abstracts and pre-proceedings baia mare september 25
TRANSCRIPT
Technical University of Cluj-Napoca, Romania
North University Center at Baia Mare
Faculty of ScienceDepartment of Mathematics and Computer Science
9th
InternationalConference of Applied Mathematics
ABSTRACTS AND PRE-PROCEEDINGS
Baia Mare
S e p t e m b e r 2 5 - 2 8 , 2 0 1 3
9th International Conference on Applied Mathematics
September 25-28, 2013organized by
Department of Mathematics and Computer Science, TUC-N, North University Center at Baia Mare,
Romanian Mathematical Society, Maramures Branch,
SINUS Association
Organizing Committee: Gheorghe Ardelean, Vasile Berinde, Dan Barbosu, Zoita Berinde, Andrei Horvat-Marc, Petrica Pop,
Nicolae Pop, Cosmin Sabo, Ioana Tascu, Ioana Zelina
Conference Secretariat: Mihaela Petric
Abstracts volume technical editor: Andrei Horvat-Marc Web site of the Conference: Cosmin Sabo, Andrei Horvat-Marc
Scientific Committee:
Dumitru Acu, University ”L. Blaga”, Sibiu, Romania
Octavian Agratini, ”Babes-Bolyai” University, Romania
Dorin Andrica, ”Babes-Bolyai” University, Romania
Mircea Balaj, University of Oradea, Romania
Dan Barbosu, TUC-N, CUNBM, Romania
Stefan Berezny, Technical University of Kosice, Slovakia
Vasile Berinde, TUC-N, CUNBM, Romania
Zoita Berinde, TUC-N, CUNBM, Romania
Lucian Beznea, Institue of Mathematics of Romanian Academy,
Bucharest, Romania
Daniel Breaz, ”1 Decembrie 1918” University, Romania
Adrian Carabineanu, University of Bucharest, Romania
Emil Catinas, ”T. Popoviciu” Institute of Numerical Analysis,
Cluj-Napoca, Romania
Aurelian Cernea, University of Bucharest, Romania
Mitrofan Choban, Univ. of Tiraspol in Kishinev, Kishinev,
Moldova
Ramesh Kumar Choudhary, APIIT SD , Panipat, India
Constantin Corduneanu, University of Texas at Arlington, USA
Marius-Eduard Craciun, ”Ovidius” University of Constanta,
Romania
Ioan Dzitac, University of Oradea, Romania
Dorel Duca, ”Babes-Bolyai” University Cluj-Napoca, Romania
Sorin Gal, University of Oradea, Romania
Ioan Gavrea, Technical University Cluj-Napoca, Romania
Vasile Glavan, State University of Chisinau, Moldova
Radu Gologan, Politehnica University Bucharest, Romania
Ghiocel Groza, Technical University of Civil Building,
Bucharest, Romania
Valeriu Gutu, State University of Chisinau, Moldova
Mircea Ivan, Technical University Cluj-Napoca, Romania
Petar Kenderov, Bulgarian Academy of Sciences, Bulgaria
Marian Klesc, Technical University of Kosice, Slovakia
Peter Kortesi, University of Miskolc, Hungary
Stefan Maruster, West University Timisoara, Romania
Mihail Megan, West University Timisoara, Romania
Dorel Mihet, West University Timisoara, Romania
Petru T. Mocanu, ”Babes-Bolyai” University, Romania
Cristinel Mortici, ”Valahia” University Targoviste, Romania
Gheorghe Munteanu, Transilvania University Brasov, Romania
Anton Muresan, ”Babes-Bolyai” University, Romania
Viorica Muresan, Technical University Cluj-Napoca, Romania
Costica Mustata, ”T. Popoviciu” Institute of Numerical Analy-
sis, Cluj-Napoca, Romania
Eugen Paltanea, Transilvania University Braov, Romania
Marcin Paprzycki, Oklahoma State University, USA
Gheorghe Paun, Institute of Mathematics of Romanian Acad-
emy, Romania
Ion Pavaloiu, ”T. Popoviciu” Institute of Numerical Analysis,
Cluj-Napoca, Romania
Adrian Petrusel, ”Babes-Bolyai” University, Romania
Cornel Pintea, ”Babes-Bolyai” University, Romania
Jan Plavka, Technical University of Kosice, Slovakia
Nicolae Pop, TUC-N, CUNBM, Romania
Petrica Pop, TUC-N, CUNBM, Romania
Constantin Popa, ”Ovidius” University of Constanta, Romania
Dorian Popa, Tehnical University Cluj-Napoca, Romania
Radu Precup, ”Babes-Bolyai” University, Romania
Vasile Preda, University of Bucharest, Romania
Mihai Postolache, Politehnica University Bucharest, Romania
Ioan Rasa, Tehnical University Cluj-Napoca, Romania
Miklos Ronto, University of Miskolc, Hungary
Ioan A. Rus, ”Babes-Bolyai” University, Romania
Tudor Sireteanu, Institute of Solid Mechanics of the Romanian
Academy, Bucharest, Romania
Mircea Sofonea, Universite de Perpignan, France
Gheorghe Stefanescu, University of Illinois, USA
Damian Trif, ”Babes-Bolyai” University Cluj-Napoca, Romania
Ioan Tomescu, University of Bucharest, Romania
Luige Vladareanu, Institute of Solid Mechanics of the Romanian
Academy, Bucharest, Romania
Cai Wen, Research Institute of Extenics and Innovation Meth-
ods, Guangdong University of Technology, Guangzhou, P.R
China
Contents
Preface 1
Part 1. Short Abstracts 3
Plenary Lectures 4Bot Radu Ioan
On primal-dual splitting algorihms for monotone inclusions with applications toconvex optimization 4
Choban MitrofanFixed points for mappings defined on generalized pseudometric spaces 4
Corduneanu, ConstantinWhat’s in the Third stage of the Fourier Analysis? 4
Dzurina JosefProperties of higher order differential equations 5
Paun GheorgheNumerical P Systems 5
Rus, Ioan A.From a Dieudonne theorem concerning the Cauchy problem to an open problem in
weakly Picard operator theory 6Rusu, Cristian
Software for Use: (Re)Defining Usability Heuristics 6Sireteanu, Tudor and Ana Maria Mitu, Ovidiu Solomon, Claudia Meglea
Assessment of equivalent linear models for experimental hysteretic loops bycorrelation method 7
Stefanescu, GheorgheOpen systems: modelling, programming, verification 7
Main and Regular lectures 81. Fixed Point Theory and Applications 8Berinde, Vasile
Fixed point theorems for nonself multi-valued almost contractions satisfyingproperty (M) 8
Bojor, Florin and Magnolia TilcaExistence and uniqueness theorem for Fredholm integral equation, via Jachymski’s
Theorem 8Bota, Monica-Felicia and Veronica Ilea, Oana Mlesnite
Fixed point theorems for α− φ contractions in b-metric spaces 8Chifu, Cristian and Gabriela Petrusel
Fixed point results for generalized multivalued contractions in b-metric spacesendowed with a graph 9
Coroian IuliaFix point theorems for multivalued contractions with respect to two topologically
equivalent metrics 9Dumitru, Dan
Generalizations of iterated function systems 9
iii
iv CONTENTS
Glavan VasileFixed points and viable sets in dynamics of relations and control 10
Gutu, ValeriuHow many contractions are needed to construct some kinds of plane compacta? 11
Horvat-Marc, AndreiFixed Point Theorems for Nonself Operators 11
Lauran, MonicaOn a functional Fredholm integral equation, via nonexpansive operators 12
Lungu, Nicolaie and Dorian PopaOn Hyers-Ulam stability of some partial differential equations 12
Muresan, Anton S.The Theory of some Asymptotic Fixed Point Theorems 13
Muresan, VioricaA Volterra Functional - integral Equation, via Weakly Picard Operators’ Technique 13
Oprea, AncaFixed point theorems for contractions of rational type in metric spaces, for
multivalued operators 13Otrocol, Diana and Veronica Ana Ilea
Qualitative properties of functional differential systems 14Pacurar, Madalina
Fixed point theorems for nonself Presic type operators 14Petric, Mihaela
Remarks on cyclic coupled fixed point theorems 14Rus, Ioan A. and Marcel-Adrian Serban
Some existence results for a system of operatorial equations 15Viorel, Adrian
Fixed point results in cone metric spaces 15
2. Optimization Theory, Operations Research and Applications 15Andreica Anca and Camelia Chira, Alexandru Agapie
Cellular Automata Topologies and Rules 15Berezny, Stefan
Generalized Algorithm of Processes of the Winter Maintenance on Airports-- see extended abstracts. 16
Drazenska, EmıliaOn the Crossing Numbers of Cartesian Products with Paths 16
Carp, Doina and Constantin Popa and Cristina SerbanModified Han algorithm for inconsistent linear inequalities 16
Chira, Camelia and Anca AndreicaEvolutionary Algorithms for Dynamic Complex Problems 17
Danciulescu, DanielaSystems of knowledge representation based on stratified graphs and their inference
process 17Deaconu, Adrian and Mihai Iolu
Inverse Generalized Maximum Flow Algorithms 18Enache-David, Nicoleta and Sangeorzan Livia
On a Markov Model for the Optimization of the Websites Structure-- see extended abstracts. 19
Marian KlescMinimal intersections in graph drawings 19
Kravecova, Daniela and Jana PetrillovaDetermination of the crossing numbers of the Cartesian product of graphs-- see extended abstracts. 19
Levit, Vadim E. and Eugen MandrescuGreedoids on Vertex Sets of B-joins of Graphs 19
CONTENTS v
Parpalea, Mircea and Grigoras, NicoletaThe maximum parametric flow in discrete dynamic networks 20
Pintea CameliaPharaoh ants for Sensor Networks Security 20
Prusinska, A. and E. Szczepanik and A.A. Tret’yakovHigh-order optimality conditions for degenerate calculus of variations problems 21
Pop, PetricaOn the multidimensional multi-way number partitioning problem 21
Sabo, CosminIntelligent methods for making the best decisions using optimization techniques and
data mining 21Scheiber, Ernest
On the Convexity of the Control Set of a Hybrid Optimal Control Problem-- see extended abstracts. 22
Stoilova, Krasimira. and Todor StoilovBi-level definition of portfolio optimization problem-- see extended abstracts. 22
Stas, MichalAxiomatic set theory for functional analysis 22
Suto, Jzsef and Stefan OnigaTesting artificial neural network for gesture recognition 22
Villar, Jose R., Silvia Gonzalez, Javier Sedano, Camelia Chira and Jose M.Trejo
Early diagnosis of Stroke: bridging the gap through wearable sensors andcomputational models
-- see extended abstracts. 23Zelina, Ioana
Communication aspects in Fibonacci type topologies 23
3. Ordinary Differential Equations and Partial Differential Equations 24Babutia, Mihai Gabriel
Input-output methods in the study of nonuniform exponential dichotomy ofevolution families 24
Balint, Agneta M. and Stefan BalintWell posed problem in sense of Hadamard, for a source produced acoustic
perturbation propagation in a lined duct, carrying a gas flow-- see extended abstracts. 24
Curt, PaulaSome remarks on certain invariant geometric properties in Hele-Shaw flows 24
Cozma, DumitruReversible cubic systems with centers 25
Groza G., M. Jianu and N. PopInfinitely differentiable functions represented into Newton interpolating series 25
Gil-Swiderska, AgnieszkaSecond order partial differential equation of parabolic type in the cosmic rays
transport studies-- see extended abstracts. 26
Ionescu AdelaMathematical models for repetitive phenomena in the excitable media. The case of
turbulent mixing 26Klincsik, Mihaly
Exact periodic patterns in quasi-linear reaction-diffusion systems with competitions 27Perjan, Andrei
Limits of solutions to the singularly perturbed abstract hyperbolic-parabolic systems 27
vi CONTENTS
Patiuc, Vladimir and Galina RıbacovaNumerical Approach for Solving Nonlinear Electromagnetic Problem 28
Perjan, A. and G. RusuSingularly perturbed problems for abstract linear differential equations with positive
powers of a positive defined operator 28Pop Nicolae
The 3D elastic contact applied to robots control 28Ronto, Andras and Miklos Ronto
Investigation of periodic solutions using interval halving 29Sfetcu, Razvan
Approximation of Kothe-Bochner spaces with subspaces of functions having finitedimensional values 29
Siluszyk, AgnieszkaA new central configurations in the planar N -body problem and their linear stability 29
Suba Alexandru, Vacaras OlgaCubic Systems with an Invariant Line at Infinity of the Maximal Geometric
Multiplicity 30
4. Advances in Numerical Analysis and Approximation Theory 30Acu, Ana Maria and Sofonea Florin
Improvement of Gruss and Ostrowski Type Inequalities and Applications 30Agratini Octavian
Approximation by Linear Discrete Operators on Weighted Spaces 30Busa Jan
Identification of a Sum of Exponential Functions Using its Taylor Series 31Babos, Alina-Mihaela
Interpolation operators on a triangle with two and three curved edges 31Barbosu, Dan and Gheorghe Ardelean
The Bernstein quadrature formula revisited 31Birou, Marius Mihai
Bernstein type operators which preserve some test functions 32Cismasiu, Cristina Sanda
Some properties of a Durrmeyer type operator associated with Bleimann-Butzer-Hahnoperator 32
Gavrea, Ioan and Bogdan GavreaAbout some inequalities in approximation theory 33
Indrea, AdrianAbout a linear and positive operator of Stancu-type with fixed points e1 and e2 33
Gavrea, Ioan and Mircea IvanOptimal rate of convergence for sequences of a prescribed form 33
Miclaus, DanOn the Stancu type bivariate approximation formula 34
Mitrea AlexandruTwo-sided estimates for the norm of the linear operators used in the convergence of
some approximation processes 34Popa, Dorian and Ioan Rasa
On the stability of some classical operators from approximation theory (II) 34Radu, Voichita Adriana
On a Class of Linear and Positive Operators 35Rasa, Ioan
Approximation processes and asymptotic relations 35Sofonea Florin, Muraru Carmen Violeta, Acu Ana Maria
Note on Approximation Properties of q-Bernstein-Schurer Operators 35
CONTENTS vii
Tascu, Ioana and Andrei Horvat-MarcGraphical reprezentations of mean square error of the bivariate operator of Stancu
type 36
5. Advances in Algebra 36Botnaru, Dumitru and Elena Baes
The Cocartesian Right Product 36Botnaru, Dumitru and Olga Cerbu
Semireflexive Subcategories 36Botnaru, Dumitru and Alina Turcan
The Right Product 37Constantinescu, Adrian
Hilbert - Mumford - Nagata Theorem on invariants and some topological aspects ofthe finite generation of subalgebras. (II) 37
Crivei SeptimiuFinitely accessible categories versus module categories 38
Kortesi, PeterAbout separation axioms in semitopological and topological invers semigroups 38
Muresan, Calin AlexeNew Methods for the Polynomial Roots Approximation 38
Olteanu, GabrielaSemisimple group algebras: primitive idempotents and group codes 38
Pelea, CosminOn some particular equivalence relations of multialgebras 39
Pop, Adina and Maria S. PopA generalization of Hyers-Ulam-Rassias stability on m-semigroups 39
Pop, VasileSimultaneous extensions of polyadic groups 40
Szanto, CsabaExtensions of modules over tame hereditary algebras 40
Teodor Dumitru ValcanAbelian groups in which any proper subgroup has the direct summand intersection
property 41
6. Software Engineering - Principles and Practices 41Berczes, Tamas and Attila Kuki, Bela Almasi, Janos Sztrik and Pascal Moyal
A new model of finite-source retrial queues with multi-state server’s breakdown-- see extended abstracts. 41
Sarvari, CsabaConstructing questions using Maple T. A. 41
Hajdu-Macelaru, Mara DianaMetrics in software quality evaluation 42
Motogna, Simona and Florin Craciun, Gabriel GlodeanfUML Formal Description 42
Ildiko Perjesi-HamoriOn-Line Testing in Higher Mathematics Education - Maple T. A. 43
Imre PillerSoftware Tools for Information Retrieval with Lattices 43
Petreanu, Emanuela and Livia SangeorzanThe use of Java technologies for web e-commerce applications 44
Sangeorzan, Livia and Mihaela Parpalea, Mircea ParpaleaA functional sentence perspective approach to preflow algorithm in parametric
networks 44Szilagyi, Szabolcs
The effects of different queuing techniques over VoIP performance: a simulation
viii CONTENTS
approach-- see extended abstracts. 45
Szabo, PeterA Max-Plus Algorithm and the Prime Numbers 45
Sztrik, Janos and Tamas BerczesTool supported analysis of queueing systems with Future Internet applications-- see extended abstracts. 45
Veres LauraApplication of rough approximations in Group Technology problems 45
Gergely Kocsis, Imre VargaInformation spreading on declining social networks-- see extended abstracts. 46
7. Applications of Mathematics and Computer Science in Science, Arts andTechnology 46
Ardelean, GheorgheNew graphical models for the basins of attraction of the real roots of a nonlinear
equation-- see extended abstracts. 46
Contras, Diana and Alina PintescuDeveloping an ontology for automated scene creation 46
Berinde Ruxandra and Vasile BerindeUsing a spatial configuration mathematical model to study the inhabited area of a
Maramures village 46Berinde, Zoita
New quantitative structure-toxicity relationship for aliphatic carboxylic acids 47Dippong, Thomas and Zoita Berinde
A topological study for a set of columnar liquid crystals 47Mare Rosca, Oana, Lucia Mihalescu, Monica Marian, Zorica Vosgan
Analysis and Interpretation of Structure and Diversity of Some MacrozoobenthicCommunities Using Mathematics Indices
-- see extended abstracts. 47Marzec, Krzysztof
Applications of computer science in impingement cooling system design-- see extended abstracts. 47
Mihali, Cristina and Gabriela Oprea, Claudia ButeanSpatial distribution maps of microelements concentration in surface soil around soil
pollution sources 47
8. Mathematical Modelling with Applications in Economics 48Boca, Gratiela Dana
Structural Optimization Model Design using TOSCA Program-- see extended abstracts. 48
Carstea, Claudia and Sangeorzan LiviaAlgorithms implementation model for software optimization-- see extended abstracts. 48
Daraba, DinuOptimizing Investment Costs for Production Systems with Discontinuous Operation
Mode-- see extended abstracts. 48
Hordau, Anne Marie AndreeaAn Questionnare Based Analyses on Labor Force in Maramures County-- see extended abstracts. 48
Rabaea, AdrianAn Implementation of Monte Carlo Method for European Option Pricing 48
CONTENTS ix
Mihoc, Ion and Cristina-Ioana FatuOn the comparison of Fisher informations of the some probability distributions 48
Sabou, Simona and Liliana Zima, Rita Toader, Corina Radulescu, Florina Hahn,Cristian Vele
The performance appraisal in human resources-- see extended abstracts. 48
Toader,Cezar, Rita Toader and Corina RadulescuResource-Oriented Applications in Product Data Management-- see extended abstracts. 48
Vele, Cristian and Cristian Anghel and Rita ToaderUsing statistical data to evaluate the strategic efforts of companies-- see extended abstracts. 48
Zima Liliana, Simona Sabou, Rita Toader, Cezar ToaderThe calculation of human resource performance-- see extended abstracts. 48
9. Variational methods and applications to ODEs and PDEs 48Breckner, Brigitte E.
Parameter-depending problems on fractals 48Bogdan, Marcel
An application to quasi-linear variational inequalities 49Faraci, Francesca
An existence result for a quasi-linear elliptic equation with dependence on thegradient 49
Inoan Daniela, Kolumban JozsefExistence theorems for intersection problems and equilibrium problems 50
Lisei, HanneloreStochastic Nonlinear Equations of Schrodinger Type 50
Laszlo, SzilardMultivalued variational inequalities and coincidence point results 50
10. Miscellanea 50Cioruta, Bogdan and Mirela Coman
Bezier Curves in GeoGebra and Computational Applications dedicated toEnvironmental Informatics 50
Cioruta, Bogdan and Mirela ComanFourier Series in GeoGebra - New Possibilities for Representation and Applications 51
T. V. Do, R. Chakka, J. Sztrik, T. Berczes, D. EfrosininAn efficient method to solve a two-server heterogeneous retrial queue with threshold
policy-- see extended abstracts. 51
Dana Debora GlitiaField extensions and Clifford theory 51
Kortesi, PeterA divisibility problem of integers 52
Marian, Claudia and Monica MarianPrognose and diagnosis in education by using statistical methods-- see extended abstracts. 52
Marian, Monica and Beatrice AgnetaStatistical Instruments Used in Environmental Assessment Validation of Newly
Introduced Species-- see extended abstracts. 52
Piscoran, Laurian Ioan and Catalin Ionel BarbuTzitzeica curves in a Minkowski space 52
Part 2. Extended Abstracts 53
x CONTENTS
Ardelean, GheorgheNew graphical models for the basins of attraction of the real roots of a nonlinear
equation 55Balint, Agneta M. and Stefan Balint
Well posed problem in sense of Hadamard, for a source produced acousticperturbation propagation in a lined duct, carrying a gas flow 58
Berezny, StefanGeneralized Algorithm of Processes of the Winter Maintenance on Airports 61
Berczes, Tamas and Attila Kuki, Bela Almasi, Janos Sztrik and Pascal MoyalA new model of finite-source retrial queues with multi-state server’s breakdown 63
Boca, Gratiela DanaStructural Optimization Model Design using TOSCA Program 66
Daraba, DinuOptimizing Investment Costs for Production Systems with Discontinuous Operation
Mode 69T. V. Do, R. Chakka, J. Sztrik, T. Berczes, D. Efrosinin
An efficient method to solve a two-server heterogeneous retrial queue with thresholdpolicy 71
Carstea, Claudia and Sangeorzan LiviaAlgorithms implementation model for software optimization 74
Enache-David, Nicoleta and Sangeorzan LiviaOn a Markov Model for the Optimization of the Websites Structure 78
Gil-Swiderska, AgnieszkaSecond order partial differential equation of parabolic type in the cosmic rays
transport studies 81Hordau, Anne Marie Andreea
An Questionnare Based Analyses on Labor Force in Maramures County 83Kravecova, Daniela and Jana Petrillova
Determination of the crossing numbers of the Cartesian product of graphs 85Kocsis Gergely and Imre Varga
Information spreading on declining social networks 88Mare Rosca, Oana, Lucia Mihalescu, Monica Marian, Zorica Vosgan
Analysis and Interpretation of Structure and Diversity of Some MacrozoobenthicCommunities Using Mathematics Indices 91
Marian, Claudia and Monica MarianPrognose and diagnosis in education by using statistical methods 93
Marian, Monica and Beatrice AgnetaStatistical Instruments Used in Environmental Assessment Validation of Newly
Introduced Species 96Marzec, Krzysztof
Applications of computer science in impingement cooling system design 98Scheiber, Ernest
On the Convexity of the Control Set of a Hybrid Optimal Control Problem 101Sabou, Simona and Liliana Zima, Rita Toader, Corina Radulescu, Florina Hahn,
Cristian VeleThe performance appraisal in human resources 104
Stoilova, Krasimira. and Todor StoilovBi-level definition of portfolio optimization problem 107
Szilagyi, SzabolcsThe effects of different queuing techniques over VoIP performance: a simulation
approach 109Sztrik, Janos and Tamas Berczes
Tool supported analysis of queueing systems with Future Internet applications 114
CONTENTS xi
Toader,Cezar, Rita Toader and Corina RadulescuResource-Oriented Applications in Product Data Management 118
Villar, Jose R., Silvia Gonzalez, Javier Sedano, Camelia Chira and Jose M.Trejo
Early diagnosis of Stroke: bridging the gap through wearable sensors andcomputational models 122
Vele, Cristian and Cristian Anghel and Rita ToaderUsing statistical data to evaluate the strategic efforts of companies 126
Zima Liliana, Simona Sabou, Rita Toader, Cezar ToaderThe calculation of human resource performance 129
Preface
The Ninth International Conference on Applied Mathematics (ICAM 9) follows some successfullyinternational conferences organized in Baia Mare since 1996 (35 Years of Higher Mathematics Educationin Maramures 1996, ICAM1: 1998; 135th Pannonian Applied Mathematics Meeting: 2001, ICAM2:2000; ICAM3: 2002; ICAM4: 2004; ICAM5: 2006; ICAM6: 2008; ICAM7: 2010 and ICAM8:2011).
The general profile and scientific programme is mainly the same as at the previous ICAM editions.Apart from Plenary Lectures (9 at ICAM9), the conference programme includes main and regular
lectures grouped on thematic minisymposia. The following symposia have been proposed for ICAM9:
• Fixed Point Theory and Applications• Optimization Theory, Operations Research and Applications• Numerical methods for Ordinary Differential Equations and Partial Differential Equations• Advances in Numerical Analysis and Approximation Theory• Advances in Algebra• Advances in Geometry• Software Engineering - Principles and Practices• Applications of Mathematics and Computer Science in Science, Arts and Technology• Mathematical Modelling with Applications in Economics• Mathematics Education Advanced Intelligent Control Applied in Robotics and Mechatronics• Variational methods and applications to ODEs and PDEs• Applications of Mathematics and Computer Science in Chemistry and Biology
Due to the considerable number of submitted papers (more than 160), a rather important numberof papers have been accepted for presentation and some of them were included in the Poster session.
One new feature of ICAM9 is the fact that the Local Organizing Committee has decided to publish,apart from the usual volume of short abstracts, several extended abstracts that form a Pre-Proceedingssection in the volume of Abstracts.
This is done in order to ensure a fast publication of those papers submitted by authors before theconference.
Extended and improved versions of the papers presented at the conference will be included inpost-Proceedings volumes published as special issues of our journals:
Carpathian Journal of Mathematics (2012 Impact factor: 0.852)Creative Mathematics and Informatics (B+ CNCSIS indexed journal)
after a rigorous peer-review process.Both journals are cover-to-cover reviewed/indexed in: Zentralblatt MATH and Mathematical
Reviews.Contributions to post-Proceedings will be submitted on-line using the submission and editorial
system SEMN of the two journals:Carpathian Journal of Mathematics: http://radu.autoportret.ro/cjm/
Creative Mathematics and Informatics: http://radu.autoportret.ro/cmi/The authors who will contribute to the post-Proceedings volumes have to select ”Special issue
ICAM9” for Article Type when submitting their contribution. More information about these journals(Editorial Board, Aims and Scope, Instruction for Authors, etc.) may be found at the followingaddresses:
http://carpathian.ubm.ro/
http://creative-mathematics.ubm.ro/
We thank all contributors to ICAM9 and hope they will enjoy their stay in Baia Mare andMaramures, where, exactly in the same period is organized the local festival ”Sarbatoarea Castanelor(Chestnuts Festival)”.
Vasile BERINDE,Chair of ICAM9
Part 1
Short Abstracts
Plenary Lectures
On primal-dual splitting algorihms for monotone inclusions with applications to convex optimization
Radu Ioan BotUniversity of Vienna, Austria
We consider the primal problem of finding the zeros of mixtures of linear compositions and parallelsums of maximally monotone operators. By formulating its Attouch-Thera-type dual inclusion problem,a class of primal-dual splitting algorithms which simultaneously solve the two problems is presented.The proposed schemes process at each iteration individually the resolvents of the maximally monotoneoperators involved and aim to overcome the shortcoming of classical splitting algorithms when dealingwith linear compositions of maximally monotone operators. The iterative algorithms are used forsolving nondifferentiable convex optimization problems arising in image and video processing. Thetalk is based on the papers [1, 2, 3].
Bibliography[1] Bot, R.I., Csetnek, E.R., Heinrich, A., A primal-dual splitting algorithm for finding zeros of sums of maximal
monotone operators, to appear in SIAM Journal on Optimization[2] Bot, R.I., Hendrich, C., A Douglas-Rachford type primal-dual method for solving inclusions with mixtures of composite
and parallel-sum type monotone operators , arXiv:1212.0326 [math.OC], 2012[3] Bot, R.I., Hendrich, C., Convergence analysis for a primal-dual monotone + skew splitting algorithm with applications
to total variation minimization , arXiv:1211.1706 [math.OC], 2012
ICAM9
Fixed points for mappings defined on generalized pseudometric spaces
Mitrofan ChobanTiraspol State University, Republic of Moldova
A generalized pseudometric space is a topological space X with a continuous pseudometric d withvalues in a Banach reticulate lattice for which any Cauchy sequence has an accumulation point. If thesets Z(x, d) = y ∈ X : d(x, y) = 0 are compacta, then the pseudometric is called perfect. For spaceswith such pseudometrics there are proved the Bishop-Phelps, Takahashi, Caristi, Caristi-Browdentheorems.
ICAM9
Constantin Corduneanu
What’s in the Third stage of the Fourier Analysis?University of Texas at Arlington, U.S.A
The aim of this paper is to present the state of the art in Fourier Analysis in its ”third stage”.
ICAM9
5
Properties of higher order differential equations
Josef DzurinaTechnical University of Kosice, Slovakia
In the talk we provide criteria for oscillation of the even order delay differential equation
y(n)(t) + p(t)y(ct) = 0
We provide detail analysis of the properties of this equation, we offer necessary and sufficient conditionsfor oscillation of studied equation and we fulfill the gap in the oscillation theory.
ICAM9
Numerical P Systems
Gheorghe PaunInstitute of Mathematics of the Romanian Academy, Bucuresti, Romania,
Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, University of Sevilla, Sevilla, Spain
Membrane computing is a branch of natural computing initiated fifteen years ago, in [1], andalready in 2003 considered by ISI a fast emerging research area in computer science. The goal is toabstract computing ideas (data structures, operations with them, ways to control these operations,computer architectures, computing models) from the structure and the functioning of the living celland for the way cells collaborate in tissues and other populations of cells, the brain included. Theobtained models are called P systems. Very shortly, they consist of cell-like or tissue-like arrangementsof membranes, delimiting compartments where multisets of objects (symbols in an alphabet, stringsor more complex objects) evolve according to various types of evolution rules; also the membranes canevolve, by specific rules. The rules are used in a nondeterministic maximally parallel way. A very largenumber of variants were considered, with mathematical, computational, or biological motivations.These computing devices proved to be both computationally powerful (in many cases, equivalentwith Turing machines) and computationally efficient (by a space-time trade-off, polynomial solutionsto computationally hard problems, typically, NP-complete problems, were proposed). Also, a largevariety of applications were reported, especially in modeling biological processes, but also in otherareas.
Numerical P systems were introduced in [3] with motivations coming from economics. Such asystem consists of a cell-like membrane structure, in the compartment of which numerical variablesare placed; these variables evolve by means of programs, consisting of two parts, a production functionand a repartition protocol. Roughly speaking, in a computation step, depending on the current valueof variables, a “total production” is computed in each compartment, which is then distributed amongthe variables in that compartment and in the neighboring compartments. A computation is a sequenceof such production-repartition steps. One of the variables is distinguished and its values form the setof numbers generated by the computation.
The talk will present the basic classes of numerical P systems (catalytic and non-catalytic, sequentialand parallel, etc.), their computing power (Turing universality in most cases) and computationalcomplexity aspects. Applications in robot control will be mentioned, as well as a series of openproblems and research topics. A quick introduction to membrane computing will be provided.
Bibliography
[1] Gh. Paun: Computing with membranes. Journal of Computer and System Sciences, 61, 1 (2000), 108–143 (andTurku Center for Computer Science-TUCS Report 208, November 1998, www.tucs.fi).
[2] Gh. Paun: Computing with Membranes: An Introduction, Springer, Berlin, 2002.[3] Gh. Paun, R. Paun: Membrane computing and economics: Numerical P systems. Fundamenta Informaticae, 73
(2006), 213–227.[4] Gh. Paun, G. Rozenberg, A. Salomaa, eds.: Handbook of Membrane Computing. Oxford University Press, 2010.[5] The P Systems Website: http://ppage.psystems.eu.
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ICAM9
From a Dieudonne theorem concerning the Cauchy problem to an open problem in weakly Picardoperator theory
Ioan A. RusBabes-Bolyai Unversity Cluj-Napoca, Romania
Let f ∈ C[a, b]× Rn,Rn). We consider the following Cauchy problem:
(1) y′ = f(x, y), y(a) = y0
and the corresponding sequence of successive approximations:
(2) yn+1(x) = y0 +
∫ x
af(s, yn(s))ds.
The following result was given by J. Dieudonne in 1945 (see [1] and [2]):Theorem 1. We suppose that the Cauchy problem (1.1) has a uniques solution. Then there exists
h ∈ (0, b− a) such that the sequence of successive approximations (2) converges to the unique solutionof (1), uniformly on [a, a+ h] if and only if the sequence (yn+1 − yn)n∈N converges to 0 uniformly on[a, a+ h].
The aim of this talk is to study the following problem rose by the above theorem.Problem. Let X be a Banach space and f : X → X be an operator. In which conditions the
following implication holds:
fn+1(x)− fn(x)→ 0 as n→ +∞ =⇒ fn(x)→ x∗(x) ∈ Ff , ∀x ∈ Xor equivalently
f is asymptotically regular =⇒ f is a weakly Picard operator.
Bibliography[1] I.A. Rus, On a theorem of Dieudonne, in Differential Equations and Control Theory (V. Barbu-Ed.), Longman, 1991,
296-298.[2] I.A. Rus and M.-A. Serban, Basic problems of the metric fixed point theory and the relevance of a metric fixed point
theorem, Carpathian J. Math., 29(2013), no.2, 239-258.
ICAM9
Software for Use: (Re)Defining Usability Heuristics
Cristian RusuPontificia Universidad Catlica de Valparaso, Escuela de Ingeniera Informtica, Valparaso, Chile
The Special Interest Group on Computer-Human Interaction (SIGCHI) of the Association forComputing Machinery (ACM) defines Human-Computer Interaction (HCI) as the discipline concernedwith the design, evaluation and implementation of interactive computing systems for human use,and with the study of major phenomena surrounding them. The ISO/IEC 9241 standard definesthe usability as the extent to which a product can be used by specified users to achieve specifiedgoals with effectiveness, efficiency and satisfaction in a specified context of use. Usability evaluationfor applications based on emerging information technology brings new challenges. Is it the classicalconcept of usability still valid? Which are the dimensions of the (new) usability? How can it bemeasured? How should we develop for (better) usability? There is a need for new evaluation methodsor at least for the use of traditional evaluations in novel ways.
Usability evaluation methods are commonly divided into inspection and testing methods. Inspectionmethods find usability problems based on the expertise of usability professionals. Testing methods findusability problems through the observation of the users while they use (and comment on) a system
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interface. Heuristic evaluation is a widely used inspection method. A group of evaluators inspect theinterface design based on usability principles (heuristics), usually Nielsens ten heuristics.
Heuristic evaluation is easy to perform, cheap and able to find many usability problems (bothmajor and minor problems). However, it may miss domain specific problems. That is why theuse of appropriate heuristics is highly relevant. Sets of usability heuristics were developed by theUseCV research group in HCI at Pontificia Universidad Catlica de Valparaso (Escuela de IngenieraInformtica), for specific applications: Grid Computing, Virtual Worlds, Interactive TV, TransactionalWeb Applications, Mobiles (among others). Heuristics were validated by experiments and seems towork better than general heuristics.
ICAM9
Assessment of equivalent linear models for experimental hysteretic loops by correlation method
Tudor Sireteanu*, Ana Maria Mitu*, Ovidiu Solomon**, Claudia Meglea****Institute of Solid Mechanics, Romanian Academy, 15 Constantin Mille, RO-010141, Bucharest
**Romanian-American University,1b Expozitiei Blvd., Bucharest
***Center of Technology and Engineering for Nuclear Projects, 409 Atomistilor, Bucharest - Magurele
Corresponding author: [email protected]
Cyclic stress-strain or force-displacement data are required for engineering application at all stagesin the design and assessment of future life prediction of materials and structures, or of stiffness anddamping properties of vibration control devices. In most practical cases the experimental data yieldhysteresis loops displaying highly non-linear behavior. The fitting of non-linear parametric modelsto experimental data is not a simple task. Moreover, in many of the existing computing programsfor structural dynamic analysis only equivalent linear visco-elastic or linear differential models canbe used to approximate the hysteresis behavior of materials, structures or devices,. In this paper ispresented a linearization method based on correlation functions of force and displacement signalsrecorded by cyclic tests, without need for analytical models of hysteresis behavior. The application ofthe proposed method is illustrated for hysteresis loops obtained by testing several devices for vibrationcontrol and anti-seismic protection. The effectiveness of linearization method based on correlationapproach is illustrated through comparative analysis of seismic response of systems with hysteresisand linear equivalent characteristics.
ICAM9
Open systems: modelling, programming, verification
Gheorghe StefanescuDepartment of Computer Science, University of Bucharest, Romania
Powerful algebraic techniques have been developed for classical sequential computation. Many ofthem are based on regular expressions and the associated regular algebra. For parallel and interactivecomputation, extensions to handle 2-dimensional patterns are often required. Finite interactivesystems, a 2-dimensional version of finite automata, may be used to recognize 2-dimensional languages.In this talk we present a blueprint for getting a formal representation of parallel, interactive programsand of their semantics. It is based on a new approach for getting regular expressions for 2-dimensionalpatterns, particularly using words of arbitrary shapes and powerful control mechanisms on composition.We extend the class of 2-dimensional expressions with new control features, progressively increasing theexpressive power of the formalism up to a level where a procedure for generating the words acceptedby finite interactive systems may be obtained. Targeted applications come from the area of modelling,specification, analysis and verification of structured interactive programs via the associated scenariosemantics.
ICAM9
8
Main and Regular Lectures
1. Fixed Point Theory and Applications
Fixed point theorems for nonself multi-valued almost contractions satisfying property (M)
Vasile BerindeDepartment of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Romania
Let X be a Banach space, K a non-empty closed subset of X and let T : K → B(X) be a non-selfmulti-valued almost contraction. We extend the results established in [1] to non-self multi-valuedalmost contractions satisfying property (M), thus also extending the results from [3] from single-valuedmappings to multi-valued ones.
Bibliography
[1] Alghamdi, Maryam A., Berinde, V. and Shahzad, N., Fixed points of multi-valued non-self almost contractions, J.Appl. Math. Volume 2013, Article ID 621614, 6 pages http://dx.doi.org/10.1155/2013/621614
[2] Alghamdi, Maryam A., Berinde, V. and Shahzad, N., Fixed points of non-self almost contractions, Carpathian J.Math. 33 (2014), No. 1 (in print)
[3] Berinde, V. and Pacurar, M., Fixed points of single-valued non-self almost contractions, Fixed Point Theory 14(2013), No. 2 (in print)
ICAM9
Existence and uniqueness theorem for Fredholm integral equation, via Jachymski’s Theorem
Florin Bojor and Magnolia Tilca
[email protected]; [email protected]
The aim of this paper is to study the existence and uniqueness of the solutions of Fredholm integralequation type. The main tools employed in this study are based on applications of the Jachymskifixed point theorem on metric spaces endowed with a graph.
Bibliography
[1] Ionescu D.V. Ecuatii diferentiale si integrale, Ed. Didactica si pedagogica, Bucuresti, 1972.[2] Jachymski J., The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc. 1
(136) (2008) 1359–1373.[3] Lungu N. Rus I.A., On a functional Volterra-Freduolm ecuation, via Picard operators, J.M.I. 3(4) (2009) 519-527.
ICAM9
Fixed point theorems for α− φ contractions in b-metric spaces
Monica-Felicia Bota*, Veronica Ilea*, Erdal Karapinar**, Oana Mlesnite**Babess-Bolyai University, Cluj-Napoca, Romania; **Atilim University, Ankara, Turkey
[email protected], [email protected], [email protected], [email protected]
Very recently, Samet et al. [4] introduced the notion of α-ψ-contractive type mapping and provedsome fixed point results for such mappings. We give some fixed and strict fixed point results in
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b-metric spaces. We consider both the singlevalued and the multivalued cases of α-ψ-contractions. Asapplications we give some Ulam-Hyers stability results.
Bibliography
[1] M. Boriceanu, A. Petrusel, I.A. Rus, Fixed point theorems for some multivalued generalized contractions in b-metricspaces, International Journal of Mathematics and Statistics, 6(2010), 65-76.
[2] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Univ. Modena, 46(1998),263-276;
[3] I. A. Rus, Remarks on Ulam stability of the operatorial equations, Fixed Point Theory, 10(2009), No. 2, 305-320.[4] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Analysis 75 (2012),
2154-2165.
ICAM9
Fixed point results for generalized multivalued contractions in b-metric spaces endowed with a graph
Cristian Chifu and Gabriela PetruselBbabes-Bolyai Unversity Cluj-Napoca, Romania
[email protected] [email protected]
The purpose of this paper is to present some fixed point results on a b-metric space endowed witha graph, using the contractive type conditions of Reich and Ciric with respect to Hausdorff-Pompeiufunctional H. The data dependence of fixed point set is also studied.
Bibliography
[1] Bota, M., Dynamical Aspects in the Theory of Multivalued Operators, Cluj University Press, 2010.[2] Czerwik S., Nonlinear set-valued contraction mappings in b-metric space, Atti Sem. Mat. Univ. Modena, 46(1998),
263-276.[3] Jachymski J., The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc.,
136(2008), 1359-1373[4] Nicolae A., O’Regan D. and Petrusel A., Fixed point theorems for singlevalued and multivalued generalized contractions
in metric spaces endowed with a graph, J. Georgian Math. Soc., 18(2011), 307-327.[5] Petrusel A., Rus I. A., Yao J.-C., Well-posedness in the generalized sense of the fixed point problems for multivalued
operators, Taiwanese J. Math., 11(2007), 903-914.
ICAM9
Fix point theorems for multivalued contractions with respect to two topologically equivalent metrics
Iulia CoroianBabes-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, Romania
Fix point theorems for multivalued contractions with respect to two topologically equivalentmetrics
In this paper, we will present some fixed point results for multivalued almost contractions withrespects to two topologically equivalent Hausdorff type metrics.
ICAM9
Generalizations of iterated function systems
Dan DumitruSpiru Haret University of Bucharest, Romania
The aim of this article is to investigate infinite iterated function systems formed by contraction typefunctions such as (ε, ϕ)-functions with ε > 0 and ϕ a comparation function, or by strong Meir-Keeler
10
functions and to prove the existence and uniqueness of the attractors of these kind of infinite iteratedfunction systems.
Bibliography
[1] J. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J., 30 (1981), No 5, 713-747[2] K. Lesniak, Infinite iterated function systems: a multivalued approach, Bull. Pol. Acad. Sci. Math., 52 (2004), No 1,
1-8
ICAM9
Fixed points and viable sets in dynamics of relations and control
Vasile GlavanSiedlce University of Natural Sciences and Humanities, Siedlce, Poland,
Moldova State University, Chisinau, Republic of Moldova
We are concerned with the dynamics of closed relations in complete metric spaces and with theiterations of set-valued functions F : X → P(X). A sequence (xn)n∈Z , such that xn+1 ∈ F (xn) for alln ∈ Z, is called a trajectory, or a chain. If instead of inclusion one has the inequality ρ(xn+1, F (xn)) ≤ δfor some δ ≥ 0, then one speaks about a δ-chain (here ρ denotes the Hausdorff-Pompeiu semi-distance).
A closed subset Y ⊆ X is called invariant, if F (Y ) = Y , and completely invariant, if F−1(Y ) =Y = F (Y ). The last equalities mean that given x ∈ Y , every chain (xn)n∈Z with x0 = x satisfies alsoxn ∈ Y for all n ∈ Z. Such a subset is said to be viable on Z+ (on Z) if for any x ∈ Y , there existsa chain (xn)n∈Z+(Z) such that x0 = x and xn ∈ Y for all n ∈ Z+ (respectively, n ∈ Z ). Obviously,completely invariant subsets, fixed points and periodic chains, as well as their reunion, represent viablesets. If the relation is contractive, then it has a unique attractor which coincides with the closure ofthe set Per(F ) of periodic points [1] and, at least in the case of an affine IFS, this attractor representsthe smallest closed viable set, containing Per(F ).
In our report we will generalize this facts for some affine Iterated Function System (Rn; f1, f2, . . . fm)with fj(x) = Ajx+ bj , where the linear operators Aj are not necessarily contractive. More precisely,we assume, that the family of matrices Aj , j = 1, 2, . . . ,m, satisfies the so called ”cone condition” (see,e.g., [2]), which means that there are two cones, one of them invariant with respect to all Aj , and
another one being invariant with respect to all A−1j , provided that all operators are invertible. This
implies that the matrices are hyperbolic and all their unstable subspaces are located in the first cone,while the stable ones are included in the second cone.
Under the ”cone condition” most of the chains are unbounded, excepting, at least, fixed pointsand periodic orbits. Denote by Λ the subset of points x ∈ Rn with the property, that there exists abounded chain (xn)n∈Z , satisfying x0 = x. We show, that Λ is non-empty, compact and viable onZ. Moreover, we prove, that Λ is the maximal subset with these properties. At the same time Λ isthe smallest closed viable set, containing all periodic chains. We also prove, that the IFS has theShadowing Property on Λ: given ε > 0, there is δ > 0 such, that for every δ-chain (xn)n∈Z , staying ina neighborhood of Λ, there exists a chain (yn)n∈Z ⊂ Λ, such that ‖ xn − yn ‖≤ ε, n ∈ Z.
In the particular case of a two-dimensional affine IFS with common linear parts we give sometopological characteristics of the viable set Λ, depending on eigenvalues of the linear operator. Wegive also some applications in control theory.
This work was partially supported by the SCSTD Grants 11.817.08.41F and 12.839.08.06F.
Bibliography
[1] Glavan, V., Gutu, V., On the dynamics of contracting relations.In: Analysis and Optimization of DifferentialSystems, Edited by V. Barbu et al., Kluwer Acad. Publ., 2003, pp.179–188.
[2] Katok, A., Hasselblatt, B., Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press,1995.
ICAM9
11
How many contractions are needed to construct some kinds of plane compacta?
Valeriu GutuMoldova State University, Chisinau, Republic of Moldova
A hyperbolic Iterated Function System (IFS) is a finite collection of contractions, usually consideredin a complete metric space. It is known that any hyperbolic IFS possesses a unique invariant compactset, called the attractor of this IFS.
The structure of attractors of hyperbolic IFS’s and their properties were studied by many authors.M. Hata (1985), M. Barnsley (1988), P. F. Duvall and L. S. Husch (1992), M. Kwiecinski (1999),
S. Crovisier and M. Rams (2006), M. J. Sanders (2009), M. Kulczycki and M. Nowak (2012), T. Banakhand M. Nowak (2013) and others have studied the possibility of compacta to be obtained as attractors,as well as some examples of compacta, which can not serve as attractor of any hyperbolic IFS (see,e.g., [1] and the bibliography therein).
We study this problem from another side:1. Which compacta can serve as attractors of hyperbolic IFS’s?2. Given a compact set, what is the minimal number of contractions of a hyperbolic IFS (provided
it exists) needed to obtain this set as attractor?Theorem 1. Any nonempty finite union of convex compacta in Rn can be realized as attractor of
a hyperbolic IFS.Theorem 2. Any plane convex compact set can be realized as attractor of a hyperbolic IFS,
consisting of at most three contractions. If the given compact set can be embedded uniquely in a figureof constant width, then this number of contractions is minimal possible.
Theorem 3. Any nonempty finite union of m plane convex compacta can be realized as attractorof a hyperbolic IFS, consisting of at most 3m contractions.
Remark. There are examples when the number of contractions in Theorem 3 is minimal possibleand other examples when this number can be diminished.
Bibliography
[1] Banakh, T., Nowak, M., A 1-dimensional Peano continuum which is not an IFS attractor, Proc. Amer. Math. Soc.,141(2013), no. 3, 931-935
ICAM9
Fixed Point Theorems for Nonself Operators
Andrei Horvat-MarcDepartment of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Romania
Most of xed point theorem are established for self mappings. The transition from this results tofixed point theorems for non-self mappings can be done via nonlinear alternative and the consequencesof this, i.e. Leray-Schauder alternative. In A. Granas and J. Dugundji [4] are presented some versionsof nonlinear, respectively Leray-Schauder, alternatives. In this work we present examples of non-selfoperators satisfies some boundary conditions which ensure the existence of fixed points.
Bibliography
[1] V. Berinde, On the approximation of fixed points of weak contractive mappings, Carpathian J. Math. 19 (2003), no. 1,7–22.
[2] V. Berinde and M. Pacurar, Fixed point theorems for nonself single-valued almost contractions, (2013).[3] K. Deimling, Nonlinear functional analysis, Springer-Verlag, Berlin, 1985.[4] A. Granas and J. Dugundji, Fixed point theory, Springer Monographs in Mathemetics, Springer, 2002.[5] Donal O’Regan, A continuation theory for weakly inward maps, Glasgow Mathematical Journal 40 (1998), 311–321.
ICAM9
12
On a functional Fredholm integral equation, via nonexpansive operators
Monica LauranNorth University Center at Baia Mare, Technical University of Cluj-Napoca, Baia Mare, Romania
In this paper we present one result relative to existence of solutions of the functional Fredholmintegral equation with deviating argument in a subset of Banach space:
u(x, y) = f(x, y, g(u)(x, y)) +
b∫a
b∫a
K(x, y, s, t, u(s, t))dsdt, x, y ∈ [a, b]
by nonexpansive operators technique.
Bibliography[1] Berinde,V., Existence and approximation of solutions of some first order iterative differential equations, Miskolc
Math. Notes,Vol. 11 (2010), No. 1, pp. 1326[2] Berinde, V.and M. Lauran, Nonexpansive fixed point technique used for solve boundary value problem for frac-
tional differential equations, Analele St. ale Univ.Al.I. Cuza Iasi, Seria Matematica, Tomul LVII, Supliment,DOI:10.2478/v10157-011-0009-0
[3] Goebel,K. and Kirk, W.A., Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge, 1990[4] Ishikawa, S., Fixed point and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc.,
59(1976), No. 1,65-71[5] Lauran, M., Existence results for some nonlinear integral equations, Miskolc Math. Notes, vol. 13 (2012), No.1,
pp.67-74[6] Lauran, M., Existence results for some differential equations with deviating argument, Filomat, 25 (2011), No. 2,
21-31.[7] Pachpatte, B.G., On Fredholm type integral equation in two variables,Diff. Eq. and Appl., 1(2009), No.1, 27-39.[8] Rus, I. A. and Petrusel, A.and Petrusel, G., Fixed point theory, Cluj University Press, 2008
ICAM9
On Hyers-Ulam stability of some partial differential equations
Nicolaie Lungu and Dorian PopaTecnical University of Cluj-Napoca, Romania
In a recent paper we obtained a stability result for a partial differential equation of order one inBanach spaces. In this paper we improve the result mentioned above and, as applications, we obtainHyers-Ulam stability results for some linear partial differential equations of second order and for somenonlinear partial differential equations.
Bibliography[1] Lungu, N. , Popa, D., Hyers-Ulam stability of a first order partial differential equation, J. Math. Anal. Appl.385(2012),
86-91.
ICAM9
13
The Theory of some Asymptotic Fixed Point Theorems
Anton S. MuresanBabes-Bolyai Unversity of Cluj-Napoca, Romania
In this paper we give and study some problems about some asymptotic fixed point theorems like:data dependence of fixed points, Ulam stability, sequences of operators and fixed points, well-posednessof fixed point problem, and limit shadowing property.
Bibliography[1] Andras, Sz., Fredholm-Volterra integral equations, Ed. Did. Ped., Bucuresti, 2005 (In Romanian)[2] Filip, A.D., Fixed point theorems in Kasahara spaces with respect to an operetor and applications, Fixed Point Theory,
12(2011), No. 2, 329-340[3] Muresan, A.S., Graphic contactions, Proceedings - ICFPTA, Cluj-Napoca, July 2012 (to appear)[4] Pacurar, M., Fixed point theory for cyclic Berinde operators, Fixed Point Theory, 12(2011), No. 2, 419-428[5] Pacurar, M., Rus, I.A., Fixed point theory for cyclic ϕ-contractions, Nonlinear Analysis, 72 (2010), 1181-1187[6] Rus, I.A., Maps with ϕ-contractive iterates, Studia Univ. Babes-Bolyai, Mathematica,XXV,4, 1980, 47-51 (in
Romanian)[7] Rus, I.A., The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory,
9(2004), No.2, 541-559[8] Rus, I.A., Some nonlinear functional differential and integral equations, via weakly Picard operator theory: a survey,
Carpathian J. Math., 26(2010), 230-258[9] Rus, I.A., Petrusel, A., Petrusel, G., Fixed Point Theory, Cluj University Press, Cluj-Napoca, 2008
ICAM9
A Volterra Functional - integral Equation, via Weakly Picard Operators Technique
Viorica MuresanTechnical Unversity of Cluj-Napoca, Romania
In this paper we consider a Volterra functional - integral equation with linear modifications of thearguments. By using Contraction principle and weakly Picard operators’ technique, we give existences,uniqueness and data dependence results for the solution.
Bibliography[1] Muresan, V., Functional - Integral Equations, Mediamira, Cluj-Napoca, 2003[2] Serban, M.A., Rus, I.A. and Petrusel, A., A class of abstract Volterra equations, via weakly Picard operators’ technique,
Math. Ineq. & Appl. (Zagreb), 13(2010), No. 2, 255-269
ICAM9
Fixed point theorems for contractions of rational type in metric spaces, for multivalued operators
Anca OpreaBabes-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, Romania
The purpose of this paper is to present a fixed point result, for multivalued operators, whichsatises the contractive conditions of rational type on complete metric spaces.We extend the resultsof I.Cabrera, J.Harjani and K.Sadarangan [2]to multivalued operators.The paper will contain also aproof for the fixed point theorems for contractions of rational type in partially ordered metric spaces.
ICAM9
14
Qualitative properties of functional differential systems
Diana Otrocol and Veronica Ana IleaT. Popoviciu” Institute of Numerical Analysis and Babes-Bolyai University, Romania
[email protected], [email protected]
In this paper we study certain qualitative properties of functional differential systems using weaklyPicard operators techniques. In the end, some applications are given.
Bibliography[1] V. Kolmanovskii, A. Mishkis, Applied theory of functional differential equations, Kluwer Academic Publisers, 1992[2] D. Otrocol, Abstract Volterra operators, Carpathian J. Math., 24(2008) no. 3, 370-377[3] J. Sremr, On the initial value problem for two-dimensional linear functional differential systems, Memoirs on Diff. Eq.
and Math. Physics, 50(2010), 1-127[4] M.A. Serban, I.A. Rus, A. Petrusel, A class of abstract Volterra equations, via weakly Picard operators technique,
Mathematical Inequalities & Applications, 13(2010), 255-269
ICAM9
Fixed point theorems for nonself Presic type operators
Madalina PacurarBabes-Bolyai University of Cluj-Napoca, Romania;
In some previous papers, [1]-[4] the authors have studied the existence and approximation of fixedpoints of single-valued self Presic type operators f : Xk → X, where k ≥ 1 is a positive integer.
The main aim of the present paper is to extend some of those results from self mappings to nonself mappings.
Bibliography[1] Ciric, L.B., Presic, S.B., On Presic type generalization of the Banach contraction mapping principle, Acta Math.
Univ. Comenianae, 76 (2007), No. 2, 143-147[2] Pacurar, M., Iterative Methods for Fixed Point Approximation, Risoprint, Cluj-Napoca, 2010[3] Pacurar, M., A multi-step iterative method for approximating fixed points of Presic-Kannan operators, Acta Math.
Univ. Comen. New Ser., 79 (2010), No. 1, 77-88[4] Pacurar, M., Fixed points of almost Presic operators by a k-step iterative method, An. Stiint,. Univ. Al. I. Cuza Iasi,
Ser. Noua, Mat. (to appear)[5] Pacurar, M., Common fixed points for almost Presc type operators. Carpathian J. Math. 28 (2012), no. 1, 117–126
ICAM9
Remarks on cyclic coupled fixed point theorems
Mihaela PetricTechnical University Cluj-Napoca, North Unversity Center Baia Mare, Romania
The objective of this lecture is to present some remarks concerning the concepts of coupled fixedpoints and coupled best proximity points for cyclical contractions.
Bibliography[1] Borcut, M., Berinde, V., Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces,
Nonlinear Anal., 74 (2011), 48894897[2] Sintunavarat, W., Kumam, P., Coupled best proximity point theorem in metric Spaces, Fixed Point Theory and
Applications 2012, 2012:93
ICAM9
15
Some existence results for a system of operatorial equations
Ioan A. Rus and Marcel-Adrian SerbanBabes-Bolyai Unversity Cluj-Napoca, Romania
[email protected] [email protected]
In this paper we study a system of operatorial equations in terms of vectorial distances and vectorialmeasures of noncompactness. The basic tools are some classical fixed point principles, the generalretraction operator principle and the cartesian hull of a subset of a cartesian product. Applications tosome systems of functional integral equations are also given.
Bibliography[1] Rus, I.A., On the fixed points of the mappings defined on a cartesian product (III), (in Romanian), Studia Univ.
Babes-Bolyai Math., 24(1979), 55-56.[2] Rus, I.A., Petrusel, A., Petrusel, G. Fixed Point Theory, Cluj University Press, Cluj-Napoca, 2008.[3] Serban, M.A., Fixed point theorems on cartesian product, Fixed Point Theory, 9(2008), No. 1, 331-350.[4] Serban, M.A., Fixed Point Theory for Operators on Cartesian Product, (in Romanian), Cluj University Press,
Cluj-Napoca, 2002.
ICAM9
Fixed point results in cone metric spaces
Adrian ViorelDepartment of Mathematics, Technical University of Cluj-Napoca, Romania
In this work we deal with cone metric spaces, generalizations of metric spaces wherein the metrictakes values in a cone rather than in R+. Cone metric spaces were (re)introduced by Huang and Zhang(2007), the authors being unaware of the fact that the concept existed under the name K-metric (orK-normed) space. Following the article of Huang and Zhang, a great deal of interest has risen aroundcone metric spaces and their corresponding fixed point theory. Recently, Amini-Harandi and Fakhar,respectively Jankovic and coworkers, proved independently that the topology generated by the conemetric coincides with the topology generated by a usual (scalar) metric. Based on this observationsome of the cone fixed point results obtained in the recent years were shown to be direct consequencesof standard metric fixed point theorems. The aim of this contribution is to extend these investigationsin the following directions: K-boundedness, compactness and K-nonexpansive operators, which arerelevant in fixed point theory.
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2. Optimization Theory, Operations Research and Applications
Cellular Automata Topologies and Rules
Anca Andreica1, Camelia Chira1, Alexandru Agapie2
1Babes-Bolyai University of Cluj-Napoca, Romania and 2University of Economic Studies, Bucharest, Romania
[email protected], [email protected], [email protected]
Cellular Automata (CAs) represent useful and important tools in the study of complex systemsand interactions. CAs can generate a complex behavior based on the local interaction of simplecomponents that evolve according to some state change rule [3]. The detection of rules that exhibitcoordinated global information processing is a challenging task highly important in the study ofcomplex systems.
In this paper we investigate different CA topologies with probability-based rules for both asyn-chronous [1] and synchronous [2] Cellular Automata. Computational experiments focus on the
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density classification task for the one-dimensional binary-state CA. This is a prototypical distributedcomputational task with the objective of finding the density most present in the initial cellular state.The discovery of rules exhibiting a high degree of global self-organization is not easily achieved sincecoordinated global information processing must rise from the interactions of components with localinformation and communication. The use of probability-based rules for the density task generates acomplex behavior with competitive performance in the correct classification of initial configurations.Results are analysed in the context of various topologies for CA with binary states.
Bibliography
[1] Agapie, A., Hns, R., Mhlenbein, H., Markov Chain Analysis for One-Dimensional Asynchronous Cellular Automata,Methodology And Computing In Applied Probability, Volume 6, Issue 2, pp 181-201 (2004)
[2] Chira, C., Gog, A., Lung, R. I., Iclanzan, D., Complex Systems and Cellular Automata Models in the Study ofComplexity, Studia Informatica series, Vol. LV, No. 4, pp. 33-49 (2010)
[3] Wolfram, S., Theory and Applications of Cellular Automata, Advanced series on complex systems, World ScientificPublishing, 9128 (1986)
ICAM9
On the Crossing Numbers of Cartesian Products with Paths
Emılia DrazenskaTechnical university, Kosice, Slovak Republic
In general, compute the crossing number for a given graph is a very difficult problem. It has beenproved that this problem is NP–complete. The crossing numbers of a few families of graphs are known.Most of them are Cartesian products of special graphs.
The crossing numbers of Cartesian products of cycles, stars and paths with all graphs of order fourare given. The crossing numbers of Cartesian products of cycles with many graphs of order five aregiven. Except for the star S5, there are given the crossing numbers of GCn for all five–edge trees G.Values of crossing numbers of the Cartesian products GCn, GSn, GPn with six–vertex graphsG are known for several graphs G.
We extend these results by giving the exact values of crossing numbers of Cartesian productsGPn for every tree G on seven vertices. There are 11 trees of order seven.
ICAM9
Modified Han algorithm for inconsistent linear inequalities
Doina Carp1, Constantin Popa2, Cristina Serban3
1 Constanta Maritime University, Romania2 Faculty of Mathematics and Computer Science, Ovidius University of Constanta, Romania3 Faculty of Civil Engineering, Ovidius University of Constanta, Romania
[email protected], [email protected], [email protected]
In the paper [2] the author described a finitely terminating algorithm for solving an inconsistentsystem Ax ≤ b of linear inequalities in a least squares sense. His algorithm uses a singular valuedecomposition of a submatrix of A om each iteration, making it impractical for all but only smallerproblems. The same disadvantages appear for the version of Hans method proposed in [1], where aQR factorization with column pivoting is used. In order to overcome these difficulties, in this paperwe show that a modification of Han’s algorithm allows us to introduce a controlled (possible iterative)approximation to the original singular value solution. We also present numerical experiments andcomparisons with the original methods from [1] and [2].
Bibliography
[1] R. Bramley, B. Winnicka, Solving linear inequalities in a least squares sense, SIAM J. Sci. Comp., 17(1) (1996),275-286.
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[2] S.-P. Han, Least squares solution of linear inequalities, tech. rep. TR-2141, Mathematics Research Center, Universityof Wisconsin - Madison, 1980.
ICAM9
Evolutionary Algorithms for Dynamic Complex Problems
Camelia Chira, Anca AndreicaBabes-Bolyai University of Cluj-Napoca, Romania
[email protected], [email protected]
Evolutionary approaches to dynamic complex problems need to be able to continously adapt thesolution to a changing environment [1]. This study focuses on the detection of dynamic communitiesin complex networks. Networks represent a central model for the description of complex phenomenaand they have been studied independently in many different fields such as mathematics, neuroscience,biology, epidemiology, sociology, social-psychology and economy. The detection of communities incomplex networks is a challenging problem recognized to be NP-hard [2]. The dynamic version ofthe problem is of great significance since most real-world networks change in time and this dynamicbehaviour should be reflected in the evolution of communities. For example, ad-hoc networks formedby communication nodes constantly change and need to be grouped in order to be able to choose themost efficient communication path. Clearly, the study of dynamic networks can facilitate predictionsabout the evolution in time of networks from various different areas. Dynamics add another dimensionof complexity to the NP-hard problem of detecting communities. An extra mechanism is needed todeal with the network at different timesteps and to include as necessary in the detection of the currentcommunity structure, the community structure that existed at the previous timestep.
Online algorithms should be able to capture the dynamic aspect of network data and adjustonline the communities as the network evolves. These features are well described by the concept ofevolutionary clustering introduced in [3] and engaged in some of the existing methods for the detectionof evolving communities [4, 5, 6]. The strategy is to look for a trade-off between snapshot quality (ameasure of how good the current community structure is) and history cost (a measure of how differentthe current community structure is compared to the previous one). In this paper, we investigate theperformance of evolutionary models for this dynamic complex problem by facilitating the adaptationof solutions to the changes in network structure during their evolution.
Bibliography
[1] Branke, J., Evolutionary optimization in dynamic environments, 2001, Kluwer academic publishers.[2] Fortunato, S., Community detection in graphs, arxiv 0906.0612, 2010.[3] Chakrabarti, D., Kumar, R., Tomkins, A., Evolutionary clustering, Proceedings of the 12th ACM SIGKDD
international conference on Knowledge discovery and data mining, KDD ’06, ACM, 554-560, 2006.[4] Lin, Y., Chi, Y., Zhu, S., Sundaram, H., Tseng, B., Facetnet: a framework for analyzing communities and their
evolutions in dynamic networks,Proceedings of the 17th international conference on World Wide Web, 685-694, ACM,2008.
[5] Kim, M.-S., Han, J., A particle-and-density based evolutionary clustering method for dynamic networks, Proc. VLDBEndow.,Vol. 2, No. 1, 622-633, 2009.
[6] Folino, F., Pizzuti, C., Multiobjective evolutionary community detection for dynamic networks, Proceedings of the12th annual conference on Genetic and evolutionary computation, GECCO ’10, 535-536, ACM, 2010.
ICAM9
Systems of knowledge representation based on stratified graphs and their inference process
Daniela DanciulescuUniversity of Craiova, Craiova, Romania
Systems of knowledge representation based on stratified graphs and their inference processThe concept of stratified graph introduces some method of knowledge representation ([8], [10]).
The inference process developed for this method uses the paths of the stratified graphs, an order
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between the elementary arcs of a path and some results of universal algebras. The order is defined byconsidering a structured path instead of a regular path. In this paper we define the concept of systemof knowledge representation as a tuple of the following components: a stratified graph G, a partialalgebra Y of real objects, an embedding mapping (an injective mapping that embeds the nodes of Ginto objects of Y) and a set of algorithms such that each of them can combine two objects of Y toget some other object of Y. We define also the concept of inference process performed by a systemof knowledge processing. The inference process is based on the concept of accepted structured path.The set of all accepted structured paths of G is organized as a partial algebra ASP(G) such thatevery accepted structured path d can be uniquely decomposed by means of two accepted structuredsubpaths of d. We show that the inference process is a morphism of partial algebras.
Bibliography[1] V. Boicescu, A. Filipoiu, G. Georgescu and S. Rudeanu, Lukasiewicz-Moisil Algebra, Annals of Discrete Mathematics
49 (North-Holland, 1991)[2] Tudor (Preda) Irina-Valentina, Considerations Regarding Formal Languages Generation Using Labelled Stratified
Graphs, International Journal of Applied Mathematics and Informatics, University Press, Issue 2, Volume 5, pp.101-108, 2011
[3] Tudor (Preda) Irina-Valentina, Generating Natural Language by Labelled Stratified Graphs, Scientific Bulletin -University of Pitesti, Matematics and Informatics Series, pg. 89-100, Nr. 17 (2011)
[4] N. Tanareanu, Knowledge Bases with Output, Knowledge and Information Systems 2/4, 438460, 2000[5] N. Tandareanu, Knowledge representation by labeled stratified graphs, Proceedings of the 8th World Multi Conference
on Systemics, Cybernetics and Informatics (2004), Vol. 5, 345-350.
ICAM9
Inverse Generalized Maximum Flow Algorithms
Adrian Deaconu and Mihai IoluUniversity Transilvania of Brasov, Department of Computer Science, Brasov, Romania
[email protected], [email protected]
In this paper we present algorithms for solving the inverse generalized maximum flow problem(denoted IGMF). A generalized maximum flow problem takes into account the gain (loss) of flow oneach arc. An inverse generalized maximum flow problem is to change the capacities of the arcs so thata given feasible flow becomes a maximum flow in the modified network and the distance between theinitial vector of capacities and the modified one is minimum.
The first problem we solve is the problem of inverse generalized maximum flow under max-typedistances (denoted IGMFM). We present an algorithm that solves this problem in O(mn · log(n))time.
We study IGMFM and the inverse generalized maximum flow under sum-type distances (denotedIGMFS) in lossy networks, in which every residual arc is lossy (the gain factor is less or equalto one). In the case of lossy networks we show that the algorithm for IGMFM improves its time
complexity to O(m · log(n)). We also present an O(mn · log(n2/m)) or O(minn2/3,m1/2 · m ·log(n2/m) · log(maxn,U)) time algorithm for IGMFS (depending on the implementation, stronglyor, respectively, weakly polynomial).
For all algorithms we present an apriori fast test that tells us if the problem has feasible solutionor not.
Bibliography[1] R.K. Ahuja, T.L. Magnanti, J.B. Orlin, Network Flows. Theory, Algorithms and Applications, Prentice Hall,
Englewood Cliffs, NJ, 1993[2] R.K. Ahuja, J.B. Orlin: Combinatorial Algorithms for Inverse Network Flow Problems, Networks (2002).[3] E. Ciurea, A. Deaconu, Inverse Minimum Flow Problem, Journal of Applied Mathematics and Computing, 23
(2007) 193-203.[4] A. Deaconu, The Inverse Maximum Flow Problem Considering L∞ Norm, RAIRO, 42 (2008), No. 3, 401-414[5] C. Heuberger, Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results, Journal of
Combinatorial Optimization, 8 (2004) 329-361[6] L. Liu and J. Zhang, Inverse Maximum Flow Problems under Weighted Hamming Distance, J. Combin. Optim., 12
(2006) 395-408
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[7] P.T. Sokkalingam, R.K. Ahuja, J.B. Orlin, Solving Inverse Spanning Tree Problems through Network Flow Techniques,Oper. Res. 47 (1999) 291-298.
[8] C. Yang, X. Chen, An Inverse Maximum Capacity Path Problem with Lower Bound Constraints, Acta Math. Sci.,Ser. B 22 (2002) 207-212.
[9] C. Yang, J. Zhang, Z. Ma, Inverse Maximum Flow and Minimum Cut Problems, Optimization, 40 (1997) 147-170[10] J. Zhang, C. Cai, Inverse Problems of Minimum Cuts, ZOR-Math. Methods Oper. Res. 47 (1998) 51-58.
ICAM9
Minimal intersections in graph drawings
Marian KlescTechnical Unversity of Kosice, Slovakia
The visualized graph should be very effective in many research areas and technical applications. Itis known that the aesthetics and readability of graph-structures heavily depends on the number ofcrossings, when the structures are visualized on a 2-dimensional medium.
The crossing number cr(G) of a graph G is the smallest number of edge crossings in any drawingof G in the plane. It was introduced by Turan [6] during the World War II. The crossing numberproblem has been vividly investigated for over 60 years, but there are only few infinite graph classesfor which the values of crossing number are known. Even for the complete and complete bipartitegraphs this invariant is known only for some few parameters. In general, computing the crossingnumber is very difficult. It has been proved by Garey and Johnson [2] that computing the crossingnumber of a graph is an NP-hard problem.
In 1973, Harary, Kainen, and Schwenk [4] established the crossing number of the Cartesian productC3 × C3 and conjectured that cr(Cm × Cn) = m(n− 2) for 3 ≤ m ≤ n. Recently has been proved byGlebsky and Salazar [3] that for any fixed m ≥ 3, the conjecture holds for all n ≥ m(m+ 1). Besidesthe Cartesian products of two cycles, there are several other exact results. In 2007, Bokal [1] provedthe conjecture given by Jendrol’ and Scerbova [5] that cr(K1,n × Pm) = (m − 1)bn2 cb
n−12 c for the
path Pm of length m. Applying the capped Cartesian product operation in combination with a newlyintroduced π– subdivision, he established the crossing numbers for the Cartesian products of K1,n
with a tree of maximum degree 3 and for the product Wn × Pm, where Wn is the wheel on n + 1vertices.
In the talk, we summarise new results concerning crossing numbers for the Cartesian products oftwo graphs, for join products of two graphs as well as for some other operations on graphs.
Bibliography
[1] D. Bokal,On the crossing numbers of Cartesian products with trees, J. Graph Theory, 56 (2007), 287-300[2] M.R. Garey, D.S. Johnson,Crossing number is NP-complete, SIAM J. Algebraic and Discrete Methods, 4 (1983),
312-316[3] L.Y. Glebsky, G. Salazar, The crossing number of Cm ×Cn is as conjectured for n ≥ m(m+ 1), J. Graph Theory, 47
(2004), 53–72[4] F. Harary, P.C. Kainen, A.J. Schwenk,Toroidal graphs with arbitrarily high crossing numbers, Nanta Math., 6 (1973),
58–67[5] S. Jendrol’, M. Scerbova, On the crossing numbers of Sm × Pn and Sm × Cn, Casopis pro pestovanı matematiky, 107
(1982), 225-230[6] P. Turan,A note of welcome, J. Graph Theory, 1 (1977), 79
ICAM9
.
Greedoids on Vertex Sets of B-joins of Graphs
Vadim E. Levit and Eugen MandrescuAriel University and Holon Institute of Technology, Israel
[email protected] and eugen [email protected]
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Let G = (V (G), E(G)) denote a simple, finite, undirected graph. A subset A of V (G) is calleda local maximum stable set of if A is a maximum stable set in the subgraph induced by its closedneighborhood [2]. The family of all local maximum stable sets of G is denoted by Ψ(G). Let G1, G2
be two disjoint graphs, and let B = (V (G1), V (G2), E(B)) be a bipartite graph. By the B-joinof G1 and G2 we mean the graph B(G1, G2), whose vertex set is V (G1)
⋃V (G2) and edge set is
E(G1)⋃E(G2)
⋃E(B).
In this talk we present various conditions for Ψ(B(G1, G2)) to be a greedoid [1], in terms of thegraphs G1, G2, and B, using some findings from [3, 4, 5].
Bibliography
[1] Korte,B., Lovsz, L., Schrader, R., Greedoids, Springer-Verlag (Berlin), 1991.[2] Levit, E. V., Mandrescu, E., A new greedoid: the family of local maximum stable sets of a forest, Discrete Applied
Mathematics, 124 (2002), 91-101[3] Levit, E. V., Mandrescu, E., Local maximum stable sets in bipartite graphs with uniquely restricted maximum
matchings, Discrete Applied Mathematics 132 (2004), 163-174[4] Levit, E. V., Mandrescu, E., Graph operations that are good for greedoids, Discrete Applied Mathematics 158 (2010),
1418-1423[5] Levit, E. V., Mandrescu, E., On local maximum stable set greedoids, Discrete Mathematics 312 (2012), 588-96
ICAM9
The maximum parametric flow in discrete dynamic networks
Mircea Parpalea and Nicoleta GrigorasNational College ”Andrei Saguna” Brasov, Romania; ”Cambridge School” of Constanta, Romania
[email protected]; nicole [email protected]
The aim of this paper is to present an approach for solving the maximum parametric flow overtime problem. The proposed algorithm consists in repeatedly finding a maximum dynamic flow fora sequence of parameter values, in their increasing order. In each of its iterations, the algorithmcomputes a new breakpoint for the maximum parametric flow value function. The complexity of thealgorithm is presented and also an example is given on how the algorithm works.
Bibliography
[1] Ahuja, R., Magnanti, T. and Orlin, J., Network Flows. Theory, algorithms and applications, Prentice Hall, Inc.,Englewood Cliffs, New Jersey, 1993
[2] Ciurea, E., Ciupala, L., ALGORITMI Introducere ın algoritmica fluxurilor ın retele Ed. MATRIX ROM. Bucuresti,2006
[3] Ciurea, E., Parpalea, M., A sequential algorithm for finding the solution of the parametric minimum flow problem,Carpathian Journal of Mathematics, 28(1) (2012), 47–58
[4] Hamacher, H. W. and L. R. Foulds, L. R., Algorithms for Flows with Parametric Capacities, ZOR - Methods Model.Oper. Res. 33 (1989), 21–37
[5] Parpalea, M., Min-Max Algorithm for the Parametric Flow Problem, Bulletin of the Transilvania University of Brasov,3(52) (2010), 191–198
[6] Parpalea, M., Ciurea, E., The quickest maximum dynamic flow of minimum cost, International Journal of AppliedMathematics and Informatics, 3(5) (2011), 266–274
[7] Ruhe, G., Complexity Results for Multicriterial and Parametric Network Flows Using a Pathological Graph of Zadeh,Zeitschrift fur Oper. Res. 32 (1988), 9–27
ICAM9
Pharaoh ants for Sensor Networks Security
Camelia PinteaTechnical University Cluj-Napoca, North Unversity Center Baia Mare, Romania
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A new conceptual model based on Pharaoh ants is introduced to solve a complex problem: thesecurity of networks. Pharaoh ants with their specific features will influence positively the results ofthe introduced algorithm.
Bibliography[1] Pintea, C-M., Pop, P.C., Sensor networks security based on sensitive robots agents. A conceptual model, Advances in
Intelligent Systems and Computing, Springer, 189(2013), 47-56[2] Pintea, C-M., Pop, P.C., Sensitive Ants for Denial Jamming Attack on Wireless Sensor Network, Advances in
Intelligent and Soft Computing Series, Springer, accepted.[3] Banerjee, S., Grosan, C., Abraham, A. IDEAS: Intrusion Detection based on Emotional Ants for Sensors. In:
Intelligent Systems Design and Applications, 344349, IEEE C.S. (2005)[4] Pintea, C-M., Dumitrescu D., Distributed Pharaoh System for Network Routing, Automat. Comput. Appl. Math.16(1-
2)(2007), 27-34
ICAM9
High-order optimality conditions for degenerate calculus of variations problems
A. Prusinska1, E. Szczepanik1 and A.A. Tret’yakov1,2
1 Siedlce University of Natural Sciences and Humanities, Siedlce, Poland2 Russian Acad. Sci., Dorodnitsyn Comp. Ctr., Moscow, Russia
The contribution is devoted to singular calculus of variations problems with constraint functionalnot regular at the solution point in the sense that the first derivative is not surjective. We pursue anapproach based on the constructions of the p-regularity theory. For p-regular calculus of variationsproblem we formulate and prove necessary and sufficient conditions for optimality in singular caseand illustrate our results by classical example of calculus of variations problem.
ICAM9
On the multidimensional multi-way number partitioning problem
Petrica PopDepartment of Mathematics and Computer Sciences, Faculty of Sciences, North University Center at Baia Mare, Technical University of
Cluj-Napoca, Romania
In this paper, we consider a generalization of the two-way number partitioning problem, calledthe multidimensional multi-way number partitioning problem (MDMWNPP), where a set of vectorshas to be partitioned into p sets (parts) such that the sums per every coordinate should be exactlyor approximately equal. We present a survey of the existiting techniques for solving this complexproblem.
Bibliography[1] J. Kojic, Integer linear programming model for multidimensional two-way number partitioning problem, Comput.
Math. Appl. 60 (2010) 2302 - 2308.[2] P.C.Pop and O. Matei, A memetic algorithm approach for solving the multidimensional multi-way number partitioning
problem, Appl. Math. Model. in press.
ICAM9
Intelligent methods for making the best decisions using optimization techniques and data mining
Cosmin SaboDepartment of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Romania
The use of database technology to manage large volumes of business data is growing at anexponential rate and leads to a phenomenon now referred to as Big Data. The size and the volume
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data being managed by the companies raise the following interesting issue: can we use intelligentmethods wherein the data to help business achieve competitive advantage? This is the major goal of ourresearch and based on our expertise on managing large volumes of data, data mining and optimizationwe will provide intelligent methods that will provide the capabilities to explore, summarize and modelthe business data.
ICAM9
Axiomatic set theory for functional analysis
Michal StasFaculty of Electrical Engineering and Informatics, Technical University of Kosice, Bozeny Nemcovej 32, 042 00 Kosice, SR
Mathematicians usually prefer to work in the Zermelo-Fraenkel axiomatic set theory ZF or ZFwith the Axiom of Choice AC denoted as ZFC. A lot of them often do not notice when they have usedAC, even in an essential way. However the common proofs of many results especially in functionalanalysis usually exploit the Axiom of Choice in spite of the fact that one can prove them in ZF orin ZF with a weak form of AC. We shall try to indicate that a weaker form of an axiom of choice issufficient for proving a statement, e.g., important results in functional analysis as the Hahn-BanachTheorem or the Baire Category Theorem with its consequences for Banach spaces.
Bibliography
[1] Bell J.L., Fremlin D.H., Geometric form of the axiom of choice, Fund. Math. 77 (1972), no. 2, 167170.[2] Blair C. E., The Baire category theorem implies the principle of dependent choices, Bull. Acad. Polon. Sci. Ser. Sci.
Math. Astronom. Phys. 25 (1977), 933–934.[3] Bukovsky L., The Structure of the Real Line, Monografie Matematyczne, Vol. 71 2011.[4] M. Foreman and F. Wehrung, The Hahn-Banach Theorem implies the existence of a non-Lebesgue measurable set,
Fundamenta Mathematicae 138, no. 1 (1991), 13–19.[5] H. Garnir, M. de Wilde and J. Schmets, Analyse fonctionelle I, Birkhuser, Basel, (1968).[6] Halpern, J.D., Levy, A., The Boolean prime ideal theorem does not imply the axiom of choice, Axiomatic Set Theory,
Proceedings of Symposia in Pure Mathematics 13 (1971) part 1, D. Scott ed., American Math. Soc., Providence,83-134.
[7] Howard P. and Rubin J.E., The Boolean prime ideal theorem+countable choice do not imply dependent choice, Math.Logic Quarterly 42 (1996) 410-420.
[8] Luxemburg, W., Two applications of the method of construction by ultrapowers to analysis, Bull. Amer. Math. Soc.68, (1962)416-419.
[9] Luxemburg, W., Beweis des Satzes von Hahn-Banach, Arch. Math (Basel) 18, (1967a) 271-272.[10] Luxemburg, W., Reduced powers of the real number system and equivalents of the Hahn-Banach theorem, Technical
Report 2, Cal. Inst. Tech. (1967b)[11] Pincus, D., Independence of the prime ideal theorem from the Banach theorem, Bull. Amer. Math. Soc. 78, (1972),
766-770.[12] Pincus, D. The strength of the Hahn-Banach theorem, Proc. Victoria Symposium on Nonstandard Analysis, Springer-
Verlag, New York, (1974), 203-208.[13] Pincus D. and Solovay R.M., Definability of measures and ultrafiltersh. Journal of Symbolic Logic 42, (1977), n. 2,
179-190.[14] Solovay R. M., A model of set theory in which every set of reals is Lebesgue measurable, Ann. of Math. 92 (1970),
156.
ICAM9
Testing artificial neural network for gesture recognition
Jozsef Suto and Stefan OnigaUniversity of Debrecen, Hungary
Neural networks are well applicable for gesture recognition. In this article we want to present theresult of a feed forward network for a simplified gesture recognition problem.
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In neural networks, the learning algorithm is very important, because the performance of neuralnetwork depends on it. One of the most known learning algorithm is the backpropagation. There aresome mathematical software which provides acceptable result for a given problem by a backpropagationbased network, but in some cases a high-level programming language implemented program can providebetter solution.
Acknowledgement The research was supported by the European Union and the State ofHungary, co-financed by the European Social Fund in the framework of TMOP 4.2.4.A/2-11-1-2012-0001 ”National Excellence Program - Elaborating and operating an inland student and researcherpersonal support system convergence program”.
The used devices and development accessories was financed by TAMOP-4.2.2.C-11/1/KONV-2012-0001 project. The acquisition of used devices and development accessories has been supported by theEuropean Union, co-financed by the European Social Fund.
Bibliography
[1] Martin T. Hagan, Howard B. Demuth, Mark Beale, Neural Network Design, ISBN 7-111-10841-8, 1996[2] Ben Krse, Patrick van der Smagt, An introduction to Neural Networks, Eight edition, University of Amsterdam,
November 1996[3] S.Oniga, I.Orha, Hardware Implemented Neural Networks used for Hand Gestures Recognition, Carpathian Journal of
Electronic and Computer Engineering, vol. 4, 11/2011[4] James A. Freeman, David M. Skapura, Algorithms, Applications, and Programming Techniques, ISBN 0-201-51376-5,
1991[5] Kouichi Murakami, Hitomi Taguchi, Gesture recognition using recurrent neural networks, CHI’91 Proceedings of the
SIGCHI Conference on Human Factors in Computing Systems, 1991[6] G. Sebestyen, A. Tirea and R. Albert, Monitoring Human Activity through Portable Devices, Carpathian Journal of
Electronic and Computer Engineering, vol. 5, (2012)[7] Analog devices, ADXL345 3 axis digital accelerometer, Rev. D, 2009[8] Digilent Inc., Chipkit Max32 Board Reference Manual, Revision: July 25, 2011,
http://www.digilentinc.com/Data/Products/CHIPKIT-MAX32/chipKIT%20Max32 rm.pdf, 2013[9] C.G. Gavrincea, A.S. Tisan, Real time EMG pattern recognition system for hand postures, Carpathian Journal of
Electronic and Computer Engineering, vol. 1, 2008[10] A. Pavelka and A. Prochzka, Algorithms for Initialization of Neural Networks,
http://dsp.vscht.cz/konference matlab/matlab04/pavelka.pdf, 2013[11] Bjarne Stroustrup, The C++ Programming Language, ISBN 9789639301191, Copyright 1997 by AT&T
ICAM9
Communication aspects in Fibonacci type topologies
Ioana ZelinaDepartment of Mathematics and Computer Science, Technical University of Cluj-Napoca, North University Center at Baia Mare, Romania
The communication is a very important issue in interconnection networks for distributed systemsbecause the exchange of information is based on message exchange. In the case of direct interconnectionnetwork a processor communicates using direct links only with its neighbors that means the networktopology is of a great importance. The interconnection network can be seen as a graph and theproperties of a network can be studied using the graph theory. The Fibonacci cube, extended Fibonaccicube and Lucas cube are topologies based on the sequence of Fibonacci numbers which provide goodproperties for an interconnection network regarding diameter, node degree, recursive decomposition,embeddability and communication algorithms. In this paper we present a survey on the algorithmsfor routing and for broadcasting a message in Fibonacci type topologies.
Bibliography
[1] W.J. Hsu, Fibonacci cubes-new interconnection technology, IEEE Transactions on Parallel and Distributed Systems4(1)(1993), 312
[2] E. Munarini, C.P. Cippo, N. Zagaglia Salvi, On the Lucas cubes, Fibonacci Quarterly 39(1)(2001), 1221
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[3] I. Zelina, G. Moldovan, P.C. Pop, Some Communication Aspects in Extended Fibonacci Cubes, IEEE Proc. ofSAINT2008, Workshop HEUNET08, Turku, Finland, publisher IEEE Computer Society Press, 2008, 245-248
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3. Ordinary Differential Equations and Partial Differential Equations
Input-output methods in the study of nonuniform exponential dichotomy of evolution families
Mihai Gabriel BabutiaWest University of Timisoara, Romania
This talk presents one of our recent results from [4] concerning the nonuniform exponentialdichotomy in the light of (Cb, L
p) admissibility. We discuss our results by making a parallel to thoseobtained by M. Megan, A. L. Sasu and B. Sasu [3] in 2002 and to the recent developments of L.Barreira and C. Valls in [1] and [2] and Jiang and Liao in [5]. Overall, our results are extendedfrom the admissibility of spaces of continuous functions to the admissibility of Lp spaces, withoutconstructing auxiliary Lebesgue spaces.
Bibliography
[1] L. Barreira, C. Valls, Admissibility for nonuniform exponential contractions, J. Differential Equations 249 (2010),2889-2904.
[2] L. Barreira, C. Valls, Nonuniform exponential dichotomies and admissibility, Discrete Contin. Dynam. Systems 30(2011), 39-53.
[3] M. Megan, A. L. Sasu, B. Sasu, On nonuniform exponential dichotomy of evolution operators in Banach spaces,Integral Equations and Operator Theory 44 (2002), 71-78.
[4] A. L. Sasu, M. G. Babutia, B. Sasu, Admissibility and nonuniform exponential dichotomy on the half-line, Bull. Sci.Math. 137 (2013), 466-484.
[5] Y. Jiang and F. Liao, Admissibility for Nonuniform (µ, ν) Contraction and Dichotomy, Abstract and AppliedAnalysis Volume 2012, Article ID 741696, doi:10.1155/2012/741696
ICAM9
Some remarks on certain invariant geometric properties in Hele-Shaw flows
Paula CurtBabes-Bolyai Unversity of Cluj-Napoca, Romania
We study the time evolution of the free boundary of a viscous fluid for planar flows in Hele-Shawcells under injection. We analyze the geometrical properties of the moving frontier for bounded andunbounded (with bounded complement) domains and discuss both zero and non-zero surface tensionmodels. Applying methods from the theory of univalent functions, we prove the invariance in timeof Φ-likeness property (a geometric property which includes starlikeness and spirallikeness) and ofα-convexity (a geometric property which makes a continuous passage from the starlike functions tothe convex functions). In the case of bounded domains we get an upper bound α0 (α0 > 0) for α, suchthat the α-convexity property of the moving boundary is preserved in time for each α ≤ α0. In thecase of unbounded domains we generalize the fact that the convex dynamics is preserved in time, byobtaining the invariance in time of α-convexity for α sufficiently close to 1. Moreover, we establish anupper bound for the order of strongly starlikeness of the classical solution in the Hele-Shaw problemwhich starts with a starlike bounded domain.
Bibliography
[1] Curt, P., Fericeanu, D., A special class of univalent in Hele-Shaw flow problems, Abstr. Appl. Anal., Vol. 2011, Art.ID 948236, 10 pp.
25
[2] Curt, P., Fericean, D., Grosan, T., φ-like functions in two-dimensions free boundary problems, Mathematica,63(76)(2011), no. 2, 121-130.
[3] Fericean, D., Strongly φ-like functions of order α in two-dimensions free boundary problems, Applied Math. andComp., 218(15)(2012), 7856-7863.
[4] Gustafsson, B., Prokhorov, D., Vasil’ev, A., Infinite lifetime for the starlike dynamics in Hele-Shaw cells, Proc. of theAmerican Math. Soc., 132(2004), no. 9, 2661-2669.
[5] Gustafsson, B., Vasil’ev, A., Conformal and Potential Analysis in Hele-Shaw Cells, Birkhauser Verlag, 2006, 231 pp.[6] Miller, S.S., Mocanu, P.T., The theory and applications of second-order differential subordinations, Studia Univ.
Babes-Bolyai, Math., 34(1989), no. 4, 3-33.[7] Polubarinova-Kochina, P. Ya., On a problem of the motion of the contour of a petroleum shell, Dokl. Akad. Nauk
USSR, 47(1945), no. 4, 254-257 (in Russian).
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Reversible cubic systems with centers
Dumitru CozmaTiraspol State University, Republic of Moldova
By using a nondegenerate transformation of variables and a time rescaling, a cubic system with asingular point with pure imaginary eigenvalues (λ1,2 = ±i, i2 = −1) can be brought to the form
x = y + ax2 + cxy + fy2 + kx3 +mx2y + pxy2 + ry3,
y = −(x+ gx2 + dxy + by2 + sx3 + qx2y + nxy2 + ly3),(1)
where the variables and coefficients in (1) are assumed to be real. Then the origin O(0, 0) is a singularpoint of a center or a focus type for (1). It arises the problem of distinguishing between a center anda focus, i.e. of finding the coefficient conditions under which O(0, 0) is, for example, a center. Weobtain the center conditions for system (1) by using the method of rational reversibility.
An algorithm for checking whether it is possible to transform a given system to one which istime-reversible by means of a bilinear transformation was described in [1] and an algorithm for findingall time-reversible systems within a given family of 2-dim systems of ODE’s whose right-hand sidesare polynomials was presented in [2]. The relation between time-reversibility and the center-focusproblem was discussed in [3]. The center conditions for cubic system (1) with two invariant straightlines was obtained in [4] by using the method of rational reversibility.
Bibliography
[1] Lloyd, N.G., Pearson, J.M., Symmetry in planar dynamical systems, J. Symbolic Computation, 33 (2002), 357-366.[2] Romanovski V.G., Time-reversibility in 2-dimensional systems, Open Sys. & Infor. Dyn., 15 (2008), no.4, 359–370.[3] Teixeira, M.A., Yang Jiazhong, The center-focus problem and reversibility, J. of Diff. Equations, 174 (2001), 237–251.[4] Cozma D., Darboux integrability and rational reversibility in cubic systems with two invariant straight lines,
Electronic Journal of Differential Equations, Vol. 2013 (2013), no.23, 1–19.
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Infinitely differentiable functions represented into Newton interpolating series
G. Groza1, M. Jianu1 and N. Pop2
1Dept. of Math. and Comp. Science, Technical University of Civil Eng. of Bucharest, Romania2Dept. of Math. and Comp. Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Baia Mare,
Romania,
[email protected], marilena [email protected], [email protected]
Given the interpolating sequence defined by α1 = 0, α2 = 1, α3 = 12 , and for k ≥ 4,
αk =2s+ 1
2m+1, when k ∈ (2m + 1, 2m+1 + 1], s = k − 2m − 2,
26
we construct the polynomials u0(x) = 1,
uk(x) =k∏j=1
(x− αj), k ≥ 1.
By extending the results of [1] and [2] we study infinitely differentiable functions f : [0, 1]→ R whichcan be represented into Newton interpolating series at αkk≥1, that is
f(x) =∞∑k=0
akuk(x).
The results are used to obtain approximate solutions of boundary value problems for ODEs.
Bibliography
[1] G. Groza, N. Pop, A numerical method for solving of the boundary value problems for ordinary differential equations,Result. Math., 53(2009), No. 3-4, 295-302.
[2] G. Groza, S. M. Ali Khan, N. Pop, Approximate solutions of boundary value problems for ODEs using Newtoninterpolating series, Carpathian. J. Math., 25(2009), No. 1, 73-81.
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Mathematical models for repetitive phenomena in the excitable media. The case of turbulent mixing
Adela IonescuDepartment of Applied Mathematics, University of Craiova, Romania
This paper focuses on some new trends in CFD (computational fluid dynamics), an exciting andattractive discipline which nowadays becomes more and more mature. It concerns the turbulenceproblem in mixing media. The mixing theory appears in an area with far from complete solvingproblems: the flow kinematics. Its methods and techniques developed the significant relation betweenturbulence and chaos. The turbulence is an important feature of dynamic systems with few freedomdegrees, the so-called “far from equilibrium systems”. These are widespread between the models ofexcitable media, and a recent challenge is to find a consistent and coherent theory to stand up that amixing model in excitable media leads to a far from equilibrium model.
Studying a mixing for a flow implies the analysis of successive stretching and folding phenomenafor its particles, the influence of parameters and initial conditions. In the previous works, the study ofthe 3D non-periodic models exhibited a quite complicated behavior. In agreement with experiments,they involved some significant events - the so-called “rare events”. The variation of parameters had agreat influence on the length and surface deformations.
In this paper there is continued the author’s work started in recent years on turbulent mixing.The 3D mixing flow phenomena had very few analytical and experimental tests, in order to provethat this model has a far from equilibrium behavior and it is very sensitive to the variation of itsparameters and orientation versors. The comparisons of deformation (in length and surface) efficiencyof 3D versus 2D case brought a very rich panel of random distributed events. An important partialconclusion was that the mixing, and especially the turbulent mixing, is introduced at irrational valuesof length and surface versors.
There is used a modern mathematical soft, MAPLE11, which has a lot of computationalappliances. Crossing over from 2D to 3D case, it is easy to deduce the requirement of a special analysisof the influence of parameters on the behavior of this complex mixing flow. Since in the precedentwork there were obtained numeric plots standing for the images of the deformation efficiency, in thispaper the standpoint is a little changed. Using specific computational appliances, from “DEplot”package, there is started a computational comparison analysis of the flow behavior in 2D and 3D case.Two analysis directions are followed:
a) The widespread isochoric 2D (non-periodic) flow model, versus the 3D mixing flow model;b) The general 2D (non-periodic) flow model versus the 2D perturbed model.
27
Thus, the panel of random distributed events would be completed with new special events andnew data would be collected for the qualitative analysis of the mixing phenomena.
Bibliography[1] A. Ionescu, Recent trends in computational modeling of excitable media dynamics, Lambert Academic Press 2010,
Saarbrucken, Germany[2] A. Ionescu, Recent challenges in turbulence: computational features of turbulent mixing, Recent advances in Continuum
Mechanics (Proceedings of the 4th IASME/WSEAS Int. Conference on Continuum Mechanics), Mathematics andComputers in Science and Engineering, Cambridge, UK, 24-26 feb 2009, 29-38
[3] J.M. Ottino, The kinematics of mixing: stretching, chaos and transport. Cambridge University Press. 1989[4] A. Ionescu, New approach for the turbulent mixing study – the behavior of vortic flows from computational standpoint,
Acta Universitatis Apulensis Journal, Special Issue – Proceedings of the International Conference on Theory andApplications of Mathematics and Informatics ICTAMI 2009, Aeternitatis Publishing House, Alba Iulia 2009, 13-22
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Exact periodic patterns in quasi-linear reaction-diffusion systems with competitions
Mihaly KlincsikUnversity of Pecs, Hungary
Modeling of some real biological pattern formations often leads to different reaction-diffusionsystems. All models for spatial pattern generation are necessarily nonlinear practical applicationsrequire numerical solutions since no non-trivial analytical solutions are available in general. Weshall present some periodic non-constant stationary solutions to the simplified Shigesada-Teramoto-Kawasaki PDE system (see in [1] and [2]), which describes the population density of two competitivespecies. The solution exhibits specific periodic spatial segregation behavior of the species in case ofone space dimension.
Bibliography[1] Shigesada N., Kawasaki K., Teramoto E., Spatial segregation of interacting species, J. Theor. Biology 79(1979), 83-99.[2] Murray J. D., Mathematical Biology, Springer Verlag, Berlin, 1989.
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Limits of solutions to the singularly perturbed abstract hyperbolic-parabolic systems
Andrei PerjanMoldova State University, Chisinau, Moldova
Let H and V be two real Hilbert spaces such that V ⊂ H continuously and densely. LetA(t) : D(A) ⊂ H → H be a family of self-adjoint positive defined operators and let B : D(B) ⊂ H → Hbe a nonlinear operator.
We study the behavior of solutions uε to the following abstract hyperbolic systemε u′′ε(t) + u′ε(t) +A(t)uε(t) +B
(uε(t)
)= fε(t), t ∈ (0, T ),
uε(0) = v0ε, u′ε(0) = v1ε,
as ε→ 0. Under some conditions on operators A(t) and B, we prove that uε → v, when v0 ε → v0 andfε → f in some topologies, where v is the solution to the following abstract parabolic system
v′(t) +A0v(t) +B(v(t)
)= f(t), t ∈ (0, T ),
v(0) = v0.
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28
Numerical Approach for Solving Nonlinear Electromagnetic Problem
Vladimir Patiuc, Galina RıbacovaMoldova State University, Republic of Moldova
[email protected], [email protected]
We consider the nonlinear problem for semiconductor diode based on drift-diffusion equations[1]. The proposed numerical approach consists of the finite volume method [2] in combination withsome iterative procedure (Gummel’s algorithm) and Newton’s method for internal linearization. Someresults of numerical simulation are presented.
Bibliography[1] Numerical Methods in Electromagnetics, Special Volume (W.H.A. Schilders and E.J.W. ter Maten, Guest Editors) of
Handbook of Numerical Analysis, Vol. XIII. Elsevier, Amsterdam, 2005[2] Li R., Chen Z., Wu W., Generalized Difference Methods for Differential Equations. Numerical Analysis of Finite
Volume Methods, Marcel Dekker Inc., New York-Basel, 2000
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Singularly perturbed problems for abstract linear differential equations with positive powers of apositive defined operator
A. Perjan1, G. Rusu2
Moldova State University, Chisinau, Moldova
[email protected] and [email protected]
Let H be a real Hilbert space endowed with the scalar product (·, ·) and the norm | · |. LetAi : D(Ai) ⊂ H → H, i = 0, 1, be two linear self-adjoint operators.
Consider the following Cauchy problem:ε(u′′ε(t) +A1uε(t)
)+ u′ε(t) +A0uε(t) = fε(t), t ∈ (0, T ),
uε(0) = u0ε, u′ε(0) = u1ε,(Pε)
where ε > 0 is a small parameter(ε 1), uε, fε : [0, T )→ H.Supposing that the operator A1 is subordinated to a positive power of the operator A0, we
investigate the behavior of solutions uε to the problems (Pε) when u0ε → u0, fε → f as ε→ 0. Weestablish a relationship between solutions to the problems (Pε) and the corresponding solution to thefollowing unperturbed problem:
v′(t) +A0v(t) = f(t), t ∈ (0, T ),v(0) = u0.
(P0)
ICAM9
The 3D elastic contact applied to robots control
Nicolae PopTechnical University Cluj-Napoca, North Unversity Center Baia Mare, Romania
This paper proposes an algorithm for the condition detection in which the slip state transitionsin a stick-slip motion, or the solution breaks down and also to study the state transition of nodesbelonging to the contact area: stick, slip or open contact state. The Coulomb friction laws on thecontact boundary in 3D elastic contact problems applied to robots control are analyzed.
Bibliography[1] Oden, J. T. and Pires, E., Nonlocal and nonlinear friction laws and variational principles for contact problems in
elasticity, ASME J. Appl. Mech. 50 (1983), 67–76[2] Cocu, M., Existence of solutions of Signorini problems with friction, Int. J. Eng. Sci 22, No. 10, 567–575[3] Klarbring, A., Exemples of non-uniqueness and non-existence of solutions to quasi-static contact problems with
friction, Ingineur-Archiv. 60 (1990), 529–541
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[4] Cho, H. and Barber, J. R., Dynamic behavior and stability of simple frictional systems, Math. Comput. Modeling28 (1998), 37–53
[5] Cho, H. and Barber, J. R., Stability of the three-dimensional Coulomb friction law, Proc. R. Soc. Lond. A 455(1999), 839–861
ICAM9
Investigation of periodic solutions using interval halving
Andras Ronto and Miklos RontoInstitute of Mathematics of the Academy of Sciences of the Czech Republic and University of Miskolc, Hungary
[email protected], [email protected]
Based on [1, 2], we show how a suitable interval halving and parametrisation technique can helpto essentially improve the sufficient convergence condition for the periodic successive approximationsdealing with periodic solutions of nonlinear non-autonomous systems of ordinary differential equations.
Bibliography[1] A. Ronto and M. Ronto, Periodic successive approximations and interval halving, Miskolc Math. Notes 13(2), 459–482.[2] A. Ronto, M. Ronto, and N. Shchobak, Constructive analysis of periodic solutions with interval halving, Boundary
Value Problems 2013, 2013:57, 1–34
ICAM9
Approximation of Kothe-Bochner spaces with subspaces of functions having finite dimensional values
Razvan SfetcuFaculty of Mathematics and Computer Science, University of Bucharest, Romania
razvan [email protected]
We consider Kothe-Bochner spaces LX(ρ) (X Banach space, ρ function norm) where X hasSchauder basis. With the help of the Schauder basis, we consider finite dimensional spaces Y ⊂ Xand the corresponding spaces LY (ρ) which approximate the space LX(ρ).
Bibliography[1] Chitescu I., Function Spaces (in Romanian), Ed. St. Encicl., Bucuresti, 1983[2] Lin P. K., Sun H., Extremal structure in Kothe function spaces, J. Math. Analysis and Applications 218 (1998),
2315-2322[3] Zaanen A. C., Integration, Nord Holland Publishing Co., Amsterdam, Interscience Publishers John Wiley & Sons,
Inc., New York, 1967
ICAM9
A new central configurations in the planarN-body problem and their linear stability
Agnieszka SiluszykUniversity of Natural Sciences and Humanities, Siedlce, Poland
In [1] has proved necessary condition for the stability the Lagrange’s triangle of the three bodiesproblem as the configuration. In [2,3] the authors have shown the stability of permanent configurationsin the problem of four bodies. In this paper we establish the existence a planar configuraion which isconsisted with N bodies situated on two different circular orbits. We show necessary and sufficientconditions for existing this configuration. Additionally, we study the problem (the condtitions) linearstability for such configuration.
Bibliography[1] Routh E.I. Proceedings of the London Mathematical Society, v.6, 1875[2] Macmilian W.D., Bartky W. Configurations in the Problem of Four Bodies, Trans.Amer.Math.Soc.,34, 838-875,
(1932).
30
[3] Roberts G.E. Stability of Relative Equilibria in the Planar n-Vortex Problem, SIAM Journal on Applied DynamicalSystems, 12, no. 2, 1114-1134 (2013).
ICAM9
Cubic Systems with an Invariant Line at Infinity of the Maximal Geometric Multiplicity
Alexandru Suba, Olga VacarasInstitute of Mathematics and Computer Science of ASM, Republic of Moldova
[email protected], vacaras [email protected]
In the work [1] for polynomial differential systems there are introduced the following definitionsof the multiplicity of an invariant algebraic curve: algebraic multiplicity, geometric multiplicity,integrable multiplicity, infinitesimal multiplicity, holonomic multiplicity and the relations betweenthese definitions are established.
The main aim of this lecture is to show that for cubic systems the geometric multiplicity of a lineat infinite is at most seven. Any cubic system having a line at infinite of the geometric multiplicityseven via affine transformations and time rescaling can be written as one of the following two forms:x = 1, y = a+ bx+ cx2 + x3 and x = −x, y = ax+ x3 + 2y, a, b, c ∈ R.
Bibliography[1] Christopher C., Llibre J. and Pereira J.V., Multiplicity of invariant algebraic curves in polynomial vector fields,
Pacific Journal of Mathematics, 329 (2007), no. 1, 63–117.
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4. Advances in Numerical Analysis and Approximation Theory
Improvement of Gruss and Ostrowski Type Inequalities and Applications
Ana Maria Acu, Florin Sofonea”Lucian Blaga” University of Sibiu, Romania
[email protected], [email protected]
Several inequalities of Gruss and Ostrowski type available in the literature are generalized andimproved. A estimation of cumulative distribution function is given. The inequality of Gruss typeproved by P. Cerone and S.S. Dragomir [1] is extended for the weighted case.
Bibliography[1] Cerone, P., Dragomir, S.S, New bounds for the Cebysev functional, Applied Mathematics Letters, 18 (2005), 603-611.
ICAM9
Approximation by Linear Discrete Operators on Weighted Spaces
Octavian AgratiniBabes-Bolyai University, Cluj-Napoca, Romania
The talk aimed at two aspects relative to linear approximation processes.We consider some sequences of positive linear operators expressed by series and we modify them
into finite sums investigating their approximation properties in weighted spaces of continuous functions.Special cases are revealed.
Beside this research, a new property of moduli of smoothness associated to certain spaces offunctions is proven. In terms of statistical convergence we determine the behavior of these specialfunctions at the point δ = 0. In this respect, Peetre’s K-functional is also investigated.
31
ICAM9
Identification of a Sum of Exponential Functions Using its Taylor Series
Jan BusaDepartment of Mathematics and Theoretical Informatics, FEI Technical University in Kosice
In the talk a problem of the correspondence between parameters of a sum of exponential functionsand its Taylor series coefficients is considered. If the coefficients of the Taylor expansion of a function(supposed to be a sum of exponential functions) are given, it is shown that parameters in exponents aresolutions to the algebraic equation, which coefficients are the solutions of a system of linear algebraicequations. This system is constructed using Taylor coefficients.
In the talk a problem of the correspondence between parameters of a sum of exponential functionsof the form f(x) =
∑nk=1Ak exp(αk ·x) and its Taylor series coefficients is considered. If the coefficients
of the Taylor expansion of the function f(x) are given, it is shown that parameters αk of exponents aresolutions to the algebraic equation, which coefficients are the solutions of a system of linear algebraicequations. This system is constructed using Taylor coefficients.
ICAM9
Interpolation operators on a triangle with two and three curved edges
Alina-Mihaela BabosLand Forces Academy ”Nicolae Balcescu”, Sibiu, Romania
alina babos [email protected]
We construct Lagrange, Hermite and Birkhoff-type operators, which interpolate a given functionand some of its derivatives on the border of a triangle with two and three curved edges. We alsoconsider some of their product and boolean sum operators. We study the interpolation properties andthe degree of exactness of the constructed operators.
Bibliography[1] Barnhil, R.E., Gregory, J.A., Polynomial interpolation to boundary data on triangles, Math. Comput. 29(131),726-735
(1975).[2] Barnhil, R.E., Birkoff, G., Gordon, W.J., Smooth interpolation in triangle, J. Approx. Theory. 8,114-128 (1973).[3] Coman, Gh., Catinas, T., Interpolation operators on a triangle with one curved side, BIT Numer Math 47, (2010).[4] Blaga, P., Catinas, T., Coman, Gh., Bernstein-type operators on triangle with all curved sides, Mediterr. J. Math. 9
(2012), 833-845.
ICAM9
The Bernstein quadrature formula revisited
Dan Barbosu and Gheorghe ArdeleanTechnical University Cluj-Napoca, North Unversity Center Baia Mare, Romania
Starting with the Bernstein approximation formula on the interval [a, b] a corresponding quadratureformula is obtained. Its coefficients an an upper bound for the remainder term is obtained. Next, thecomposite quadrature formula of Bernstein-type on [a, b] is constructed. Some numerical examples arealso presented.
Bibliography[1] Acu,A., M., Sofonea, D.,F., Some numerical integration methods based on interpolation polynomials, Carpathian J.
Math.,29(2013), No.1, 1-8[2] Arama, O., Some properties concerning thesequence of S.N.Bernstein (Romanian), Studii si Cerc. Mat., 8(1957),
195-210[3] Barbosu, D., A Schurer-Stancu type quadrature formula, Carpathian J. Math., 23(2007), No.1-2, 27-31
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[4] Barbosu, D., Miclaus, D., On the composite Bernstein type quadrature formula, Rev. Anal. Numer. Theor. Approx.,39(2010), 3-7
[5] Bernstein,S.,N., Demonstration du theoreme de Weierstrass fondee sur le calcul de probabilites, Commun. Math.Kharkow, 13 (1912-19130, no.2, 1-2
[6] Stancu, D.,D., Quadrature formulas constructed by using certain linear positive operators, Numerical Integration(proc.Conf. Math. Res. Inst. Oberwolffach)(G.Hammerlin,ed.), Birkhauser (1982), 241-251
[7] Stancu, D.D., Vernescu, A., On some remarkable positive polynomial operators of approximation, Rev. Anal. Numer.Theor. Approx., 28(1999), 85-95
ICAM9
Bernstein type operators which preserve some test functions
Marius Mihai BirouTechnical University of Cluj Napoca, Romania
In this paper we construct a sequence of Bernstein type operators which fix some polynomials. Westudy the convergence of this sequence and establish a result of Vornovskaya type. Also, we present acomparison of these operators with the classical Bernstein operator related to the approximation error.
ICAM9
Some properties of a Durrmeyer type operator associated with Bleimann-Butzer-Hahn operator
Cristina Sanda CismasiuTransilvania University of Brasov, Romania
2000 Mathematics Subject Classification: 41A36, 41A35.Keywords and phrases: Positive linear operators, Bleimann - Butzer - Hahn operators, approxima-
tion properties.Our lecture refers to a new linear positive operator of Durrmeyer type which is associated with
Bleimann-Butzer-Hahn operator
Cn(f ;x) = pn,0(x)f(0) +n−1∑k=1
pn,k(x) ·
∞∫0
f(t)pn+2,k−1(t)dt
∞∫0
pn+2,k−1(t)dt
+ pn,n(x)f(n)
= pn,0(x)f(0) +n−1∑k=1
pn,k(x) · 1
B(k, n− k + 2)
∞∫0
f(t)tk−1
(1 + t)n+2dt+ pn,n(x)f(n),
defined for any function f ∈ CB [0,+∞) and x ≥ 0, with pn,k(x) =(nk
) xk
(1 + x)n, x ≥ 0, 0 ≤ k ≤ n,
n ∈ N. We studied some of its approximation properties.
Bibliography[1] Adell, J. A., De la Cal, J., San Miguel, M., Inverse Beta and Generalized Bleimann Butzer - Hahn Operators, J.
Approx. Theory 76 ( 1994), 54-64.[2] Agratini, O., Approximation properties of a generalization of Bleimann, Butzer and Hahn operators, Mathematica
Pannonica 9 (1998)2, 165-171.[3] Bleimann, G., Butzer, P. L., Hahn, L. A., Bernstein - type operator approximating continuous functions on the
semi-axis, Indag. Math. 42 (1980), 255-262.[4] Cismasiu, C. S., A new linear positive operator of Durrmeyer type associated with Bleimann-Butzer-Hahn oprator,
Bull. Of Transilvania Univ. Brasov, Vol 6(55), No. 1 2013, Series III: Mathematics, Informatics, Physics, 1-8.[5] Ivan, M., A note on the Bleimann - Butzer - Hahn operator, Automat. Comput. Appl. Math. 6 (1997), 11-15.
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33
About some inequalities in approximation theory
Ioan Gavrea and Bogdan GavreaTechnical University Cluj-Napoca, Romania
We present some inequalities that appear in approximation theory. Some improvements andgeneralizations of Chebysev-Gruss type inequalities are given.
ICAM9
About a linear and positive operator of Stancu-type with fixed points e1 and e2
Adrian IndreaTechnological High School of Tarna Mare, Romania
The objective of this paper is to introduce an operator of Stancu-type, with the properties thatthe test functions e1 and e2 are reproduced. Also, in our approach, a theorem of error approximationand a Voronovskaja-type theorem for this operator is obtained.
In this paper, we introduce a general class which preserves the test functions e1 and e2. For ouroperators approximation properties, a convergence theorem and a Voronovskaja-type theorem areobtained.
The paper is organized as follows. In section 2 we recall some results obtained in [?] which areessentially used for obtaining the main results of this paper. Section 3 is devoted to the constructionof the general class of a new linear and positive operators. In Section 4 we obtain a Stancu typeoperator which is an operator that preserves the test functions e1 and e2.
Bibliography
[1] Agratini, O., An asymptotic formula for a class of approximation processes of King’s type, Studia Sci. Math. Hungar.,47 (2010), Number 4, 435-444
[2] Barbosu, D., Introduction in numerical analysis and approximation theory, Ed. Univ. de Nord Baia Mare, 2009[3] Braica, P.I., Pop, O.T., Barbosu, D. and Piscoran, L., About a linear and positive operator of Stancu-type with
fixed points e0 and e1 (submitted)[4] Braica, P.I., Pop, O.T. and Indrea, A.D., About a King-type operator, Appl. Math. Inf. Sci, No. 6 (1)(2012), 191-197[5] Gadjiev, A.D., Ghobanalizadeh, A.M., Approximation properties of a new type Berstein - Stancu polynomials of one
and two variables, Appl. Math. Comp., (2010), No. 216, 890-901[6] Indrea, A.D., A particular class of linear and positive Stancu-type operators, Acta Univ. Apulensis, No. 31(2012),
249-256[7] King, J. P., Positive linear operators which preserve x2, Acta Math. Hungar., 99 (2003), No. 3, 203-208[8] Oancea, Ingrid A., Berstein - Stancu type operator wich preserves e2, An. St. Univ. Ovidius Constanta, Vol. 17(1)
(2009), 145-152[9] Pop, O. T., The generalization of Voronovskaja’s theorem for a class of liniar and positive operators, Rev. Anal.
Numer. Theor. Approx., 34 (2005), No. 1, 79-91[10] Pop, O.T., Indrea, A.D. and Braica, P.I., Durrmeyer operators of King-type, Annals of the University of Craiova,
Math.Comp.Sci.Ser. 39(2), (2012), 288-298[11] Stancu, D.D., On a generalization of the Bernstein polynomials, Studia Univ. ”Babes - Bolyai”, Scr. Math - Phis 14,
(1969), 31-45 (in Romanian)
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Optimal rate of convergence for sequences of a prescribed form
Ioan Gavrea and Mircea IvanTechnical University of Cluj-Napoca, Romania
We provide a highly convergent version of the generalized Euler sequence and we determine theelement with the optimal rate of convergence in several classes of sequences of a prescribed form. The
34
new approach extends and unifies many previous efforts in this direction. In addition, we answer anopen problem on the asymptotic expansion of the Harmonic number sequence.
ICAM9
On the Stancu type bivariate approximation formula
Dan MiclausTechnical University of Cluj-Napoca
North Unversity Center at Baia Mare, Romania
In the present paper we establish the form of remainder term associated to the bivariate approx-imation formula for Stancu type operators, using the bivariate divided differences. We also shallestablish an upper bound estimation for the remainder term, in the case when approximated functionfulfills some given properties.
Bibliography
[1] Lupas, L. and Lupas, A., Polynomials of binomial type and approximation operators, Studia Univ. Babes-Bolyai,Mathematica 32 (1987), No. 4, 61–69
[2] Miclaus, D., The revision of some results for Bernstein-Stancu type operators, Carpathian J. Math., 28 (2012), no. 2,273–284
[3] Stancu, D. D., Approximation of functions by a new class of linear polynomial operators, Rev. Roum. Math. Pures etAppl. 13 (1968), 1173–1194
ICAM9
Two-sided estimates for the norm of the linear operators used in the convergence of someapproximation processes
Alexandru MitreaTechnical University of Cluj-Napoca, Romania
Two-sided estimates concerning the norm of some linear operators involved in approximationprocesses are obtained. Further, based on these estimates, we derive convergence-type results and weestablish the topological structure of the set of unbounded divergence for some particular approximationprocedures, such as quadrature formulas of product-type on Legendre nodes, numerical differentiationformulas associated to a Chebyshev node matrix and numerical differentiation on Sturm-Liouvilletype node matrix.
ICAM9
On the stability of some classical operators from approximation theory (II)
Dorian Popa and Ioan RasaTecnical University of Cluj-Napoca, Romania
[email protected], [email protected]
Let C[0, 1] be endowed with the supremum norm. For 0 ≤ a ≤ b, consider the Stancu operatorsSn : C[0, 1]→ C[0, 1]
Snf(x) =
n∑k=0
(n
k
)xk(1− x)n−kf
(k + a
n+ b
).
we investigate the Hyers-Ulam stability of the operators Sn and prove that the HUS constant of Sn is(2n
2[n2
])/( n[n2
]).
35
This corrects, generalizes and improves a result in our paper [1] concerning the Bernstein operator Bn,which is obtained when a = b = 0.
We consider also the case when C[0, 1] is endowed with the L1−norm.Moreover, we discuss an extremal property of the Bernstein operators concerning the Hyers-Ulam
stability constants.
Bibliography[1] D. Popa, I. Rasa, On the stability of some classical operators from approximation theory, Expo. Math., in press,
http://dx.doi.org/10.1016/j.exmath.2013.01.007.
ICAM9
On a Class of Linear and Positive Operators
Voichita Adriana Radu”Babes-Bolyai” University, FSEGA, Deparment of Statistics-Forecasts-Mathematics, Cluj-Napoca, Romania
The focus of this paper is to gather the most significant properties of the Bernstein-Stancuoperators:
Cn : Y → Πn
(Cnf
)(x) =
n∑k=0
(an)knk
(n
k
)[0,
1
n, ...,
k
n; f
]xk.
ICAM9
Approximation processes and asymptotic relations
Ioan RasaTechnical University of Cluj-Napoca, Romania
We discuss two approximation processes: general King operators and Campiti-Metafune operators.They are related by similar Voronovskaja formulas. Their shape preserving and global smoothnesspreserving properties are investigated and compared.
ICAM9
Note on Approximation Properties of q-Bernstein-Schurer Operators
Florin Sofonea1, Carmen Violeta Muraru2, Ana Maria Acu1
1 ”Lucian Blaga” University of Sibiu, Romania;2 ”Vasile Alecsandri” University of Bacau
[email protected]; carmen [email protected]; [email protected];
In 2011, C. Muraru [1] introduced a generalization of the Bernstein-Schurer operators based onq-integers. In this paper we will propose a new variant of q-Bernstein-Schurer operators which preservethe linear function. A Bohman-Korovkin type approximation theorem of these operators is considered.The rate of convergence by using the first modulus of smoothness is computed. Also, a Durrmeyervariant of q-Bernstein-Schurer operators is considered.
Bibliography[1] Muraru, C.V., Note on q-Bernstein-Schurer operators, Stud. Univ. Babes-Bolyai Math. 56 (2011), No.2, 489-495.
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36
Graphical representations of mean square error of the bivariate operator of Stancu type
Ioana Tascu and Andrei Horvat-MarcDepartment of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Romania
[email protected]; [email protected]
In this paper are represented the errors obtained from approximation of a continuous function by abivariate operator. Starting from [1], we represent some quantitative estimation of approximation. Wetake the definition of the Stancu bivariate operator obtained by the tensorial product of parametricextensions.
Bibliography
[1] I. Tasu and I. Zelina, On the mean square error of the bivariate operator of Stancu type, Carpathian J. Math.,19(2003), No. 2, 141-146
[2] Stancu D.D., Vernescu A., On some remarkable positive polynomial operators of approximation, Revue dAnalyseNumerique et de Theorie de lApproximation, Tome 28, 1(1999), 85-95
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5. Advances in Algebra
The Cocartesian Right Product
Dumitru Botnaru, Elena BaesState University from Tiraspol, Technical University of Moldova, Chisinau
[email protected], [email protected]
We examine a construction that allows to obtain new reflective subcategories. For notions andnotation see [1]. Let K be a coreflective subcategory, and R be a reflective subcategory in the categoryC2V of the locally convex topological vector Hausdorff spaces. For an arbitrary object X of thecategory C2V we consider the following constructions: kX : kX −→ X, that is the K-coreplique;rkX : kX −→ rkX, that is R-replique; vX · kX = uX · rkX , that is the cocartesian square.
Full subcategory of all objects isomorphic to objects of type vX is called the cocartesian rightproduct of subcategories K and R, and is denoted by V = K ∗dc R.
Theorem. Let (K,R) be a pairs of conjugate subcategories and R a reflective subcategory of thecategory C2V. Then: 1. K ∗dc R = QεL(R), QεL(R) is the full subcategory of all (εL)-factorobiectsof the objects of the R subcategory; 2. K ∗dc R is a reflective subcategory of the category C2V; 3.The subcategory K ∗dc R is closed under εL-factorobjects; 4. v · k = r · k; 5. If r(K) ⊂ K, then thecoreflector functor k : C2V −→ K and the reflector one v : C2V −→ K ∗dc R commute: k · v = v · k.
Bibliography
[1] Botnaru D., Structures bicategorielles complementaires, ROMAI J., 2009, v.5, nr.2, p.5-27.
ICAM9
Semireflexive Subcategories
Dumitru Botnaru, Olga CerbuState University from Tiraspol, State University Moldova, Chisinau
[email protected], [email protected]
In the category C2V of the locally convex topological vector Hausdorff spaces are introduced thenotions: semireflexive subcategories [2], the right product of two subcategories [3] and pairs of theconjugate subcategories [1]. The relations between semireflexive subcategories via the right product of
37
two subcategories and pairs of the conjugate subcategories are examined. We construct and describesome old and new examples.
Bibliography
[1] Botnaru D., Structures bicategorielles complementaires, ROMAI J., 2009, v.5, nr.2, p.5-27.[2] Botnaru D., Cerbu O., Semireflexive product of two subcategories, Proceedings of the Sixth Congress of Romanian
Mathematicians, Bucharest, 2007, v.1, p.5-19.[3] Botnaru D., Turcanu A., The factorization of the right product of two subcategories, ROMAI Journal, 2010, v. VI N
2, p.41-53.
ICAM9
The Right Product
Dumitru Botnaru, Alina TurcanState University from Tiraspol, Technical University of Moldova, Chisinau
[email protected], [email protected]
In the category of the locally convex topological vector Hausdorff spaces are introduced the notions:the right product of two subcategories, where one is coreflective and the other is reflective [1]. Thisproduct is never a reflective subcategory. There are highlighted the properties of the right product andare indicated the conditions where this product is a reflective subcategory. We construct examples.
Bibliography
[1] Botnaru D., Turcanu A., The factorization of the right product of two subcategories, ROMAI Journal, 2010, v. VI N2, p.41-53.
ICAM9
Hilbert - Mumford - Nagata Theorem on invariants and some topological aspects of the finitegeneration of subalgebras. (II)
Adrian Constantinescu”Simion Stoilow” Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Recall the well known central Theorem of the Invariant Theory:Theorem[Hilbert - Mumford - Nagata] Let k be an algebraically closed field, A a k-algebra of finitetype and G a reductive ( in particular linearly reductive ) algebraic Lie group over k acting rationallyon A. Then the subalgebra of invariants AG = a ∈ A|ga = a for each g ∈ G is finitely generatedover k.
In this talk we will use the universally 1-equicodimensional rings and schemes - a class of objectsdefined by us by means of a universally topological property , as well as a class of scheme morphismsdefined also by a universally topological property to establish the Theorem above, at least in thesituation when G is linearly reductive. For a subalgebra of an algebra of finite type over a field k,the property of universally 1-equicodimensionality control completely the finite generation of thesubalgebra.
Some variants of this class of scheme morphisms, defined also in a universally topologically manner,will be discussed in relation to other situations of finite generation of subalgebras of algebras of finitetype over a field k.
Bibliography
[1] A. Constantinescu, Schemes dominated by algebraic varieties and some classes of scheme morphisms.II, PreprintsSeries of ”Simion Stoilow” Institute of Mathematics of the Romanian Academy, ISSN 0250 3638, Preprint nr.8/2010,36 p.
[2] D. Mumford, Geometric Invariant Theory, Springer Verlag, 1965.
[3] M. Nagata, A theorem on finite generation of a ring, Nagoya Math. 27 (1966), p. 193-205.
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38
Finitely accessible categories versus module categories
Septimiu CriveiBabes-Bolyai University, Cluj-Napoca, Romania
An additive category is called finitely accessible if it has direct limits, the class of finitely presentedobjects is skeletally small, and every object is a direct limit of finitely presented objects. Any finitelyaccessible category C may be embedded via the covariant Yoneda functor as a full subcategory of thecategory Mod(A) of unitary right modules over a certain ring with enough idempotents A, called thefunctor ring of C. This allows one to relate properties of C with properties of the module categoryMod(A). We shall review the main connections between them, and present some new ones, especiallyrelated to purity and approximations.
Bibliography[1] S. Crivei, M. Prest and B. Torrecillas, Covers in finitely accessible categories, Proc. Amer. Math. Soc. 138 (2010),
1213–1221.[2] M. Prest, Definable additive categories: purity and model theory, Mem. Amer. Math. Soc. 210, No. 987 (2011).
ICAM9
About separation axioms in semitopological and topological invers semigroups
Peter KortesiInstitute of Mathematics, University of Miskolc, Hungary
[email protected]; [email protected]
It is well-known that T0separation aximoms are equivalent to Hausdorf fseparation in toopologicalgroups. However, if we weaken the relation between the two structures - semitopolocal case, or wetake more general algebraic structures - invers semigroups, this property disappears. We will studysome separation axioms for inverse semigroups, and some shadow separation properties as well.
ICAM9
New Methods for the Polynomial Roots Approximation
Calin Alexe MuresanUniversity of Petroleum and Gas, Romania
Our results, about one of the product of distances between the polynomial roots, in complexspace, can be used for the polynomial roots isolation. These, conduce as to many evaluations of thecomplexity of the isolation, located in the finest class known.
ICAM9
Semisimple group algebras: primitive idempotents and group codes
Gabriela OlteanuDepartment of Statistics-Forecasts-Mathematics
Babes-Bolyai University
In [3, 4, 6, 7], Jespers, Olteanu, del Rıo and Van Gelder described a complete set of orthogonalprimitive idempotents in each Wedderburn component of a semisimple group algebra FG for variousclasses of finite groups G and F being the field of rational numbers or a finite field, using strong Shodapairs and the description of the Wedderburn decomposition of FG given by Olivieri, del Rıo and
39
Simon in [5] and [2]. We shall describe some of these methods to compute complete sets of orthogonalprimitive idempotents in semisimple group algebras FG.
In [6], the computation of primitive idempotents in finite group algebras is used in order to providealgorithms to construct minimal left group codes for a large class of groups and fields. To illustratethese methods, we provide alternative constructions to some best linear codes over F2 and F3. Weshall present some examples of best linear codes. The methods to construct minimal left group codeswere implemented using the programming language provided by the computer algebra system GAPand we included them in the GAP package Wedderga [1].
Bibliography
[1] O. Broche, A. Konovalov, A. Olivieri, G. Olteanu, A. del Rıo, I. Van Gelder, Wedderga - Wedderburn Decompositionof Group Algebras, Version 4.5.1 (2013). http://www.gap-system.org/Packages/wedderga.html
[2] O. Broche, A. del Rıo, Wedderburn decomposition of finite group algebras, Finite Fields and their Applications 13(2007), no. 1, 71–79.
[3] E. Jespers, G. Olteanu, A. del Rıo, Rational group algebras of finite groups: from idempotents to units of integralgroup rings, Algebr. Represent. Theor. 15 (2012), 359–377. http://arxiv.org/abs/1001.1236
[4] E. Jespers, G. Olteanu, A del Rıo, I. Van Gelder, Group rings of finite strongly monomial groups: central units andprimitive idempotents, J. Algebra 387 (2013), 99–116. http://arxiv.org/abs/1209.1269
[5] A. Olivieri, A. del Rıo, J.J. Simon, On monomial characters and central idempotents of rational group algebras,Comm. Algebra 32 (4), 1531–1550 (2004).
[6] G. Olteanu, I. Van Gelder, Construction of inimal non-abelian left group codes, submitted.http://arxiv.org/abs/1302.3747
[7] I. Van Gelder, G. Olteanu, Finite group algebras of nilpotent groups: a complete set of orthogonal primitive idempotents,Finite Fields Appl. 17 (2011), 157–165. http://arxiv.org/abs/1302.3882
ICAM9
On some particular equivalence relations of multialgebras
Cosmin PeleaBabes-Bolyai University, Cluj-Napoca, Romania
The equivalence relations of a multialgebra which determine universal algebras are importanttools in multialgebra theory. Our talk is a survey (based on [1] and [2]) on the class of these relationsof a given multialgebra 〈A,F 〉. We give a special attention to the image α(θ) of a binary relation θof A through the closure operator they determine. We will discuss some problems concerning theconstruction of α(R) for particular relations R and special cases of multialgebras.
Bibliography[1] Pelea, C., Hyperrings and α∗-relations. A general approach, J. Algebra 383 (2013), 104–128[2] Pelea, C., Purdea, I., Stanca, L., Fundamental relations in multialgebras. Applications, preprint, arXiv:1305.6141
ICAM9
A generalization of Hyers-Ulam-Rassias stability onm-semigroups
Adina Pop and Maria S. PopTechnical University of Cluj Napoca, North Univ Center of Baia Mare, Department of Mathematics and Computer Science, Baia Mare,
Romania
adina p [email protected]; maria [email protected]
In this paper we investigate the generalized Hyers-Ulam-Rassias stability of mappings ofm−semigroupsm ∈ N;m ≥ 3 into Banach spaces. For m = 3 the results can be found in Amyari and Moslehian[ Approximately ternary semigroup homomorphisms, Lett. Math. Phys. 77(2006), 1-9 ] with themention that they are true in the class of normal m−semigroups which is larger than the class ofcommutative m−semigroups. For m = 2 we find certain results of Hyers [ On the stability of thelinear functional equation, Proc. Nat. Acad. Sci. USA, 27 (1941), 222-224 ], Rassias, Th. M. [Onthe stability of the linear mapping in Banach space, Proc. Amer. Math, Soc. 72 (1978), 297-300 ]
40
and Rassias, J. M. [ Solution of a Problem of Ulam, J. Approx. Theory Math. 57 (1989), 268-273 ].In addition, we establish the superstability of m−ary homomorphims into Banach algebras endowedwith multiplicative norms, generalizing the results of Szekelyhidi [ On a theorem of Baker, Lawrenceand Zorzitto, Proc. Amer. Math. Soc., 84 (1982), 95-96 ] and Amyari and Moslehian (2006) .
Bibliography[1] Amyari, M. and Moslechian, M.S., Approximately ternary semigroup homomorphisms, Lett. Math. Phys. 77(2006),
1-9[2] Dehghanian, M. and Modarres, M.S., Ternary Weighted Function and Beurling Ternary Banach Algebra lω1 (S), Abs.
and Appl. Analysis, (2011), doi:10.1155/2011 206165[3] Gavruta, P.,A generalization of the Hyers-Ulam-Rassian stability of approximately additive mappings, J. Math. Anal.
Appl. 184 (1994), 431-436[4] Hyers, D.H.,On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA, 27 (1941), 222-224[5] Kerner, R., Ternary and non-associative algebraic structures and their applications in physics, Univ. P. and M.
Curie, 2000[6] Moslehian, M. S., Szekelyhidi, L., Stability of ternary homomorphisms via generalized Jensen equation , Result.
Math. 49 (2006) 286-300, doi: 101007/s00025-006-0225-1[7] Post, E. L., Polyadic groups, Trans. Amer. Math. Soc. 18(1940), 208-350[8] Rassias, Th. M., On the stability of the linear mapping in Banach space, Proc. Amer. Math, Soc. 72 (1978), 297-300[9] Rassias, Th. M., The Problem of S.M. Ulam for Approximately Multiplicative Mappings, J. Math. Anal. Appl. 246,
(2000), 352-378[10] Rassias, J. M., Solution of a Problem of Ulam, J. Approx. Theory Math. 57 (1989), 268-273[11] Szekelyhidi, L. On a theorem of Baker, Lawrence and Zorzitto, Proc. Amer. Math. Soc., 84 (1982), 95-96[12] Ulam, S. M., A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, no. 8,
Interscience Publishers, New York, NY, USA, 1960.[13] Zettl, H., A characterization of ternary rings of operators, Adv. Math. 48 (1983), 117-143
ICAM9
Simultaneous extensions of polyadic groups
Vasile PopTechnical University of Cluj-Napoca, Department of Mathematics, Cluj-Napoca, Romania
[email protected] reduction of two polyadic groups of arbitrary arity to the same group was studied by I.
Corovei, I. Purdea and V. Pop. In this paper we give necessary and sufficient conditions under whichtwo polyadic groups of (m+ 1) and (n+ 1)-arity can be extended to the same (k + 1)-group, where kis multiple of m and n.
Bibliography[1] Corovei, I., Purdea, I., The reduction of (m + 1)-groups and its extensions to the same group, Preprint sem. of
algebra 5(1988), Babes-Bolyai Univ., 63-68.[2] Dornte, W., Untersuchungen uber einen verallgemeinderten Gruppenbegrieff, Math. Z., 29(1929), 1-19.[3] Dudek, W.A., Michalski, J., On a generalization of Hosszu Theorem, Dem. Math., 3(1982), 783-805.[4] Hosszu, M., On explicit form of n-group operation, Publ. Math. Debrecen, 10(1963), 88-92.[5] Pop, V., Reduction of two polyadic groups to a group, Aut. Comput. Appl. Math., 14(2005), no. 1, 9-16.
ICAM9
Extensions of modules over tame hereditary algebras
Csaba SzantoUBB Cluj, Faculty of Mathematics and Computer Science, Romania
Consider a finite dimensional tame hereditary algebra (path algebra of a noncyclic affine quiver)and its finite dimensional right modules. An indecomposable module is called exceptional if it hasno self extensions. Two modules X,Y are called orthogonal if Hom(X,Y ) = Hom(Y,X) = 0. Anorthogonal exceptional pair to an indecomposable M is a pair of orthogonal exceptional modules(Y,X) such that there is a short exact sequence 0→ uX →M → vY → 0 with Ext1(X,Y ) = 0 (here
41
uX = X ⊕ · · · ⊕X u-times). Schofields theorem tells us that if M is exceptional then there existsorthogonal exceptional pairs to M , however there is no convenient method to determine these pairs.In case the quiver is Dynkin (not affine) Bo Chens theorem shows that the pair (M/T, T ), where T isthe Gabriel-Roiter submodule of M , is orthogonal exceptional to M . We generalize this result fortame cases using Ringel-Hall algebras.
ICAM9
Abelian groups in which any proper subgroup has the direct summand intersection property
Teodor Dumitru Valcan”Babes-Bolyai” University of Cluj-Napoca, Romania
We say that an R-module (abelian group) M has the direct summand intersection property (inshort D.S.I.P.) if the intersection of any two direct summands of M is again a direct summand in M .In this work we will present three classes of abelian groups (torsion, divisible, respectively torsion-free)which have the property that any proper subgroup has D.S.I.P. and we are going to show that thereare not such mixed groups.
Bibliography
[1] Albrecht, U., Hausen, J., Modules with the quasi-summand intersection property, Bull. Austr. Math. Soc., 44, 1991,189-201
[2] Albrecht, U., Hausen, J., Mixed Abelian Groups with the Summand Intersection Property, Lecture Notes in Pure andApplied Math., 182, Aekker, New York, 1996, 123-132
[3] Arnold, D.M., Hausen, J., A characterization of modules with the summand intersection property, Comm. Algebra,18(2), 1990, 519-528
[4] Fuchs, L., Infinite Abelian Groups Theory, Vol.I, Academic Press, New York and London, Pure and AppliedMathematics, 36, 1970
[5] Hausen, J., Modules with the summand intersection property, Comm. Algebra, 17, 1989, 135-148[6] Kamalov, F.F., Intersection of direct summands of abelian groups, (in Russian), Izv, Vyssh. Uchebn. Zaved. Mat. 5,
1977, 45-56[7] Kuros, A., The Groups Theory, (in Russian), Ed. Nauka, 1967[8] Valcan, D., Abelian groups with the direct summand intersection property, (in Romanian), The Annual Conference of
the Romanian Society of Mathematical Sciences, 1977, May 29 - June 1, Bucharest, Romania, 111-120
ICAM9
6. Software Engineering - Principles and Practices
Constructing questions using Maple T. A.
Csaba SarvariUniversity of Pecs, Pollack Mihaly Faculty of Engineering and Information Technology, Hungary
Under an EU project two English-language collections of exercises are being developed at theUniversity of Pecs. The titles of the exercise books are: Algebra and number theory, Multivariatefunctions and series. For the development the MAPLE T.A test and assessment system [1], [2] isused. Using this system not only multiple choice questions can be framed, but there are possibilitiesto check the partial results as well. During the evaluation of the answers the Maple computer algebrasystem runs in the background, thus the system automatically evaluates the variously formulatedanswers of the person completing test and compares it to the correct solution.
In our presentation we cover some mathematical didactic issues raised by the task development.Our examples are selected from themes of differential equations and linear algebra and multivariate
42
functions. We investigate the process of constructing questions and present some special forms ofquestions, e.g. questions based on relation analysis.
Bibliography[1] Andre Heck, Leendert van Gastel, Diagnostic Testing with Maple T.A. , In: M. Seppalla, O. Xambo, O. Caprotti
(eds.) WebALT 2006 Proceedings. pp 37 - 51.[2] Stefanie Winkler, Andreas Korner, Vilma Urbonaite, Maple T.A. in Engineering Educations, 7th Vienna Conference
on Mathematics Modelling Febr. 15-17, 2012
ICAM9
Metrics in software quality evaluation
Mara Diana Hajdu-MacelaruTechnical University Cluj-Napoca, North Unversity Center Baia Mare, Romania
Software metrics can be classified into three categories: product metrics, process metrics, andproject metrics. In current paper we will detail the existing software quality metrics , their importanceand accuracy . We will also improve some of the existing metrics and state which of the metrics countsmore when evaluating the software quality.
ICAM9
fUML Formal Description
Simona Motogna, Florin Craciun and Gabriel GlodeanDepartment of Computer Science, Babes Bolyai University, Cluj-Napoca, Romania
[email protected]; [email protected]
Constructing software automatically from high-level models is one of the challenges in softwareengineering nowadays. There is an urgent need for adequate methods to ensure high quality of models.The Executable Foundational UML (fUML) has been proposed as a computationally complete andcompact subset of UML. A fUML model is supposed to be executed and tested in the early stage ofthe software development process. A complete and sound formalization of fUML operational semanticsis still in its early stages, and although several proposals to execute and verify fUML models have beenissued, this problem is still open. Our project aims to develop a novel K-based approach for executingand verifying fUML models. K is a rewrite-based executable semantic framework. This paper focuseson the formalization of the fUML activities execution. We define an intermediate language to describefUML activity graphical components and we introduce a fully concurrent K-based execution model ofthe fUML activities and actions. Initial set of experiments have shown that our K-based approach isfeasible.
Bibliography[1] OMG, Concrete Syntax for UML Action Language (Action Language for Foundational UML - ALF), OMG, 2010.[2] E. Planas, J. Cabot, and C. Gomez, Lightweight verification of executable models, in ER, 2011, pp. 467475.[3] G. Rosu and T. F. Serbanuta, An overview of the K semantic framework, Journal of Logic and Algebraic Program-
ming,2010.[4] V. Rusu and D. Lucanu, A k-based formal framework for domain-specific modelling languages, in FoVeOOS, 2011,
pp. 214231.
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43
On-Line Testing in Higher Mathematics Education - Maple T. A.
Ildiko Perjesi-HamoriUniversity of Pecs, Pollack Mihaly Faculty of Engineering and Information Technology, Hungary
Under a EU project two English-language collections of exercises are being developed at theUniversity of Pecs. The titles of the exercise books are: Algebra and number theory, Multivariatefunctions and series. For the development the MAPLE T.A test and assessment system [1], [2] isused. With the help of this system not only multiple choice questions can be framed, but there arepossibilities to check the partial results as well. During the evaluation of the answers the Maplecomputer algebra system runs in the background, thus the system automatically evaluates the variouslyformulated answers of the person completing test and compares it to the correct solution. (For exampleif the question is about the comparison test of series convergence there are infinite number of correctanswers, the system is able to check whether the answer is correct or not.)
In our presentation we cover some mathematical didactic issues raised by the task development.Our examples are selected from themes of numerical and function series, and from the integration ofmultivariate functions.
Bibliography
[1] Andre Heck, Leendert van Gastel, Diagnostic Testing with Maple T.A. , In: M. Seppalla, O. Xambo, O. Caprotti(eds.) WebALT 2006 Proceedings. pp 37 - 51.
[2] Stefanie Winkler, Andreas Korner, Vilma Urbonaite, Maple T.A. in Engineering Educations, 7th Vienna Conferenceon Mathematics Modelling Febr. 15-17, 2012
ICAM9
Software Tools for Information Retrieval with Lattices
Imre PillerUniversity of Miskolc, Hungary
The information retrieval became one of the most important topic in informatics in the last decade.There are various structures and methods for representing the information and store as a data inefficient way, this work shows some of them from the simpler structures to the more general ones. Inthis consideration the lattice is the preferred structure because it is able to describe complex relationsbetween objects in a hierarchical manner [2].
There are many possible structures for representing information. The key-value pair is a wellknown elementary structure which appears almost in all informational systems. The relational modelis more flexible and closer to the human thinking in complicated cases. Where the hierarchy has akey role we need to create trees or lattices. It is important to provide tools which are able to presentthese structures and help to emphasize their advantages and disadvantages.
The theory of formal concept analysis is an arising area of mathematics and computer science. Ithas a pure theoretical foundation and has many real world application [1]. There are many researchwhich shows the importance of the theory in information retrieval [3].
The aim of this work is to present available software tools for the examination of conceptualstructures. There are many advantages of the integration of special topics in a common platform. Ithelps to solve the common tasks (for example visualization) in an easier way and the users can use afamiliar interface. The GeoGebra is a widely used educational software but has a minimal support forthe mentioned structures. This work makes steps to extend the functionality in this direction in thehope that the theory of formal concept analysis will be a popular area in the future.
Bibliography
[1] Bernhard Ganter, Gerd Stumme, Rudolf Wille, Formal Concept Analysis, Foundations and Applications, Springer-Verlag Berlin Heidelberg 2005
[2] Uta Priss Lattice-based Information Retrieval., Knowledge Organization, Vol. 27, 3, 2000, p. 132-142.
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[3] Uta Priss, Formal Concept Analysis in Information Science., Cronin, Blaise (ed.), Annual Review of InformationScience and Technology. Vol 40, 2006, p. 521-543.
ICAM9
The use of Java technologies for web e-commerce applications
Emanuela Petreanu and Livia SangeorzanDepartment of Mathematic and Computer Science, Transilvania University of Brasov, Romania
The e-commerce sector, in the century of speed and information, must find an answer for everybodywho wants to solve their shopping needs as quickly as possible, if possible by just giving a mouse click.The Internet is providing a range of solutions and useful information in all fields, including a largevariety of online shops. The Internet became an important environment for presenting and marketingof the company products in real time that is available to everyone. The web applications offer peoplethe possibility to buy products for every activity in their life, work or spending their vacations..The paper presents a structure of a site, using Java web technologies, which permits access the webapplication Mountain Expert in order to buy sport products. Through this application when you leavein a trip in nature, you might want to buy sport clothes and accessories, and if you are in a hurry anddont have time, a web shop is the best solution. The web application Mountain Expert has appliedrules and techniques of accessibility from WAI (Web Accessibility Initiative). The server applicationis implemented using Java JSF and Primefaces libraries. Java web technologies has a great flexibilityallowing to be used with other technologies and also using these languages /technologies makes possiblethe obtaining of remarkable results. This paper will present a new development approach of the webapplications implementation based on MVC pattern with JavaServer Faces technology. This approachis based on the separation of the user presentation part and business logic behind the application.
Bibliography
[1] June Cohen, The Unusually Useful Web Book, New Riders , ISBN-10: 0735712069, ISBN-13: 978-0735712065, 2003[2] David R. Heffelfinger, Java EE 6 Development with NetBeans 7, Packt Publishing, ISBN 978-1-84951-270-1, 2011[3] Bill Dudney, Jonathan Lehr, Bill Willis, LeRoy Mattingly Mastering JavaServer Faces Wiley, ISBN: 978-0-471-
46207-1, 2004[4] Ian Hlavats JSF 1.2 Components, Packt Publishing, ISBN 978-1-847197-62-7, 2009[5] Damiano Distante, Model Driven Development of Web Application with UWA,MVC and JavaServer Faces, Proceeding
ICWE’07 Proceedings of the 7th international conference on Web engineering, pages 457-472[6] http://en.wikipedia.org/wiki/NetBeans[7] http://db.apache.org/derby/[8] http://en.wikipedia.org/wiki/Object diagram[9] http://www.w3.org/standards/webdesign/accessibility
ICAM9
A functional sentence perspective approach to preflow algorithm in parametric networks
Livia Sangeorzan1, Mihaela Parpalea2, Mircea Parpalea3
1Department of Mathematic and Computer Science, Transilvania University of Brasov, Romania2Department of Foreign Languages, Transilvania University of Brasov, Romania3National College Andrei Saguna, Brasov, Romania
[email protected]; [email protected]; [email protected]
The present paper proposes a fractal-like approach to the parametric flow problem, derived fromthe rules and recursion of generative linguistics, based on the Functional Sentence Perspective (FSP)which describes the German word order. The same as any sentence can be analysed in terms oftheme of the sentence (that which is spoken about in the sentence) and rheme of the sentence (thatwhich is said about the theme in the sentence), in a preflow-push algorithm, a partitioning push (anon-cancelling push of flow in the parametric residual network) might leave the node unbalancedfor only a subinterval of the range of the values of the parameter. This will lead to separating the
45
problem for the two disjoints subintervals, which allows the algorithm to continue after the samerules, independently, on each of the partitioned subintervals. The algorithm runs as the template-likestructure of a dialogue act which reveals a design where information about the items (part-of-speech)is a two sections vector with one segment for each of the used part of speech categories.
Bibliography
[1] Ahuja, R., Orlin, J., Distance-directed augmenting path algorithms for maximum flow and parametric maximumflow problems, Naval Research Logistics, 38(1990), 413-430.
[2] Brill, E., A simple rule-based part of speech tagger. Proceedings of the Third Conference on Applied NaturalLanguage Processing, 1992, 152155.
[3] Hamacher, H.W., Foulds, L.R., Algorithms for Flows with Parametric Capacities. ZOR - Methods and Models ofOperations Research, 33(1989), 21-37.
[4] Parpalea, MM., German Word Order. Bulletin of the Transilvania University of Brasov, Series IV, Vol.2, 51(2009),175-182.
[5] Parpalea, M., Min-Max algorithm for the parametric flow problem, Bulletin of the Transilvania University of Brasov,Series III: Mathematics, Informatics, Physics, Vol.3, 52(2010), 191-198.
[6] Ruhe, G., Complexity Results for Multicriterial and Parametric Network Flows Using a Pathological Graph of Zadeh,Zeitschrift fr Operations Research, 32(1988), 9- 27.
[7] Ruhe, G., Algorithmic Aspects of Flows in Networks, Kluwer Academic Publishers, Dordrecht, The Netherlands,1991.
[8] Sangeorzan, L., Kiss-Iakab, K., Parpalea, M., Runtimes for Parallel Fractals. Proceedings On the 31st AnnualCongress of the American Romanian Academy of Arts and Sciences, 5(2007), 549-552.
[9] Tarjan, R., Ward, J., Zhang, B., Zhou, Y., Mao, J., Balancing Applied to Maximum Network Flow Problems.AlgorithmsESA, Springer 4168(2006), 612-623.
ICAM9
A Max-Plus Algorithm and the Prime Numbers
Peter SzaboTechnical University of Kosice, Department of Aerodynamics and Simulations, Slovakia
Let us consider the following task:
maxti−1 + x1, ti−2 + x2, · · · , t0 + xi, xi+1, · · · , xn = λ+ xi
for all i = 1, 2, · · · , n. It is assumed that input values ti are nonnegative real numbers for alli = 0, 1, · · · , n − 1. The λ, x1, · · · , xn ∈ R values are the solutions of the equations. One of theeffective solution of this problem is based on using special partitions of number n, see [1]. Thisproperty enables to investigate different partition problems. In this work, we examine the possibilityto prove the Goldbach conjecture.
Keywords : Goldbach conjecture, max-plus algebra, Toeplitz matrix.
Bibliography
[1] Szabo,P. : An Iterative Algorithm for Computing the Cycle Mean of a Toeplitz Matrix in Special Form, Kybernetika,2013 in press.
ICAM9
Application of rough approximations in Group Technology problems
Laura VeresUniversity of Miskolc, Hungary
The notion of rough sets was introduced by Z. Pawlak in the early eighties deals with incompleteinformation about objects. As an application to Group Technology problems, I developed a newmethod and an algorithm, based on rough approximations and modal operators defined on a context,for determinig the master parts corresponding to a manufacturing process.
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ICAM9
7. Applications of Mathematics and Computer Science in Science, Arts andTechnology
Developing an ontology for automated scene creation
Diana Contras and Alina PintescuAutomation Department, Technical University of Cluj-Napoca
This article presents an ontology meant to be used by algorithms for automated creation of scenes.At any time and in any place we encounter scenes: in plays, in paintings, in film frames, at hospitals,at police stations, at schools, at restaurants, at stores, everywhere. Depending on where it is located,a scene can contain more types of elements: backgrounds, objects, characters connected through theirspatial relationships. Our intention is to offer the possibility of realizing many combinations of thechosen elements in order to obtain the waned scene. In practice is difficult to obtain such a result,that is why we intend to design an automatic system, which will automatically generate the scenes.The possible elements of scenes together with their relationships are grouped in an ontology which ispresented in this article.
Bibliography[1] Gruber, Thomas R. A Translation Approach to Portable Ontology Specifications, 1993[2] Sowa, John Knowledge Representation: Logical, Philosophical and Computational Foundations, 1999[3] Gmez-Prez, Asuncion; Fernndez-Lpez, Mariano; Corcho, Oscal Ontological Engineering: With Examples from the
Areas of Knowledge Management, E-commerce and the Semantic Web, Springer, 2004[4] Gmez-Prez, Asuncion; Fernndez-Lpez, Marianol Overview and analysis of methodologies for building ontologies, 2002[5] Noy, Natalya F.; McGuinness, Deborah L. Ontology Development 101: A Guide to Creating Your First Ontology,
Technical Report KSL0105, Stanford Knowledge Systems Laboratory, 2001[6] Alatrish, Emhimed Salem Comparison of Ontology Editors, e-RAF Journal on Computing, Volume no. 4, 2012[7] Matei, Oliviu Ontology-Based Knowledge Organization for the Radiograph Images Segmentation, Advances in
Electrical and Computer Engineering, 8(15), 2008[8] Panagi, P.; Dasiopoulou, S.; Papadopoulos, G.T.; Kompatsiaris, I.; Strintzis, M.G. A Genetic Algorithm Approach
to Ontology-driven Semantic Image Analysis, Visual Information Engineering, 2006[9] Matei, Oliviu Defining an Ontology for the Radiograph Images Segmentation, 9th International Conference on
Development and Application Systems, 2008[10] O. Matei, Evolutionary Computation: Principles and Practices, Risoprint, 2008.
ICAM9
Using a spatial configuration mathematical model to study the inhabited area of a Maramures village
Ruxandra Berindea and Vasile Berindeb
aSchool of Architecture, University of Sheffield, United Kingdom;bDepartment of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Roma-
nia;
[email protected]; [email protected]
We use the Space Syntax theory, i.e., the concept of JPG (Justified Plan Graph) as surveyed in[1], in order to mathematically describe and analyze the configuration aspects of the inhabited area ofthe Maramures village Budesti.
Bibliography[1] Ostwald, M.J., The mathematics of spatial configuration: revisiting, revising and critiquing Plan Graph Theory,
Nexus Network J., 13 (2011), 445–470
ICAM9
47
New quantitative structure-toxicity relationship for aliphatic carboxylic acids
Zoita BerindeDepartment of Chemistry and Biology, North University Center at Baia Mare, Technical University of Cluj-Napoca, Romania
The paper reports on a quantitative structure-activity relationship (QSAR) study of the toxicityof 38 aliphatic carboxilic acids. This is done by modelling as molecular graphs the chemical structureof the compounds and then by extracting several topological indices from the corresponding weightedconnectivity matrices, which are then correlated with some biological properties of aliphatic carboxilicacids, amongst which the most important is their toxicity.
ICAM9
A topological study for a set of columnar liquid crystals
Thomas Dippong and Zoita BerindeDepartment of Chemistry and Biology, North University Center at Baia Mare, Technical University of Cluj-Napoca, Romania;
[email protected]; [email protected]
The paper reports on a study that searches for a possible relationship between the chemicalstructure of a class of columnar liquid crystals and some of their physico-chemical properties.
Monovariable as well multivariable correlation studies between the transition temperature andone or more molecular descriptors (like topological indices or Van der Waals parameters) have beenperformed
ICAM9
Spatial distribution maps of microelements concentration in surface soil around soil pollution sources
Cristina Mihali, Gabriela Oprea, Claudia ButeanTechnical University of Cluj Napoca, North University Center at Baia Mare, Romania
Spatial distribution maps of pollutant microelements in the soil are important tools for theassessment of pollution degree around the pollution sources. The concentrations of microelements (Pb,Cd, Zn and Cu) were measured for sampling points distributed around the main soil pollution sourcesin Baia Mare area. The pollution sources were a lead smelter and tailing ponds [1]. The samplingpoint coordinates (latitude and longitude) were registered with a GPS (Global Positioning System)instrument. Considering the coordinates of each sampling point and the corresponding concentrationof the considered microelement in the sampling point, a matrix XYZ was obtained where X was thelongitude; Y was the latitude and Z the concentration of the microelements [2]. A continuous surfacewas generated beginning with each sampling point. Origin program was applied for gridding withcorrelation method. The spatial distribution maps of the microelements indicated some area highpolluted around the lead smelter especially for Pb and Cd.
Bibliography
[1] Mihali, C., Michnea, A., Oprea, G., Gogoasa, I., Pop, C., Senila, M., Grigor, L., Trace element transfer from soilto vegetables around the lead smelter in Baia Mare, NW Romania, Journal of Food, Agriculture & Environment,10(2012), 828-834.
[2] Levei, E.A., Freniu, T., Ponta, M., Senila, M., Miclean, M., Roman, C., Cordo, E., Characterization of soil qualityand mobility of Cd, Cu, Pb, and Zn in the Baia Mare area Northwest Romania following the historical pollution,International Journal of Environmental Analytical Chemistry, 89(2009), 635-649
ICAM9
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8. Mathematical Modelling with Applications in Economics
An Implementation of Monte Carlo Method for European Option Pricing
Adrian RabaeaTUCN-NUCBM, Romania
Pricing options[1] often requires use of parallel computing and Monte Carlo methods[2] in financialindustries. We describe and analyze the performance of a multi-core processors of personal computersdedicated to Monte Carlo simulation[3] on the evaluation of financial derivatives.
Bibliography[1] Black, F., Scholes, M.: The pricing of Options and Corporate Liabilities, Journal of Political Economics 81, 1973,
637-659[2] Jenny X. Li, Gary L. Mullen, Parallel computing of a quasi-Monte Carlo algorithm for valuing derivatives, Parallel
Computing 26, 641-653, 2000[3] Rabaea A., Rabaea M. - Experiments with Parallel Monte Carlo Simulation for Pricing Options using PVM, Lecture
Notes in Computer Science 1908 - Recent Advances in Parallel Virtual Machine and Message Passing Interface,Springer-Verlag Berlin Heidelberg, 330-337, 2000.
ICAM9
On the comparison of Fisher informations of the some probability distributions
Ion Mihoc(1) and Cristina-Ioana Fatu(2)
(1)Faculty of Mathematics and Computer Science, ”Babes-Bolyai” University of Cluj-Napoca,(2) Faculty of Economics, Christian University ”Dimitrie Cantemir”, Cluj-Napoca, Romania
[email protected], [email protected]
Fisher information plays an important role in the statistical inference connection with theproperties of the estimators for an unknown vector parameter θ which lie in some parameter spaceDθ, Dθ ⊂ Rk, k ≥ 1.
In this paper, we study some properties of the Fisher information for some probability distributionswhich belong to an exponential family.
Bibliography[1] Gupta, R.D. and Kundu, D. Generalized exponential distrinutions, Australian and New Zealand Journal of
Statistics, 41 (2002), 173-188[2] Mihoc, I., Fatu, C.I., About some properties of the F isher information in the sample theory, Automation
Computers Applied Mathematics, ISSN 1221-437X, 19 (2010) No. 2, 97-108
ICAM9
9. Variational methods and applications to ODEs and PDEs
Parameter-depending problems on fractals
Brigitte E. BrecknerBabes-Bolyai Unversity, Cluj-Napoca, Romania
The talk is based on the recent papers [1] and [2], jointly written with Csaba Varga. There aretreated nonlinear elliptic problems defined on the Sierpinski gasket, a highly non-smooth fractal set.Even if the structure of this fractal differs considerably from that of (open) domains of Euclideanspaces, the talk emphasizes that PDEs and systems of PDEs defined on it may be studied (as in the
49
Euclidian case) by means of certain variational methods, involving also some abstract multiplicitytheorems by B. Ricceri (see [3] and [4]).
Bibliography
[1] Breckner, B.E., Varga, Cs., Multiple solutions of Dirichlet problems on the Sierpinski gasket, submitted[2] Breckner, B.E., Varga, Cs., A note on gradient-type systems on fractals, submitted[3] Ricceri, B., A class of nonlinear eigenvalue problems with four solutions, J. Nonlinear Convex Anal., 11 (2010),
503–511[4] Ricceri, B., A further refinement of a three critical points theorem, Nonlinear Anal., 74 (2011), 7446–7454
ICAM9
An application to quasi-linear variational inequalities
Marcel Bogdan”Petru Maior ”Unversity of Tırgu Mures, Romania
In the present exposition we consider a variational inequality coming from a boundary valueproblem, governed by a topological pseudomonotone operator in the Brezis’s sense, classified asquasi-linear [3].
Our purpose is to relate a Ritz-Galerkin scheme type by our approach in [1, 2] that involves asequence of operators.
Bibliography
[1] Bogdan, M., Kolumban, J., Some regularities for parametric equilibrium problems, J. of Global Optimization, 44(2009),481-492
[2] Bogdan, M., On parametric quasivariational inequalities, Scientific Bulletin of the Petru Maior University of TırguMures, 9(2012), 26-27
[3] Zeidler, E., Nonlinear Functional Analysis and its Applications, Vol. III, Springer Verlag, Berlin, Germany, 1990.
ICAM9
An existence result for a quasi-linear elliptic equation with dependence on the gradient
Francesca FaraciUniversity of Catania, Italy
In this lecture we present an existence theorem for a quasilinear elliptic problem with dependenceon the gradient of the following type
−∆pu = f(x, u,∇u) in Ωu = 0 on ∂Ω,
under general growth conditions of the nonlinearity on u and ∇u. Our aim is to combine variationaltechniques with fixed point methods in order to prove the existence of a solution. More precisely ourapproach is based on sub-supersolution techniques, extremal solutions for an auxiliary parametricproblem and Schaefer’s fixed point theorem. A multiplicity theorem is also obtained.
Based on a joint work with D. Motreanu and D. Puglisi (see [1]).
Bibliography
[1] Faraci F., Motranu D., Puglisi D., Quasi-linear elliptic equations with dependence on the gradient, preprint.
ICAM9
Existence theorems for intersection problems and equilibrium problems
Daniela Inoan, Jozsef KolumbanTechnical University of Cluj-Napoca, Babes Bolyai University of Cluj-Napoca
50
[email protected], [email protected]
Necessary and sufficient conditions for the existence of an x ∈ X such that f(x, y) ≥ 0, for ally ∈ Y , are given. Here X is a subset of a Hausdorff topological vector space, Y is an arbitraryset independent of X, and f : X × Y → R is a given function. Our results extend the Knaster-Kuratowski-Mazurkiewicz Lemma, Ky Fan’s minimax inequality and Brezis-Nirenberg-StampacchiaTheorem.
ICAM9
Stochastic Nonlinear Equations of Schrodinger Type
Hannelore LiseiBabes-Bolyai University, Cluj-Napoca, Romania
We consider a stochastic nonlinear equation of Schrodinger type, which is perturbed by an infinitedimensional Wiener process. The existence of the solution is proved by using the Galerkin method. Wealso construct a splitting method for these equations: we approximate the solution of our problem bya sequence of solutions of two types of equations: one without stochastic integral term, but containingthe Laplace operator and the nonlinear term, and the other one containing only the stochastic integralterm. The two types of equations are connected to each other by their initial values. We prove that thesolutions of these equations both converge strongly to the solution of the Schrodinger type equation.
ICAM9
Multivalued variational inequalities and coincidence point results
Szilard LaszloTechnical University of Cluj-Napoca, Romania
In this paper, we establish some existence results of the solutions for several multivalued variationalinequalities involving elements belonging to a class of operators that was recently introduced inthe literature. As applications we obtain some new coincidence point results in Hilbert spaces.Bibliography
[1] Laszlo, S., Multivalued variational inequalities and coincidence point results, J.Math.Anal.Appl., 404(2013), 105-114[2] Laszlo, S., Some existence results of solutions for general variational inequalities, J.Optim.TheoryAppl., 150(2011),
425-443
ICAM9
10. Miscellanea
Bezier Curves in GeoGebra and Computational Applications dedicated to Environmental Informatics
Bogdan Cioruta, Mirela ComanNorth University Center at Baia Mare, Technical University of Cluj-Napoca, Baia Mare, Romania
[email protected]; [email protected]
Bezier is one of the influent polynomial and important tool for interpolation. The Bezier interpo-lating curve always lies within the convex hull and it never oscillates wildly away from the controlpoints. Bezier polynomial has several applications in the fields of engineering, science and technologysuch as highway or railway rout designing, networks, Computer Aided Design system, animation,environment design, robotics, communications, Environmental Informatics and many other disciplines
51
or areas of interest because it is easy to compute and is also very stable. One of the main approachesto robot motion, for example, is through the use of Quadratic and Cubic Bezier spline functions.
In CAD systems and in Environmental Information (Computational) Systems, parametric rep-resentation of curves and surfaces and its shape control are under wide consideration and research,and it is very important to choose the appropriate basis functions. Based on their good properties,the classical Bezier curves play a significant role in CAD system, so in recent years, the parametricrepresentation of curves and surfaces with shape parameters has received attention especially inEnvironmental Informatics for the landslide geomorphology, the simulation of a waste deposit / landfillcompactation, contours and mapping.
The purpose of this workpaper is to introduce the possibilities to represent in a particular way,using GeoGebra open-source mathematic software, some types of the generalized Bernstein basisfunctions associated with the shape parameters and Bezier curves and surfaces which seems to beentirely new in environmental science and engineering domain, but for perspective in the long-termresearch because the curves and surfaces have simpler form and geometric meaning.
ICAM9
Fourier Series in GeoGebra - New Possibilities for Representation and Applications
Bogdan Cioruta, Mirela ComanNorth University Center at Baia Mare, Technical University of Cluj-Napoca, Baia Mare, Romania
[email protected]; [email protected]
The Fourier series have long provided one of the principal methods of analysis for mathematicalphysics, engineering and signal processing; it has also spurred generalizations and applications thatcontinue to develop right up to the present. While the original theory of Fourier series appliesto periodic functions occurring in wave motion, such as with light and sound, its generalizationsoften relate to wider settings, such as the time-frequency analysis underlying the recent theoriesof trigonometric analysis. Methods based on the Fourier series are used in virtually all areas ofengineering and science, and by the circuit designers, spectroscopists, crystallographers and anyoneworking in signal processing and communications.
In this paper we try to give an introduction to the Fourier series (or trigonometric series) thatcould be suitable for students with the calculus and graphical representation specific to the open-sourcemath software GeoGebra. Without getting too hung up on details we present the useful terminologyand start to analyse and apply our knowledge in finding different possibilities to represent, use anddevelop Fourier analysis for concrete functions that could be occur in many domain of activitiesconnected to mathematics and informatics.
ICAM9
Field extensions and Clifford theory
Dana Debora GlitiaBabes-Bolyai Unversity of Cluj Napoca, Romania
We study Clifford theory in connection with the action of the Galois group of a field extension inthe context of group graded algebras.
Let G be a finite group, let K/F be an algebraic field extension, and let R =⊕
g∈GRg be a finitedimensional strongly G-graded F -algebra. A simple R1-module, as well as a simple K ⊗F R1-module,define a “Clifford theory”. The main idea is that the R-module induced from a simple R1-modulegenerates an abelian subcategory of the category of R-module which is equivalent to the categoryof modules over its endomorphism algebra. The author investigates the relationships between thesetheories. One of the main results says that a G-graded derived equivalence over F preserves the
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Clifford theory defined by corresponding simple modules, and also preserves Galois actions and Schurindices.
Bibliography[1] Dade, E.C., Clifford theory for group-graded rings. J. Reine Angew. Math., 369 (1986), 40–86.[2] Dade, E.C., Clifford theory for group-graded rings. II. J. Reine Angew. Math. 387 (1988), 148–181.[3] Glitia, D.D., Group graded bimodules over a commutative G-ring, (2013), to appear.[4] Karpilovsky, G., Projective representations of finite groups. Marcel Dekker, 1985.[5] Marcus, A., Representation theory of group graded algebras. Nova Science Publishers, 1999.[6] Marcus, A., Characters and equivalence classes of central simple group graded algebras. Commun. Algebra, 36 (2008),
1394–1412.[7] Marcus, A., Derived invariance of Clifford classes, J. Group Theory, 12 (2009), 83–94.[8] Turull, A., The Brauer-Clifford group. J. Algebra 321 (2009), 3620–3642.[9] Turull, A., Clifford theory and endoisomorphisms. J. Algebra 371 (2012), 510–520.
ICAM9
A divisibility problem of integers
Peter KortesiInstitute of Mathematics, University of Miskolc, Hungary
[email protected]; [email protected]
We will show the way how a nice property of divisibility of integers, equivalent to Fermat’s smalltheorem has been studied in the Self-Made Mathematics Group of the University of Miskolc, and wewill emphasize the way how Computer Algebra tools influenced the findings related to the property.
ICAM9
Tzitzeica curves in a Minkowski space
Laurian Ioan Piscoran1 and Catalin Ionel Barbu2
1Technical University of Cluj-Napoca, North University Center of Baia Mare, Romania2”Vasile Alecsandri” National College, Bacau, Romania
[email protected]; kafka [email protected]
Using the Minkowski-Pythagorean hodograph, or short MPH-curves, in this paper we will studythe existence of Tzitzeica-MPH curves in the Minkowski space R2,1.
ICAM9
Part 2
Extended Abstracts
Pre-Proceedings of
9th
International
Conference
on
Applied
Mathematics
25-28 September, 2013Baia Mare, Romania
Editor: Petrica Pop Sitar
Baia Mare2013
EDITURA BIBLIOPHILISBN 978-606-93094-8-3
55
New graphical models for the basins of attraction of the real roots of a nonlinear equation
Gheorghe ArdeleanDepartment of Mathematics and Computer Science, Technical University of Cluj-Napoca, North University Center at Baia Mare, Romania
ardelean [email protected]
Abstract. In this paper we present two new graphical models for the basins of attraction of real roots,
generated by iterative methods for solving nonlinear equations. Even if the images generated are not as
spectacular as in the complex case, this shows some behaviors of iterative methods for solving nonlinear
equations (such range of convergence and speed of convergence).
1.1. Introduction. Newton’s method is the best known iterative method for solving nonlinearequations. Let f : R→ R be a function and α a root of the equation f(x) = 0, that is f(α) = 0. It isknown that if f ′(α) 6= 0, x0 is sufficiently close to α and under some conditions, the classical Newton’smethod defined by
(1) xn+1 = xn −f(xn)
f ′(xn), n = 0, 1, 2, . . .
generates a sequence xn∞n=0 that converges to α.The mapping
(2) Φ(x) = x− f(x)
f ′(x)
is called the Iteration Function (abbrev. I. F.) [9] of the method defined by (1).It is known that Newton’s method converges quadratically in a sufficiently small neighborhood of
the root α.The fractal pictures of the basins of attraction generated by Newton’s method for complex
polynomials are well known [2,3,5,7,8,10].A new third-order newton-type iterative method for solving nonlinear equations we introduce in
[1].In this paper we present graphical representations for the basins of attraction of real roots for two
examples of nonlinear equations and two Newton-type methods.
1.2. The basin of attraction and sample methods and equations. Let f : [a, b]→ R be afunction and α a root of the equation f(x) = 0, that is f(α) = 0, α ∈ [a, b] and let x0 ∈ [a, b].
If starting from x0 the sequence generated by the iterative relation (1) converges to α then we saythat x0 is attracted to α.
The basin of attraction of the root α is the set of all starting points x0 ∈ [a, b] which are attractedto α.
To show the graphical view of the basins of attraction, we considered the classical Newton’s methoddefined by the relation (1) and the harmonic mean Newton’s method [4,6] defined by
(3) xn+1 = xn −f(xn)(f ′(xn) + f ′(yn))
2f ′(xn)f ′(yn), n = 0, 1, 2, . . .
where yn = xn − f(xn)f ′(xn) ,
and two nonlinear equations f1(x) = 0 and f2(x) = 0 , where
(4) f1 : [−8, 8]→ R, f1(x) = 2xsinx− 2
(5) f2 : [−1, 3]→ R, f2(x) = x4 − 4x3 + 6x2 − 4x
The roots of the equation f1(x) = 0 in the interval I1 = [−8, 8] are α1 ≈ −6.439, α2 ≈ −2.773,α3 ≈ −1.114, α4 ≈ 1.114, α5 ≈ 2.773 and α6 ≈ 6.439, and the roots of the equation f2(x) = 0 in theinterval I2 = [−1, 3] are β1 = 0 and β2 = 2.
We present two versions for graphical view of the basins of attraction.
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1.3. Graphical views of the basins of attraction. a) The ”sinusoidal” model for the basinsof attraction
To generate, for example, the basins of attraction for the roots of the equation f1(x) = 0 on theinterval I1 = [−8, 8] using classical Newton’s method, we divide the interval I1 into n+1equidistantpoints tini=0 (in this case n = 500, t0 = −8 and t500 = 8). We solve the equation (4), by usingclassical Newton’s method, starting from each point tini=0.
If ti attempts a root α of the equation, α ∈ I1 ,with a tolerance ε = 10−5 in a maximum of 14iterations, then we draw a line between the points (ti, 0) and (ti, f1(ti) in a color associated to theroot α.
Nothing to draw if ti is not attracted by any root α ∈ I1. So, the white regions means that herethe method does not converges to any root in I1.
Figure 1.”Sinusoidal” view for Newton’s method and the equation f1(x) = 0
In the Figure 1, we can see that some values are not attracted by the nearest root. We say thatthese are out of the base basin of attraction of any root in the interval I1. If we denote B(α) to bethe basin of attraction of the root α, then we define the base basin of attraction B∗(α) to be thelargest open interval such that α ∈ B∗(α) ⊆ B(α). As one can see in Figure 1, from starting pointx0 = −7.712 the next point is x1 = Φ(x0) = −4.254 and then x2 = Φ(x1) = −1.547. Because x2 is inthe base basin of α3 ≈ −1.114 it results that x0 ∈ B(α3). (Geometrically, the tangent in(x0, f1(x0))intercept Ox axes in x1 and the tangent in(x1, f1(x1)) intercept Ox axes in x2).
To generate the basins of attraction we used Mathcad 14.0 package.b) The”bars” model for the basins of attractionTo generate, for example, the basins of attraction for the roots of the equation f1(x) = 0 on the
interval I1 = [−8, 8] using classical Newton’s method, we divide the interval I1 into n+1 equidistantpoints tini=0 (n = 500). We solve the equation (4), by using classical Newton’s method, starting fromeach point tini=0. If ti attempts a root α of the equation, α ∈ I1,with a tolerance ε = 10−5 in k ≤ 14iterations then we draw in ti a vertical bar with height equal to k and in a color associated to the rootα.
If ti is not attracted by any root α ∈ I1, then we draw at ti a red bar under the Ox axes.In fact, in this case, ti is attracted by a root out of the interval I1 (the equation f1(x) = 0 has an
infinity of roots!).
57
Figure 2 .”Bars” view for Newton’s method and the equation f1(x) = 0
This kind of representation is more relevant as the ”sinusoidal” one because it shows us the numberof iterations. So, using this representation for the basins of attraction, we can compare some iterativemethods for solving nonlinear equations.
1.4. Conclusions. Our graphical representations allow us to see the behavior of iterative methodsfor solving nonlinear equations and compare them.
Bibliography[1] G. Ardelean, A new third-order newton-type iterative method for solving nonlinear equations, Appl. Math. and
Comp., 219 (2013) 9856–9864.[2] G. Ardelean, A comparison between iterative methods by using the basins of attraction, Appl. Math. and Comp., 218
(2011) 88–95.[3] B. Kalantari, Polinomiography and applications in art, education and science, Computers&Graphics, 28 (2004)
417–430.[4] H.H.H. Homeier, On Newton-type methods with cubic convergence, J. Comp. Appl. Math., 176 (2005) 425–432.[5] St. Maruster, Numerical experiments on attraction basins, Annals Computer Science Series, 2nd Tome 1st Fasc.,
(2004) 167–171.[6] A. Y. Ozban, Some new variant of Newton’s Method, Appl. Math. Lett., 17 (2004) 677–682.[7] M. L. Sahari, I. Djellit, Fractal Newton basins, Discrete Dynamics in Nature and Society (2006) Article ID 28756.[8] H. Susanto, N. Karjanto, Newton’s method basin of attraction revisited, Appl. Math. and Comp., 215 (2009)
1084–1090.[9] J. F. Traub, Iterative Methods for the Solution of Equations, Chelsea publishing company, New York, 1997.
[10] J. L. Varona, Graphic and numerical comparison between iterative methods, Math. Intell., 24 (2002) 37–46.
ICAM9
58
Well posed problem in sense of Hadamard, for a source produced acousticperturbation propagation in a lined duct, carrying a gas flowAgneta M. Balint1 and Stefan Balint2
1Physics Faculty West University of Timisoara, Romania2Mathematics and Computer Science Faculty, West University of Timisoara, Romania
[email protected], [email protected]
Abstract. The purpose of this paper is to replace Brambley’s concept of ”well posed differential equation”
[1] related to the source produced acoustic perturbation propagation in a rectangular lined duct carrying
a gas flow with that of ”well posed problem in Hadamard sense”. The reason is that the concept
introduced by Brambley is confusing, i.e. the same equation can be well posed or ill posed depending on
the functional framework. For the source produced acoustic perturbation (SPAP) propagation problem
the concept of ”well posed problem in Hadamard sense” is defined as follows: for any SPAP, from a given
set of SPAP-s, there exists a unique solution to the problem of propagation and the solution depends
continuously on the SPAP. Necessary and sufficient conditions are derived for that the propagation
problem be well posed in sense of Hadamard.
1.1. Introduction. In the context of a large number of published results concerning acousticperturbation propagation in a lined duct carrying a gas flow, in this section the mathematicalconsiderations made in this paper are motivated.
1.2. Preliminary results. The propagation problem of the SPAP (described by the functionsF (x, y, t), G(x, y, t), H(x, y, t)) is: find u′(x, y, t), v′(x, y, t), p′(x, y, t) which satisfy equations
(1)
∂u′
∂t+ U0 (y) · ∂u
′
∂x+ v′ · dU0
dy+
1
ρ0· ∂p
′
∂x= F (x, y, t)
∂v′
∂t+ U0 (y) · ∂v
′
∂x+
1
ρ0· ∂p
′
∂y= G(x, y, t)
∂p′
∂t+ γ · p0 ·
∂u′
∂x+ γ · p0 ·
∂v′
∂y+ U0 (y) · ∂p
′
∂x= H(x, y, t)
boundary conditions
(2) a · ∂2v′
∂t2+ b · ∂v
′
∂t+ c · v′ = ∓∂p
′
∂tfor y = −h and y = h
and ”initial” condition:
(3) u′(x, y, t) = 0 v′(x, y, t) = 0 p′(x, y, t) = 0 for any t negative
Definition. Following the usage of Hadamard, we will say that the propagation problem (1), (2), (3)is well set if:(i) for any SPAP from a given class of SPAP-s, there is a unique solution to the problem;(ii) the solution varies continuously with the SPAP.The mathematical treatment of the propagation problem (1), (2), (3) in this paper is made under thefollowing assumptions :I. the set B of SPAP-s is that of the functions which satisfy :
1. are identically equal to zero for t non positive,2. are bounded and infinitely differentiable3. for any t fixed the functions have compact support with respect to the spatial variables x,y and
their support is included in Ω = (−∞,+∞)× (−h, h) .II. the solution of the problem (1), (2), (3) (if exists) belongs to the set S of system of functions
u′
= u′(x, y, t), v
′= v
′(x, y, t), p
′= p
′(x, y, t) which are continuously differentiable and rapidly
decreasing with respect to x .Under the above assumptions the magnitude of a SPAP from B at the moment of time t can beevaluated by ‖F (, , t) ‖ = sup
x∈R′sup
y∈[−h,h]|F (x, y, t) | and so on;
59
and the magnitude of the corresponding solution (if exists) at the moment of time t can be evaluatedby ‖u′ (, , t) ‖ = sup
x∈R′sup
y∈[−h,h]|u′ (x, y, t) | and so on.
1.3. Existence, uniqueness and continuity. The following result holds:Proposition 3.1. If for an SPAP from B the following conditions hold:
(i) the propagation problem (1) ,(2) ,(3) has a solution u′
= u′(x, y, t), v
′= v
′(x, y, t), p
′=
p′(x, y, t) in S .
(ii) for any (x, y) ∈ (−∞,+∞)× [−h, h] the solution possesses Laplace transform Lt with respectto t
(iii) the Fourier transform with respect to x, Fx , of the solution commutes with its Laplace
transform, Lt, i.e. u (α, y, ω) = Fx Lt · u′(x, y, t) = Lt Fx · u
′(x, y, t) and so on,
then there exists a real number µ such that for any α ∈ R′ and any ω ∈ C with Im ω > µ for theFx Lt transforms u (α, y, ω), v (α, y, ω), p (α, y, ω) (of the solution) the following equalities hold:
(4)
d2p
dy2+
2α
ω−α·U0 (y)· dU0
dy· dpdy
+
[(ω−α · U0 (y))2
c20
−α2
]· p= i·ρ0 ·α·F (α, y, ω)+
+2·ρ0 ·α
ω−α·U0 (y)· dU0
dy·G (α, y, ω)+ρ0 ·
dG
dy+i (ω−α · U0 (y))
c20
·H (α, y, ω)
(5)
u (α, y, ω) =α
ρ0 (ω − α · U0 (y))· p (α, y, ω)− 1
ρ0 (ω − α · U0 (y))2 ·dU0
dy· dpdy
+
+i
ω − α · U0 (y)· F (α, y, ω) +
1
(ω − α · U0 (y))2 ·dU0
dy· G (α, y, ω)
(6) v (α, y, ω) = − i
ρ0 (ω − α · U0 (y))· dpdy
+i
ω − α · U0 (y)· G (α, y, ω)
(7) v (α,∓h, ω) = ∓ 1
Z (ω)· p (α,∓h, ω)
Here: ω = i · z and z is the Lt transform variable; α is the Fx transform variable; F (α, y, ω),
G (α, y, ω), H (α, y, ω) are the Fx Lt transforms of the SPAP (F, G, H); Z (ω) = −a · i ·ω+b− c
i · ωis the wall impedance.Proposition 3.2. If there exists a real number µ such that for α ∈ R′ and ω ∈ C with Im ω > µ theboundary value problem:
(8)d2p
dy2+
2α
ω − α · U0 (y)· dU0
dy· dpdy
+
[(ω − α · U0 (y))2
c20
− α2
]· p = 0
(9) i · ρ0 · ω · p (α,∓h, ω)± Z (ω) · dpdy
(α,∓h, ω) = 0
possesses only the zero solution, then if exists a solution to the problem of propagation (1), (2), (3)having the properties i), ii), iii) (from Proposition 3.1), it is unique.Proposition 3.3. If the set of the imaginary parts Imω of the zero’s ω of the dispersion relations isbounded from above by µ, then the B.V.P. (4), (9) has a unique solution given by:
(10) p (α, y, ω) =
∫ h
−hI(y, y′;α, ω
)· f(α, y′, ω
)dy′
where: f (α, y′, ω) the right hand member of (4); I (y, y′;α, ω) is the Green’s function defined fory ∈ [−h, h], y′ ∈ [−h, h], α ∈ R′, ω ∈ C with Im ω > µ , by the formula:
60
(11) I(y, y′;α, ω
)=
[ω − α · U0 (0)] 2
E0 (α, ω)· p1
(α, y′, ω
)· p2 (α, y, ω) for − h ≤ y′ ≤ y ≤ h
[ω − α · U0 (0)] 2
E0 (α, ω)· p1 (α, y, ω) · p2
(α, y′, ω
)for − h ≤ y ≤ y′ ≤ h
with:
(12) E0 (α, ω) = p1 (α, 0, ω) · dp2
dy(α, 0, ω)− p2 (α, 0, ω) · dp1
dy(α, 0, ω)
and p1 (α, y, ω), p2 (α, y, ω) are solutions of the eq. (8) which satisfy the conditions:
(13) p1 (α,−h, ω) = 1 anddp1
dy(α,−h, ω) = − i · ρ0 · ω
Z (ω)
(14) p2 (α, h, ω) = 1 anddp2
dy(α, h, ω) =
i · ρ0 · ωZ (ω)
respectively.Proposition 3.4. If the set of the imaginary parts Im ω of the zero’s ωof the dispersion relations isbounded from above by a real number µ and the Green function satisfies
(15)∣∣ I (y, y′;α, ω) ∣∣ ≤ | P (α) | α ∈ R′ and Im ω > µ
(16)∣∣ ω · I (y, y′;α, ω) ∣∣→ 0 for |ω | → ∞ and Im ω > µ
then for every SPAP (F, G, H) from B , the propagation problem (1), (2), (3) has a unique solutionhaving the properties i), ii), iii).
1.4. Acknowledgement. This work was supported by a grant of the Romanian National Au-thority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0171.
Bibliography[1] Brambley, E. J., Fundamental problems with the model of uniform flow over acoustic liner, J. Sound and Vibrations,
322 (2009) 1026-1037
ICAM9
61
Generalized Algorithm of Processes of the Winter Maintenance on Airports
Stefan BereznyDepartment of Mathematics and Theoretical Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Kosice,
Kosice, Slovak Republic
Abstract. The paper describes a generalized algorithm, which describes the simulation of winter main-
tenance of airports. It is a model of the winter maintenance of airport motion areas. Purpose of this
algorithm is a simulation of snow cover at the airport movement areas with respect at varying weather
conditions. This algorithm was created, based on the data and algorithms that have been developed for
Kosice airport. The result of this work is a flowchart of the algorithm, according to which it is possible
to create a program that can simulate winter maintenance of motion areas on any airport with respect
to the initial limitations.
1.1. Introduction. First algorithm which generalizes given problem of winter maintenance waspublished in [2]. This algorithm generalizes the algorithm, which was published in the proceedings[1]. The basic scheme was published in the work [3], that used the methodology of work [6]. Basicparameters used for Kosice airport are included in the work [5]. Optimization operations of wintermaintenance was published in the journal [4].
1.2. The inputs of the algorithm. The main difference generalization of this algorithm is thatthe model can be used universally on almost any airport and not just the particular specified airfieldsof airports. Input data for the algorithm are represented by basic parameters:
Parameters airport:
Runway j ∈ 1, . . . , k1 PRj = WRj × LRj
Taxiway j ∈ 1, . . . , k2 P Tj = W Tj × LTj
Connecting roads j ∈ 1, . . . , k3 PCj = WCj × LCj
Apron j ∈ 1, . . . , k4 PAj = WAj × LAj
Parameters and variables of the algorithm:
Name Type DescriptionHSC Matrix of real numbers Snow depth at defined parts of the airfieldsISnow Series of real numbers Intensity of snowCHSnow Series of real numbers Current snow depthEtime Series of real numbers Estimated time of clean-up airfieldsEtimex Series of real numbers Estimated time of clean-up airfield x of the airport,
where x ∈ R, T,C,AQSnow Series of real numbers Quality of snowHSnow Real number Snow depth obtained from the sensorMP Series of real numbers The performance of the mechanization meansTimer Integer Timer clockCCSc Integer Current cleaned of aerodrome surfaceNSc Integer Number of aerodrome surfaceN Integer Number of dividing the movement area of the airportSSnow Real number Amount of snowhr Integer Hourmin Integer Minutek1 Integer Number of runwaysk2 Integer Number of taxiwaysk3 Integer Number of connecting roadsk4 Integer Number of apronsW xj Real number Width of the airfield x, where
x ∈ R, T,C,ALxj Real number Length of the airfield x, where
62
x ∈ R, T,C,AP xj Real number Surface area of the airfield x, where
x ∈ R, T,C,AStartT imexInteger Starting time: Number of time cycle, in which
began winter maintenance of airfields x, wherex ∈ R, T,C,A
1.3. The outputs of the algorithm. Estimated Time of clean-up the airport movement areax ∈ R, T,C,A is given by:
ETimax :=(QSnow · CHSnow · P x · 0.01)
MPThe total estimate of the time of clean-up the aerodrome movement area of airport is given by:
Etime := maxx∈R,T,C,A
1
6· StartT imex + ETimex
Parameters and variables are updated in ten minute intervals. Snow depth due to the intensity
of snowfall and running of cleaning airfields is updated. Based on these changes of variables, theexpected time of completion of maintenance of airport movement areas is modified.
Based on the well-established schema of algorithm for processes of winter maintenance would becreated realistic simulator of these processes and software solutions for winter maintenance. Suchrealistic simulator would be provide timely and properly respond to the situation and minimizecatastrophe risk in aviation safety at the airport, which are associated with closing the airport or theevent of poor maintenance of airport runway.
Bibliography[1] BEREZNY Stefan: Algorithms of Processes of the Winter Maintenance on Koice Airport, In: MOSATT 2011: pro-
ceedings of the International Scientific Conference Modern Safety Technologies in Transportation: 20. - 22.September2011, Zlat Idka, Slovakia - Koice: Suprema Ltd, 2011 S. 24-29. - ISBN 978-80-970772-0-4 - ISSN 1338-5232.
[2] BEREZNY Stefan: Generalized Algorithm of Processes of the Winter Maintenance on Kosice Airport, In: ICAM8:Proceedings of the International Conference of Applied Mathematics: October 27-30, 2011, Baia Mare – Romania
[3] KLACANSKY Matus: Mathematical Model Design of Simulation of 24-hours Cycle of Maintenance of Airport Area,Bachelor thesis, Koice, Technical University of Koice, Faculty of Electrical Engineering and Informatics, SlovakRepublic, 2011, 36 p.
[4] KOSCAK Peter BEREZNY Stefan - FERENC Jan: Optimization operations of winter maintenance of airport, In:International Journal of Traffic and Transportation Engineering. Vol. 1, no. 3 ,(2012), p. 40-45. - ISSN 2325-0062
[5] KOSCAK Peter BEREZNY Stefan: Optimal Attaching Means Winter Maintenance of Airport, Proceeding of The9th International Scientific Conference: New Trends in Aviation Development, Gerlachov High Tatras, September16. - 17. 2010, Slovak Republic, ISBN: 978-80-555-0475-5.
[6] PSENCIKOVA Jana: Algoritmizace, Computer Media s. r. o., Czech Republic, 2009, 128 p. ISBN: 978-80-7402-34-6
ICAM9
63
A new model of finite-source retrial queues with multi-state server’s breakdown
Tamas Berczes1, Attila Kuki1, Bela Almasi1, Janos Sztrik1 and Pascal Moyal2
1Department of Informatics Systems and Networks at the Faculty of Informatics, University of Debrecen, Hungary2Universite de Technologie de Compiegne, Compiegne, France
[email protected]; [email protected]; [email protected]; [email protected], [email protected]
Abstract.This paper deals with unreliable systems, where the performance of the system can be experi-enced in different levels of health between the perfect and the failed states.
The underlying model is a single server retrial queue with a finite number of homogeneous sources ofrequests and a single non-reliable server. The server is subject to random deteriorations and breakdownsdepending on whether it is busy or idle. The operations of the system might be blocked or unblockedby the failure of the server and the service of the interrupted request may be resumed or the requestcan be transmitted to the orbit. All random variables involved in the model constructions are supposedto be exponentially distributed and totally independent of each other.
The novelty of the investigation is the levels of goodness of a system in case of finite sources of
requests. The transitions of states of the server depend on its working status (ie., busy or idle), which
makes the system rather complicated. The MOSEL-2 tool was used to formulate and solve the problem.
The main performance and reliability measures were calculated.
1.1. Introduction. Retrial queues have been widely investigated and used to model manyproblems arising in telephone switching systems, telecommunication networks, computer networks,optical networks, etc. The main characteristic of a retrial queue is that a customer who finds theservice facility busy upon arrival is obliged to leave the service area, but some time later he comesback to re-initiate his demand. Between the trials a customer is said to be in the orbit. The literatureon retrial queueing systems is very extensive. For a recent account, readers may refer to the recentbooks of Falin and Templeton [1], Artalejo and Gomez-Corral [7] that summarize the main modelsand methods. Since in practice some components of the systems are subject to random breakdowns(see for example [2], [3],[4]) it is basically importan to study the reliability of retrial queues with serverbreakdowns and repairs because of limited ability of repairs and heavy influence of the breakdowns onthe performance measures of the system. However, so far the repairable retrial queues were analyzedonly in the case when the server could be in two states: operable or failed. For related literature thereader is referred to the works [5], [6] where infinite-source non-reliable retrial queues were treated.
In general, systems used in industries always suffer from stochastical deterioration and may undergomany deteriorating states before failure.
In this paper, a finite-source system is investigated with the following assumptions. Consider asingle server queueing system, where the primary calls are generated by K, 1 < K <∞ homogeneoussources. We assume that the system deterioration condition can be described by a finite number oflevels 1, 2..,m+ 1. Level 1 denotes the best health condition meaning that the system is as good as anew one, while m denotes the most deteriorated condition. Finally, m + 1 indicates that the systemhas failed.
The server can be in three states:
• idle state: The server level is between 1..m and the server can start serving the arrivingrequests.• busy state: The server is in busy state, when the server is in available state (the server level
is between 1..m) and one request is under service.• failed state: The server is in failed state, when the server level is m + 1. It can not start
serving any arriving requests until it is repaired.
We assume, that the service times are exponential distributed with parameters µ1,· · · ,µm, corre-sponding to server levels 1,· · · ,m
If a source is free at time t, it can generate a primary call during interval (t, t+dt) with probabilityλdt + o(dt). If the server is idle at the time of arrival of a call, then the servive of the call startsimmediately, the source moves into the under service state and the server moves into busy state. Theservice is finished during the interval (t, t+dt) with probability µidt+o(td), i = 1..m, according to theserver level. If the server is busy, then the source starts generation of a Poisson flow of repeated callswith rate ν until it finds the server idle. After service the source becomes free, and it can generate a
64
new primary call, and the server becomes idle so it can serve a new call. The server can step into thenext level during the interval (t, t+ dt) with probability δdt+ o(dt) if it is idle, and with probabilityγdt + o(dt) if it is busy. If δ = 0, γ > 0 or δ = γ > 0 active or independent breakdowns can bediscussed, respectively. If the server step reaches the level m + 1, that is the server is failed, twodifferent cases can be treated. The first one is the blocked sources case, when all the operations arestopped, that is no new calls are generated. The second one is the unblocked sources case, when onlythe service is interrupted but all the other operations are continued. In this paper we investigate onlythe unblocked sources case. If the server fails in a busy state, the interrupted request returns to thesources. The repair times are exponentially distributed with a finite mean 1/τ . All the times involvedin the model are assumed to be mutually independent of each other.
Because of the fact, that the state space of the describing Markov chain is very large, it is ratherdifficult to calculate the system measures in the traditional way of writing down and solving theunderlying steady-state equations. To simplify this procedure we used the software tool MOSEL(Modeling, Specification and Evaluation Language), see Begail et al. [8], to formulate the model andto obtain the performance measures.
1.2. The M/M/1//K retrial queueing model with multi-state unreliable server. Tomaintain theoretical manageability, the distributions of inter-event times (i.e., request generationtime, service time, retrial time, available state time, failed state time) presented in the network are byassumption exponential and totally independent.
We introduce the following notations:
• y(t) represents the server states at time t, y(t) = 1 · · ·m if the server is up with thecorresponding service rates µ1,· · · ,µm and y(t) = m+ 1 if the server is failed.• c(t) = 0 if the server is idle, c(t) = 1 if the server is busy• o(t) is the number of jobs in the orbit at time t.
The system state at a time t corresponds to a Continuous Time Markov Chain (CTMC) with 3dimensions:
X(t) = (y(t); c(t); o(t))
The steady-state distributions are denoted by
P (y; c; o) = limt→∞
P (y(t) = q, c(t) = r, o(t) = j), q = 1..m+ 1, r = 0, 1, j = 0, ...,K − 1.
Note, that the state space of this Continuous Time Markovian Chain is finite, so the steady-stateprobabilities surely exist. For computing the steady-state probabilities and the system characteristics,we use the MOSEL software tool in this paper.
As soon as we have calculated the distributions defined above, the most important steady-statesystem characteristics can be obtained in the following way:
• Utilization of the server
US =m∑y=1
K−1∑o=0
P (y, 1, o)
• Availability of the server
AS =m∑y=1
1∑c=0
K−1∑o=0
P (y, c, o)
• Average number of jobs in the orbit
O = E(o(t)) =
=m+1∑y=1
1∑c=0
K∑o=0
oP (y, c, o)
65
• The mean number of calls staying in the orbit or in service
M = E[o(t) + c(t)] = O +
m+1∑q=1
K−1∑o=0
P (q, 1, j).
• The mean rate of generation of primary calls
λ =
λE[K − c(t)− o(t); y(t)in(1, ..,m)], for blocked case,
λE[K − c(t)− o(t)], for unblocked case.
• The mean response time
E[T ] = M/λ.
• The mean waiting time
E[W ] = N/λ.
Acknowledgment. The publication was supported by the TAMOP-4.2.2.C-11/1/KONV-2012-0001 project. The project has been supported by the European Union, co-financed by the EuropeanSocial Fund. The research was also supported by the European Union with the help of the GOP-1.3.2-08-2009-0007 program.This research was partially granted by the Hungarian Science and Technology Foundation, Hungarian-French Bilateral Cooperation under grant TeT 10-1- 2011-0741, FR- 25/2010. The work of Janos
Sztrik was realized in the frames of TAMOP 4.2.4. A/2-11-1-2012-0001 National Excellence Program -Elaborating and operating an inland student and researcher personal support system. The projectwas subsidized by the European Union and co-financed by the European Social Fund.The work of Tamas Berczes was realized in the frames of TAMOP 4.2.4. A/2-11-1-2012-0001 NationalExcellence Program Elaborating and operating an inland student and researcher personal supportsystem The project was subsidized by the European Union and co-financed by the European SocialFund.
Bibliography[1] Falin G.I. and Templeton J.G.C. Retrial queues, Chapman and Hall, London, 1997.[2] Kovalenko I.N., Kuznetsov N.Yu. and Pegg P.A. Mathematical theory of reliability of time dependent systems with
practical applications, John Wiley and Sons, Chichester, 1997.[3] Ravichandran N. Stochastic methods in reliability theory, John Wiley and Sons, New York, 1990.[4] Trivedi K. S. Probability and statistics with reliability, queueing and computer science applications, Prentice-Hall,
Englewood Cliffs, 1982.[5] Artalejo J.R. New results in retrial queueing systems with breakdown of the servers, Statistica Neerlandica 48(1994),
23–36.[6] Aissani A. and Artalejo J. R. On the single server retrial queue subject to breakdowns, Queueing Systems Theory
and Applications 30(1998), 309–321.[7] Artalejo, J.R. and Gomez-Corral, A. Information theoretic analysis for queueing systems with quasi-random input,
Mathematical and Computer Modelling 22(1995) 65–76.[8] Begain K., Bolch G. and Herold H. Practical performance modeling, application of the MOSEL language, Kluwer
Academic Publisher, Boston, 2001.
ICAM9
66
Structural Optimization Model Design using TOSCA Program
Gratiela Dana BocaTechnical University of Cluj Napoca, North Unversity Center of Baia Mare, Romania
Abstract.The present work shows some of the typical computational tools and algorithms which areoften applied in industrial optimization.
The industry usually has existing CAD and CAE procedures that can handle large-scale finite
element calculations for complex geometries. Structural optimization using TOSCA structure helps to
find optimized design proposals in a very early phase of the product development cycle and dramatically
reduces the overall development costs and time. In the industry structural calculations is often done by
finite element modeling. Normally, the degrees freedom of the finite element models is constrained by
the capacity of computer power available for solving the model. Frequently, an industrial designer will
also prefer to use his daily preprocessor for constructing the finite element models for the optimization.
The purpose of the present paper is to show that optimization allows to be conducted in an already
existing CAD flow for large-scale models having a high number of degrees freedom, a realistic geometry
and boundary conditions, which finally can be done in an earlier faze of design product which assure
the robustness reliability of product.
1.1. Introduction. The general Robust Optimization formulation is:Minimize f0(x)
Subject to fi(x;ui) ≤ 0;∀ui ∈ Ui; i = 1 . . .m (1)
here x ∈ Rn is a vector of decision variables, f0, fi are as before, ui are disturbance vectors orparameter uncertainties, and Ui are uncertainty sets, which, for our purposes, will always be closed.By introducing a new constraint if necessary, we can always take the objective function to haveno uncertainty. The goal of (1) is to compute minimum cost solutions x among all those solutionswhich are feasible for all realizations of the disturbances ui within Ui. If Ui is a singleton, then thecorresponding constraint has no uncertainty. Intuitively, this problem offers some measure of feasibility,protection for optimization problems containing parameters which are not known exactly.
Frequently, an industrial designer will prefer to use his daily preprocessor for constructing thefinite element models for the optimization. Normally, the degrees freedom of the finite element modelsis constrained by the capacity of computer power available for solving the model. The purpose of thepresent paper is to show that non-parametric optimization allows the optimization to be conductedin an already existing CAD flow for large-scale models having a high number of degrees freedom, arealistic geometry and boundary conditions. This also allows an efficient handling of the definition ofthe optimization problem. Following the total quality management we must to start from the data andinformation, especially for our industry which still uses old generation machine and tools. The qualityis the only factor who can assure the top market competition and also the customers expectation.
FE DESIGN - proven partner for industrial manufacturers and suppliers.Demands for state of-the -art product development are stronger than ever. Nowadays all industries aresubject to accelerating changes in production and development and increasing aggressive competition.Complex demands can be fulfilled by applying simulation and optimization technologies in a virtualproduct developing process. The use of structural optimization in the early design phase leads tooptimal design proposal that eliminate the need to perform numerous design variations.
The FE DESIGN approach goes beyond the usual analysis of single engineering problems. Thereforecustomers are able to make better product development decisions in the earlier design phase using amulti-disciplinary approach which includes the combination of static and dynamic FE analyses withsimulation, with durability analyses, or calculation with life cycle predictions. Using existing CAEsolvers for solving optimization problems is essential in the industry. It ensures that the importantknow-how regarding the CAE-solvers and their results are reserved in the optimization computations.Additionally, standard pre and post-processors can be used in the optimization process. Figure 1. Thevirtual simulation of product can be done to different torques and materials and factors which canpresent the future work activity and work condition considering the real parameters from industry.
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Figure 1 Optimization added to an existing CAD and CAE workflow [6]
Modeling and design quality product.Having the solutions a specialist will consider the results as a suggestion for a future optimize of flankprofile of the teeth a problem which can be solve with the help of TOSCA program, by using thesimilar mathematical model realize with the FEM method who is consider the base of data.
In this way we can discover earlier the possible factors and the parameters which can improvethe quality. That solution brings benefits from economical point of view, material; reduce the cost,increasing the quality and the optimization of technological process. The present work shows some ofthe typical computational tools and algorithms which are often applied in industrial optimization.The industry usually has existing CAD and CAE procedures that can handle large-scale finite elementcalculations for complex geometries.
Structural optimization using TOSCA Structure helps to find optimized design proposals in a veryearly phase of the product development cycle and dramatically reduces the overall development costsand time. In the industry structural calculations is often done by finite element modeling. Elementgroups, node groups, sets, property numbers and/or material numbers defined in your preferredCAE preprocessor can directly be applied in optimization solutions, discussing and distributing 3Doptimization results without restraints using freely distributed 3D plug-in viewer and post processingof optimization results in personal preferred. Normally, the degrees freedom of the finite elementmodels is constrained by the capacity of computer power available for solving the model. Frequently,an industrial designer will also prefer to use his daily preprocessor for constructing the finite elementmodels for the optimization. The purpose of the present paper is to show that optimization allows tobe conducted in an already existing CAD flow for large-scale models having a high number of degreesfreedom, a realistic geometry and boundary conditions, which finally can be done in an earlier faze ofdesign product which assure the robustness reliability of product
1.2. Conclusion. The rapid development of models or prototypes may largely reduce the de-velopment cost and the product development cycle. Since it is based on technological changes orimprovements, the development of such models or prototypes is usually conducted by technologist,who has no regard for the cost of such a development.
Using the new programs as ANSYS, TOSCA, FEMFAT, the future for quality product it is a reality,in this way we can improve quality from the first stage of life cycle of the product. Each individualissue requires typically dedicated analyses and modeling tools, which leads to the introduction ofvarious fields of application and corresponding domain and research. The use of structural robustoptimization tools in the early stage of the development process offers new potential in the processchain. This method in design product will help customers to: make early decision in the design cycle,reduce the product development cycle, improve time-to market and reduce design and manufacturingcost: reduce design cycle, reduce cost of materials, reduce number of prototypes and physical testes.The algorithm identify the life cycle of the product design and the evolution of specific elements which
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can influence the robust design of the product but the economical and trust solution it is the FEsolution, which mean reduce costs, robust design from the first stage of product design.
The benefits are: fast improvement of existing FE models, reduction of stress calculation, increasedurability, no need to run nonlinear analysis after optimization, robust reliability, practical conceptualdesigning for weight reduction considering manufacturing constraints → material savings
- fast conceptual designing for Eigen frequency optimization → sound reduction and avoidingfrequency interactions
- reliable conceptual designing considering different structural constraints in each load case →feasible design for several load scenarios without time consuming trial and error process
- combined conceptual designing for both static and dynamic properties → obtaining newdesign which is not intuitive
- straightforward maximal stress reduction for complex surfaces and geometries → increasinglife-span
- increase of durability using shape optimization → fatigue resistant design- combined stress reduction and increase of durability → design fulfilling misuse load cases
and long life excitations- general reduction of the development time and development cycles → cost saving
The equation of flexibility and knowledge product can be written in function of following variablesfor our improvement product matrix were: Qp represent quality perception, Qa = quality action, Qd =quality decision, Pq,-quality perception , Pa-action perception, Pp- precision perception, T -technology,M -man, manufacture power, A-affect variable.
(1) EKP = f(Qp, Qa, Qd, Pq, Pa, Pd, T,M,A)
Bibliography[1] Albers, A. and Weiler, H., (2009) Impact of Distribution Functions of Input Parameters on the Quality of Robustness
Analysis in Simulation. Nafems Seminar: VIRTUAL TESTING, Simulations verfahren als integrierter Baustein einereffizienten Produktentwicklung, 10-11.05.06, Wiesbaden, ISBN 1-874376-14-X
[2] Bangert, C.and Jiang, J.(2006), Optimization and robustness analysis with deep drawing simulation, INPRO Workshop”Robust Processes with Modern Steels”, Berlin
[3] Bendsoe, M.P. and Sigmund, O.(2003), Topology optimization: Theory, Methods and Applications. Springer-Verlag,Berlin Heidelberg New York
[4] Emmrich, E., (2004), Entwicklung einer FEM-basierten Methode zur Gesaltung von Sicken fr biegebeanspruchte Leit-sttzstrukturen im Konstruktionsprozess, Forschungsberichte des Instituts fr Produktentwicklung, Band 13, Karlsruhe
[5] W. Huber, W., Fischer and M. and Himmler, G., ( 2003), Stress Reduction in an Inter stage Air Seal using TOSCA(MSC.Construct) for Increasing the LCF Fatigue Life, MSC Virtual Product Development Conference, Bad Neuenahr
[6] Pedersen, C.B.W. and Allinger, P., (2005), Recent Developments in the Commercial Implementation of TopologyOptimization, TopoptSYMP2005 - IUTAM-Symposium- Topological design optimization of structures, machines andmaterial status and perspectives, Copenhagen, Denmark, pp:123-132
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Algorithms implementation model for software optimization
Carstea Claudia1, Sangeorzan Livia2
1Departament of Informatics and Mathematic, George Baritiu University from Brasov, Romania2Faculty of Mathematics and Computer Science, University Transilvania of Brasov, Romania
[email protected]; [email protected]
This paper deals with significant aspects of the process of making an evaluation system for theinformation system project management and optimize the software with genetic algorithms. Thisnew era requires a new breed of software, service and support solutions. It is critical to be able tovisualize what is going on in your IT infrastructure and implement solutions that not only monitor,but deliver proactive management capabilities. Over time, those elements have become dispersed anddistributed across wide networks. As the complexity of infrastructures increased, so did the need formanagement software to handle this complexity, anticipate problems and resolve them before theyimpact the business.
1.1. Introduction. The ESSENCE of mathematics is not to make simple things - complicated,but making complicated things SIMPLE. In the computer science field of artificial intelligence, a geneticalgorithm (GA) is a search heuristic that mimics the process of natural selection. This heuristic isroutinely used to generate useful solutions to optimization and search problems. In a genetic algorithm,a population of candidate solutions (called individuals, creatures, or phenotypes) to an optimizationproblem is evolved toward better solutions. [2,15] Each candidate solution has a set of properties (itschromosomes or genotype) which can be mutated and altered; traditionally, solutions are represented inbinary as strings of 0 s and 1s, but other encodings are also possible. The evolution usually starts froma population of randomly generated individuals, and is an iterative process, with the population ineach iteration called a generation. In each generation, the fitness of every individual in the populationis evaluated; the fitness is usually the value of the objective function in the optimization problembeing solved.
Figure 1 Iterative cycle for genetics algorithms
The more fit individuals are stochastically selected from the current population, and each individ-ual’s genome is modified (recombined and possibly randomly mutated) to form a new generation. [3]The new generation of candidate solutions is then used in the next iteration of the algorithm. Com-monly, the algorithm terminates when either a maximum number of generations has been produced, ora satisfactory fitness level has been reached for the population. (Figure 1) A typical genetic algorithmrequires:
• a genetic representation of the solution domain,• a fitness function to evaluate the solution domain.
1.2. Why Genetic Algorithms? Genetic algorithms tend to thrive in an environment in whichthere is a very large set of candidate solutions and in which the search space is uneven and has manyhills and valleys. True, genetic algorithms will do well in any environment, but they will be greatlyoutclassed by more situation specific algorithms in the simpler search spaces. Therefore you must
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keep in mind that genetic algorithms are not always the best choice. Sometimes they can take quite awhile to run and are therefore not always feasible for real time use. They are, however, one of themost powerful methods with which to (relatively) quickly create high quality solutions to a problem.Now, before we start, I’m going to provide you with some key terms so that this article makes sense.[7, 8, 11] Genetic algorithms are a very effective way of quickly finding a reasonable solution to acomplex problem. Granted they aren’t instantaneous, or even close, but they do an excellent job ofsearching through a large and complex search space. Genetic algorithms are most effective in a searchspace for which little is known. You may know exactly what you want a solution to do but have noidea how you want it to go about doing it. This is where genetic algorithms thrive. They producesolutions that solve the problem in ways you may never have even considered. Then again, they canalso produce solutions that only work within the test environment and flounder once you try to usethem in the real world. Put simply: use genetic algorithms for everything you cannot easily do withanother algorithm. (Figure 2)
Figure 2 GA concepts
Genetic algorithms were formally introduced in the United States in the 1970s by John Holland atUniversity of Michigan. The continuing price/performance improvements of computational systemshas made them attractive for some types of optimization. In particular, genetic algorithms work verywell on mixed (continuous and discrete), combinatorial problems. They are less susceptible to gettingstuck at local optima than gradient search methods. But they tend to be computationally expensive.Genetic algorithms are one of the best ways to solve a problem for which little is known. They are avery general algorithm and so will work well in any search space. All you need to know is what youneed the solution to be able to do well, and a genetic algorithm will be able to create a high qualitysolution. Genetic algorithms use the principles of selection and evolution to produce several solutionsto a given problem. You have to remember that f and d functions depend by particularity of problemto have resolve. (Figure 3)
Figure 3 Performance function
Some examples of Genetic Algorithm Software are:GENOCOP III Genetic Algorithm for Constrained Problems in C (by Zbigniew Michalewicz)DE Differential Evolution Genetic Algorithm in C and Matlab (by Rainer Storn). DE has won the
third place at the 1st International Contest on Evolutionary Computation on a real-valued functiontestsuite
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Figure 4 Activities Diagram
PGAPack - Parallel Genetic Algorithm in Fortran and C (from Argonne National Laboratory)PIKAIA - Genetic algorithm in Fortran 77/90 (by Charbonneau, Knapp and Miller)GAGA = Genetic Algorithm for General Application in C (by Ian Poole)GAS Genetic Algorithm in C++ (by Jelasity and Dombi)GAlib C++ Genetic Algorithm Library (by Matthew Wall)GADS Genetic Algorithm and Direct Search Toolbox inMatlab - (from MathWorks)GEATbx - Genetic and Evolutionary Algorithm Toolbox for MatlabGAOT Genetic Algorithms Optimization Toolbox inThe software development process is usually affected by many risk factors that may cause the loss
of control and failure, thus which need to be identified and mitigated by project managers. Softwaredevelopment companies are currently improving their process by adopting internationally acceptedpractices, with the aim of avoiding risks and demonstrating the quality of their work. [12]
The optimization method was tested with several software risk prediction models that have beendeveloped based on the literature and using data from a survey which collected information fromin-house and outsourced software development projects in the Chilean software industry. Thesemodels predict the probability of success of a project based on the activities undertaken by the projectmanager and development team. The results show that the proposed method is very useful to identifythose activities needing greater allocation of resources, and which of these will have a higher impacton the projects success probability.
1.3. Activities Diagram. The managerial philosophy and the leading manner affect the wayin which any company is administrated, no matter the field of operation. We can include in thiscategory factors such as: taking the risks, instituted politics and procedures, giving responsibilities,the attitude in regard of financial reports. The control medium is strongly influenced by the degreein which the employees are aware of their role in reaching the companys targets. But the employeesethical manner is not enough. Their abilities are another essential element of the control medium.The ability, that is knowledge and aptitudes necessary in every line of work, must be mentioned bythe leaders. It is in the interest of every company to have the best employees. (Figure 4)
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Figure 5 The evaluation model diagrame
A regular monitoring assures a dynamic reaction to the changes that appear, so that the projectmanager has pertinent information for the politics of the companys implementations (Figure 5).
Bibliography[1] Baker, D., Bridges, D., Hunter, R., Johnson, G., Krupa, J., Murphy, J. and Sorenson, K. Guidebook to Decision-
Making Methods, WSRC-IM-2002-00002, Department of Energy, 2002[2] Buchmann Robert, Mocean Loredan, Xml Connectivity within Flash Presentations, in Information And Knowledge
Age Proceedings Of The 7th International Conference On EInformatics Bucharest, 2012[3] Claudia Carstea, Plesea Doru, The future in marketing tests and management programs, International Conference,
Plovdiv, 2003, pag.462, ISSN 0477-0250[4] Jeffrey L. Whitten, Lonnie D.Bentley, Systems analyses and Design Methods, McGrow-Hill Companies Inc, 1998[5] J. McGovern, Enterprise Service Oriented Architectures: Concepts, Challenges, Recommendations, Springer, 2006[6] B. Henderson-Sellers, P. Giorgini, Agent- Oriented Methodologies, Idea Group Publishing, USA, 2005[7] W. H. Immon, Building the Data Warehouse, John Wiley & Sons, 1996[8] M. Roost et al, A Model of Information Systems Development for Learning Virtual Organizations, Information
Systems Development: Advances in Theory, Practice and Education, O. Vasilecas etc., Ed. Springer, 2010[9] N.L. Russo, Expanding the horizont of information systems development, Organizational and social perspectives of
information technology: Proceedings of the IFIP TC8/WG8.2 International Working Conference, Aalborg, Denmark,2000
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Optimizing Investment Costs for Production Systems with Discontinuous Operation Mode
Dinu DarabaDepartment of Engineering and Technological Management, Technical University of Cluj-Napoca, North University Center at Baia Mare,
Baia Mare, Romania
Abstract.In case of the investment process, the optimization is based on a mathematical model or a range
of mathematical models which describe the process. The Choice of the most appropriate mathematical
model is the guarantee to obtain useful information for investors. This paper presents a classic analytical
method of decreasing the investment cost in the batch production systems that are specific to the
engineering industry.
1.1. Introduction. For the efficient use of the investment resources, the investment processin the field of technical systems requires the use of the mathematical optimization methods basedon static linear programming (geometric methods, analytical methods and sequential methods) anddynamic linear programming, when taking into account the influence of the time factor. Dependingon the potential of the mathematical model, the concept of optimum could have a double meaning:a permanent or relative one. The closest to the optimum variant, resulting from the application ofmathematical methods, provides the investors with useful information to adopt the solution withthe lowest investment risk, in order to achieve the closest economic efficiency to the proposed one.Modeling and solving the optimization problems involve the following sequential steps [2]:
(1) Choice of the aimed function - usually it is the criterion of economic efficiency to be achievedand which is to meet some specific, immediate and prospective needs. A benchmark to bemaximized or minimized will be selected accordingly.
(2) The main and secondary restrictions are determined the minimum level for some economiceffects to be achieved, the minimum level of the production costs, the minimum amount ofthe resources.
(3) The objective function is created, starting from its dependence on the variables of the solutionsunderlying the formulated alternatives.
(4) Solving the algorithm formed by the system of equations and inequalities as well as the aimedfunction.
(5) Verifying the stability of the optimal solution identified in relation to the adopted hypothesesand considering whether there are other alternative variants that would provide suitableresults with fewer risks under those hypotheses.
(6) Recommendation for investors on the variant that would be adopted, presenting its advantagesover other alternatives.
(7) Recommendation for investors on the variant that would be adopted, presenting its advantagesover other alternatives.
1.2. Mathematical model. Considering that a batch of products is manufactured by a produc-tion system comprised of some technological equipment operating in discontinuous mode and others insemi-continuous mode. Mathematically, it is assumed that the production system made up of a stringof X technological equipment in batch operation mode and Y equipment in semi-continuous operationmode, to form the G group of equipment. The total manufacturing time of a batch of parts will be [1]:
D =X∑i=1
ti +Y∑j=1
dj
where: ti and dj are durations of the manufacturing processes.Denoting with Q the production task of a batch of parts, the manufacturing system productivity
could be expressed as [1]:
W =Q
D.
The imposed restrictions also refer to the cost of the technological equipment. To determine the costof the technological equipment, their number is considered, corresponding to various technological
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operations i with discontinuous operation mode, which are necessary to meet the production taskQ, are different but proportional to Q; expressions to determine the cost of their purchase can beexpressed in the form [1]:
Ci = uiXαii = ui · (Ki ·Q)αi = ai ·Qαi , i = 1, , X
where : ai and αi are specific constants of the batch mode operating equipment;ui- unit cost of the equipment;Ki - constant of proportionality.
Using the same rationale for the batch mode operating equipment we could assume[1]:
Ck = bk ·(Q
θk
)βk, k = 1, ., Y.
where: bk and βk are the specific constants of the semi-continuous mode operating equipment;θk the operation time that is necessary to manufacture a batch of products.The total investment cost, which also represents the aimed function, will be:
(1) CT =X∑i=1
ai ·Qαi +Y∑i=1
bk ·(Q
θk
)βkMinimizing this expression with respect to the variables ti and dj should be done by respecting therestrictions relative to the respective production, expressed by the relation:
(2) W =Q
D=
QX∑i=1
ti +G∑j=1
dj
Using the substitution of the Q (2), production task into the aimed function (1), an equivalent equationwithout restrictions is obtained:
CT =X∑i=1
ai ·Wαi ·Dαi +Y∑k=1
bk ·Wαi
(D
θk
)βkFinally we obtain a system whose solution will offer the best solution. This allows the investor the
choice of equipment with the features needed productive activity.
Bibliography[1] Loorkar, Y. and Robinson, J.D., Minimization of Capital Investment for Batch Proceses. Calculation of Optimum
Equipment Sizes, Industrial Engineering Chemistry and Process. Design Development, Vol. 9, No. 4, (1970), pp.625-629
[2] Stancu, F., Prvu, D., Dumitru, M., Stoian, M. and Vasilescu, I., Eficienta economica a investitiilor, Ed. D. P.,Bucuresti, 1995.
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An efficient method to solve a two-server heterogeneous retrial queue with threshold policy
T. V. Do1, R. Chakka1, J. Sztrik2, T. Berczes2, D. Efrosinin3
1Department of Networked Systems and Services, Budapest University of Technology and Economics, Hungary2Faculty of Informatics, University of Debrecen, Hungary3Johannes Kepler University, Linz, Austria
[email protected], [email protected]
Efrosinin and Sztrik [1] considered a two-server heterogeneous retrial queue with threshold policy.They model the system as a quasi-birth-and-death (QBD) process with threshold dependent block-tridiagonal infinitesimal matrix and apply the general theory of matrix-geometric solutions. Thus, thecomputation of the rate matrix R (the minimal non-negative solution to the matrix equation) is basedon the iteration algorithm. However, R can be expressed in a closed formula.
1.1. Level-dependent Band-QBD Solution. From the form of Λ (see page 214 of [1]) weobserve that has two QBD-bands (see [2]):
• In band 1, we have the balance equations
(1) πi−1A01 + πiA10 + πi+1A21 = 0, 1 ≤ i ≤ q2 − 2.
• the balance equations of band 2 is expressed as follows.
(2) πi−1A02 + πiA12 + πi+1A22 = 0, i ≥ q2 + 1.
Note that if the size of the orbit is finite, then the range of index i in equation (2) is upper boundedby N − 1. That is, q2 + 1 ≤ i ≤ N − 1.
1.2. Infinite Orbit Size. The boundary balance equations are
(3) π0A00 + π1A21 = 0,
(4) πq2−2A01 + πq2−1A11 + πq2A22 = 0.
MGM (Matrix Geometric Method):From eq. (1), we obtain (see [3, 4])
πi = π0Ri1 + πq2−1R
q2−1−i2 , ∀i = 0, . . . , q2 − 1,(5)
where R1 and R2 are the minimal non-negative solution of the quadratic matrix equations
A01 +R1A10 +R21A21 = 0,(6)
A21 +R2A10 +R22A01 = 0,(7)
respectively.The matrix geometric solution for πi, i ≥ q2 is given by
(8) πi = πq2Ri−q2, i ≥ q2,
where R is the minimal non-negative solution of the quadratic matrix equation
(9) A02 +RA12 +R2A22 = 0.
SE (Spectral Expansion):
Following [2], we obtain the expression for πi, 0 ≤ i ≤ q2 − 1, from equation (1)
πi =
4∑k=1
a1,kψ1,kxi1,k +
4∑k=1
b1,kφ1,kyq2−1−i1,k , ∀i = 0, . . . , q2 − 1,(10)
where a1,k’s and b1,k’s are the coefficients to be determined, and (x1,k,ψ1,k) (k = 1, 2, 3, 4)are the eigenvalue, left-eigenvector solution pairs of the matrix equations
(11) ψ1,.[A01 +A10x1,. +A21x21,.] = 0,
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and (y1,k,φ1,k) (k = 1, 2, 3, 4) are the eigenvalue, left-eigenvector solution pairs of the matrixequation
(12) φ1,.[A21 +A10y1,. +A01y21,.] = 0.
The probability πi, i ≥ q2, is given by
πi =4∑
k=1
a2,kψ2,kxi−q22,k , ∀i ≥ q2,(13)
where (x2,k,ψ2,k) (k = 1, 2, 3, 4) are the eigenvalue, left-eigenvector solution pairs of thematrix equations
(14) ψ2,.[A02 +A12x2,. +A22x22,.] = 0.
Note that |x2,k| < 1 for k = 1, 2, 3, 4.
The R matrix. Following [5], the characteristic matrix polynomial associated to eq. (2) isQ(x) = A02 + xA12 + x2A22 (note that we use the same notations of [1]). We obtain
(15) Q(x) =
−(γ + λ)x x(λ+ γx) 0 0
µ1x −(γ + λ+ µ1)x 0 x(λ+ γx)µ2x 0 −(γ + λ+ µ2)x x(λ+ γx)0 µ2x µ1x λ− (λ+ µ1 + µ2)x
.It yields
Det[Q(x)] = x3(x− 1)[λ((γ + λ)2 + γµ1)(γ + λ+ µ2)
−γ(µ1(γ2 + 2λ2 + γ(3λ+ µ1)) + ((γ + λ)2 + 2(γ + 2λ)µ1 + µ21)µ2 + (γ + λ+ µ1)µ2
2)x
+γ2µ1(µ1 − µ2)x2]
= x3(x− 1)[ω0 − ω1x+ ω2x2](16)
where
ω0 = λ((γ + λ)2 + γµ1)(γ + λ+ µ2),
ω1 = γ(µ1(γ2 + 2λ2 + γ(3λ+ µ1)) + ((γ + λ)2 + 2(γ + 2λ)µ1 + µ21)µ2 + (γ + λ+ µ1)µ2
2),
ω2 = γ2µ1(µ1 − µ2).
As a consequence, Det[Q(x)] has three zero roots (x2,1 = x2,2 = x2,3 = 0), one root equal to 1. Inaddition,
• Det[Q(x)] has one root x∗2,4 = γ2λ+2γλ2+λ3+γλµ2γµ2(2γ+3λ+2µ2) if µ1 = µ2.
• Det[Q(x)] has two roots x2,4 =ω1−√ω21−4ω0ω2
2ω2and x2,5 =
ω1+√ω21−4ω0ω2
2ω2if µ1 6= µ2.
Note that the eigenvalues of eq. (14) are the roots of Det[Q(x)]. Following the same argument asin [5], if the QBD process is ergodic, Q(x) should have four eigenvalues inside the unit circle. As aconsequence, |x∗2,4| < 1 (for µ1 = µ2) and |x2,4| < 1 (for µ1 6= µ2). In what follows, we also use x2,4 torefer to x∗2,4 when µ1 = µ2.
It is easy to check that independent left-eigenvectors corresponding to three null-eigenvalues areψ2,1 = [1, 0, 0, 0], ψ2,2 = [0, 1, 0, 0],. . . ,ψ2,3 = [0, 0, 1, 0].
Let ψ2,4 = [ψ2,4,1, ψ2,4,2, ψ2,4,3, 1] be the eigenvector corresponding to x2,4. Utilizing ψ2,4Q(x2,4) =0, we get
ψ2,4,1 =2γµ1µ2 + 2λµ1µ2 + µ2
1µ2 + µ1µ22
(γ + λ+ µ2)(γ2 + 2γλ+ λ2 + γµ1 − γµ1x2,4),
ψ2,4,2 = −−γ2µ2 − 2γλµ2 − λ2µ2 − λµ1µ2 − γµ2
2 − λµ22 − γµ1µ2x2,4
(γ + λ+ µ2)(γ2 + 2γλ+ λ2 + γµ1 − γµ1x2,4),
ψ2,4,3 =µ1
γ + λ+ µ2.
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Following [5], we get R = Ψ−1 · diag(0, 0, 0, x2,4) ·Ψ, where Ψ = [ψ2,1,ψ2,2,ψ2,3,ψ2,4]T . Hence,
(17) R = x4
0 0 0 00 0 0 00 0 0 0
ψ2,4,1 ψ2,4,2 ψ2,4,3 1
.1.3. Finite Orbit Size. The matrix geometric solution for πi, i ≥ q2 is given by
(18) πi = πq2Ri−q23 + πNR
N−i4 , q2 ≤ i ≤ N,
where R3 and R4 is the minimal non-negative solution of the quadratic matrix equations
A02 +R3A12 +R23A22 = 0,(19)
A22 +R4A12 +R24A02 = 0,(20)
respectively.The alternative expression for πi, i ≥ q2, is given by
πi =
4∑k=1
a2,kψ2,kxi−q22,k +
4∑k=1
b2,kφ2,kyN−i2,k , ∀q2 ≤ i ≤ N,(21)
where (x2,k,ψ2,k) (k = 1, 2, 3, 4) are the eigenvalue (of least absolute value), left-eigenvector solutionpairs of the matrix equations
(22) ψ2,.[A02 +A12x2,. +A22x22,.] = 0,
and (y2,k,φ2,k) (k = 1, 2, 3, 4) are the eigenvalue (of least absolute value), left-eigenvector solutionpairs of the matrix equation
(23) φ2,.[A22 +A12y2,. +A02y22,.] = 0.
AcknowledgementThe publication was supported by the TAMOP-4.2.2.C-11/1/KONV-2012-0001 project. The
project has been supported by the European Union, co-financed by the European Social Fund.The work of Tamas Berczes was funded in the frames of TAMOP 4.2.4.A/2-11-1-2012-0001
“National Excellence Program Elaborating and operating an inland student and researcher personalsupport system”. The project was subsidized by the European Union and co-financed by the EuropeanSocial Fund.
Bibliography[1] Dmitry Efrosinin and Janos Sztrik. Performance analysis of a two-server heterogeneous retrial queue with threshold
policy. Quality Technology and Quantitative Management, 8(3):211–236, 2011.[2] Tien V Do, Ram Chakka, Orhan Gemikonakli, and Denes Papp. Level dependent band-QBD processes: Steady state
solution and applications. In Second International Working Conference on Performance Modelling and Evaluation ofHeterogeneous Networks, pages WP8/1–6, Ilkley, United Kingdom, 2004.
[3] N. Akar and K. Sohraby. Finite and Infinite QBD Chains: A Simple and Unifying Algorithmic Approach. InProceedings of IEEE INFOCOM, pages 1105–1113, 1997.
[4] Nail Akar, Nihat Cem Oguz, and Khosrow Sohraby. A Novel Computational Method for Solving Finite QBD processes.Commun. Statst.- Stochastic Models, 16(2):273–311, 2000.
[5] Tien Van Do and Ram Chakka. An Efficient Method to Compute the Rate Matrix for Retrial Queues with LargeNumber of Servers. Applied Mathematics Letters, 23:638–643, 2010.
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On a Markov Model for the Optimization of the Websites Structure
Nicoleta Enache-David and Livia SangeorzanFaculty of Mathematics and Informatics, Transilvania University of Brasov, Romania
[email protected], [email protected]
Abstract.In this paper we propose a Markov model for a web site. We introduce the typical navigation
trail notion and we determine the length of the typical navigation trails in a web site, using the entropy
of the Markov chain that we have considered. Finally, we propose a method for the optimization of the
structure of a web site, based on the length of the typical navigation trails.
1.1. Introduction. The websites have a hierarchical organization of content. Logical informationarchitecture makes a website more interesting to both search engines and visitors by ensuring that thecontent is accessible in a logical way. In this paper we propose a method for the optimization of thestructure of a website.
Log files provide a list of the page requests made to a given web server in which a request ischaracterized by the IP address of the machine placing the request, the date and time of the requestand the URL of the page requested. From this information it is possible to reconstruct the usernavigation sessions within a website, where a session consists of a sequence of web pages viewed by auser in a given period of time.
1.2. A Markov Model for a Website. Let us consider a Markov chain M = (X,P, µ) definedby a set of states X = (Xi)i=1,n, a transition matrix P = (pij)ij=1,n and a vector of initial probabilities
µ = (µi)i=1,n. The states Xi, i = 1, n are represented by the pages in website [1].The transition matrix P contains the transition probabilities which are estimated as the proportion
of times the corresponding link was traversed from the anchor. The initial probability of a state isestimated as the proportion of times the corresponding page was requested by the user.
Definition 1. A trail in M is a finite sequence T = X1, X2, . . . , Xt of states in M such that(Xi, Xi+1), i ∈ 1, . . . , t− 1 are consecutive pages in the web site.
The probability p (T ) of a trail T of length t is given by:
(1) p (T ) = Pk1Pk1k2Pk2k3 · Pki−1ki ,
where k1, . . . , kt is a permutation of 1, 2, . . . t, [2].Definition 2. A typical trail in a web site is a trail T whose estimated probability is above a
specified cut-point λ ∈ (0, 1).We denote by Tλ the estimated length of a trail T and we obtain:
(2) tλ ≤ −lnλ
H (M) ln 2
where H (M) is the entropy of the Markov chain M .
1.3. Website Structure Optimization. In order to optimize the structure of a website, weuse the FBT (Finding Backtrack Pages) algorithm that we have presented in [6]. FBT has as inputthe pages of the website, the transition matrix, a collection of navigation trails and the target pageTP , and as output the set of backtrack pages M and the target page TP .
The main idea is to create additional links between the pages from the set M and the target pageTP . This way, the visitors can have an easier access to the target page.
Let us consider the set of backtrack pages M returned by the FBT algorithm. We propose theSSO (Site Structure Optimization) algorithm that will consider only those pages from the set M thatare on a typical trail that have the length less or equal with tλ, λ ≤ 1 from (2).
SSO algorithm has as input the set of backtrack pages M , the target page TP , the start page andthe length of the typical trails, and as output we obtain an optimized structure of the website.
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Figure 1 The initial structure of the website
Figure 2 The optimized structure of the website
1.4. Experimental Results. Our experimental results have been obtained on an ecommercewebsite having 10 pages denoted by X1, X2, . . . , X10, where the start page is X1. We apply the SSOalgorithm for the website structure optimization and we conclude that we must create a new linkbetween the pages X9 and X1. In figure 1 we present the initial structure of the site and in figure 2we present the optimized structure of the site.
1.5. Conclusion. Our key insight is that visitors of a website will backtrack if they do not findinformation where they expect it. The page from where they backtrack is the expected location for
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the page. This way we can improve the structure of the website by creating an additional link fromhomepage to the expected location for the page and one can offer an easier access to the information.
Bibliography[1] Borges, J., Levene, M., An Average Linear Time Algorithm for Web Usage Mining, International Journal of
Information Technology and Decision Making, Vol. 3, 2004.[2] Cover, T. M., Thomas J. A., Elements of Information Theory, John Wiley and Sons, Inc., 2006.[3] Haggstrom, 0., Finite Markov Chains and Algorithmic Applications, Cambridge University Press, ISBN: 0-511-
01941-6, 2002[4] Borges, J., Levene, M., Evaluating Variable-Length Markov Chain Models for Analysis of User Web Navigation
Sessions, IEEE Transactions on Knowledge and Data Engineering, 19(4): 441-452, 2007[5] Wu, X. et al, Top 10 algorithms in data mining, Knowledge and Information Systems, 14:1-37, Springer, 2008[6] David, N., Consideratii asupra entropiei si aplicatii, International Session of Scientific Papers Scientific Research
and Education in the Air Force, Henri Coanda Air Force Academy, May 16-17, Brasov, Romania, 699-704, ISBN:978-973-8415-56-0, 2008
[7] David, N., Aspects Regarding the Length of Typical Trails in a Web Site, Proceedings of the 10th WSEAS InternationalConference on Mathematical Methods, Computational Techniques and Intelligent Systems (MAMECTIS 08), October26-28, Corfu, Greece, 203-207, ISBN: 978-960-474-012-2, ISSN: 1790-2769, 2008
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Second order partial differential equation of parabolic type in the cosmic rays transport studies
Agnieszka Gil-SwiderskaInstitute of Mathematics and Physics, Siedlce University, Siedlce, Poland
Abstract. The propagation of cosmic rays is described by Parker’s transport equation (Parker, 1965),
which is a second order parabolic type partial differential equation. It is time-dependent 4- variables
(with ρ, θ, ϕ, R, meaning: distance from the Sun, heliolatitudes, heliolongitudes, and particles’ rigidity,
respectively) equation, which is a well-known instrument for studying problems connected with solar
modulation of cosmic rays. Transport equation contains all basic processes taking place in the helio-
sphere’s vicinity. In our paper we investigate a topic of the 27-day variation of the galactic cosmic rays
intensity, which is connected with solar rotation. We numerically solve the Parker’s transport equation
involving in situ measurements of solar wind speed and heliospheric magnetic field.
1.1. Parker’s transport equation. Galactic cosmic rays (GCR) are highly energetic nuclei ofextra solar source. When they are propagating through the heliosphere (being a region totally drivenby the Sun’s magnetic activity), they are partially modulated by the solar wind and heliosphericmagnetic field (HMF). Moreover, heliosphere changes in time and those changes influence GCR indifferent time scales (e.g. [1]).The Parker’s transport equation [2] contains all elementary processes taking place in the heliosphere:convection, diffusion, energy changes of the GCR particles owing to the interaction with solar wind’sinhomogeneities, drift due to the gradient and curvature of the regular HMF and on the heliosphericcurrent sheet (HCS):
(1) ∇i(κij∇jf)−∇i(Uif) +1
3R2
∂(fR3)
∂R(∇iUi) =
∂f
∂t
where f is the omnidirectional distribution function, R is the rigidity of the GCR particles, U is thesolar wind velocity and t - time. The anisotropic diffusion tensor κij for the 3-D magnetic field istaken in to account as in ([3, 4]).The GCR intensity in the interstellar space is taken according to [5] as:
I =21.1T−2.8
(1 + 5.85T−1.22 + 1.18T−2.54),
where T is the particles’ kinetic energy.
In article by Moraal [6] is presented a noteworthy review regarding Parker’s transport equation. Itis impossible to solve analytically, in general, Parker’s equation without the substantial simplificationswhich makes the mathematical model to paltry to represent the processes in the heliosphere. Thus, itneeds to be solved numerically. Many methods have been developed to solve this equation numerically,most of them employing the finite difference technique (e.g. [7] ). The other approach is stochastic,where Parker’s transport equation is considered as the Fokker-Planck equation equivalent to a set offirst-order ordinary stochastic differential equations of the Ito’s type containing a speedily fluctuatingrandom term (e.g. [8]). First attempt to apply this method to this problem was done by [9] and [10].In our paper Eq. (1) is reduced to the linear algebraic system of equations by finite difference schemeand numerically solved using the Gauss - Seidel iteration method (e.g. [11]) for one rotation of theSun, i.e. for instant state of the heliosphere, when the distribution of the GCR density is determinedby the time independent parameters included in Eq. (1). The current sheet drift is taken into accountaccording to the boundary condition method [12].
Bibliography
[1] Kudela K., Space weather near Earth and energetic particles: selected results, Journal of Physics: Conference Series,409, 1, 012017, DOI: 10.1088/1742-596/409/1/012017 (2013)
[2] Parker, E.N., The passage of energetic charged particles through interplanetary space, Planetary and Space Science,Vol. 13, 9-49 (1965)
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[3] Alania, M.V., Dzhapiashvili, T. V., The Expected Features of Cosmic Ray Anisotropy due to Hall-Type Diffusionand the Comparison with the Experiment, In Proceedings of 16th International Cosmic Rays Conference, Vol. 3,19-24 (1979)
[4] Alania, M.V., Stochastic variations of galactic cosmic rays, Acta Physica Polonica B, Vol.33, 1149-1166 (2002)[5] Webber, W.R., Lockwood, J.A., Voyager and Pioneer spacecraft measurements of cosmic ray intensities in the
outer heliosphere: Toward a new paradigm for understanding the global solar modulation process: 1. Minimum solarmodulation (1987 and 1997), Journal of Geophysical Research, Vol. 106, 29323-29332 (2001)
[6] Moraal, H., Cosmic-Ray Modulation Equations, Space Science Reviews, Vol. 176, 299-319 (2013)[7] Jokipii, J.R., Levy, E. H. , Effects of Particle Drifts on the Solar Modulation of Galactic Cosmic Rays, Astrophysical
Journal, Vol. 213, 85 -88 (1977)[8] Gardiner, C. W., Handbook of Stochastic Methods, Springer Verlag, Berlin, 1989[9] Zhang, M., , A Markov stochastic process theory of cosmic-ray modulation, Astrophysical Journal, Vol. 513, 409-420
(1999)[10] Gervasi, M., Rancoita, P. G., Usoskin, I. G., Kovaltsov, G. A., Monte-Carlo approach to Galactic Cosmic Ray
propagation in the Heliosphere, Nuclear Physics B , Vol. 78, 26-31 (1999)[11] Kincaid, D.R., Cheney, E.W., Numerical analysis: mathematics of scientific computing, AMS Bookstore, 2009[12] Jokipii, J.R., Kopriva, D. A., Effects of particle drift on the transport of cosmic rays. III - Numerical models of
galactic cosmic-ray modulation, Astrophysical Journal, Vol. 234, 384-392 (1979)
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An Questionnare Based Analyses on Labor Force in Maramures County
Anne Marie Andreea HordauTechnical University of Cluj-Napoca, North University Centre of Baia Mare, Romania
This article is part of a major research on labour market in Romania after 1990. During thisresearch, analyses of labour market and unemployment, in Romania and in Maramures County, weremade on the basis of official data. To present a real picture of the situation at the county level,as representative, we considered necessary also the application of a questionnaire among managersfrom economic area. The main goal was to capture the characteristics of the decisions related toemployees and hiring process and redundancy. In addition to introductory questions relating tothe organization’s properties (size, type, industry), questionnaire includes ideas related to hiring,unemployment process, involving economic areas in the process of continuous training of employees,etc. Random, 100 companies of different size were selected by businesses in Maramures county, towhom were sent questionnaires. Of these 74 responded. We consider this response rate satisfactory,especially since, as you can see from the results presented below, the characteristics of the labourmarket in the county from the standpoint of the economic agent are very clear-cut. Additionalcompanies examined would lead only to a confirmation of these results. First, we were interested indemographic characteristics of the companies analyzed. The majority of these, 92% are private, only5.5% of public institutions (city halls, hospitals, etc.). Two of the responding firms are under otherforms of organization.
Of great importance for developing analysis is to establish the size of the organization. In ourstudycase the majority of firms are small, with fewer than 10 employees. They represent nearly 50percent of all firms surveyed. The remaining firms are divided roughly equally into two groups-between10 and 49 employees, and over 50 employees (even with a larger share of the latter).
Before the actual analysis of the hiring process-dismissal, another important aspect is linked tothe skill level of employees. It knows very well that the labour market in Romania is poor at theirjobs for persons with higher education. The majority of publications ”Labour Exchange” organisedacross the country are seeking predominantly persons with secondary education, with secondary-schoolstudies or post-graduate. Unlike other issues analysed before, which have differentiated MaramuresCounty attribute, in this case the analysis proves that economic agents in this county have the samepreferences as those in the rest of the country. Thus, 44 of the firms surveyed, representing 60% mostemployees with secondary education graduated. Almost 40% (28 companies) have several employeeswith higher education and only 1 operator working in the field of provision of services has the majorityof employees with completed master degree studies.
Starting 2008, the international financial crisis began to feel and in Romania. To be able tocapture its effects, we asked the operators in the county where people have committed over the pastthree years and how many people have been fired over the past three years. Most of them have hiredless than 5 people . What is interesting, however, is that, even in times of crisis, there were companiesthat have hired more consistent-13 companies from the 74 hirred on average10 people in the pastthree years, while the 19 companies have pledged around 15 people. Analyzing the activity field, itemerged that most of the hires have made businesses related to trade. Another specificity is thatthey have hired more people in manufacturing than in services. These results, and the tests applied,they found a meaningful connection between local labour market activity and the number of personsemployed in the past three years, characterized by international and national economic crisis. Verygratifying is the fact that most businesses have not fired any person in the last 3 years. Among thosewho fired, majority have fired less than 5 people.
It is very important to be seen and which is the distribution of firms based on the number of newpeople engaged and the number of people laid off in the past three years. In fact, we wanted to see ifthose who have fired or dismissed people have hired other people for the available positions.
It seems that most companies have employed but also dismissed people in the same three-yearperiod. This shows that the layoffs were not based on the financial and economic situation precariousfound nationally, but the reasoning more on characteristics of employees. And, as will be seen laterin the analysis, the lack of interest, skills of employees are considered by employers as main reasons
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for the determination of obtaining the status of unemployed. However, statistical analysis revealedthe existence of a link between persons employed and those laid off, the number. We were interestedthen why employees were sent into unemployment. Unfortunately, half of the businesses surveyedhave avoided to answer this question. As we expected, in most cases, the main reason was linked tofinancial problems (for those who have chosen a reason).
Employees sent in unemployment were evaluated on different criteria. In the questionnaire wereincluded criteria which referred to issues relating to their level of training, labour costs or punctualityand other criteria. Most employers have framed the reasons in the fourth group-other criteria. Actually,as this group is followed by the employers ’ group which were based on the level of training in thechoice of people to be laid off. Few have had as main criteria-outs or punctuality of employees wagecosts. In recent years, discussions of increasingly are worn on the correlation of University studies withlabour market requirements. For this reason, we wanted to see employers ’ opinion of the issues thatshould put greater emphasis on the higher education institutions in Romania with an overwhelmingmajority is apparent that employers prefer creative people who come up with new ideas for theirbusiness. Higher level education institutions should, therefore, to think about the study programmesso as to develop the creative ability of the future employee. In this way we have, from the pointof view of the business environment in Maramures County, a better integration of recent graduateson the labour market. The effect would be extremely important, taking into account the results ofthe analysis of the labour market at national level, showing an unemployment rate extremely high(over 20% in recent years) among young people. Keeping higher education department, we analyzedthe degree of collaboration between business and academic area in Maramures. The most importantaspect of this collaboration, which discerned the effects on labour market relates to students ’ practice.Unfortunately, a large majority of companies do not have any kind of collaboration on this very pathwith institutions of higher education. It appears so, a lack of communication between employer andeducator that is not only detrimental to employees.
Bibliography[1] Matei, L & Matei, A, (2010) Local employment policies in the context of the economic crisis:Influences of the European
Community structural instruments,Online at http://mpra.ub.uni-muenchen.de/23086/ MPRA Paper No. 23086.[2] Nstase C & Kajanus M (2009), The impact of the global crisis on SME and entrepreneurship behavior Romania
and Finland cases, Article provided by Academy of Economic Studies - Bucharest, Romania in its journal TheAMFITEATRU ECONOMIC journal, number 3, 2009, pages 751-762
[3] Newberry, D., (2006), The role of small and medium sized enterprises in the futures of emerging economies, WorldResource Institute
[4] Roman, M. (2010), The effciency analysis applied for the evaluation of labour market policies: Study case for Romania,Online at http://mpra.ub.uni-muenchen.de/20332/ MPRA Paper No. 20332.
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Determination of the crossing numbers of the Cartesian product of graphs
Daniela Kravecova and Jana PetrillovaDepartment of Mathematics and Theoretical Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Kosice,
Kosice, Slovakia
[email protected], [email protected]
Abstract. The problem of determination and reducing the number of crossings in a graph is studiednot only in the theory of graphs, but also in computer science. It is well known that the problemof determination of the crossing numbers of graphs is NP-complete. The exact values of the crossingnumbers are known only for some graphs or some families of graphs. Some Cartesian products of specialgraphs are one of few graph classes for which the exact values of crossing numbers were obtained. Thereare known several exact results of the crossing numbers of the Cartesian product of a some special graphswith paths, cycles and stars.
In this paper we determine exact value of the crossing numbers of the Cartesian product of graphson six vertices with the path.
1.1. Introduction. Let G be a simple graph with vertex set V and edge set E. A drawing ofa graph is a mapping of a graph into a surface. We assume that in a drawing (a) no edge passesthrough any vertex other than its end-points, (b) no two edges touch each other (i.e., if two edgeshave a common interior point, then they properly cross at this point), and (c) no three edges crossat the same point. It is easy to see that a drawing with minimum number of crossings (an optimaldrawing) is always a good drawing, meaning that no edge crosses itself, no two edges cross more thanonce, and no two edges incident with the same vertex cross each other. The crossing number cr(G) ofa graph G is the number of edge crossings in an optimal drawing of G in the plane. The Cartesianproduct G1 G2 of two graphs G1 and G2 has vertex set V (G1)× V (G2) and two vertices (u, u′) and(v, v′) are adjacent in G1 G2 if and only if u = v and u′v′ ∈ E(G2) or u′ = v′ and uv ∈ E(G1).
According to their special structure, Cartesian products of special graphs are one of few graphclasses for which the exact values of crossing numbers were obtained. Let Cn be the cycle of length n,Pn be the path of length n, and Sn be the star isomorphic to K1,n.
Several authors have been researched the crossing numbers of the Cartesian products GCn,GPn and GSn for some specific graphs G. Beineke and Ringeisen [1] started to study the crossingnumbers of Cartesian products of cycles with all graphs on at most four vertices. Jendrol’, Scerbovain [2] and Klesc in [3], [4], [5] continued with determination of the crossing numbers of Cartesianproducts of cycles, paths and stars with all 4-vertex graphs. The crossing numbers of Cartesianproducts of paths with all graphs of order five are collected in [6]. It seems natural to enquire aboutcrossing numbers of Cartesian products of paths with other graphs. There are known the crossingnumbers of products GPn for some 6-vertex graphs G, see [8], [9], [10], [11], [12] and the crossingnumbers of Cartesian products of paths with 40 graphs of order six are collected in [7]. In this paperwe extend the results given in [7] by determining the crossing numbers of the Cartesian products ofother three graphs on six vertices with the path.
1.2. Main results. Let us consider three graphs G, H, and J in Figure 1.
G H J
a
a
a
b
b
bcc
c
d
d de
e
e ff
f
Figure 1 The graphs G, H, and J .
Let be n ≥ 1. First we determine the crossing number of the graph GPn. We find it convenientto consider the graph GPn in the following way. It has 6(n + 1) vertices, which we denote xifor x = a, b, c, d, e, f and i = 0, 1, . . . , n. The edges belong to n+ 1 copies of the subgraphs isomorphicto G and six paths of length n, see Figure 2(a). We will denote each of subgraphs isomorphic to G
by G(i), i = 0, 1, . . . , n. For i = 0, 1, . . . , n, let bi and ei be the vertices of G(i) of degree three, ci anddi the vertices of degree two and let ai, fi be the vertices of degree one.
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(a) (b)
Figure 2 The drawing of the graph GPn with 2(n − 1) crossings and HPn with 2(n − 2)crossings.
The next lemma help us to prove that the crossing number of the graph GPn is 2(n − 1) forn ≥ 1.
LemmaIf D is a good drawing of the graph GPn, n ≥ 3, in which every subgraph G(i), i =0, 1, . . . , n, has at most one crossing on its edges, then there are at least 2(n− 1) crossings in D.
Theorem cr(GPn) = 2(n− 1) for n ≥ 1.
Figure 2(a) shows the good drawing of the graph GPn with 2 crossings on every copy G(i),i = 1, 2, . . . , n− 1. Clearly, cr(GPn) ≤ 2(n− 1). The reverse inequality is proved by induction withrespect n.
Now we determine the crossing number of the graph HPn. We find it convenient to considerthe graph HPn in the following way: it has 6(n+ 1) vertices and edges that the edges are in n+ 1
copies of H(i), i = 0, 1, . . . , n, and in six paths of length n. For i = 0, 1, . . . , n, let ai, bi, ci and ei bethe vertices of H(i) of degree two, di the vertex of degree three and let fi be the vertex of degree one.
The graph HP1 is planar. The crossing number of the graph HP2 is at least one, becausethe graph S3P2 is its subgraph and cr(S3P2) = 1 (see [2]). The reverse inequality cr(HP2) ≤ 1follows from the drawing in Figure 2(b). The next lemma help us to prove that the crossing numberof the graph HPn is 2(n− 2) for n ≥ 3.
Lemma If D is a good drawing of the graph HPn, n ≥ 3, in which every of the subgraphs H(i),i = 0, 1, 2, ..., n, has at most one crossing on its edges, then there are at least 2(n− 2) crossings in D.
Theorem cr(HPn) = 2(n− 2) for n ≥ 3.
The drawing in Figure 2(b) shows that cr(HPn) ≤ 2(n − 2), because every copy of H(i),
i = 2, 3, ..., n−2, is crossed two times, H(1) and H(n−1) are crossed once and there is no other crossingsin the drawing. The proof of the reverse inequality proceeds by the induction on n.
In the last case we determine the crossing number of the graph JPn. We find it convenient toconsider the graph JPn in the following way: it has 6(n+ 1) vertices and edges that the edges are in
n+ 1 copies of J (i), i = 0, 1, . . . , n, and in six paths of length n. For i = 0, 1, . . . , n, let bi, ci and di bethe vertices of J (i) of degree three and ai, ei and fi the vertices of degree one.
Figure 3 The drawing of the graph JPn with 3(n− 1) crossings.
The next result help us to prove that the crossing number of the graph JPn is 3(n− 1) for n ≥ 1.
Lemma If D is a good drawing of the graph JPn, n ≥ 3, in which every of the subgraphs J (i),i = 0, 1, 2, ..., n, has at most two crossing on its edges, then there are at least 3(n− 1) crossings in D.
Theorem cr(JPn) = 3(n− 1) for n ≥ 1.
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The drawing in Figure 3 shows that cr(JPn) ≤ 3(n − 1), because every copy of J (i), i =1, 2, ..., n− 1, is crossed three times and there is no other crossings in the drawing. The proof of thereverse inequality proceeds by the induction on n.
Acknowledgment. This work was supported by the Slovak VEGA grant No. 1/0309/11.
Bibliography[1] L. W. Beineke, R. D. Ringeisen, On the crossing numbers of products of cycles and graphs of order four, J. Graph
Theory, 4, 145–155 (1980)[2] S. Jendrol’, M. Scerbova, On the crossing numbers of Sm × Pn and Sm × Cn, Casopis pro pestovanı matematiky,
107, 225–230 (1982)[3] M. Klesc, The crossing numbers of Cartesian products of stars and paths or cycles, Mathematica Slovaca, 41, 113–120
(1991)[4] M. Klesc, The crossing numbers of products of paths and stars with 4-vertex graphs, J. Graph Theory, 18, 605–614,
(1994)[5] M. Klesc, The crossing numbers of products of 4-vertex graphs with paths and cycles, Discuss. Math Graph Theory,
19, 59–669 (1999)[6] M. Klesc, The crossing numbers of Cartesian products of paths with 5-vertex graphs, Discrete Math., 233, 353–359
(2001)[7] M. Klesc, J. Petrillova, The crossing numbers of products of path with graphs of order six, Discuss. Math Graph
Theory (to appear).[8] D. Kravecova, The crossing number of P 2
5 × Pn, Creative Mathematics and Informatics, 21, 1, 65–72 (2012)[9] Y. H. Peng, Y. C. Yiew, The crossing number of P (3, 1) × Pn, Discr. math., 306, 1941–1946 (2006)
[10] J. Wang, Y. Huang, The crossing number of K2,4 × Pn, Acta Math. Sci., Ser A, Chin Ed., 28, 251–255 (2008)[11] L. Zhao, W. He, Y. Liu, X. Ren, The crossing number of two Cartesian products, International J. Math. Combin., 1,
120–127 (2007)[12] W. Zheng, X. Lin, Y. Yang, Ch. Cui, On the crossing number of KmPn, Graphs Combin., 23, 327–336 (2007)
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Information spreading on declining social networks
Gergely Kocsis and Imre VargaFaculty of Informatics, University of Debrecen, Hungary
[email protected], [email protected]
Abstract. In this paper we examine the spreading of information on on-line social networks that are
in their final phase of their life. In this state a number of users (nodes) have left the network making
it less connected, and after a while, breaking it into separate pieces. Our final question is if it worth
to advertise on these networks or not. Using a previous model of ours we executed simulations on
a real sample network of more than 5 ∗ 107 nodes and many generated networks. Results were found
highlighting the way how social networks loose their users, and even some first findings are presented
answering the main question of ours.
1.1. Introduction and motivation. The life cycle of an online social network (such as Facebook,Myspace, etc.) can be described by 4 distinct states (see Fig. A ). First when it is introduced, theamount of users starts to increase slowly because of the low awareness of the network. After a while –as more and more users are connected to the network – this increasing speeds up. This phase is calledthe growing of the network. After a while the network reaches its possible maximum number of users.The growing slows down and for a more or less long time the social network stays in its mature state.History shows however that this state is not the last in the life of a social network. With time a newrival always appears and sooner or later the network enters to its final phase of declining [3].
Fig. A Life cycle of a social network [3]
It is easy to understand that advertising insocial networks in their first 3 states – espe-cially in the middle 2 – is very worthy. Thesenetworks have almost clean scale free topol-ogy [2]. This property makes the spreadingof information very rapid. However the sameis not proven to be true for declining socialnetworks.
In the followings first we try to find a method to reproduce real networks based on a huge setsample of Facebook data. After that we examine the effect of attacking the network on the spreadingof information.
1.2. Real, generated and attacked networks. From the work of M. Gjoka et al. [5] we got aset of data from a real piece of the global Facebook social network. Besides this network we also triedto reproduce the network by generation. In this way we can produce networks with similar structureas real networks, but in smaller size than in our sample data. Later these networks can be attackedin order to represent networks in the declining phase. Nevertheless starting examinations on thesenetworks makes it possible to find out what will happen later on the real network.
Examining the degree distribution of our sample network it turns out that it has a power lawdegree distribution with a slightly lower degree distribution exponent as the theoretical one γ = 3.To generate scale-free networks with variable degree distribution exponent we used the model of Leeet al. [1]. This is a mixture of the popularity-driven BA algorithm and the fitness-driven algorithm.In this each new node connect to the network according to BA model with probability p and thefitness-driven connection has 1− p probability. Using this mixed algorithm we were able to produce asimilar network as the sample.
Using the above process we became able to generate networks having almost the same degreedistribution exponent as our sample network. To simulate a declining network we have to use aso called attack process. We used three different ways to attack the network based on the degreeof nodes. Namely i.) removing nodes with the same probability (general attack), ii.) removing thehigh degree nodes more likely (central attack) and iii.) removing the low degree nodes more likely(peripheral attack). In addition the attack can be described by the attack rate η = N−/N0, where
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N− is the number of removed nodes. Finally the parameters of these model networks at each attacktypes are the original number of nodes N0, the dominance of BA model p and the attack rate η. Asit is well-known, the scale-free networks are very resistant against general attack [2]. The degreedistribution has almost the same exponent γ even if the attack rate η is close to 0.5, only the rangeof the distribution is shrinking. The exponent γ seems to be constant also in case of significant sizeperipheral attack. It is understandable while removing recently joined nodes with small k leads to astate which is similar to an earlier and smaller one if the BA based system is large enough. Whenthe nodes with larger number of link are damaged frequently the slope of the degree distribution ofcentrally attacked network is decreasing very fast.
1.3. Information spreading. In a previous work Kocsis and Kun proposed a model for infor-mation spreading on complex networks [4]. In our current work the simulations are based on thismodel. The model in short builds up as the following:
The socio-economic system is represented by a set of agents which have a complex topology ofsocial contacts. Agents take place on the nodes of the underlying network topology and the socialcontacts are represented by the edges. The state of agents during the time evolution of the systemis characterized by an integer variable Si, which takes the value 0 if the agent is informed and 1 inthe opposite case. Initially all agents are in the state Si = 1, i = 1, . . . , N0, where N0 denotes thetotal number of agents. In the model the primary source of information is a homogeneous externaldriving field E. For simplicity this strength is set to E = 1. The sensitivity of agents to the externalinformation field is described by a parameter β. The information can be also transmitted betweeninteracting agents resulting in a horizontal flow of information. The sensitivity of agents to this sourceof information is presented by α that is a real value. We cast the total amount of information Ii agenti receives through the information channels into following form
(1) Ii = αSi
ki∑j=1
(1− Sj) + βSi,
where ki denotes the number of social contacts of agent i. Agents get informed with a certainprobability A, which is a monotonically increasing function of the available information Ii
(2) A(Ii) = 1− e−Ii/λ,
where λ is a scale parameter. Note that Ii is the total amount of new information received by agent i.Since the surroundings of a selected agent changes due to the agents which have become aware of theinnovation, the total amount of new information Ii and the resulting awareness probability A(Ii) areboth functions of time.
1.4. Results of simulations. To prove that the way of spreading is size-independent we ransimulations of networks of different sizes for all three types of attack. The parameters of the modelwere set to the values proven to be the closest to the real world scenarios previously [4]. Namely weset α = 0.01 and β = 0.001 in order to balance the effect of the two channels. During the simulationswe chose the ratio of informed agents as the key indicator of the spreading. The results are presentedon Fig. 1/a). Note that the spreading process behaves the same way independently of the size of thenetwork.
As a next step we compared our results on the real network with the ones on a simple unattackedgenerated network. Slightly surprisingly the results proven to be different in these two cases indicatingthat the sample Facebook network which we are using is not any more a simple scale-free graph ratheran attacked one. This implies the interesting fact, that it is currently about to enter to its decliningphase.
Because of this, we tried all three attack methods, to get a parameter set, that results a networkwith about the same degree distribution and spreading properties as the real graph. Technically weran the same simulations on both networks and compared the trends of the informed agents as afunction of time. Our results are presented on Fig. 1/b). As we found all three ways of attack mayresults in a network that is close to have the same behavior as the real network. The amount of nodesto be removed in each case are the followings: about 46% in the peripheral case, about 16% in the
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Figure 1 a) Ratio of informed nodes in the system as a function of time t. Networks attacked in the same way show the same
fashion of spreading independent of the size of the network. b) The effect of attack on the spreading. The direction of the arrow shows
the increase of the number removed nodes (10%, 20%, 30%, 40%, 50%).
general phase and less than 1% in the case of the central attack. These numbers mean that the futureof spreading highly depend on the way how the network declines.
Knowing how to generate a network that coincides with the real social network we can examinehow our model reflects if we attack the network in several different ways. What became clear directlyfrom our previous simulations is that the different ways of attacking have different consequences onthe spreading. Naturally in all cases with the increase of the number of removed nodes the spreadingbecomes slower. However the same amount of removed nodes affect the spreading in different ways.As it was seen above, if low degree nodes are removed from the network, the structure of it does notchange. This is why we see on Fig. 1/b) that even if we remove 50% of the lowest degree nodes, thebehavior of spreading does not change too much. Focusing on the case of general attack shows, that inthis case a smaller amount of removed nodes can imply the same effect. The third case however evenif we remove only a few nodes from the network following this rule, the spreading slows dramatically.
1.5. Summary. In our work we tried to find an aswer to the question ”How information spreadson a declining social network?”. In order to make our results as close as possible to the real networkswe used a set of data from real Facebook users. We generated scale-free networks with changeabledegree distribution exponent using a mixture of popularity-driven and fitness-driven models of growingnetworks. Then the networks were attacked using three different ways of attack to model the effectsof declining. We examined the effect of three attacking methods. We found that while the peripheralattack hardly changes the process, the equal attack affects it more while the central attack dramaticallychanges it.
1.6. Acknowledgment. The publication was supported by the TMOP-4.2.2.C-11/1/KONV-2012-0001 project. The project has been supported by the European Union, co-financed by theEuropean Social Fund.
Bibliography[1] H. Y. Lee, H. Y. Chan, and P. M. Hui, Scale-free networks with tunable degree distribution exponents, Phys. Rev. E,
69, 067102 (2004)[2] R. Albert and A.-L. Barabsi, Statistical mechanics of complex networks, Rev. Mod. Phys. 74, 47-97 (2002)[3] B. M. Varghese, The Life Cycle of a Social Network, Techpedia (http://www.techipedia.com/2011/social-network-
life-cycle/ - last visited: Juna20.2013) (2011)[4] G. Kocsis and F. Kun, Competition of information channels in the spreading of innovations, Phys. Rev. E, 84,
026111 (2011)[5] M. Gjoka, M. Kurant, C. T. Butts and A. Markopoulou, Walking in Facebook: A Case Study of Unbiased Sampling
of OSNs, Proc. of IEEE INFOCOM ’10, San Diego, CA, (2010)
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Analysis and Interpretation of Structure and Diversity of Some Macrozoobenthic Communities UsingMathematics Indices
Oana Mare Rosca, Lucia Mihalescu, Monica Marian, Zorica VosganCluj-Napoca Technical University, Baia Mare North University Center,
Abstract.Modification of the structure of aquatic communities occurs in response to different types of
stress, including anthropogenic pollution. In order to sense some aspects of the level of contamination
and the ecological status of rivers the following environmental indicators are often used: analytical
(abundance, frequency, dominance), synthetic (ecological significance index) and diversity (Shannon-
Wiener index, Margalef index and Simpson index).
1.1. Introduction. Macrozoobenthic communities consist of small invertebrates that live on orin the substrate on rivers bottoms (worms, crustaceans, insect larvae, mollusks). In order to capturesome aspects of the numerical weight of the contribution and role of macrozoobenthos taxa, theanalytical environmental indices (density, frequency, abundance) and synthetic (ecological significanceindex) are often used. Diversity indices get the environmental instability affecting the life of theaquatic communities. These are the most used diversity indices in the interpretation of such toxicpollution: Shannon-Wiener-H index, Margalef -d1 index and Simpson index-D.
1.2. Methods. The overview of data structures and how they are distributed is obtained byapplying the analytical, synthetic and diversity ecologic indices.
1.3. Discussion. The zoobenthos community structure reflects the state of the entire aquaticecosystem. Changing specific richness and numerical abundance that occurs in response to pollution(Tudorancea, 2004) can also be captured using analytical indices (abundance, frequency, dominance),respectively, synthetic indices (index of ecological significance). Numerical abundance representsthe absolute number of individuals of a species present in a given area. Frequency (F), expressesin percentage the presence of a certain species within the collected samples. Thus, it highlights thedensity (abundance number), homogeneity or heterogeneity of a particular species within a particularbiocoenosis. The calculation is:
F =p
P· 100
where is p is the number of samples in which the considered species is present and P is the totalnumber of collected samples (Varvara et all., 2001).
Constancy (C) is the notion which expresses the continuity of species in a given habitat (Varvaraet al., 2001). The higher the indicator value, the better the species is adapted to the conditions offeredby the biotope.
Dominancy (D). Dominancy expresses the influence exercised by a species within a community(Balogh, 1958, quoted by Stugren, 1982).
D =nA
N· 100
where: nA- total number of individuals of the A species found in the checked samples,N - total number of individuals of all the species found in all the checked samplesTo highlight the role of species in coenosis, we used the ecological significance index (W).
This index expresses the ratio between the frequency and dominance, as follows:
W =FA
DA· 100
where: FA- frequency of A species,DA- dominancy of A species.Diversity indices focus the information in a numerical value that allows researchers to objectively
assess the state of the studied communities. These indices capture the instability of the environmentalfactors affecting the aquatic invertebrate communities, being frequently used in elucidating the degreeof deterioration of lotic systems (Washington, 1984; Moldoveanu et al., 2011). But diversity indices donot capture the changes in species composition and as a result they will be complemented by biotic
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indices (Moldoveanu et al, 2011). Basically, a diversity index of a high numerical value implies abetter structuring of the species that is a higher stability and implicitly balanced biotic relationships.Among the many known diversity indices the following will be presented: Shannon-Wiener index,Simpson index and Margalef diversity index.
Shannon Wiener diversity index (H) measures the degree of organization (or disorganization)of a system.
H ′ = −s∑i=1
pi ln (pi)
where: pi = niN ; ni- number of individuals of the i species within a sample,
N - total number of individuals within the sample.K- factor for converting base 10 logarithms to base 2, it is equal to 3, 321928.Simpson index (D) summarizes the probability of occurrence of each species; it reflects how the
ecosystem is dominated by a small number or a large number of species.
D = 1−∑ ni (n1 − 1)
N (N − 1)
where: ni- number of individuals of the i species within a sample,N - total number of individuals within the sampleMargalef index (d1) assesses the information from a sample of a certain size.
d1 =S − 1
lnNwhere: S- total number of the species.
N - total number of individuals of all the species.
1.4. Conclusions. Environmental indices are relatively easy to use and provide useful informationabout the state of degradation of lotic ecosystems. Interpretation of the overall ecological status loticecosystems will be made linking all the values of the analyzed indicators, including the biotic ones,and not by singularly analyzed values.
Bibliography[1] Moldoveanu, M., Rnoveanu, G., Chiriac, G. Ecological indices for monitoring and assessing ecological status of lotic
system. Conferinta stiintifica anuala, 1-3 Noiembrie INHGA, 2011.[2] Stugren, B.,Bazele ecologiei generale, Ed. Stiintifica si Enciclopedica, 1982, Bucuresti, 435 p.[3] Tudorancea, M. M, Ecologia unor populaii de chironomidae (Diptera) din rul Someul Mic i bazinul de drenaj al
rului Criul Repede, Tez de doctorat, Cluj Napoca, 2004, 97.[4] Varvara, M., Zamfirescu, t., Neacu, P.Lucrari practice de ecologie, Ed. Univ. Al. I. Cuza, Iai, 2001, p. 153.[5] Washington, H., G., Diversity, Biotic and Similarity indices. A review with special relevance to aquatic ecosystems,
Water Res. Vol. V (6), 1984, 653-694.
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Prognose and diagnosis in education by using statistical methods
Claudia Marian and Monica MarianTechnical University Cluj-Napoca, North Unversity Center Baia Mare, Romania
Abstract.This paper aims to exemplify a concrete way in which the methods and statistical indicators can
help to direct a formative approach of adult education. Descriptive statistical methods, like media and
frequency, and comparative study methods - analysis of variance (ANOVA) one/ two way will be used
as tools for initial evaluation of the knowledge, the joint analysis of the types of mental maps, selection
of vulnerable groups and post-intervention assessment of the effectiveness of training program.
1.1. Introduction. Contemporary education is largely subordinated to the requirements ofergonomics and competitiveness. In general, this requires a careful management of human resources,of the methods used to achieve the stated objectives, of the expected results, a careful monitoringof the cost / benefits, anticipating the evolutionary routes, assessing possible risks, etc. Statisticalinstrument are a good means of achieving these objectives by forecasting and diagnostic continuousevolution of the whole educational endeavor.
An example of this was the need to implement an educational programs which, in the long run, todetermine protection, conservation and fund raising of biodiversity in declared areas Natura 2000. Tooptimize the formative approach of experimental design are required several steps:
1. an initial assessment to know, on the one hand, which is the local people’s knowledgeregarding the basic concepts of what a Natura 2000 site requires (attitudes that they havetowards the site, knowledge about resources of flora and fauna in the area, the impact that aprotected area has on economic development of the region) On the other hand, pragmaticapproach require criteria for predictions of groups vulnerability and also identifying cognitivedistortions that prevent proper assimilation and reporting the information taught.
2. the second step consists in implementing a training program, applied mainly on vulnerablegroups, the program takes into account the need to offset the distortions and deficienciesfound in the initial phase
3. final evaluation as a feedback of the whole project, which monitor the dynamics of thepost-outreach project and which constituted the starting point for necessary measures to betaken on long term by those who manage the site.
The study group consisted of 1273 people, inhabitants of the Natura 2000 site, based on statisticalcriteria of representativeness and heterogeneity; the group included people of ages and in differentgenres from different backgrounds, different levels of education and different responsibilities withincommunities.
Statistical methods of data collection were based on the Likert scale questionnaire with 10 levelsand items requesting choice of correct between answer or either completing them.
Statistical methods chosen for processing raw data were as follows:
-: Descriptive statistical methods - media and frequency-: Comparative study methods - analysis of variance (ANOVA) one/ two way.
The independent variables used: age, gender, origin, place of belonging, schooling level and typeof activity, and the dependent variables are the awareness of the population and attitudes towardbiodiversity of the site. Statistical analysis was performed using SPSS version 17.
After processing the data has arrived at the following results: first of all, the initial outreach onthe particularities of a Natura 2000 site and a protected area looks like this: only 32.8% recognizedall three specific characteristic of an protected area, 30.9% admit only 2 marks characteristic, 28.8%identifies a single feature and 7.5% seem to be foreign to the concept of protected area recognizingnothing special. Of these, only 62.1% identified an area protected by his fundamental distinguishingcriteria (species of plants / animals, biogeographic formations, etc. of environmental, cultural scientificimportance.
Regarding the correlation between the concept of biodiversity and protected areas, the distributionof correct answers / wrong is this: importance of protected areas for biodiversity conservation isassumed by 90.3% of respondents. Major discrepancies between the two data types, logically connected
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to each other, demonstrate the existence of ”mental maps” incomplete and fragmentary. In the sameregistry, more than half of the population does not know even a plant species at the site, while only3.3% can name 5 species! (with a mean of 0.96 species group). For animals the situation is better, butfar from ideal - and here 41% of the subjects do not know even one species fauna of the site, but 21%were able to name five species. (with a mean of 2.27 species group)
Congruent with this finding, information concerned the economic impact of protected areas onthe economic development of the region is validated only by half of the respondents, which betraysmisunderstanding of the mechanisms behind these dynamics. It’s important to understand thisdynamic - the public awareness of the economic value that biodiversity implicitly protected area canplay in their own welfare could be a motivating factor for its preservation. When analyzing howvarying the information related to the concepts of protected areas and biodiversity according to agegroups and genders, it appears that there are significant differences between the three age groupsanalyzed (under 20 years, 21-40 and over 41) on the one hand and between the awareness of women /men on the oher. The average response of those under 20 year is the lowest comparable with thatof ages between 21-40 years (men and women alike) and with those over 41, which has the highestaverage correct answers. Men over 41 years old have the highest level of information, significantlyhigher than women of the same age. These differences are statistically significant (Fage = 17.008with p = 0.000 and p = Fgen = 4.798 to 0.008), with a risk of error below 0.8%. Same distributionanalysis by level of education and area of origin - urban / rural does not indicate significant differencesbetween their benefits.. Also, subjects in all localities analyzed have a comparable level of information.Similarly, the activities that peoples has in community does not induce significant differences in thelevel of awareness of the general notion of a protected area.
Regarding the attitude that people have towards the presence of Natura 2000 site in their area,recorded on a scale of 1 to 10, the average yield is 7.4 - a situation that will improve the final evaluationstatistically significantly (p = 0.007), reaching an average of 8.6. In addition, the trend registeringa significant decrease in the inferior (1-5 points) and polarization responses to positive attitudesfavorable to this site in their area.
Future directions in educational intervention suggested by these statistical trends are:
-: Educational interventions focusing on basic concepts and clarifying connections betweenthem
-: Increasing concrete information about the flora and fauna of the site-: Explanations focus on emphasizing the economic benefits provided by the site-: Inclusion in the training group mainly those aged under 41, regardless of gender, education
level, type of affiliation urban / rural and activity in the community
They were the basis for the batch application and implementation of educational approachThe results of the training process and post-intervention assessment records following progress:
-: Compared to the situation at the initial evaluation, it is observed that the final evaluation,significantly increases the number of those who recognize two features of protected areas, andalso those that recognize all three basic features (it’s true, to an extent smaller), and diminishthe number of those that recognize a single feature or none. This increase is significant for asignificance threshold of p = 0.03. The most significant increases (for a significance thresholdof p = 0.009) are recorded at the extreme age categories, while the population aged 21-40years remains stable as level information.
-: Further, those over 41 years have the highest level of knowledge (average correct answers is2.5 - 2.7 of 3 possible). Another trend is to close the level of awareness of women to men inthe same age category.
-: Understanding the concept of biodiversity register significant progress as a result of publicawareness / information made under the project. The number of those who know this notionincreased significantly (p = 0.02) from 81.6% at baseline in 94.3% in the final evaluation.
-: Analyzing the correspondence between biodiversity and protected areas remains constantbetween the two assessments, initial and final weight was not significantly different responses(p = 0.427 for an increase of 90.3% correct responses in the initial evaluation to 91.2% in thefinal evaluation).
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-: constantly keeps the trend: despite the theoretical knowledge of the concept of biodiversityand mental connection with the concept of protected area, this does not reflect a proportionalpragmatic recognition of its economic value, where even if percentage of correct responsesincreased significantly (p = 0.014) from 52.6% to 63.7% it is still low This trend respectthe psychological dynamics of assimilation into a faster pace of information theory, followedsomewhat slower then by forming attitudes.
-: Knowing the specific protected areas included in the analyzed site made a statisticallysignificant progress (p <0.001) between the two assessments
If in the initial assessment, the knowledge concerning Sit protected areas vary significantlydepending on the type and age of subjects (F = 6.349 for age p = 0.002 and F = 4.785 a kind p =0.009), (information increases with age, male gender beating the one female) for final evaluation, thegender differences are insignificant, as well as the age groups records the uniformity of this cognitivelevel, the general population average know a mean of over 2 sites from 5 presented
under between over20 years old 21-40 years old 41 years old
Initial assessment Masculine gender 1,7 1,4 2
Feminine gender 1,3 1,3 1,8
Final assessment Masculine gender 2,4 2,3 2,6
Feminine gender 2,1 2,2 2,4
1.2. Conclusions. The conclusions that can be made for the measures to be taken for long termare that formative approach must be focus mainly on the pragmatic aspects and on attitudinal one,and the focus group must be compose by young population under 40 years.
Bibliography[1] Howitt, D., Cramer D., 2006, Introducere in SPSS pentru psihologi, versiunile SPSS 10, 11, 12 si 13, Polirom , Iasi[2] Labar A. V., 2008, SPSS pentru stiintele educatiei, Polirom, Iasi[3] Radu, I., si colab, 1993, Metodologie psihologica si analiza datelor, Sincron, Cluj Napoca[4] Sava, F.A., 2004, Analiza datelor in cercetarea psihologica. Metode statistice complementare, ASCR Cluj Napoca[5] Stan, A., Clocotici V., 2000, Statistica aplicata in psihologie, Polirom, Iasi
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Statistical Instruments Used in Environmental Assessment Validation of Newly Introduced Species
Monica Marian1, Beatrice Agneta Szilagyi2
1Technical University of Cluj-Napoca, North University Center at Baia Mare, Romania2University of Agricultural Sciences and Veterinary Medicine, Faculty of Horticulture, Cluj-Napoca, Romania
[email protected], nitella [email protected]
Abstract.Introduction of the new species of plants in the context of environmentally is a challenge, both
in terms of acclimatization, as well as potential hazards on the statute invasively. The results of the
measurement of physiological parameters, as well as germination, the undercoat of germination, intensity
of photosynthesis, plant growth, are processed statistical summary, thus contributing to the validation
decision on whether introduction of the new species in a more environmentally sensitive again. Such
statistical procedures have been followed up for testing suitability for introduction in Romania of the
species Asimina triloba (L.) Dunal, a North American shrub well-trained fruit.
1.1. Introduction. In temperate climates, Asimina triloba (L.) Dunal is the only cultivatedmember of the Annonaceae family, with its generally subtropical and tropical species, and is popularlyknown as the banana of the north.
In order to arrive at a precise interpretation of results regarding the influence of experimentalfactors and calculate growth predictions made on Asimina triloba (L.) Dunal plants used in the study,seedlings were divided into multiple categories. The hypotheses from which we started in our collectionof experimental data are:
- the initial size of seedlings significantly affects stem length, distance between internodes,diameter of main and secondary stems, the number of branches and leaves on the main andsecondary stems as well as their parameters (leaf length and width);
- the plant location has a significant predictive value for plant evolution in terms of theparameters analyzed;
- the plant age significantly affects growth.
1.2. Materials and methods. Data analysis was accomplished with the aid of the statisticalprogram SPSS (Statistical Package for the Social Sciences), version 17. In the present work, weused descriptive statistics as a working method for interpreting stochastic data. The statisticalapparatus used for confirming the initial hypotheses were uni and bifactorial variant analysis(anova uni and bifactorial). The F indicator (variance report) that it generates indicates the existenceof differences between the various groups analyzed, starting with several selection criteria; thehierarchical regression calculation permits evaluating the weight that one of more causal factorscontributes to the variation in the effect; the calculation of correlation coefficients was meant to defineextant links between growth in various vegetable organs of the Asimina triloba (L.) Dunal plant.
In the present work, we show the results obtained through a variance analysis of biological aspectsin Asimina triloba (L.) Dunal and its growth predictions.
1.3. Results and discussion. We combined the two analysis criteria, plant location (Lpuel andBaia Mare) and their age (one, two or three years). The bifactorial anova calculation revealed whetherdifferences in stem length exist among the 5 (five) subgroupsin other words, if age and plant locationsignificantly influence growth in the main stem. An analysis of the variance report values (F) and thep-values (p) leads to the following conclusions:
When comparing average stem lengths among the three subgroups of Asimina triloba (L.) Dunalplants aged one, two and three years, one observes that these lengths differ significantly (F=117.603).This allows us to state with certainty (error risk of 0, as p=0.000) that stem length increasessubstantially every year. Thus, plant age as a variance factor is significant for main stem growth inthe Asimina triloba (L.) Dunal plant.
Likewise, if we analyze average main stem length in the Asimina triloba (L.) Dunal plant in termsof location, we observe that the two subgroups (in Baia Mare and Lpuel) are significantly different(F=21.760). The error risk we assume for this statement is 0 (p=0.000). This fact allows us to affirmthat plant location, along with age, is a significantly influential factor in terms of growth in length ofthe main stem in Asimina triloba (L.) Dunal plants.
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Combining the two variance factors of plant age and location and comparatively analyzing averagemain stem lengths of the five (5) subgroups that they generate, we observe that these averagessignificantly differ among themselves (m1 bm=5.850, m2 bm=9.207, m2 lpuel=8.203, m3 bm=34.130,m3 lpuel=21.320). The value of the variation report F=16.006 indicates significant differences amongthe subgroups (p=0.000).
Prediction model R2 r p1 age 0,453 0,676 0,000∗∗
2 age∗ location 0,541 0,780 0,000∗∗
Prediction of main stem length growthin terms of age and location of the Asimina triloba (L.) Dunal plant
Calculating the variance analysis allowed us to conclude that the subgroups formed by combiningcriteria of plant location and age generate differences in main stem length of the Asimina triloba (L.)Dunal plant. A multiple regression analysis allows us to know and to quantify the weight that the twofactorslocation and agecontribute to growth of the main stem in the plants studied. To this purpose,table 2 condenses values of the correlation coefficients (r) and of the determinant coefficients (R2),together wth the associated p-values.
In our case, in order to predict growth in length of the main stem of the Asimina triloba (L.)Dunal plant, we used two prediction models. The first calculates the extent to which plant age affectsmodification of the main stem length. The second model analyzes the extent to which the two factorsof age and plant location, taken as a whole, affect main stem growth. The correlation coefficient valuesfor both models are significant (rmodel 1=0.676 p=0.000 and rmodel 2=0.780 p=0.000), meaning thatas the plant ages, length of the main stem will increase proportionally. Stem length is greater in BaiaMare than in Lpuel.
1.4. Conclusions. Analyzing the data obtained following a statistical analysis, we found that forAsimina triloba (L.) Dunal plants, conditions present in Baia Mare (temperature, exposure, wetness)are significantly favorable for growth in length of the main stem. We can affirm that the two criteria(plant age and location) taken together are significant in terms of main stem growth in the Asiminatriloba (L.) Dunal plant. We can also say, based on the results obtained, that in terms of importancethe two factors have in main stem growth, plant age has a weight of 45.3% in main stem growth ofthe Asimina triloba (L.) Dunal plant (R2model 1=0.453), while adding the location factor boostsvariation a further 8.8% (R2model 2=0.541), so that model 2 contributes 54.1% of main stem growth.
Bibliography[1] Desmond, R. Layne. (1996). The Pawpaw [Asimina triloba (L.)Dunal], A New Fruit Crop for Kentucky and the
United States, HortScience, Vol. 31(5), 777-784.[2] Kral, R. (1960). A revision of Asimina and Deeringothamnus (Annonaceae) Brittonia, 12, 233-278.[3] Layne, D. R. and R. N. Peterson. (1996) The pawpaw regional variety trial (RVT), Background, rationale and early
data HortScience 31:667.
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Applications of computer science in impingement cooling system design
Krzysztof MarzecMTU Aero Engines Polska employee, Phd student at Rzeszw University of Technology, Department of Thermodynamics and Flow Me-
chanics, Poland
Abstract.Jet impingement heat transfer cooling systems plays significant role in many industrial appli-
cations. This is due to the fact that the impinged jet provides higher rate of heat and mass transfer.
Applications such as electronic chip cooling, cooling of photovoltaic cells, de-icing of aircraft wings, an-
nealing of metals, heat exchangers in automotive and aeronautical applications, cooling of gas turbine
blades and other are a few examples of jet impingement cooling. Influence of the grid density, flow
mechanism and heat transfer, consisting of a numerical model of an impingement cooling jet directed to
the flat surface were investigated. The simulation were performed using Computational Fluid Dynamics
(CFD) code Ansys CFX that solves implicitly turbulent equations of continuity, momentum and energy
using the Reynolds Averaged Navier-Stokes approach. Numerical analysis of the different mesh density
resulted in good convergence of the GCI index what excluded mesh size dependency. The numerically
simulated values of the heat transfer coefficient and Nusselt number have also been compared with the
results obtained from the formulas coming from the physical experiments. The agreement was generally
good.
1.1. Introduction. The literature includes many investigations of a single impingement jets orjet arrays. A variety of geometrical and physical parameters for the impingement cooling have beenstudied. For example Goldstein [1] reported a fundamental analysis of heat transfer behavior under acircular impingement jet. Present literature contain many numerical simulations of the impingementcooling affecting both circular and slot types of the jets [2-4]. Zuckerman and Lior [5] presented reviewof the various types of the geometries and designs of the impingement jet cooling. They also presentedcomparison of different CFD turbulence models used in impingement jets problems.
An impingement jet is a jet of high velocity fluid which is made to strike a target surface. Animpinging jet can be classified as submerged jet or free jet. If the fluid issuing from the jet is of thesame density and nature as that of the surrounding fluid then the jet is called a submerged jet. If thefluid issuing from the nozzle is of a different density and nature than that of the surrounding fluidthen the jet is called a free Jet. Fig. 1 describes these two different types of the jets configurations.
Figure 1 a) submerged jet, b) free jet
Further classification between jets can be made as confined and un-confined jets. In the case ofconfined jets, the jet remains bounded between the two surfaces during its flow. There is very lessentrainment of air from the atmosphere. Un-confined jets are free to expand after they impinge onthe target surface.
1.2. Numerical Setup. In this section, an overview on the numerical setup investigated ispresented. The numerical grid density is taken into consideration.
Computational Domain
The chosen computational domain corresponded to a single cooling impingement jet directed toa flat surface. In this study the nozzle diameter D=4mm was constant for all analysis. The nozzle
99
Figure 2 a) un-confined jet, b) confined jet
exit-plate distance y/D=20 mm and was also constant for all simulations. The total length of thetarget plate measured L=15mm. This ensured that the outlet boundaries were far away from thesection of interest where the jet impinged onto the target plate.
The numerical calculations were carried out using unstructured grids with hexahedral elementsgenerated with Ansys CFX. The purpose of the simulation was to investigate the influence of thenumerical grid density on the results of the heat transfer coefficient and Nusselt number in stagnationregion. Therefore 4 analysis with cell size in the area of the interface (between air flow and flat surface)was taken into consideration. For detail sizing of the mesh in area of the interface see table 1.
Table 1 parameters of the grids used in simulations
grid number number of cells cell size in interface area ∆X [mm]1 28887 0,082 145559 0,043 265679 0,034 315679 0,025
1.3. Numerical Methods. In the following, the flow solver used for the present investigation ispresented. The accuracy of the results will be discussed in details.
Numerical solver
The simulation were performed using Computational Fluid Dynamics (CFD) code Ansys CFX,that solves equations of continuity, momentum end energy using Reynolds-Averaged Navier-Stokesapproach. In the present investigation the k ω shear stress transport (SST) turbulence model wasused. The SST model combines the k ω model near the wall and the k ε model farther from the wallto utilize the strengths of each. Zuckerman and Lior [5] reported that SST model can produce betterpredictions of fluid properties in impinging jet flows and are recommended as the best compromisebetween solution speed and accuracy. Typical Nuo errors of 20-40%.
Numerical accuracy
To investigate the sensitivity of the results of the numerical analysis Grid Convergence Index(GCI) was performed.
GCI =|Uh2−Uh1
Uh1|
rp−1 · 100%
In presented test for the grid number 3, a GCI value of 0,63% was obtained. Therefore furtherchanges of the grid density had no sense because of the extra time consumption with negligible qualityimprovement. It can be concluded that numerical results on the fine grid are grid independent andadequate grid density was chosen for the study.
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Table 2 Grid Convergence Index
grid number density factor r Uh[K] GCI (%)1 - 328,864 -2 2,000 324,249 1,4033163 1,333 324,78 0,6316574 1,200 324,74 0,083973
1.4. Results and Discussion. This section provides analysis of the flow field behavior of theimpingement jet in the stagnation region with obtained GCI value of 0,63% . The results of heattransfer coefficient and dimensionless Nusselt number are shown and compared to the results fromthe literature. This is interesting to note that, the impingement values of heat transfer have beenelaborated by Mohanty and Tawfek [6] in the experimental configurations and the stagnation pointNusselt numbers have been correlated. This paper presents comparison of the Mohanty and Tawfek[6] correlations based on experiments with numerical calculations. Comparison has given followingresults:
• heat transfer coefficient h=19,2% discrepancy• Nusselt number Nuo=15% discrepancy
Taking into account that numerical model was simplified by using steady state two-dimensionalanalysis, the fluid physical properties were constant, and the effect of the gravity and radiation wasneglected we can assume that numerical experiments gives satisfying results and can be used todescribe physical phenomena and flow behavior in stagnation region. Moreover the obtained GCIindex 0,63% gave adequate grid resolution and excluded dependency of mesh density on the results ofthe numerical experiment. Further analysis of the Nusselt number and heat transfer coefficient notonly in stagnation region can be made based on analyzed numerical model.
1.5. Conclusions. The aim of the work was the numerical simulation of the flow in stagnationregion based on an impinged cooling jet directed to the flat surface. Four analysis with differentmesh density using numerical solver Ansys CFX were done. Achieved GCI index 0,63% for the gridwith 0,03 mm in the interface region excluded mesh size dependency on the results. Obtained valuesof the heat transfer coefficient and Nusselt number were compared with the correlations based onphysical experiments Mohanty and Tawfek [6]. Comparison of the mentioned correlations with valuesfrom numerical experiments had given satisfying results of the flow characteristic in stagnation region.Presented numerical model might be a basis for further researches for example of the average Nusseltnumber along the impinged surface.
Bibliography[1] Goldstein, R.J., Sobolik, K.A. and Seol, W.S. 1990., Effect of entrainment on the heat- transfer to a heated circular
air-jet impinging on a flat surface, ASME Journal of Heat Transfer, 112(3), Aug., pp. 608-611.[2] Jian-Jun Shu, Heat transfer on a hot surface impinged by a cold circular liquid jet, V European Conference on CFD,
ECCOMAS CFD 2010.[3] F. Ben Ahmed, B. Weigand, K. Meier, Heat transfer and pressure drop characteristics for a turbine casing
impingement cooling system, Proceedings of International Heat Transfer Conference, Aug. 2010, Washington, USA.[4] Wael M. El-Maghany, Ahmed A. Hanafy, Khaled M. Abdou, Mohamed A. Teamah, Numerical simulation for
confined rectangular slot jets impingement on isothermal horizontal plate, European Journal of Scientific Research,Vol. 76, pp. 553-566, 2012.
[5] N. Zuckerman, N. Lior, Jet impingement heat Transfer: Physics, Correlations and Numerical Modeling, Advancedin Heat Transfer Vol 39, 2006.
[6] Mohanty, A.K.; Tawfek, A.A., Heat transfer due to a round jet impinging normal to a flat plate, Int. J. Heat MassTransfer 36 (1993) 1639-1647.
ICAM9
101
On the Convexity of the Control Set of a Hybrid Optimal Control ProblemScheiber ErnestDepartment of Mathematics and Computer Science, Transilvania University, Brasov, Romania
Abstract.The purpose of this paper is to state that the set of the control functions for a type of hybrid
optimal control problem may be not convex. In order to simulate a hybrid system, the main difficulty
is to generate admissible control functions, i.e. the corresponding trajectory of a control function
reaches the switching manifolds. For a test problem we compute a suboptimal solution using a heuristic
optimization procedure based on the parametrization of the problem data. The attention is focused on
the use of admissible control functions. The implementation is done within the Mathematica software.
1.1. Introduction. The purpose of this paper is to re-examine a hybrid optimal control sampleproblem presented in [1]. We have found that the set of admissible control functions may be notconvex. We were interested to verify the numerical result reported in the above mentioned paper, too.Unfortunately, this task is not a simple one. The details of used algorithm are only sketched. Even theproblem involves first order linear differential equations with constant coefficients, the computationsrequires a computer program.
Numerical methods to solve hybrid optimal control problems are presented in [3], [2], but withoutproviding the implementations of the algorithms.
We have used heuristic methods based on the particular definition of the test problem. Theinvolved control functions will be admissible.
1.2. The hybrid optimal control problem. Following [1],[3] a hybrid control system (HS) isdefined by
• Q a finite set of discrete states;• U ∈ Rm the set of admissible control values;• fq : [0, 1]×Rn×U → Rn, q ∈ Q, setting the right hand side of ordinary differential equations;• (Iq)q∈Q a family of subintervals of [0, 1]. The length of each subinterval is less than 1;• There exists r ∈ N∗ and the unknown switching times
0 = t0 < t1 < . . . < tr < tr+1 = 1
such that(1) [ti−1, ti) ⊆ Iqi ;(2)
(3) x(t) = fqi(t, x(t), u(t)), t ∈ [ti−1, ti), qi ∈ Q;
for i ∈ 1, 2, . . . , r + 1 and x(0) = x0.We suppose that a switching time ti occurs when the trajectory of (3) reaches a switching
manifold Mi,i+1, i ∈ 1, 2, . . . , r.The vector Rr+1 = (q1, . . . , qr+1), q1, . . . , qr+1 ∈ Q is called discrete trajectory and it
will be prescribed.• U = u ∈ L∞m [0, 1] : u(t) ∈ U, a.e.[0, 1]; inducing the discrete trajectoryRr+1 the set of admissible control functions;
There is supposed that for any u ∈ U there exists a continuous trajectory xu(t) such thatxu|[ti−1,ti) is the solution of (3).
Attaching to the HS a cost functional J(u) we obtained a hybrid optimal control problem (HOCP).If J(u) = φ(xu(1)) then there is defined a Meyer type HOCP.In order to simulate a HS, the main difficulty is to generate an admissible control function, i.e.
the corresponding trajectory reaches the switching manifolds. This constraint will be satisfied in thecase of controllable differentiable systems.
Further we suppose that
• fqi(t, x, u) = aqix+ bqiu, x, u, aqi , bqi ∈ R, i ∈ 1, 2, . . . , r + 1;• the switching manifolds are Mi−1,i = x ∈ R : x− x0
i = 0.In other words, the switching time ti occurs when xu(ti) = x0
i .
102
If
(4) u(t) =2aqibqi
eaqi (ti−1−ti)x0i − x0
i−1
1− e2aqi (ti−1−ti)eaqi (ti−1−t), t ∈ [ti−1, ti),
then the solution of the differential equation
x(t) = aqix(t) + bqiu(t)
will satisfy the equalities x(ti−1) = x0i−1 and x(ti) = x0
i . The solution is given by
(5) x(t) = eaqi (t−ti−1)x0i−1 + bqi
∫ t
ti−1
eaqi (t−s)u(s)ds.
It results that in this case U 6= ∅. As for the convexity of this set we state that:Theorem. The set of admissible controls U may not be convex.To prove this statement, let be r = 1, R2 = 1, 2 and the switching manifold M1,2 = x ∈ R :
x− x01 = 0.
Let u1, u2 ∈ U be two control functions and t11 < t21 such that xu1(t11) = xu2(t21) = x01.
We suppose that xu1(t), xu2(t) are increasing, 0 < x0 < x01 and that t11, t
21 are the smallest reaching
times. If follows that xu2(t) 6= x01, ∀t ∈ [t11, t
21).
Now we define
u1(t) =
u1(t), t ∈ [0, t11]u2(t), t ∈ (t11, 1]
.
Then u1 ∈ U .For 0 ≤ λ ≤ 1, we consider the control function
uλ(t) = λu1(t) + (1− λ)u2(t) =
λu1(t) + (1− λ)u2(t), t ∈ [0, t11]u2(t), t ∈ (t11, 1]
.
uλ ∈ U if and only if the corresponding trajectory xλu1+(1−λ)u2(t) reaches the manifold M1,2, ie.
there exists tλ1 ∈ (0, 1) such that xλu1+(1−λ)u2(tλ1) = x01.
For t ∈ [0, t11] we shall have x0 ≤ xu1(t) ≤ x01, x0 ≤ xu2(t) < x0
1 and consequently xλu1+(1−λ)u2(t) =λxu1(t) + (1− λ)xu2(t) < x0
1.Let us suppose the existence of tλ1 ∈ (t11, 1]. For t11 < t ≤ tλ1 we have
xλu1+(1−λ)u2(t) = λxu1(t) + (1− λ)xu2(t) =
= λ
(xu1(t11) + b1
∫ t
t11
ea1(t−s)u2(s)ds
)+ (1− λ)
(xu2(t11) + b1
∫ t
t11
ea1(t−s)u2(s)ds
)=
= λx01 + (1− λ)xu2(t11) + b1
∫ t
t11
ea1(t−s)u2(s)ds =
= λ(x01 − xu2(t11)) + xu2(t).
For t = tλ1 , from the equality λ(x01 − xu2(t11)) + xu2(tλ1) = x0
1 we obtain the contradiction
λ =xu2(t)− x0
1
xu2(t11)− x01
> 1.
1.3. The test problem. The test HOCP is
minimize J(u) =1
2
(∫ t1
0(x2
1 + u21)dt+
∫ t2
t1
(x22 + u2
2)dt+
∫ 1
t2
(x21 + u2
1)dt
)subject to
x1(t) = −x1(t) + 4u1(t) t ∈ [0, t1)
x2(t) = −2x2(t) + 2u2(t) t ∈ [t1, t2)
x3(t) = −4x3(t)− 5u3(t) t ∈ [t2, 1]
103
with x1(0) = x0 = 5. The control functions must satisfy the inequalities |uk(t)| ≤ 40, k ∈ 1, 2, 3.The switching times t1 < t2 are unknown and the switching occurs when the trajectory reaches themanifolds
M1,2 = x+ 3 M2,3 = x− 8.
The controls functions must involve the reaching of the switching manifolds.In this case the discrete trajectory is prescribed as R = 1, 2, 3.Here we present only the obtained numerical results: x0
3 = 3.5 (the final state), t1 = 1/3, t2 =0.854167, J(u) = 64.72.
The plot of the control function shows that the boundary constrain is satisfied, too.Finally, we mention that the plots of the optimal control function and the corresponding state
have similarities with that given in [1].
Bibliography[1] Azhmyakov V., A gradient-type algorithm for a class of optimal control processes governed by hybrid dynamical
systems. IMA J. of Mathematical Control and Information, 28(2011), 291-307.[2] Silva J.M.E., Computational Methods for Dynamic Optimization of Hybrid Systems: a Survey., 2008.[3] Zhang H., James M.R., Optimal Control for a Class of Hybrid Systems Under Mixed Costs. Proceedings of the 44th
IEEE Conference on Decision and Control, and the European Control Conference, Seville, Spain, December 12-15,2005.
ICAM9
104
The performance appraisal in human resources
Simona Sabou, Liliana Zima, Rita Toader, Corina Radulescu, Florina Hahn, CristianVeleTechnical University of Cluj Napoca, North University Center at Baia Mare, Romania
simona [email protected]
Abstract.This paper presents a new models of performance assessment, performance assessment objec-
tives and the problem of performance evaluation. A performance management system needs to be based
on the organisations business strategy and human resources strategy. The potential problems that need
consideration in approaching performance assessment as a component of the performance management
system. Implementing a performance management strategy involves adopting a management style that
encourages continuous communication between employee and management, feed-back often in both di-
rections and fostering teamwork. The main purpose of the adoption of such strategies is to bring added
value to the organization by promoting and encouraging the development of performance skills. Per-
formance management involves: defining and clarifying the responsibilities associated with each post;
defining and tracking of performance standards; communication roles, indexes and standards; assess-
ing and documenting the performance level of each employee; tracking the evolution of the skills and
knowledge of each employee.
1.1. The mathematical model of performance assessment. From the mathematical mod-eling point of view, its about a non-linear regression with an independent variable
f(x) = b0 + b1x+ b2x2 + . . .+ bnx
n
This problem can be reduced at a multiple linear regression problem, but this thing necessitatesto many calculations. The use of orthogonal Tchebashevs polynomials is more indicated to find thesearched polynomial and its optimum degree.
The working algorithm is specified below:
• It must be specified the number of the values N , the counter k = 1, 2...N and the indexj = 0, 1..n, where n is the maximum degree of the polynomial it depends of N , [3].• Determination of the average xm of x variable:
xm =1
N
N∑k=1
xk
• It must be determined the step h of the x variable;• The variable x is changed with variable u:
u =x− xmh
• The average ym of the y values are determined:
ym =1
N
N∑k=1
yk
• By recurrence, the values of the report Hj and Hj−1 are determined :
Hj
Hj−1=j2(N2 − j2)
4 (4j2 − 1), j = 1, 2 . . . n
• By recurrence, the values of the terms Hj are calculated:
H0 = N, Hj = Hj−1Hj
Hj−1, j = 1, 2 . . . n
105
• The orthogonal Tchebashevs polynomials are determined, by recurrence:
p(u)0 = 1 , p(u)1 = u, p(u)j+1 = u p(u)j −Hj
Hj−1p(u)j−1, j = 1, 2 . . . n
• It must be determined the coefficients cj of the polynomial f(u):
c0 = ym, cj =1
Hj
N∑k=1
yk p(u)k, j = 1, 2 . . . n
• It must be determined the optimum degree of the f polynomial by calculating the terms Sj :
S0 =N∑k=1
(yk − ym)2, Sj = Sj−1 − c2j Hj , j = 1, 2 . . . n
If the calculated values Sj have the same size order, starting with a certain index j0,then we can consider that j0 is the optimum degree of the f polynomial. Otherwise, thedegree of the polynomial is n.• It must be formed the expression in u variable of the f polynomial having j0 degree:
f(u) = c0 + c1u+ c2u2 + . . .+ cj0u
j0
• Knowing that the u variable u = u(x), then f(u) must be replaced with f(x) by replacingu(x) in f(u)s expression. So, it will be obtained the polynomial f(x) = f(u(x)) as following:
f(x) = b0 + b1x+ b2x2 + . . .+ bj0x
j0
The algorithm of calculation presented above can be implemented in any high level programming .The evaluation criteria of individual performance are the following:
• the level of meeting the performance standards;• assume responsibility;• adequate labour complexity;• initiative and creativity.
The regression equation obtained according to the proposed model is the following:
y1 = 65, 7− 1, 25x1 − 0, 5x2 − 4x3
1.2. Conclusions. I think it is very important to adapt the performance indicators of the fiecaripeople at personal development plan and framing in the development strategy of the company.
The professional performance evaluation constitutes an undisputable motivational element withregard to the professional activity of every employee.
Performance assessment has a special influence upon the social-economical activity, the organiza-tional environment in any business organisation.
An important aspect of human resources management is represented by performance assessmentwithin the organisation, because through evaluation we can better understand the dynamic nature ofprofessional development.
It is very important to establish criteria for evaluating performance.Tracking the evolution of performances by referencing the data and results for multiple campaigns
through evaluation using multiple assessment tools, among which the evaluation forms The advantageof an informal performance assessment system resides in the fact that it requires a smaller amountof time for designing and administering, as compared to a formal assessment programme. This iswhy informal performance assessment is used especially in those situations when the available time islimited or when an interruption of the employees activity is not possible.
Bibliography[1] Burloiu, Petre, Human Resources Management, Editura LUMINA LEX, Bucuresti, 1997, pg. 612;[2] Certo C. Samuel, Modern Managemen, Editura Teora, Bucuresti, 2001;[3] Cole G. A. Personnel Management, Editura CODECS, Bucuresti, 2000;[4] Cole G. A. Management. Theory and Prcatice, Editura Stiinta, Chisinau, 2004.
106
[5] Chisu Ana Viorica, The Human Resources Specialists Manual, Casa de editura IRECSON, Bucuresti, 2002;[6] Manolescu Aurel, Human Resources Management, Editura Economica, Bucuresti, 1999;[7] Mathis L. Robert, Panait C. Nica, Rusu Costache, Human Resources Management, Editura Economica, Bucuresti,
1999;[8] Panisoara Georgeta, Panisoara I. Ovidiu, Human Resources Management, Editura Polirom, 2004;[9] Pitriu H. D., Human Resources Management Professional Performance Assessment, Editura All Beck, 2000;
ICAM9
107
Bi-level definition of portfolio optimization problem
Krasimira Stoilova, Todor StoilovInstitute of Information and Communication Technologies-Bulgarian Academy of Sciences, Bulgaria
Abstract.The investment process is formalized by hierarchical coordination for solving bi-level optimiza-
tion problem. The optimal resource allocation of sets of securities, available at the financial market can
be done by solving multi-criterion optimization task, leading to maximization of portfolio return and
minimization of portfolio risk. Two-level hierarchical approach for solving the portfolio optimization
problem is applied. The optimal Sharp ratio of risk versus return is minimized at the upper level. As a
result is determined the investors preferences for taking risk on the basis of objective considerations.
1.1. Introduction. An investment process targets the maximization of the portfolio return andminimization of the investment risk [2, 3, 4, 5, 7, 8]. The term risk reflects the undetermined andnon-predictable future. The financial risk cannot be predicted because of the dynamical and stochasticmarket behaviour. In order to formalize the investment process, allocation of the financial resourceshas to be done.
For the finance modelling and risk assessment essential contribution has the theory of Markowitz[6]. This theory is based on both optimization and probability theory. For the practical utilization ofthe portfolio theory, the relation between the return and risk is the main parameter for the investor.The portfolio risk is minimized according to two types of arguments: the portfolio content and theparameter of the investors risk preference. The last usually is done by subjective investors assumptionsfor the relation portfolio risk/return. The paper targets the decrease of the subjective influences in theinvestment process. The unknown investors coefficient for undertaking risk is determined according tooptimization problem. The portfolio investment is formalized by a bi-level optimization problem. Theparameter of the investors risk preference is evaluated at the upper level. This parameter is used foroptimal resource allocation of the portfolio optimization problem by minimizing risk and maximizingreturn. As a result the definition of the portfolio problem is performed without subjective influences.
1.2. Portfolio Optimization Problem. The portfolio theory is developed to support decisionmaking for allocation of investment to financial assets by selling and buying securities/bounds at thestock exchange [1]. The resource allocation means to invest financial resources per different assets orgoods. Later these assets will give return to the investor after a period of time. The portfolio containsa set of securities. For the investment process the target is to maximize the return and to minimizethe risk of the portfolio [8]. The analytical relations among the portfolio risk Vp, portfolio return Epand the values of the investment per type of assets xi, according to the portfolio theory, are [9]
Ep =n∑i=1
Eixi = ETxVp =n∑j
n∑i=1
xixjcov (i, j) = xT cov (·)x,
where xi - the relative amount of the investment, allocated for buying asset i; Ei - the average valueof the return of asset i; ET = (E1, E2, . . . , En)T - a vector with dimension 1 × n; cov (i, j) - theco-variation coefficient between the assets i and j.
The component Vp = xT cov (·)x formalizes the quantitative assessment of the portfolio risk. Thecomponent Ep = ETx is the quantitative evaluation of the portfolio return. The portfolio problemsolutions xi, i = 1, n determine the relative amounts of the investment per security i.
The portfolio theory defines the so called standard optimization problem by [9]:min
[12x
T cov (·)x− σETx]
xT .1 = 1
wherecov (·)x is a symmetric positively defined square matrix n× n;E is a (n× 1) vector of the average profits of the assets for the period of time T = [1, 2, . . . , N ];
1 = |1 . . . 1|T is the unity vector, n× 1;σ - is a parameter of the investors preferences to undertake risk in the investment process.
108
1.3. Hierarchical bi-level optimization problem. For the bi-level optimization problemsthe upper level solves optimization problem, which solutions influence the lower level optimizationproblems. The lower level solutions influence on its turn a set of parameters for the upper levelproblem. Because of this mutual interrelation between the upper and lower level optimization problemswith their solutions, the resulting global problem is a bi-level one. From application considerations,the solution of such problem is a difficult task. The complexity of the bi-level optimization problemsrequires its solution to be made with numerical iterative calculations.
Currently, the portfolio problem is solved by quantitative assessment of σ∗ in advance, withoutapplying interconnected hierarchical optimization. The value of σ∗ is estimated intuitively or empiricallyby an expert. The paper suggests the solution of the bi-level portfolio problem to be performed usingthe concept of the non-iterative coordination [10, 12]. The concept of the non-iterative coordinationin hierarchical systems defines analytical ap- proximations of the inexplicit functions, used by theupper and lower optimization problems. In that manner, analytical relations between the investorspreferences for the risk σ and the solutions xi are derived [11]. Such relations support fast solution ofthe bi-level problem and respectively allow real time decision making. The upper level problem isdefined with a goal function, which minimizes the Sharp ratio: portfolio risk versus portfolio return.The argument of this optimization problem is the investors preferences for taking risk σ. Applying thenon- iterative methodology [10, 12], analytical relations between the portfolio problems parametersEp(σ) Vp(σ), the portfolio solutions xi(σ) from the parameter of the investors preference σ are derived.These relations allow speeding up the decision making process and the investment decisions can bedone in real time.
1.4. Conclusions. The process of decision making is presented as a two-level optimization system.The upper level defines the optimal value of the parameter of risk preferences of the investor σ byminimizing Sharp ratio (portfolio risk versus portfolio return). The lower optimization level uses σand solves the portfolio optimization problem. The bi-level formalism in a unique way defines the mostappropriate value of σ by optimizing the Sharp ratio. In that manner, the bi-level formalism achievestwo benefits: it reduces the subjective assessment of the investors risk preferences and it applies theoptimal value of σ by minimizing the Sharp ratio. These two outcomes considerably improve thecontent of the portfolio problem with the bi-level definition in comparison with the classical definitionof one level portfolio optimization problem. The paper develops and applies a special method forsolving the optimization problem, titled non-iterative coordination. It allows to be defined explicitlyin analytical way the upper level optimiza- tion problem for solving and to derive explicit analyticalrelations between the portfolio problem solutions and σ, x(σ).
ACKNOWLEDGEMENT This work is partly supported by project AComIn-Advanced Com-puting for Innovation, Grant Agreement: 316087, 2012-2016
Bibliography[1] Bodie, Z., Kane, A., Marcus, A., Investments. Naturela, Sofia (2000)[2] Kohlmann, M., Tang, S., Minimization of risk and linear quadratic optimal control theory, SIAM J. Control optim,
Vol. 42, No. 3 (2003) 11181142[3] Korn, R., Continuous-Time Portfolio Optimization Under Terminal Wealth Constraints, ZOP-Mathematical Methods
of Operations Research, Vol. 42 (1995) 69-92[4] Magiera, P., Karbowski, A., Dynamic portfolio optimization with expected value-variance criteria, Bucharest (2001)
308-313[5] Markowitz, H. M., Portfolio selection, J. of finance, Vol. 7 (1952) 77-91[6] Mateev, M., Analysis and assessment of investment risk, University publisher Economy, Sofia (2000) In Bulg.[7] Sharpe W., Alexander, G., Bailey J., Investments, Prentice Hall, England Cliffs, New Jersey (1999)[8] Sharpe, W., Portfolio theory & Capital markets, Mc Grow Hill, No4 (2000)[9] Stoilov, T., Stoilova, K., Noniterative Coordination in Multilevel Systems, Kluwer Academic Publisher, Dor-
drecht/Boston/London (1999)[10] Stoilova K., Stoilov, T., Noniterative Coordination Application in Solving Portfolio Optimisation Problems, Proceed-
ings of the International Conference Automatics and Informatics, Vol. 1. Sofia (2003) 159-162.[11] Stoilova, K., Predictive Noniterative Coordination in Hierarchical Two-level Systems, Comptes rendus de lAcadmie
bulgare des Sciences, Vol. 58, 5 (2005) 523-530
ICAM9
109
The effects of different queuing techniques over VoIP performance: a simulation approach
Szabolcs SzilagyiDepartment of Computer Science, University of Oradea, Oradea, Romania
Abstract. This paper presents one of the features of DS (Differentiated Services) architecture, namely
the queuing or congestion management. Packets can be placed into separate buffer queues, on the basis
of the DS value. Several forwarding policies can be used to favor high priority packets in different
ways. The major reason for queuing is that the router must hold the packet in its memory while the
outgoing interface is busy with sending another packet. Our main goal is to compare the performance
of the following queueing mechanisms: FIFO (First-In First-Out), CQ (Custom Queuing), PQ (Priority
Queuing), WFQ (Weighted Fair Queuing), CBWFQ (Class Based Weighted Fair Queuing) and LLQ
(Low Latency Queuing).
1.1. Introduction. At the beginning computer networks were designed mainly for data transfersuch as FTP and email, where delay was considered to be unimportant. In most cases the deliveryservice was effective, and the TCP protocol dealt with data losses. As the multimedia applicationsbecame popular (voice transfer, video conferences), separate telephone and video communicationnetworks were set up. Nowadays, office and company networks are transformed into one convergednetwork (see [1]), in which the same network infrastructure is used to ensure all the requested services.
Although converged networks have many advantages, there are some disadvantages too, namely thecompetition for network resources (buffers of routers), which leads to congestion. Delay in deliveringthe packets, jitter, loss of packets are all consequences of congestion. Not each application is sensitiveto these issues. For example, FTP is not impacted by delay and jitter, whereas the multimediaapplications (video, voice) are very sensitive to them and the loss of packets too. QoS was introducedto handle this problem, and it is able to provide better multimedia performance (see [2]).
In the IP header there are some fields which can be used to make distinction between the packetsof different applications, for example the Type of Service field. Different technics such as congestionmanagement (PQ, CQ, WFQ, CBWFQ, LLQ), prevention of congestion (WRED), resource efficiencyinsurance (fragmenting the packets, and compressing), traffic shaping and traffic policing are usedby the QoS technology in order to control data traffic. This article focuses on the most importantcomponent, the congestion management.
Speed mismatches and path aggregations (see [1]) are the main causes of congestion in computernetworks. There are different algorithms which can overcome the mentioned problematic situations.Our purpose is to analyze and evaluate the efficiency of these algorithms using simulations. We aregoing to examine the following methods: FIFO, PQ, CQ, CBWFQ, WFQ and LLQ. It is important tonote that these algorithms have real effect only in case of congestion (see [3]).
The OPNET IT Guru Academic Edition (see [4]-[6]) was used to perform the simulation. Thenetwork topology for the testing is identical with the one occurred in former articles (see e.g. [6]-[8]).In this paper we continue to study the queueing technologies for congestion management. In [7] and [8]the authors considered three algorithms: FIFO, PQ and WFQ. The conclusion was that WFQ is themost efficient for multimedia applications. In addition to these we investigate three new algorithms:CQ, CBWFQ and LLQ. The main result of this paper is that for multimedia applications (mainlyvoice transfer) LLQ is more efficient then WFQ.
The mentioned algorithms has been examined in several papers (see e.g. [10] ).
1.2. Simulation environment and settings. We used the following network topology inOPNET IT Guru Academic Edition:
The measurement environment consists of 2 routers, 2 switches and 6 hosts. The routers areconnected with a point-to-point link, having the speed of ppp-DS1. The rest of the hosts are connectedwith 10BaseT. The part between the two routers is actually a narrow cross-section where congestioncan happen. For this reason the congestion management algorithm is activated in this area (see[11]-[12]).
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Figure 1 Simulation network topology
1.3. Simulation results. Simulation makes possible to perform several measurements andstatistical analysis. The following main indicators are investigated: the packet loss rate, the number ofreceived packets, the delay of packets between the endpoints and jitter. The length of the simulationwas 5 minutes in each case. Congestion management algorithms are activated only in the case ofcongestion. The graph below presents this fact: it is the 105th second when the congestion managementalgorithm becomes active and its performance study can be started. Figures 2-7 show the results ofthe simulation.
The highest rate of packet loss (see Fig.2.) was produced by the FIFO rule, as it could be expected.In the case of PQ, the loss of audio packets is zero, due to the existence of the highest priority queue.The loss of video and FTP packets is extremely high in this case (see Fig.3.), as the highest priorityqueue (voice traffic) blocks the video and FTP communication. Using CQ we can get better resultsthan using PQ, concerning the packet loss, but it requires a lot of fine-tuning work. WFQ, CBWFQand LLQ are the most efficient mechanisms concerning the packet loss.
In the case of voice communication there were examined the following performance parameters:the number of received voice packets, the delay of voice packets and the variation in the delay of voicepackets (see Fig.3-7). Concerning the number of received voice packets the performance of the PQ,WFQ, CBWFQ and LLQ mechanisms is the most efficient. CQ and FIFO show a bit worse resultsbut they are acceptable too. Interactive voice communication requires a maximum of 150 ms delay forvoice packets (see [13]). FIFO and CQ cannot fulfill this criterion. QoS also requires that the jitter donot exceed 30ms. FIFO and CQ didn’t fulfill this criterion too.
Finally, the four most efficient algorithms (PQ, WFQ, CBWFQ, LLQ) were compared in respectof the delay of voice packets and jitter. The reason of choosing the voice packets is that they arevery sensitive to delay and jitter. The result is interesting (see Fig.5 and 7.). Previous articles (seee.g. [6]-[7]) showed that WFQ is the most efficient for voice packets. It can be observed that WFQand CBWFQ have the highest dispersion for the delay. WFQ has the highest value for jitter, muchhigher than in the case of PQ and LLQ. It is obvious (see Fig.5. and 7.) that LLQ has much betterperformance for voice packets than WFQ.
1.4. Conclusions. In this paper ∗ we tried to present a short overview of congestion managementalgorithms used by routers. We managed to evaluate three more algorithms beside the ones publishedin former articles (see e.g. [6]-[7]). The simulation environment was provided by the OPNET IT GuruAcademic Edition application, based on mathematical models. We used a generalized, extendable andfactual network topology. The article concludes that LLQ is the most efficient algorithm for voice
∗The work was supported by the TAMOP-4.2.2.C-11/1/KONV-2012-0001 project. The project has been supportedby the European Union, co-financed by the European Social Fund.
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Figure 2 IP packet loss
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Figure 3 VoIP: Packet received
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data transfer. Our next research topic is to examine and test the algorithms presented in the currentarticle in a real network environment, as it is also a widely used by reasearchers (see e.g. [14]) toperform traffic measurements.
Bibliography
[1] QOS, Implementing Cisco Quality of Service, Student Guide, Vol. 1-2, Ver. 2.2, c©Cisco Systems Inc., 2006[2] A. S. Ranjbar, CCNP ONT Official Exam Certification Guide, Cisco Press, 2007[3] B. Durand, J. Sommerville, M.Buchmann, R. Fuller, Administering Cisco QoS in IP Networks, Syngress Publishing,
Inc., 2001[4] www.opnet.com[5] T. Svensson, A. Popescu, Development of laboratory exercices based on OPNET Modeler, Master thesis, Blekinge
Institute of Technology, Department of Telecommunications and Signal Processing, 2003[6] A. Kuki, Tools for Performance Evaluation and Modeling in Higher Education of Informatics, Informatics in the
Hungarian Higher Education, Debrecen, Hungary 70-77, 2010[7] M. M. G. Rashed, M. Kabir, A Comparative Study of Different Queuing Techniques in VoIP, Video Conferencing
and FTP, Daffodil International University Journal of Science and Technology, Volume 5, Issue 1, January 2010[8] S. Akhtar, E. Ahmed, A. k. Saka, K. S. Arefin Performance Analysis of Integrated Service over Differentiated Service
for Next GenerationInternet, c©JCIT, ISSN 2078-5828 (print), ISSN 2218-5224 (online), Vol. 1, Issue 1, 2010[9] S. Farhangi, S. Golmohammadi, A comparative study between combination of PQ and MWRR Queuing techniques
in IP network based on OPNET, Advances in Computer Science and its Applications, Vol. 1, No. 1, c©World SciencePublisher, United States, March 2012
[10] Sz. Szilagyi, B. Almasi, A Review of Congestion Management Algorithms on Cisco Routers, Journal of ComputerScience and Control Systems, University of Oradea, Vol.5, Nr.1, ISSN 1844-6043, 2012
[11] A. S. Sethi, V.Y. Hnatyshin, The Practical OPNET User Guide for Computer Network Simulation, CRC PressTaylor & Francis Group, NW, 2012
[12] L. L. Peterson, B. S. Davie, Computer Networks: A System Approach - Network Simulation Experiments Manual,3rd Edition, c©Elsevier Inc., 2011
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Figure 4 VoIP: Traffic delay
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Figure 5 VoIP: Traffic delay for PQ, WFQ, CBWFQ and LLQ
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[13] P. K. Verma, L. Wang, Voice over IP Networks - Quality of Service, Pricing and Security, Lecture Notes in ElectricalEngineering, Vol. 71, Springer, 2011
[14] B. Almasi, A. Harman, An Overview of the Multipath Communication Technologies, Proceedings of the Advances inWireless Sensor Networks (AWSN), Debrecen, Hungary, 2013 (to appear)
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Figure 6 VoIP: Traffic jitter
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Figure 7 VoIP: Traffic jitter for PQ, WFQ, CBWFQ and LLQ
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Tool supported analysis of queueing systems with Future Internet applications
Janos Sztrik and Tamas BerczesFaculty of Informatics, University of Debrecen, Hungary
[email protected], [email protected]
Abstract. This paper deals with the role of performance modeling tools for investigation of queueing
systems. Advantages and drawbacks are considered when modeling and analysis issues are treated. For
illustration the authors introduce 4 major tool developer centers. Due to the growing importance in
practical applications, for example in Future Internet engineering, the reliability analysis of finite-source
retrial queueing system is presented by using the MOdeling, Specification and Evaluation Language
(MOSEL) software. A sample numerical example is given demonstrating the effect of failure of server
on the mean response time of sources. Finally, investigating this model benchmarks to compare the
efficiency of MOSEL and PRobabIliStic Model Checker (PRISM) tools concerning execution time, model
construction time, model checking time are carried out.
1.1. Some recent modeling tools. In the following 4 major tool developer centers are intro-duced briefly.
Tools at Faculty of Informatics, University of Dortmund, Germany This traditionallyfamous center has developed several software packages which can be downloaded from the site:http://ls4-www.informatik.uni-dortmund.de/tools.html.
Parallel to their methodological work the center continuously developed and used tools for performanceevaluation and performability. Their intention is to provide facilities for a model description close tothe original system specification and hiding details of the analysis techniques. Such tools map themodel specification automatically to an analyzable model.
Mobius Tool Mobius is a software tool for modeling the behavior of complex systems. It is oneof the major research projects of the Performability Engineering Research Group (PERFORM) inthe Coordinated Science Laboratory at the University of Illinois at Urbana-Champaign, USA. Manyadvanced modeling formalisms and innovative and powerful solution techniques have been integratedin the Mobius framework.The package can be found at http://www.mobius.uiuc.edu/.
MOSEL ToolPerformance modeling tools usually have their own textual or graphical specification language
which depends largely on the underlying modeling formalism. MOSEL ( MOdeling,Specificationand Evaluation Language) tool, developed at the University of Erlangen, Germany, is based on thefollowing idea: Instead of creating another tool with all the components needed for system description,state space generation, stochastic process derivation, and numerical solution, it focuses on the formalsystem description part and exploit the power of various existing and well tested packages for thesubsequent stages. In order to reuse existing tools for the system analysis, the environment is equippedwith a set of translators which transform the MOSEL model specification into various tool-specificsystem descriptions. For further details see [2].MOSEL-2 provides means by which many interesting performance or reliability measures and thegraphical presentation of them can be specified straightforwardly. All information can be found athttp://www4.informatik.uni-erlangen.de/Projects/MOSEL/.
PRISM ToolThe PRobabIliStic Model checker PRISM provides a high-level modeling language for describing
systems that exhibit probabilistic behavior, with models based on continuous-time Markov chains(CTMCs) as well as discrete-time Markov chains (DTMCs) and Markov decision procedures (MDPs).For specifying system properties, PRISM uses the continuous stochastic logic (CSL) for CTMCs andprobabilistic computation tree logic (PCTL) for DTMCs and MDPs, both logics being extensions ofcomputation tree logic (CTL), a temporal logic that is used in various classical model checkers forspecifying properties. For further details, see for example [7].The package can be downloaded from http://www.prismmodelchecker.org.
1.2. Finite-source retrial queues with a single server subject breakdowns and repairs.Due to the growing importance of using retrial queueing systems for modeling complex communication
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systems in Future Internet applications we show an example for using MOSEL to analyze a retrialqueueing system with the following assumptions. Consider a single server queueing system, wherethe primary calls are generated by K, 1 < K <∞ homogeneous sources. The server can be in threestates: idle, busy and failed. If the server is idle, it can serve the calls of the sources. Each of thesources can be in three states: free, sending repeated calls and under service. If a source is free attime t it can generate a primary call during interval (t, t + dt) with probability λdt + o(dt). If theserver is free at the time of arrival of a call then the call starts to be served immediately, the sourcemoves into the under service state and the server moves into busy state. The service is finished duringthe interval (t, t+ dt) with probability µdt+ o(dt) if the server is available. If the server is busy atthe time of arrival of a call, then the source starts generation of a Poisson flow of repeated calls withrate ν until it finds the server free. After service the source becomes free, and it can generate a newprimary call, and the server becomes idle so it can serve a new call. The server can fail during theinterval (t, t+ dt) with probability δdt+ o(dt) if it is idle, and with probability γdt+ o(dt) if it is busy.If δ = 0, γ > 0 or δ = γ > 0 active or independent breakdowns can be discussed, respectively. If theserver fails in busy state, it either continues servicing the interrupted call after it has been repaired orthe interrupted request transmitted to the orbit. The repair time is exponentially distributed with afinite mean 1/τ . If the server is failed two different cases can be treated. Namely, blocked sources casewhen all the operations are stopped, that is neither new primary calls nor repeated calls are generated.In the unblocked (intelligent) sources case only service is interrupted but all the other operations arecontinued (primary and repeated calls can be generated). All the times involved in the model areassumed to be mutually independent of each other. More information about retrial queueing systemscan be read, for example in [1], [4], [5, 6].
For illustration our main objective is to demonstrate how the mean response time of calls dependon server’s failure rates. To achieve this goal MOSEL is used to formulate and solve the problem.
The system state at time t can be described by the processX(t) = (Y (t);C(t);N(t)), where Y (t) = 0 if the server is up, Y (t) = 1 if the server is failed, C(t) = 0 ifthe server is idle, C(t) = 1 if the server is busy, N(t) is the number of sources of repeated calls at time t.
Because of the exponentiality of the involved random variables this process is a Markov chain with afinite state space. Since the state space of the process (X(t), t ≥ 0) is finite, the process is ergodicfor all reasonable values of the rates involved in the model construction, hence from now on we willassume that the system is in the steady state.
We define the stationary probabilities:
P (q; r; j) = limt→∞
P (Y (t) = q, C(t) = r,N(t) = j),
q = 0, 1, r = 0, 1, j = 0, ...,K∗,
where K∗ =
K − 1 for blocked case,K − r for unblocked case.
The advantage of using tools is that we do not have to deal with the numerical problems of findingthe steady-state probabilities. We have to concentrate how to formulate the problem by the help of adescribing language ( usually Petri nets ) and then the whole process is automatic. In our case, thestates and transition rates of the continuous time finite state Markov chain is constructed and thestationary distribution is calculated by the help of a so-called solver. The problem arising in practicalproblems is the state space explosion which causes numerical problems due to the large number ofunknowns. It should be noted that there is no closed form solution to this problem. However, asusual an algorithmic approach could be used to get the steady-state probabilities, see [1],[8] . Thismeans an extra work in programming and displaying the results graphically which is in our case is anbuilt-in module that is why we can omit it.
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1.3. Numerical examples. We used the tool SPNP which was able to handle the model withup to 126 sources. In this case, on a computer containing a 1.1 GHz processor and 512 MB RAM,the running time was approximately 1 second. A more detailed investigation was published in [3]illustrating other effects as well.
Figure 1 E[T ] versus server’s failure rate
In Figure 1 we can see the mean response time for the reliable and the non-reliable retrial systemwhen the server’s failure rate increases. The input parameters are collected in Table 1.
K λ µ ν δ, γ τFigure 1 6 0.8 4 0.5 x axis 0.1
Table 1 Input system parameters
CommentsIn Figure 1, we can see that in the case when the request returns to the orbit at the breakdown
of the server, the sources will have always longer response times. Although the difference is notconsiderable it increase as the failure rate increase. The almost linear increase in E[T ] can be explainedas follows. In the blocked (non-intelligent) case the failure of the server blocks all the operations andthe response time is the sum of the down time of the server, the service and repeated call generationtime of the request (which does not change during the failure) thus the failure has a linear effect onthis measure. In the intelligent case the difference is only that the sources send repeated calls duringthe server is unavailable, so this is not an additional time.
Benchmarks In the following we give some comparisons between the MOSEL and PRISM toolsshowing how the number of terminals (NT) influences the execution time and total execution time.
The following preliminary conclusions can be drawn from benchmark:
• The execution times of the MOSEL system almost stay constant independently of NT ;
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Figure 2 Execution Time
• The execution times of the PRISM system increase rapidly with the increase of NT.• The model construction time in PRISM dominates the execution time rather than the model
checking time.
While MOSEL is thus more efficient for smaller models, with PRISM also larger models can beanalyzed. Furthermore, once a PRISM model is constructed, it can be arbitrarily often model checkedwith different parameter values. For such scenarios, the model checking time is more relevant thanthe model construction time.
Acknowledgment: This research was partially granted by the Hungarian Science and TechnologyFoundation, Hungarian- French Bilateral Cooperation under grant TeT 10-1-2011-0741, FR- 25/2010.
The publication was also supported by the TAMOP-4.2.2.C-11/1/KONV-2012- 0001 project. Theproject has been supported by the European Union, co- financed by the European Social Fund.
Bibliography[1] Artalejo, J.R. and Gomez-Corral, A., Retrial Queueing Systems, Springer, 2008[2] Begain, K. and Bolch, G. and Herold, H., Practical performance modeling, application of the MOSEL language,
Kluwer Academic Publisher , 2001[3] Berczes, T. and Guta, G. and Kusper, G. and Schreiner, W. and Sztrik, J., Evaluating a probabilistic model checker
for modeling and analyzing retrial queueing systems, Annales Mathematicae et Informaticae, Vol. 37, 51-75 (2010)[4] Berczes, T. and Orosz, P. and Moyal, P. and Limnios, N. and Georgiadis, S. and Sztrik, J., Tool supported modeling
of sensor communication networks by using finite-source priority retrial queues, Carpathian Journal of Electronicand Computer Engineering, Vol. 5, 13-18 (2012)
[5] Do, V.T. , An efficient solution to a retrial queue for the performability evaluation of DHCP , Computers & OR,Vol. 37, 1191-1198 (2010)
[6] Do, V.T. , A new computational algorithm for retrial queues to cellular mobile , Computers & Industrial Engineering,Vol. 59, 865-872 (2010)
[7] Kwiatkowska, M. and Norman, G. and Parker D., PRISM: Probabilistic Model Checking for Performance andReliability Analysis, ACM Sigmetrics Performance Evaluation, Vol. 36, 40-45 (2009)
[8] Lakatos, L. and Szeidl, L. and Telek, M., Introduction to Queueing Systems with Telecommunication Applications,Springer, 2012
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Resource-Oriented Applications in Product Data Management
Cezar Toader, Rita Toader and Corina RadulescuDepartment of Economics, Faculty of Sciences, Technical University of Cluj-Napoca, North University Centre of Baia Mare, Romania
[email protected]; [email protected]; [email protected]
Abstract.The increasing importance of better customization of industrial products has led to development
of configurable products. Description and management of a large variety of products within a single data
model is challenging and requires a solid conceptual basis. This paper refers to important aspects of the
evolution of Web applications architecture, according to the evolution of the Web, through creation of
new levels of abstracting, while a special importance to scalability and adaptability was given. Due to
a growing importance given to resource-oriented Web services, in the last years, this paper brings into
discussion the principle of organizing the algorithmic resources in multi-level hierarchy and the principle
of uniform access to resources. Finally, in order to implement these principles, the author promotes an
architectural model of Web Applications.
1.1. Introduction. Product families, product configuration and product data management areresearch areas with great deal of practical importance for traditional products, i.e., mechanical andelectronic products. A configurable product, or a product family, is such that each product individualis adapted to the requirements of a particular customer order on the basis of a predefined configurationmodel, which describes the set of legal product variants.
One challenge is to find the correct concepts for modeling configurable products so that thedescriptions can be kept up to date as the product evolves. The challenge has not been adequatelyanswered by the research in product configuration, product modeling standards or commercial productdata management (PDM) systems [3].
Configuration modeling does not fit nicely into the data modeling view for various reasons. Firstly,configuration models need new concepts, such as has-part relation with alternative parts, not availableas traditional data modeling concepts. Secondly, as companies develop their products, product familydescriptions are constantly changed. Thirdly, individuals of configurable products have long lifetimesand histories of their own. They evolve independently since customers may change their products asthey please.
1.2. Product configuration concepts. Configurable products clearly make a separation be-tween the process of designing a product family and the process of generating a product individualaccording to the product configuration model. This places configurable products in between massproducts and one-of-a-kind products by enabling customer specific adaptation without losing allthe economic benefits of mass-products. Knowledge based systems for configuration tasks, productconfigurators, have recently become an important application of artificial intelligence techniques forcompanies selling products adapted to customer needs [5].
The difficulties in managing configuration models are widely recognized, the vast majority of themodels ignore all aspects related to the evolution of configuration models.
Versionis a concept for describing the evolution of products. Versions typically represent theevolution of a generic object that, in turn, has a set of versions. A generic object is sometimes alsocalled a generic version or generic instance. There can be two kinds of component references toversions: statically bound and dynamically bound [6].
Schema evolution is a relevant issue for databases. The approaches to schema evolution can beclassified to filtering, persistent screening and conversion. In filtering, a database manager needs toprovide filters so that an operation defined on a particular type version can be applied to any instanceof any version of the type [4].
1.3. Resource Oriented Architectures. The concept of Resource Oriented Architectures(ROA) gradually developed and some authors made several comparisons between these architec-tures and those based on services or those based on activities. Resource oriented architecturesdeveloped based on the concepts of: resources, their identification, their representation, and linksbetween them.
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Figure 3 Layered architecture of a distributed application
The technology of Uniform Resource Identifiers is fundamental for the Web because allows theinterconnection of Web resources. The principles that URI technology is based on are described byTim Berners-Lee back in 1996, [1]. Resource oriented architectures follow several principles, describedbelow:
• Addressability. A Web application based on ROA exposes an URI for every resource.• Statelessness. Every HTTP request is completely isolated from the other requests.• Connectedness. The resources have to be interconnected in their representation and, as a
consequence, a Web service can be put in different states by calling different links.• Uniform interfaces to resources. The access to any Web resource can be made using
standardized HTTP methods: GET, PUT, POST, DELETE, HEAD, and OPTIONS.
Two important characteristics must be emphasized here: the way a resource is addressed, and thelack of state information between HTTP requests. The Web was developed by creating new levels ofabstracting, but its initial simplicity was necessary at that moment. The subsequent developmentof the Web and development of Web services required a special attention given to scalability andadaptability.
When Fielding published his doctoral thesis Architectural Styles and the Design of Network-basedSoftware Architectures, he promoted a set of principles defining a Web-based architectures programmingstyle named REST (Representational State Transfer), [5]. Since then, the architectures following thoseprinciples have got the attribute RESTful.
A large Web application having a modularized interface, can be as shown in Fig.1. Differentareas in application interface are, basically, interfaces of specialized task-oriented applications runningbehind the scene. On the highest level, these specialized Web applications are waiting for requestsfrom the network. In order to fulfill the requests, these applications need to access different kind ofresources: static or dynamic HTML, static XML, Web services based on XML, etc.
According to their role in a complex application, several layers can be defined in order to groupthese resources. Starting from top to bottom, it is necessary to define these layers: Task Layer, EntityLayer, and Utility Layer, as we can see in Figure 1.
The highest level of the proposed architecture is Task Layer. It contains several Web applicationswhich can be called by external software, for example by a Web browser. In order to fulfill specifictasks, an application on this level executes a set of operations:
• it builds the URI of requested resource according to the established hierarchy;• it accepts the redirection toward a certain resource situated on Entity Layer;• it gets a representation of data, usually in a form of XML file;• it builds the response in HTML format, according to a specific template.
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Figure 4 RESTful Multilayer architecture of a Web application
The Web applications situated on the higher level are oriented, by their design, to specific tasks.Their reusing potential for other tasks is relatively low. According to the request made by the client,the applications on the Task Layer access resources situated on Entity Layer.
The Entity Level is subordinated to the application on the Task Layer. This level contains varioussoftware modules, specifically designed for the application, which are considered Web resources for thehigher level. The resources on the Entity Level can deal with RPC-style requests. Modern applicationsuse Web services in order to have a uniform type of access to data. Web services offer datasets inXML format. Web resources on Entity Layer request data from the Web services offered by the lowerlevel, Utility Layer. Applications having such complex architecture are often developed during manyyears, by many programmers, and using different technologies. It is very likely that these old resourcesare RPC-style. If so, the applications situated on the highest level should use RPC-style URIs insteadof REST-style URIs.
1.4. Restful multilayer architectures. In this paper, the authors propose a solution for thefollowing issue: how to modify the application architecture in order to permit the highest levelapplications to use RESTful URIs and, without their knowledge, the lowest level resources to be calledusing RPC-style URIs?
One solution of this problem which consists in creation of a specific method to transform theRPC-style URIs in REST-style URIs, with respect of existing resource hierarchy.
The proposed solution consists in inserting a new adapting layer between Task Layer and EntityLayer. Hence a new architecture is created where the highest level applications can use only REST-styleURIs to access all resources on the lowest level, no matter that they are REST-style or RPC-style.One appropriate name is RESTful Multilayer Architecture [7].
The goal of RESTful Multilayer Architecture is to permit the client applications to use theREST-style URIs when accessing both, the new REST-style resources, and the existing old RPC-styleresources, without the need to redesign these resources, as it can be seen in Fig.2.
This adaptation of RESTful requests sent by client applications and arrived on Task Layer, to thereal resource identifiers used on Entity Layer is made by Resource Dispatcher.
Within this architecture, Resource Dispatcher can be treated as a new entity called URI AdaptingLayer [7]. Important actions take place on URI Adapting Layer:
• a REST-style request, pointing to a resource situated on a lower level, is received;
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• the received URI is parsed and main entities are identified (elements, methods);• a new request is build, either RPC-style or REST-style;• the caller is redirected using the new URI.
The client application has no knowledge about these actions. The Resource Dispatcher operationsare influenced by the existing resource hierarchy within the distributed application. Many resourcescalled before in different styles can be now called according to a uniform identification principle.
The goal is to permit the client applications to use only REST-style identifiers when they sendrequests to Web modules situated on Task Layer. The existence of new URI Adapting Layer permitsthe implementation of two very important ROA principles:
• The principle of resource addressability;• The principle of uniform interfaces to resources.
1.5. Final conclusions. The concepts used in traditional products modeling seem to be suitableto product families modeling as well. Utilizing the concepts from traditional product families andadapting them for representing the architecture and variation of software product families, could leadto concise and manageable models.
It is safe to say that methods for modeling and management of variation of traditional products aremore advanced than that of software product families. Nevertheless, two major areas were identifiedfor transferring results from software product families to traditional configurable products.
This paper describe one possible approach of the problem of resources organization within amodern distributed application, supporting Product Data Management implementation. Beyond that,this paper shows a way of integration the old RPC-style resources in the new REST-style applications,without heavy redesign of entire applications.
The authors propose a modern way to design and organize the algorithmic resources of Webapplications in order to implement the REST architectural principles, which further leads to abetter structure of resources, to an increased degree of uniformity in resources addressability, and toadvantageous utilization of HTTP.
Bibliography[1] Berners-Lee, T., Universal Resource Identifiers - Axioms of Web Architecture, Accessible at:
http://www.w3.org/DesignIssues/Axioms.html, 1996.[2] Fielding, R.T., Architectural Styles and the Design of Network-based Software Architectures, PhD Dissertation, USA,
University of California, Irvine, 2000.[3] Mannisto, T., A conceptual modeling approach to product families and their evolution, Doctoral thesis, Helsinki
University of Technology, 2000.[4] Mannisto, T., Peltonen, H., Sulonen, R., View to product configuration knowledge modeling and evolution,
Configuration-papers from the 1996 AAAI Fall Symposium, AAAI Press, 1996.[5] Petrovan, A., Toader, C., Modern Concepts in Product Data Management, International Multidisciplinary Conference,
7th Edition, Univ. de Nord Baia Mare, 2007, pp. 609-612.[6] Tiihonen, J., Soininen, T., Product Configurators Information system Support for Configurable Products, TAI
Research Centre and Laboratory of information Processing Science, Product Data Management Group, HelsinkiUniversity of Technology, 1997.
[7] Toader, C., RESTful multilayer architectures for Web-based learning systems, Creative Mathematics and Informatics,nr.18, pp. 208-216, 2009.
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Early diagnosis of Stroke: bridging the gap through wearable sensors and computational models
Jose R. Villar1, Silvia Gonzalez2, Javier Sedano2, Camelia Chira2 and Jose M. Trejo3
1 Computer Science Department, University of Oviedo, Spain2 Instituto Tecnologico de Castilla y Leon, Spain3 Neurology Department of the Burgos Hospital, Spain
[email protected], [email protected], [email protected], [email protected], [email protected]
Abstract. Stroke is a cerebrovascular disease defined as a circulatory disorder that causes either atemporary or a permanent disorder of one or more areas of the brain. The most common symptom ofstroke is loss of the ability to move voluntarily the limbs, either left, right or both. The hand is usuallymore severely affected compared to the leg [6, 9]. For the more prevalent cerebral infarction (85% ofthe cases) there existsa thrombolytic drug that disrupts the thrombus occluding a cerebral artery. Inthe first one and a half ”golden hour”, one out of three patients treated will recover to his/her previouslife.
Unfortunately, only a minority (5-15% of people suffering a stroke) arrive early enough to actuallyreceive the treatment [2, 7]. Thus, a device that helps people notifying a rather possible stroke episodecan make a big difference in reducing death, disability and health costs in thousands of patients eachyear. In addition, the algorithms to be implemented should be embedded in real hardware platforms sothey can be introduce in wearable products. In spite of the increasing computing power and internalresources, the algorithms still have to be as light as possible and should constrain to scenarios of reducedpower consumption and small memory capacity.
In this study, a new specific algorithm for Human Activity Recognition (HAR) is presented and
compared with a well-known HAR technique [3, 13]. Moreover, a simple algorithm for generating
alarms due to possible stroke cases is presented. Furthermore, evidence of more complex models are
provided and left as future work. The obtained results are expected to be included in a specific device
for early stroke diagnosing.
Acknowledgments. This research has been supported through the Spanish Ministry of Science andInnovation TIN2011-24302 project.
1.1. Introduction. As stated in [5], stroke is a cerebrovascular disease defined as a circulatorydisorder that causes either a temporary or a permanent disorder of one or more areas of the brain. Asthe author stated, ”Stroke is the second most common cause of death and major cause of disabilityworldwide. Because of the ageing population, the burden will increase greatly during the next 20years, especially in developing countries.” Paralysis is the most common symptom of stroke, speciallythe paralysis of the limbs. The paralysis could be either partial -one side of the body- or total -bothsides-, and the upper limbs are usually more severely affected than the lower limbs [6, 9].
Cerebral infarction makes up to around 85% of all strokes [1, 2]. For the rest 15% of cerebralhemorrhages there is no approved treatment, but for the more prevalent cerebral infarction, thereis one that can make a big difference: a thrombolytic drug that disrupts the thrombus occluding acerebral artery. If successful, cerebral tissue will recover and so will function, but that depends onhow fast the treatment is given. In the first one and a half ”golden hour”, one out of three patientstreated will recover to his/her previous life.
In spite of this golden hour drug, only a minority (5-15% of people suffering a stroke) arrive earlyenough to actually receive the treatment [2, 7]: the main concern is related with the identification ofthe stroke episode by the relatives or because the episode occurs when the subject is alone. Thus,a device that helps people notifying a rather possible stroke episode can make a big difference inreducing death, disability and health costs in thousands of patients each year.
In this study a method for the early diagnosing of the stroke is introduced. Up to our knowledge,this is the very first study that propose low cost wearable sensors in the identification of this disease.For doing so, two wearable triaxial accelerometers -one in each wrist- would allow to identify the mostremarkable stroke symptoms. The method includes a human activity recognition (HAR) method and,afterwards, a stroke paralysis alarm generator. As these algorithms should run in micro controllersthe lowest the computational costs the better. The improvements found in this study include a novellight HAR method and the algorithm for early stroke diagnosing. Additionally, it is worth mentioningthe proposed adaptation of well-known time series representation for the focused problem.
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This study is organized as follows. Next section outlines the most remarkable behaviour of thesubjects suffering a stroke episode. Then, the time series representation used in this paper are brieflydescribed. Sect. 1.4 deals with the HAR method proposed in this study, while Sect. 1.5 presents thealgorithm for alarm generation. These two latter sections also show experiment results and discussion.Finally, some conclusions and future work are included as a final section.
1.2. A brief description of Stroke’s paralysis symptoms. The most common symptom ofstroke is loss of the ability to move voluntarily the limbs, either left, right or both. The hand is usuallymore severely affected compared to the leg. In fact, arm paralysis is so common in stroke that it isused in scales by paramedics such as the Prehospital Cincinatti Stroke Scale. It has also been includedin the FAST acronym, in public campaigns aimed at stroke early recognition (FAST stands for Facedrooping, Arm paralysis, Speech difficulties, Time to act) [9]. Hand paralysis is also non-subjective soit can be monitored by a movement-detection device.
If we pay attention to these symptoms, they are usually described as an asymmetrical movementsbetween both sides of the subject body: one part moves as usual as possible while the other is ratherstill. In addition, the main symptom is the collapse of the subject: this may occur after the subjecthad sat in a chair or fell in a bed, but also the subject might suffer a falling and then a collapse.Therefore, knowing the current human activity (cHA) could allow to differentiate between the collapse,falling or body asymmetries.
In addition, each combination of these possible remarkable states and the cHA would require itsco-occurrence during a different amount of time. We must differentiate between the lack of movementin one part of the body when walking, reading or resting -whether it can be having a nap or sleepingor a collapse-; each of these combinations will take a different time to be consider worth alarming.
1.3. A light introduction to PAA and SAX. As detailed in [4], many techniques have beenpresented in the literature for time series (TS) representation and distance measuring, the PiecewiseAggregate Approximation (PAA) [11] and Symbolic Aggregate approXimation (SAX) [12] amongothers. These two latter have shown the best performance on aperiodic TS. As far as the availabledata from human activity is rather aperiodic, these two techniques are outlined.
Let X be a TS of length n previously normalized to zero mean and standard deviation of one.
Let the desired representation domain dimension w. PAA finds the w size vector Xi = [x1, . . . , xw]
calculated as xi = wn
∑ nwi
nw
(i−1)+1 xj : the overall process consists in splitting the X in w intervals and
each xi computed as the mean value within the corresponding interval.Additionally, if the alphabet size is fixed to as, SAX divides the domain of the values of the X in as
statistically equiprobable intervals taking advantage of the previous data normalization, each intervalis assigned with one symbol. Whenever a PAA component falls within an interval the correspondingsymbol is assigned in the SAX vector component. Furthermore, SAX also provides with a distancemeasure among SAX vectors.
1.4. A light human activity recognition method. Using triaxial accelerometers inducesthat the measurement obtained from the sensors should be decomposed in the gravity acceleration(G) and the body acceleration (BA) -which is due to the human movement, bxi , byi and bzi -. Let
BAi =√bxi
2 + byi2
+ bzi2 measured for each sample of the TS.
In our approach, we make use of two wrist bracelets -each one with a triaxial accelerometersampled at 16 Hz-. Let mBA and sBA be the mean and standard deviation of the movements duringactivities of daily living of the subject, both calculated by means of a initial test.
The algorithm proposed in this study for HAR is shown in Algorithm 1, though for the sake ofbrevity it is shown rather schematically; our real implemented algorithms are a bit more complex. Thereare some issues that need further study, like the learning of the membership functions and its tuningto the focused subject as well as the method for measuring similarities between TS representation.Interestingly enough, the computational cost and resources needed for implementing this algorithmare kept rather small, which is one of the main enhancement of this technique. The last part of thealgorithm is related with the stroke episode alarm generation.
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Algorithm 1 Simplified SAX based HAR algorithm: µA/A, ∀ARequire: X, a normalized TS of size n using mBA and sBAEnsure: Computes the possible activities and their certainties
Determine X = SAX(X)for each A ∈ Registered Activities do
for each Ymov ∈ RegisteredActivityMovement(A) do
Compute similarity between X and Ymov → simXY
Update the certainty of X of class A according to simXYend for
end forif Resting State is believed then
Determine the resting activity level HIGH, LOW, NONEIncrement the corresponding counters
end if
1.5. A simple algorithm for stroke diagnosing. Similarly to the previous algorithm, thisstudy proposes the use of the SAX representation and some quite simple algorithms to detect anomaloushuman behaviors. The TS from both bracelets are used in this case, and the state of resting should bepreviously detected independently for each hand. In case of resting state, the BA is normalized usingthe muRBAh and sRBAh, the mean and standard deviation of the signal of the BA when the subjectis resting; the h subindex is related with the hand -left or right-. These values should be calculated inan initial test.
Algorithm 2 briefly outlines the propose approach; as in the former section, the algorithms arevery roughly explained due to the space limitations. Firstly, some counters and the current restinglevel are determined in the previous algorithm. Afterwards, the similarity of the signal from eachhand is compare with the typical sequences of inactivity. In case that the total inactivity keeps goingon, the certainty of generating the corresponding alarm for the partial or total paralysis, and even fora falling detection alarm.
Algorithm 2 Simplified Alarm Generation Algorithm
Require: Xh, a normalized TS of size n with mRBAh and sRBAh, ∀h ∈ left, rightRequire: STATES and CERTAINTIES of the subjectRequire: RESTING LEVEL: HIGH,LOW,NONEEnsure: Generates the suitable alarms
Determine Xh = SAX(Xh)for each Ymov ∈ RegisteredAlarmSequences do
Compute similarity between Xh and Ymov → simXYif simXY is HIGH then
Mark the detection of a inactivity, fallingend if
end forUpdate time of inactivity countersif time of inactivity is HIGH for the corresponding RESTING LEVEL or a falling has been detectedthen
Generate the corresponding alarmend if
1.6. Experimentation and further discussion. Experiments carried out in this very prelimi-nary study include two young subjects. Ten runs of the well-known stroke patients rehabilitation test(for short, SRT) [10]. Moreover, more tests were carried out with the subjects sleeping during a night.Neither tabular nor figures can be included in this extended abstract due to the length restrictions.We test to discriminate between resting and walking and the results were really impressive, with aperfect discrimination of the class, though this specific problem by itself is not very complex.
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The algorithm for alarm generation seems to be coherent with the specifications given by themedical staff, though more work is needed to identify the sequences for identifying activity whileresting. Furthermore, the results shows that the algorithms work as expected though the differentthreshold and the simplifications as well as the distance measure should be greatly improved.
1.7. Conclusions and future work. This study proposes two novel algorithms: a former onefor human activity recognition, the latter for stroke early diagnosing. These algorithms require ratherlow both computational costs and resources. Obtained results are really promising, even with thesimplifications of using only thresholds. Nevertheless, there are still plenty of research to carry out.Firstly, several intelligent algorithms should be designed for learning the different simplified parameters.Secondly, the algorithms should be refined. Thirdly, the experimentation should include the higherobjective population as possible, as well as should include young people. We do expect to start theexperiments by the final quarter of this year.
Bibliography[1] R. D. Adams., Principles of Neurology, McGraw Hil, 1997[2] H. P. Adams, G. del Zoppo, M. J. Alberts, D. L. Bhatt, L. Brass, A. Furlan, R. L. Grubb, R. T. Higashida, E. C.
Jauch, C. Kidwell, P. D. Lyden, L. B. Morgenstern, A. I. Qureshi, R. H. Rosenwasser, P. A. Scott and E. F.M.Wijdicks. Guidelines for the Early Management of Adults With Ischemic Stroke, Stroke, 38(2007), 1655-1711
[3] A. Avarez-Alvarez, G. Trivino, O. Cordon., Body posture recognition by means of a genetic fuzzy finite state machine,IEEE 5th International Workshop on Genetic and Evolutionary Fuzzy Systems (GEFS), IEEE Conference Publisher,Paris France, (2011), 409-413
[4] H. Ding, G. Trajcevski, P. Scheuermann, X. Wang and E. Keogh.Querying and mining of time series data: experimentalcomparison of representations and distance measures, Proc. VLDB Endow. 1:2 (2008), 1542–1552
[5] G. A Donnan, M. Fisher, M. Macleod and S. M. Davis- Stroke, The Lancet, 371:9624 (2008), 1612-1623[6] A.D. Dromerick and S. A. Khader., Medical complications during stroke rehabilitation, Advances in Neurology, 92
(2003), 409-413[7] E. Duarte, B. Alonso, M.J. Fernandez, J.M. Fernandez, M. Florez, I. Garcıa-Montes, J. Gentil, L. Hernandez, F.J.
Juan, J. Palomino, J. Vidal, E. Viosca, J.J. Aguilar, M. Bernabeu, I. Bori, F. Carrion, A. Deniz, I. Dıaz, E. Fernandez,P. Forastero, V. Inigo, J. Junyent, N. Lizarraga, L. Lopez de Munaın, I. Manez, X. Miguens, I. Sanchez and A. Soler.Stroke rehabilitation: Care model, Rehabilitacion, 44:1 (2010), 60-68
[8] F.J. Fernandez-Gomez, F. Hernndez, L. Argandoa, M.F. Galindo, T. Segura and J. Jordn.Pharmacology of neuropro-tection in acute ischemic stroke, Rev Neurol. 47:5 (2008), 253-60
[9] C.S. Hogdson. To FAST or not to FAST, Stroke, 38 (2007), 2631-2632[10] K. HollandsWhole body coordination during turning while walking in stroke survivors, School of Health and Population
Sciences. Ph.D. thesis, University of Birmingham (2010)[11] E. Keogh, K. Chakrabarti, M. Pazzani and S. MehrotraDimensionality Reduction for Fast Similarity Search in
Large Time Series Databases Journal of Knowledge and Information Systems 3 (2000), 263-286[12] J. Lin, E. Keogh, L. Wei and S. Leonardi.Experiencing SAX: a Novel Symbolic Representation of Time Series, Data
Mining and Knowledge Discovery 15:2 (2007), 107-144[13] S. Gonzalez, J. R. Villar, J. Sedano and C. Chira. A preliminary study on early diagnosis of illnesses based on
activity disturbances, Distributed Computing and Artificial Intelligence, 10th International Conference, Berlin, 2013
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Using statistical data to evaluate the strategic efforts of companies
Cristian Vele, Cristian Anghel and Rita ToaderTechnical University of Cluj Napoca, North University Center at Baia Mare, Romania
cristian [email protected]
Abstract. Why some companies can manage to grow and develop, while other companies fail and go
bankrupt? What is the secret? The answers reside in the strategic efforts of every company and in
their specific actions and decision taken in order to overpass their competitors and become the market
leader. Following this, the present article whishes to present the main strategies used by companies in
the construction industry and analyze them with the help of specialized statistical models.
1.1. Introduction. Choosing the most efficient strategy represents, from many points of view,the central elements of strategic management, the main concern being the companys future and theactions through which will be able to face the many external influences. Also, it is very important, inorder to ensure their long term sustainability, for strategies to be realistic, not only in relation to theirexternal environment, but also with their internal capabilities (Johnson & Scholes, 1999: 255, Dikmenet. Al, 2009, 291). In the opinion of Aras and Crowther (Aras & Crowther, 2010: 568) there arefour major aspects of sustainability which need to be recognized and analyzed: (1) the influence onsociety, more specifically the companys impact in terms of social contracts, and also the influence ofits stakeholders, (2) the impact on the environment, which is comprised of all the companys actions onthe geophysical environment, (3) the corporate culture, comprised of the relations between employeesand (4) finances, evaluated based on the financial results registered by the company.
In order, for a company, to choose the best strategy, first of all it must understand the advantagesand disadvantages of every strategic option. That is why, the strategic planning process must beexplicit, transparent and participative (Karnani, 2008: 31) and also it must be focused on increasingthe organizational performance (Grant, 2003: 515). One of the most efficient models to manage thestrategic planning process is based on three major categories of factors: the structural conditions, inwhich the company is conducting its business, its resources and capabilities and its strategic experience(Kim & Mauborgne, 2009: 74). As a consequence, the strategic process is represented by thosedecisions related to (Finlay, 2000: 341): product portfolio, strategic positioning, necessary resources,ways to access the resources and financing sources.
The first step in formulating the competitive strategy is to establish what are the long termgoals that need to be met. Starting from the fact that short term maximization of profit does notensure long term sustainability and development, companies must pay great attention to establishingstrategic goals in relation with the following elements (Pearce & Robinson, 2007: 164): profitability,productivity, competitive position, employee development, employee relations, technological leadershipand social responsibility.
In order to be successful, a strategy must be formulated in a very simple and clear manner, inorder for every employee to be able to understand it. Thus, the formulation of a competitive strategymust be comprised of three major parts:the objective (where do you want to arrive), the purpose (theindustry in which the company is activating) and advantage (how will you reach the objective) (Collins& Rukstad, 2008: 84 85). Also, the strategies need to be formulating in accordance with the differentorganizational levels: at the corporate level, business unit level and functional level.
1.2. Empirical research regardubg the strategies used by companies in the construc-tion undustry. Our research is focused on the construction industry and it is based on the answersgiven by 220 companies in the North Western region of Romania, which is comprised of the countiesof Bihor, Bistrita Nasaud, Cluj, Maramures, Satu Mare and Salaj. The main goal of our researchis to identify and analyze the efforts of companies in the construction industry to gain sustainablecompetitive advantages. In order to achieve this, a questionnaire, containing questions regarding theimplemented strategies, was given to construction companies to be filled. The answers were gatheredand, by using specialized statistical software, were analyzed in order to identify the importance givenby companies in the construction industry to specific competitive strategies, such as: the diversificationof products and services, the use of cutting edge technologies, the focus on a market niche or becominga cost leader.
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Figure 1 The diversification of products and services.
Figure 2 The use of cutting edge technologies.
Based on the answers given we can observe that 81,8% of the companies are diversifying theiroffer in order to expand their market coverage and to provide the customers with integrated services.By doing this, the companies in the construction industry are trying to counteract the decreasingmarket demand and ensure their long term sustainability.
Another key aspect noticed in our research, as shown in FIGURE 2, is the importance given totechnological innovation. 83,8% of the companies presented in our study consider important and veryimportant the use of cutting edge technologies both for offering high quality products and servicesand for keeping the production costs at the lowest possible. In doing this, companies are seeking toincrease sales, lower production costs and grow the profits.
The significant decline of the construction industry, from 2008 until present, has pushed numerouscompanies into bankruptcy, while the remaining ones struggled to survive. However, some companieshave found out that focusing on a market niche, such as wood constructions or industrial constructions,can be profitable. During our study we discovered that half of the participants, as shown in FIHURE3, consider important and very important to focus on a market niche, not only to survive, but todevelop and grow.
Not least, our study allowed us to observe and confirm the companies attention and importancegiven to reducing the costs as much as possible and becoming the company with the lowest cost in theindustry. Of course, becoming a cost leader is a very difficult task, but companies do not need tobecome the leader, but merely to reduce their cost as much as possible. By doing this, they can keepthe prices unchanged and increase the profit margins. As shown previously, the use of technologicalinnovation can be a very efficient way to reduce the costs, also, increasing work productivity, findingbetter supply channels or using highly qualified work force, can be useful ways to keep costs down. Asshown in FIGURE 4, 92,3% of the participants declared that reducing the costs at the lowest levelpossible in important and very important.
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Figure 3 Focusing on a market niche.
Figure 4 The implementation of cost leadership.
1.3. Conclusions. The highly competitive business environment today forces companies, morethan ever, to seek and gain sustainable competitive advantages in order to ensure their survival andlong term development. However, to gain competitive advantages is a very complex process thatinvolves collecting data from numerous sources and analyzing it with the help of mathematical modelsin order to formulate the most efficient business strategy. At the same time, specializes statisticalmodels can help researches build a complex framework of companies in a certain industry, and helpmanagers select the best path for their company in accordance with their characteristics.
Bibliography[1] Aras, G. & Crowther, D. (2010), Sustaining Business Excellence, Total Quality Management, vol. 21, no.5: 565 576[2] Collins, D.J., Rukstad, M.G. (2008), Can You Say What Your Strategy Is?, Harvard Business Review, April: 82 - 90[3] Dikmen, I., Birgonul, M.T., Budayan, C. (2009), Strategic Group Analysis in the Construction Industry, Journal of
Construction Engineering and Management, April: 288 - 297[4] Johnson, G. & Scholes, K. (1999), Exploring corporate strategy fifth edition, Prentice Hall, Londra[5] Karnani, A. (2008), Controversy: The essence of strategy, Business Strategy Review, Winter: 28 34[6] Grant, R.M. (2003), Strategic Planning In A Turbulent Environment: Evidence From The Oil Majors, Strategic
Management Journal, vol. 24: 491 517[7] Finlay, P.N. (2000), Strategic management: an introduction to business and corporate strategy, Pearson Education,
England[8] Kim, W.C., Mauborgne, R. (2009), How Strategy Shapes Structure, Harvard Business Review, September: 73 80[9] Pearce, J.A. & Robinson Jr., R.B. (2007), Strategic Management: formulation, implementation and control,
McGraw-Hill Irwin, New York, USA
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The calculation of human resource performance
Liliana Zima, Simona Sabou, Rita Toader and Cezar ToaderTechnical University Cluj-Napoca, North Unversity Center Baia Mare, Romania
lili [email protected]
Abstract.This paper presents some aspects of calculation of individual performance according to the
performance assessment criteria, the problem of performance evaluation and new models of performance
assessment.
1.1. Introduction. In the first part of the article, we describe the main objectives assessmentand evaluation criteria.
Performance assessment is an important component of the supervisor-employee relationship. It ispart of an ongoing process of performance planning, management, and improvement and representsa culmination of past years discussions between the supervisor and employee about the employeesperformance.
The actual performance assessment serves several purposes. It encourages employee involvement,provides a formal mechanism for employees to receive feedback regarding job performance andexpectations, and allows the employee to work closely with the supervisor to establish goals andpriorities for the next year. Performance assessment also facilitates growth and development ofemployees and results in a documented history of employee performance.
A correct assessment system has to meet the following conditions:
• careful preparation and dissemination of the value system and performance assessmentprocedures with the aim of preventing adverse reactions or challenging the results;• the existence of a formal assessment tool;• using criteria that limit the absolute power of management;• personally knowing the assessed person and permanent contact with them;• continuous training for managers regarding the assessment activity;• the existence of a revising system for incorrect assessments, done by superiors;• counselling and support for those with poor performances in order to offer Human resources
must be used efficiently and rationally in order to ensure the improvement of labour produc-tivity, the improvement of quality, and the worthiness of products and services achieved.
1.2. New models of performance assessment. The second part presents one example ofindividual performance assessment calculation and the problem of performance evaluation and newmodels of performance assessment.
Pt = (p1 × C1) + (p2 × C2) + (p3 × C3) + (p4 × C4)
where Pt - total pointsp1, p2, p3, p4 - points givenC1, C2, C3, C4 - the weight of assessment criteria.
Example of individual performance calculation
Evaluation criteria % EX FB B S N1. The level of meeting the performance standards 35 5p - - - -2. Assuming responsibility 25 - 4p - - -3. Adequate labour complexity 15 - - - - -4. Initiative and creativity 25 - 4p - - -TOTAL:
General equation:
P = f (c1, c2, c3) ,
P = b0 + b1c1 + b2c2 + b3c3 + b12c1c2 + b23c2c3 + b13c1c3.
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Variation level x1(%) x2(%) x3(%)
Superior level (+1) 3.5 5 4.5
Basic level (0) 2.5 3.5 3
Inferior level (-1) 1.5 2 1.5
Variation interval (∆xi) 1 1.5 1.5
Further we establish the experimental matrix EFC 23
Nr. exp x0 x1 x2 x3 x1x2 x2x3 x1x3
1 +1 +1 +1 +1 +1 +1 +12 +1 -1 +1 +1 -1 +1 -13 +1 +1 -1 +1 -1 -1 +14 +1 -1 -1 +1 +1 -1 -15 +1 +1 +1 -1 +1 -1 -16 +1 -1 +1 -1 -1 -1 +17 +1 +1 -1 -1 -1 +1 -18 +1 -1 -1 -1 +1 +1 +1
The matrix being orthogonal, coefficients b0, b1, b2, b3, b12, b23, b13 are determined with theformulae:
bi =
N∑u=1
xiuyu
N∑u=1
x2iu
and bij =
N∑u=1
xiuxjuyu
N∑u=1
(xiuxju)2
The regression equation obtained according to the proposed model is the following:
y1 = 48.25− 1.5x1 − 1.25x2 − 5x3 − 1.25x1x2 − 0.75x1x3.
1.3. Conclusion. Performance assessments are exactly what they sound like: they are anevaluation of how employees’ are currently performing on the job and a plan for making any necessaryimprovements. Performance assessments are an essential tool in the Human Resources arsenal asthey provide data for other departmental functions (compensation, position determination, employeetraining, and employee development, etc).
In order to be efficient, performance assessment has to integrate into an adequate human resourcesmanagement system, in which the fundamental features of assessors should be professionalism, fairnessand reliability.
The most important performance assessment objectives to the management practice, are thefollowing:
• appropriate unfolding of activities in the field of human resources;• balanced rewarding of personnel;• providing employees with the information necessary for their own development, by offering
them trust in their own resources;• identifying individual training and development needs of personnel, as well as evaluating the
results of the training and development programmes;• discussing the long term plans of employees, as well as the objectives of their careers;• integrating human resources planning within the framework of all other personnel activities;• validating selection programmes;• improving motivation of employees;• improving the manager-employee relationship;
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• improving communication and intensifying cooperation between managers or superiors andemployees;• applying the equal opportunity principle.
The potential problems that need consideration in approaching performance assessment as acomponent of the performance management system are the following:
- the necessity of creating a performance culture;- involving managers at higher levels in the assessment process in order to satisfy both individual
and organisational needs;- the influence of performance management upon the role of its assessment through the
appropriate functioning of feedback.
For the success of the performance assessment activity I suggest the usage of certain mathematicalmodels and computer programmes well conceived and easy to be implemented.
Bibliography[1] Cole G. A., Management. Theory and Prcatice, Editura Stiinta, Chisinau, 2004.[2] Chisu Ana Viorica, The Human Resources Specialists Manual, Casa de editura IRECSON, Bucuresti, 2002.[3] Panisoara Georgeta, Panisoara, I. Ovidiu Human Resources Management, Editura Polirom, 2004.[4] Pitriu H. D., Managementul resurselor umane Human Resources Management Professional Performance Assessment,
Editura All Beck, 2000.[5] Varzaru Mihai, Human resources in Enterprises, Editura Tribuna Economica, Bucuresti, 2002.
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