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i

4 th INTERNATIONAL CONFERENCE ON

RECENT ADVANCES IN PURE AND APPLIED

MATHEMATICS, KUSADASI, TURKEY

11-15 MAY 2017

Abstract Book

ii

4th INTERNATIONAL CONFERENCE ON RECENT

ADVANCES IN PURE AND APPLIED

MATHEMATICS, KUSADASI, TURKEY

11-15 MAY 2017

Abstract Book

List of Major Sponsors

Istanbul Commerce University

The Turkish Academy of Sciences

Republic of Turkey Prime Ministry Turkish Cooperation and Coordination Agency

Albaraka Turk

Simurg

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4th INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN PURE AND APPLIED

MATHEMATICS, KUSADASI, TURKEY, 11-15 MAY 2017

Honorary Chairs of Scientific Committee

Prof. Dr. B. E. Rhoades, USA Prof. Dr. H. M. Srivastava, Canada Prof. Dr. Ljubisa Kocinac, Serbia Prof. Dr. Mubariz Tapdigoglu Garayev, Saudi Arabia Prof. Dr. Sadek Bouroubi, Algeria Prof. Dr. Ali M. Akhmedov, Azerbaijan Prof. Dr. Werner Varnhorn, Germany Prof. Dr. Emine Mısırlı, Turkey Prof. Dr. Huseyin Cakalli, Turkey Prof. Dr. G. Das, India Prof. Dr. M. Perestyuk, Ukraine Prof. Dr. O. Boichuk, Ukraine Prof. Dr. I. Shevchuk, Ukraine Prof. Dr. Anatoliy M. Samoilenko, Ukraine Prof. Dr. V. Guliyev, Turkey Prof. Dr. M. Abbas, S.Africa Prof. Dr. M. Mursaleen, India Prof. Dr. W. Sintunavarat, Thailand Prof. Dr. V. Kalantarov, Turkey Prof. Dr. Cihan Orhan, Turkey Prof. Dr. Metin Basarir, Turkey

Organizing Committee

Prof. Dr. Ekrem Savas, Istanbul Commerce University Prof. Dr. Richard Patterson, North Florida University Prof. Dr. Mehmet Gürdal, Suleyman Demirel University Prof. Dr. Martin Bohner, Missouri S&T Prof. Dr. Ram Mohapatra, Uni. of Central Florida Prof. Dr. Fairouz Tchier, King Saud University Prof. Dr. Mehmet Dik, Rockford University Prof. Dr. Lubomira Softova, Second University of Naples Prof. Dr. Agron Tato, Polytechnic Uni. of Tirana Prof. Dr. Debasis Giri, Haldia Institute of Technology Prof. Dr. Naim Braha, Uni. of Prishtina Assoc. Prof. Dr. Yusuf Zeren, Yildiz Technical University Assoc. Prof. Dr. Rahmet Savas, Istanbul Medeniyet University Assoc. Prof. Dr. Erhan Deniz, Kafkas University Assoc. Prof. Dr. Mahpeyker Ozturk, Sakarya University Assoc. Prof. Dr. Esra Duman, Gazi University Assist. Prof. Dr. Sukran Konca, Bitlis Eren University Assist. Prof. Dr. Gokhan Cuvalcioglu, Mersin University Assist. Prof. Dr. Emel Asici, Karadeniz Technical University Assist. Prof. Dr. Arzu Akgul, Kocaeli University Assist. Prof. Dr. Hafize Gumus, Necmettin Erbakan University Dr. Veli Capali, Süleyman Demirel University Dr. Lakhdar Ragoub, Alyammah University Dr. Nora Mahloul, University of Scien. and Tech. Houari Boumedien

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Local Organizing Committee

Rabia Savas, Sakarya University Sefa Anil Sezer, Istanbul Medeniyet University Dr. Ulas Yamanci, Suleyman Demirel University Sevim Ertug, Ankara University A. Buyukkaya, Sakarya University Oya Mert, Kemerburgaz University Gulsemay Yigit, Kemerburgaz University

Scientific Committee Prof. Dr. Huseyin Cakalli, Turkey Prof. Dr. Jeff Connor, USA Prof. Dr. Lubomira Softova, Italy Prof. Dr. Reza Langari, USA Prof. Dr. Mikail Et, Turkey Prof. Dr. S. A. Mohiuddine, S. Arabia Prof. Dr. Narendra Kumar Govil, USA Prof. Dr. T. A. Chishti, India Prof. Dr. Ayhan Serbetci, Turkey Prof. Dr. Bilal Altay, Turkey Prof. Dr. Ismail Ekincioglu, Turkey Prof. Dr. A. Sinan Cevik, Turkey Prof. Dr. Leiki Loone, Estonia Prof. Dr. Akbar B. Aliyev, Azerbaijan Prof. Dr. Vali M. Gurbanov, Azerbaijan Prof. Dr. Faqir M. Bhatti, Pakistan Prof. Dr. Said Melliani, Morocco Prof. Dr. Abdalah Rababah, Jordan Prof. Dr. Radouane Yafia, Morocco Prof. Dr. Sudarsan Nanda, India Prof. Dr. Seyit Temir, Turkey Prof. Dr. Halit Orhan, Turkey Prof. Dr. Vatan Karakaya, Turkey Prof. Dr. Amir Khosravi, Iran Prof. Dr. Seifedine Kadry, Kuwait Prof. Dr. Ali M. Akhmedov, Azerbaijan Prof. Dr. Ziyatkan Aliyev, Azerbaijan Prof. Dr. Poom Kumam, Thailand Prof. Dr. Agacik Zafer, Kuwait Prof. Dr. Tunay Bilgin, Turkey Prof. Dr. Gangaram S. Ladde, USA Prof. Dr. Claudio Cuevas, Brazil

Prof. Dr. Reza Saadati, Iran Prof. Dr. Salih Aytar, Turkey Prof. Dr. Charles Swartz, USA Prof. Dr. Yagub A. Sharifov, Azerbaijan Prof. Dr. Niyazi A. Ilyasov, Azerbaijan Prof. Dr. Aref Jeribi, Tunisia Prof. Dr. Husamettin Coskun, Turkey Prof. Dr. Maria Zeltser, Estonia Prof. Dr. Kamalmani Baral, Nepal Prof. Dr. Ants Aasma, Estonia Prof. Dr. Ismail N. Cangul, Turkey Prof. Dr. Murat Tosun, Turkey Prof. Dr. Yilmaz Simsek, Turkey Prof. Dr. Harry Miller, Bosnia Prof. Dr. Ali Fares, France Prof. Dr. Ibrahim Canak, Turkey Prof. Dr. Naim Braha, Kosova Prof. Dr. Mustapha Cheggag, Algeria Prof. Dr. Fahrettin Abdullayev, Kırgizistan Prof. Dr. Praveen Agarwal, India Prof. Dr. P. D. Srivastava, India Prof. Dr. Naila Rozi, Pakistan Prof. Dr. Emine Can, Turkey Prof. Dr. Hemen Dutta, India Assoc. Prof. Dr. Bayram Ali Ersoy, Turkey Assoc. Prof. Dr. Ayhan Aydın, Turkey Asst. Prof. Vishnu Narayan Mishra, India Dr. Lejla Miller Van-Wieren, Bosnia Dr. Mayssa Alqurashi, S. Arabia Dr. Fardous Taoufic, S. Arabia Dr. Ammar Edress Mohamed, Iraq

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Dear Collogues;

First of all I wish to offer you a warm welcome to the fourth International Conference on

Recent Advances in Pure and Applied Mathematics (ICRAPAM 2017).

The last conference of this series was organized in Bodrum, Turkey, during 19-23 May

2016 and it was attended by 350 scientists from 48 different countries, contributing 300 oral

presentations and 50 posters.

As the past conference, the aim of this conference is to provide a platform for

mathematicians to present their recent Works, exchange ideas and new methods in several

important areas of Mathematics and to provide an opportunity to improve collaboration

between local and international participants in the wonderful historic city of Istanbul. Further

we believe that, the development in various fields of Mathematics lead to new research areas in

Mathematics and the richness of the new results can also provide basis for interdisciplinary

collaborations. That is why; we have planned to provide a common forum for scientists to

communicate their original results in various fields of analysis and applied mathematics.

We would like to thank all the invited speakers who have kindly accepted our invitation

and have come to spend their precious time by sharing their ideas during the conference.

Finally, we would also like to thank all of the members of the Scientific Advisory Committee

and the Organizing Committee of this conference.

Again we would like to convey our heartiest welcome to each of you who have come to

attend this conference and we wish for an enjoyable high scientific level conference and hope

to meet you again in the future.

With our best wishes and warm regards,

Prof. Dr. Ekrem SAVAS

Chair of the Conference

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INVITED TALKS

The Sturm-Liouville Theory and Fourier Analysis Prof. Dr. Mohammed Al-Gwaiz

1 1

Topological Spaces with an -base Prof. Dr. Taras Banakh

2

Schwarz Problem for Higher-order Equations in a Polydisc Prof. Dr. A. Okay Celebi

3

Gelfand Theory Unplugged Prof. Dr. Robin Harte

4

Decision Models for Autonomous Vehicles Prof. Dr. Reza Langari

5

Summation and Quadrature Processes for Slowly Convergent Series Prof. Dr. Gradimir V. Milovanović

6

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4th INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN PURE AND APPLIED MATHEMATICS, KUSADASI, TURKEY, 11-15 MAY 2017

LIST OF TALKS

New Iterative Methods for Solving Non-Linear Equations

Osama Y. Ababneh

7

Solution of Animplicit Complementarity Problem on Isotone Projection Cones

Mujahid Abbas

Analysis and Modeling the Drought Hydrologic by the Copulas in North Algeria

Rassoul Abdelaziz

8

9

Rayleigh-Marangoni Convection in a Layer of Nanofluid

Abdullah A. Abdullah

10

On the Properties of the Orthogonal Polynomials along a Contour

Fahreddin.G.Abdullayev and Gülnara.A.Abdullayev

11

Modeling and Classifying by using Binary Logistic Regression Analysis Application on Hepatitis Disease

Data

Qais Mustafa Abdulqader

13

Residual Power Series Approach to Handle a Class of Fractional Differential Equations

Ayed H. Adamat

14

On the Existence and Uniqeness of Positive Solution for a Fractional Boundary Value Problem with New

Fractional Derivative

Asghar Ahmadkhanlu

15

On Derivation of a Subclasses of Filiform Leibniz Algebras

AL-Nashri AL-hossain Ahmed

Global Existence and Uniqueness of Weak Solution to a Chemotaxis Model

N. Aïssa and A. Balehouane

16

17

A Generalization of Hereditary Noetherian Prime Rings

Evrim Akalan

On Some Inequalities of Analytic and Biunivalent Functions Given by Subordination

Arzu Akgul

18

19

Compact Finite Differences Method for Burgers-Huxley Equation

Canan Akkoyunlu

Approximation Solution of System of Volterra Integro Differential Using Finite Element Method

Adel Alamarashi

20

21

Fixed Point Theorem in FM-Spaces

Rateb AlBtoush 22

viii

Bounds for the Zeros of Polynomials by Using Similar Matrices

Mohammad. Al-Hawari

23

An Application of Decision Tree for Evaluating a Classroom Teaching Practice

Sadri Alija and Halil Snopce

24

Existence of Positive Solution of Boundary Value Fractional Quadratic Differential Equations

Youssef Allaoui, Khalid Hilai and Guida Karimi

25

Some Applications of Cozero Sets in Topological Spaces

Ahmad Al-Omari

26

An Efficient Analytical-Numerical Technique for Handling Model of Fuzzy Differential Equations of

Fractional-Order

Mohammad Aloroud, Mohammed Al-Smadi, Rokiah Rozita Ahmad, Ummul Khair Salma Din

Adaptation of Fractional Power Series Method for Solving Fuzzy BVPs

Mohammad Alaroud, Rokiah Rozita Ahmad, Mohammed Al-Smadi and Ummul Khair Salma

Din

27

29

Solving Fuzzy Mixed Integral Equations of Second Kind in Hilbert Spaces

Mohammed Al-Smadi

Numerical Algorithm for Solving Time-Fractional Bvps in a Simplified Reproducing Kernel Space

Mohammed Al-Smadi

31

33

Semiregularization of Almost Countably Compact Spaces

Zuhier Altawallbeh

Generalization on Countably Compact Spaces via Hereditary Classes

Zuhier Altawallbeh

35

36

Hybrid Master Equation of the Jump Diffusion Approximation

Derya Altintan and Heinz Koeppl

37

Coefficient Bounds for a Subclass of Analytic Functions with Respect to Symmetric Points

Osman Altintas and Oznur Ozkan Kilic

On The Relationship Between A Family of Fibonacci And Lucas Numbers

Ipek Altun, Ali Aydogdu and Engin Ozkan

39

40

Convergence, Consistency and Stability in Intuitionistic Fuzzy Differential Equations

Bouchra Ben Amma, Said Melliani and Lalla Saadia Chadli

41

SQCQP Descent Scheme for Multi-objective Optimization Problem

Md Abu Talhamainuddin Ansary and Geetanjali Panda

42

On Gauss Balancing and Gauss Cobalancing Numbers

Mustafa Asci and Mustafa Yilmaz

43

An Overview of Ordering Based on Nullnorms

Emel Asici

44

Analytical-Numerical Solutions for a class of Systems of Differential Equations Using Reproducing Kernel

Method

Ali Mahmud Ateiwi

A Fuzzy Project Scheduling with Constrained Resources

Lyazzat Atymtayeva, Ardakbek Kungaliyev and Daniyar Artykov

45

47

ix

A Convergent Two-Level Linear Scheme for the Generalized Rosenau-Kdv-RLW Eqution

Ayhan Aydin

Fuzzy Soft Metric and Fuzzifying Soft Topology Induced by Fuzzy Soft Metric

Ebru Aydogdu, Abdulkadir Aygunoglu, Halis Aygun

Some Identities Associated With Hecke Operators

Aykut Ahmet Aygunes

48

49 50

Some Rough Convergence Criteria for the Sequences of Intervals of Fuzzy Numbers

Salih Aytar

Modified Simple Equation Method and its Applications to Some Nonlinear Physical Equations

Gizel Bakicierler and Emine Misirli

51

52

Jacobi Elliptic Function Solutions of the Space-Time Fractional Symmetric Regularized Long Wave

Equation

Dilek Varol Bayram, Sevil Çulha and Ayşegül Daşcıoğlu

53

Functional Quadratic Integral Equations in the L1loc (R+) space

Latifa Benhamouche and Smail Djebali

Suborbital Graphs for a Non-Transitive Action of the Normalizer

Murat Besenk, Bahadır Ozgur Guler and Abdurrahman Buyukkaya

54 55

On Spherically Symmetric Solutions of the Einstein-Maxwell Field Equations

Rashida Bibi and Azad A. Siddiqui

56

A Numerical Approximation Based on Collocation Method for the Solutions of Telegraph Equation

Kübra Erdem Bicer

57

Rotating Disk Cryptosystem: RDC

Sadek Bouroubi and Louiza Rezkallah

58

Free Convection inside a Porous Enclosure

Canan Bozkaya

59

Tauberian Theorems for the Cesáro Second Order Operators for Sequences of Fuzzy Numbers

Naim L. Braha

60

Estimating the Distortion Parameter of the Proportional Hazards Premium for Heavy-Tailed Losses

Brahimi Brahim

On Some Fixed Point Results Related to Almost Generalized (α,β)-(ψ,ϕ)-Weakly Contractive Mappings in

S Metric Spaces

Abdurrahman Buyukkaya and Mahpeyker Ozturk

61

62

Beyond statistical quasi Cauchy sequences

Huseyin Cakalli

63

A Study on Strongly Lacunary Ward Continuity

Huseyin Cakalli and Huseyin Kaplan

64

A Study on Abel Statistical Quasi Cauchy Sequences

Huseyin Cakalli and Iffet Taylan

65

Graph Theoretical Applications of Molecular Graphs

Ismail Naci Cangul

66

x

A Study on Public Transit Users’ Route Choice and Assignment Function

Buket Capali and Halim Ceylan

67

A New Developed Semi–Empirical Formula for Nuclear Reaction Cross–Section Calculations

Veli Capali, Mert Sekerci, Hasan Ozdogan and Abdullah Kaplan

68

On Uninorms on Bounded Lattices

Gül Deniz Cayli and Funda Karacal

69

On Statistical Dunford and Pettis Integration

Anita Caushi

71

On The Cardinality of Category Spaces

Bahaettin Cengiz and Banu Gunturk

72

Remarks and Observations on Some Special Arithmetical Sums

Elif Cetin and Yilmaz Simsek

73

S-Generalized Mittag-Leffler Function

Aysegul Cetinkaya, I. Onur Kiymaz and M. Baki Yagbasan

74

Jacobi elliptic function solutions of time-fractional KdV-Zakharov-Kuznetsov equation

Sevil Culha, Dilek Varol Bayram and Aysegul Dascioglu

75

A Fix-And-Optimize Heuristic for the Integrated Fleet Sizing and Replenishment Planning Problem with

Predetermined Delivery Frequencies

Niousha Karimi Dastjerd and Kadir Ertogral

76

Catalogue of Degree Sequences of Molecular Graphs

Sadik Delen and Ismail Naci Cangul

77

Streamline Topology of Vortex Breakdown Bubbles near the Re-Entrant Corner

Ali Deliceoglu and Ebutalib Celik

78

Optimality Conditions for a Linear Differential System with Two Delays

Hanna Demchenko

α-Convexity of Some Struve and Lommel Functions

Erhan Deniz, Halit Orhan and Murat Çağlar

79

80

Fuzzy Soft Topolical Spaces and the Related Category FST

Tugbahan Simsekler Dizman and Naime Tozlu

Fuzzy Soft Ditopological Spaces

Tugbahan Simsekler Dizman, Naime Tozlu and Şaziye Yüksel

On The Difference Method for Approximating of Second Order Derivatives of a Solution of Laplace's

Equation in a Rectangular Parallelepiped

Adiguzel A. Dosiyev and Hediye Sarıkaya

81

82

83

Kolmogorov Inequality on Variable Exponent Lebesgue Spaces

Ismail Ekincioglu, Esra Kaya

An Application of Functional Variable Method For Semi-Analytical Solutions of Nonlinear Evolution

Equations

Berfin Elma and Emine Misirli

84

85

New Types of Soft Separation Axioms and Soft Compactness in Soft Topological Spaces

M. E. El-Shafei, M. Abo-Elhamayel and T. M. Al-shami

86

xi

On Quaternion n-Spaces

Fatma Ozen Erdogan and Atilla Akpinar

87

Decomposition of Soft Continuity via Soft Locally b-Closed Set

Zehra Guzel Ergul, Naime Tozlu and Saziye Yuksel

Periodic Solutions for a Third-Order Delay Differential Equation

Nouioua Farid and A. Ardjuoni

88

89

Copula Conditional Tail Expectation for Multivariate Financial Risks

Benatia Fatah and Brahim Brahimi

90

New Properties of Fractional Derivatives Defined Using Mittag Leffler Kernel

Arran Fernandez and Dumitru Baleanu

Nodal Solutions for Indefinite Robin Problems

Michael Filippakis

91

92

On Slowly Oscillating Double Sequences

Goksen Findik, Ibrahim Canak and Umit Totur

93

A Bayes Minimax Result for a Large Class of Distributions

Dominique Fourdrinier, Fatiha Mezoued and William E. Strawderman

94

A Search for Designs with the Same Parameters as 2-(256,64,21) Design with 2-Rank 25

Mustafa Gezek

95

Compact and Matrix Mappings on the Space |Afθ|k

Fadime Gokce and G.Canan Hazar Gulec

On Some Classes of Fractional Differential Equations of Parabolic Type

Dilovar Guljonov

Some Results about ΔI-Statistically Pre-Cauchy Sequences with an Orlicz Function

Hafize Gumus, Omer Kisi and Ekrem Savas

96

97

98

A Numerical Analysis of FLMM for Semilinear Time Fractional Schrödinger Equations

Betul Hicdurmaz

On Modified FLMM Methods for Fractional Population Equations

Betül Hicdurmaz and Emine Can

99

100

Coincidence Best Proximity Points for Geraghty Type Proximal Cyclic Contractions

Azhar Hussain

Estimation of a Loss Function for Spherically Symmetric Distribution with Constraints on the Norm

Ouassou Idir

101

102

An overview on Fuzzy AHP and Its Priority Derivation

Iftikhar and Musheer Ahmad

103

Solutions of (n) (n 1)od od When n 1 Has Three Distinct Odd Primes

Nazli Yildiz Ikikardes, Daeyeoul Kim and Lianrong Ma

104

Hypersurfaces of a Kenmotsu Space Form

Mohammad Ilmakchi

105

On Some Classes of Fractional Integrodifferential Equations in Hilbert Space

Mamadsho Ilolov 106

xii

The Generators of Regular, Quasi-regular Representations and Casimir Operator

Yasemin Isik and Mehmet Sezgin

108

Some Properties of Cartan Null Curves in Semi-Euclidean 4-space with index 2

Esen Iyigün

Proximal Point Algorithms Involving Cesaro Type Mean of Total Asymptotically nonexpansive Mappings

in CAT(0) Spaces

Amna Kalsoom and Hafiz Futhar ud Din

Semi–Empirical Systematic Development for Photon Induced Nuclear Reaction Cross–Section Calculations

Abdullah Kaplan, Hasan Ozdogan, Mert Sekerci and Veli Capali

Positive Solutions for Fractional-Order Boundary Value Problems

Ilkay Yaslan Karaca

The Existence of Positive Solutions of Boundary Value Problems with P-Laplacian on the Half-Line

Ilkay Yaslan Karaca and Aycan Sinanoglu

The Dimension of Digital Khalimsky Manifolds

Ismet Karaca and Gokhan Temizel

Some Properties of Persistent Homology Groups

Ismet Karaca and Hatice Sevde Denizalti

On Digital Cohomology Groups

Ismet Karaca and Ozgur Ege

Some Common Fixed Point Theorems on Complex Valued Gb-Metric Spaces

Ismet Karaca and Ozgur Ege

109

110 111

112

113

114 115 116 118

On Some Deddens Subspaces of Banach Algebras

Mubariz Karaev, Mehmet Gurdal and Havva Tilki

Duhamel Operator and Existence of Invariant Subspace

Mubariz Karaev, Mehmet Gurdal and Mualla Birgul Huban

119

120

On Extended Eigenvalues and Extended Eigenvectors of Toeplitz Operators

Mubariz Karaev, Mehmet Gurdal and Mualla Birgul Huban

121

A generalization on the Incidence Energy and Laplacian-Energy-Like Invariant

Ezgi Kaya and A. Dilek Maden

A Data Mining Approach: Application to the Extraction of the Characteristics of IARD Products in the

Insurance Sector

Sadi Khadidja and Lounici Mosbah Nora

122

123

The Le Corbusier Approach in the Relationship between Architecture and Mathematics

Murat Kilic and Melih Kurnali

124

The Absolute Möbius Divisor Function and Euler function

Daeyeoul Kim, Umit Sarp and Sebahattin Ikikardes

126

S-Generalized Lauricella’s Hypergeometric Functions

I. Onur Kiymaz, M. Baki Yagbasan and Aysegul Cetinkaya

127

Some Remarks on Fuzzy Anti-Normed Spaces

Ljubiša D.R. Kočinac 128

xiii

On Asymptotically f-Statistical Equivalent Sequences

Sukran Konca and Mehmet Kucukaslan

Some Permanents of Hessenberg Matrices

Sibel Koparal, Nese Omur and Cemile Duygu Sener

Best Proximity Points for Generalized Geraghty Proximal Contraction Mapping in Elliptic Valued

Metric Space

Isil Arda Kosal, Hidayet Huda Kosal and Mahpeyker Ozturk

129 130

131

Characterizations of , ,p q - Convex Sequences

Xhevat Z. Krasniqi

132

A Note on the Numbers Yn(Λ) and the Polynomials Yn(X;Λ) and Their Generating Functions

Irem Kucukoglu and Yilmaz Simsek

133

Modelling Worldwide CO2 Emissions and Oil Consumption based on the L1, L2 and L∞-norm Regressions

Pranesh Kumar and Mohamadtaghi Rahimi

134

Some Symmerty Identities for Modified Degenerate Apostol-Bernoulli and Modified Degenerate Apostol-

Euler Polynomials Related to Multiplier Sums

Burak Kurt

135

Univalency Conditions of a General Nonlinear Integral Operator of Analytic Functions with Different

Domains

Shuhai Li and Huo Tang

136

Certain Subclasses of Harmonic Univalent Functions Defined By Convolution and Subordination

Shuhai Li and Huo Tang

137

Refinement of Some Inequalities Concerning to Bn-Operator of Polynomials with Restricted Zeros

A. Liman

138

Gaussian Approximation to the Estimator of the Mean of a Heavy-Tailed Distribution under Random

Censoring

Djamel Mearghni

139

Industrial Application of Fuzzy Logic Control for Torque-ripple Minimization in Electricals Machines

Zineb Mekrini and Seddik Bri

140

On Optimal Control of Stochastic Mean Field Systems

Brahim Mezerdi

141

Ring Theory Approaches to Solve Cauchy-Euler Differential Equations of Several Variables

Assal Miloud

142

Subgradient Method of Solving the Problem of Linear Stochastic Programming with Bifurcation Effect

Fakhriddin Mirzoahmedov

143

Modelling Asymmetric Magnetic Recording Heads with an Underlayer Using Superposition

Ammar Edress Mohamed

144

G-compactness for Topological Groups with Operations

Osman Mucuk and Huseyin Cakalli

145

Topological Aspects of Monodromy Groupoids for Group-Groupoids

Osman Mucuk and Serap Demir

147

xiv

A Characterization of the Two-Weight Inequality for Riesz Potentials on Cones of Radially Decreasing

Functions

Ghulam Murtaza

149

On The Fourth Geometric-Arithmetic Index of Graphs

Y. Nacaroglu and A. Dilek Maden

150

Laplace Transform of Fractional Differential Equations

Khaled I. Nawafleh

151

Gaussian Approximation of a New Tail Index Estimator for Right-Censored Pareto-Type Distributions

Abdelhakim Necir

On Residual Algebraic Free Extensions of Valuations

Figen Oke

152

153

Statistically (C,1,1) Summable Double Sequences of Fuzzy Numbers and a Tauberian Theorem

Zerrin Onder, Ibrahim Canak and Umit Totur

154

The Sheffer Stroke Basic Algebras on the Intervals

Tahsin Oner and Tugce Katican

155

A Reduction of Basic Algebras: Sheffer Stroke Basic Algebras

Tahsin Oner and Ibrahım Senturk

156

Applications on Weak and Strong Forms of Fuzzy α-Open (Closed) Sets

Hakeem A. Othman

157

Code Verification Using Method of Manufactured Solutions for CFD Problems

Hatice Ozcan

158

On the Existence of Einstein Weyl Manifold with a Special Metric Connection

F. Ozdemir and M. D. Turkoglu

159

Repeat Codes, Even Codes, Odd Codes and Their Equivalence

Mustafa Ozkan and Figen Oke

160

Tauberian Theorems for the Weighted Mean Summability Methods of Integrals

Firat Ozsarac and Ibrahim Canak

161

On Lifting Polynomials and Distinguished Pairs

Burcu Ozturk, Figen Oke

On Some Fixed Point and Common Fixed Theorems in b-Metric-Like Spaces

Mahpeyker Ozturk

162

163

Experimental Evidence of Landau Damping in a Fluid at a Macroscopic Scale

Eric Padilla, William Cody Wilson and Andrei Ludu

A Boundary Value Problem for an Irrational Order Partial Equation

A.A. Pashavand, N.A. Aliyev and A.Y. Delshad Gharegheshlaghi

164

165

Generalized Close to Convex Functions with q-Properties

Yasar Polatoglu, Oya Mert and Asena Cetinkaya

Steady-State Modeling of the Biological Network via Long-tailed Symetric Distribution

Vilda Purutcuoglu and Melih Agraz

166

167

xv

Quadrature Formula with High Degree of Exactness

Abedallah Rababah

Best Cubic Spline Interpolation Based on Minimizing the Error

Abedallah Rababah and Mohammed Bani Khalid

169

170

On Chebyshev Collocation Method and Applications to Nonlinear Integral Equations Abdalah Rababah, Benferhat Leila, Hichem Ramoul and Nora Mahloul

171

The Treatment of Fractional Singular Lagrangian

Eqab Rabei

172

MHD Convective Flow due to a Curved Surface with Thermal Radiation and Chemical Reaction

Madiha Rashid

173

On The Isolated Points of the Spectrum of M-Paranormal Operators

Mohammad Rashid

174

Existence of Homoclinic Orbit in Generalized Planar System of Lienard Type

Vahid Roomi

175

Some Results of the Picard-Krasnoselskii Hybrid Iterative Process

Aynur Sahin and Metin Basarir

176

Optimal Coincidence Best Proximity Point Results in Fuzzy Metric Spaces

Naeem Saleem

177

New Concept of Determinants with Three Indexes (3D Determinants) and Possibilities of Use

Armend Salihu

Boundedness Properties of Some Operators on M (P, Q) ( d)

Ayse Sandikci

178

179

On Approximate Biprojectivity of Banach Algebras

M. H. Sattari

On Some New Sequence Spaces Defined By Almost Lacunary Bounded Variation Ekrem Savas

On Filter Convergence of Nets in Uniform Spaces

Ekrem Savas and Ulas Yamanci

180

181 182

On E-J Hausdorff Transformations for Double Sequences

Rabia Savas and Hamdullah Sevli

Double Lacunary Statistical Boundedness of Order α

Rabia Savas and Mahpeyker Ozturk

Statistical Convergent Functions Via Ideals With Respect To The Intuitionistic Fuzzy 2-Normed Spaces

Rahmet Savas

183

184 185

Submanifolds in 1

2H ( 1)m with Finite Type Pseudo-Hyperbolic Gauss Map

Ruya Yegin Sen and Ugur Dursun

186

On the Determination of Validity of Categorical Syllogisms by Using a Mathematical Model

Ibrahım Senturk and Tahsin Oner

187

xvi

Converse Theorems for Statistical Convergence

Sefa Anil Sezer, Rahmet Savas and Ibrahim Canak

188

Cesàro Summability of Sequences in 2-Normed Spaces

Sefa Anil Sezer and Rahmet Savas

189

Applications of the Schwarz Lemma to Inequalities for Polynomials with Restricted Zeros

Lubna Wali Shah

190

Growth of Maximum Modulus of Polynomials and Rational Functions in the Complex Domain

Wali Mohammad Shah

Trace Formula for Witt Vector Rings

Mokhfi Siham

191

192

On Parametrization of the q-Bernstein Basis Functions

Yilmaz Simsek

Control of the Performance of the Panel of Judge in Sensory Analysis by a Functinal Principal Component

Analysis of Probability Densities Function

Yousfi Smail

193

194

Optimization of an Execution Time for Parallel Matrix Multiplication by adding a New Set of Processors

on the Array

Halil Snopce, Sadri Alija, Azir Aliu and Artan Luma

195

From Dido to Morrey: Variational Problems and Regularity Theory!

Lubomira G. Softova

196

A Publicly Verifiable Authenticated Encryption Scheme Based on Chaotic Maps and Factoring Problems

Nedal Tahat

197

Third-Order Differential Sandwich-type Results Involving the Liu-Owa Operator

Huo Tang, M. K. Aouf, Shigeyoshi Owa and Shu-Hai Li

198

Second-Order Differential Superordination for Analytic Functions in the Upper Half-Plane

Huo Tang, H. M. Srivastava, Guan-Tie Deng and Shu-Hai Li

199

Capacity Sizing and Pricing with Heterogeneous Products and Flexible Resources

Salih Tekin

201

A New Class of the r-Stirling Numbers and the Generalized Bernoulli Polynomials

Meriem Tiachachat

202

Degree Sequences and Inverse Problem on Graphs

Muge Togan, Aysun Yurttas and Ismail Naci Cangul 203

Notes on Permuting tri-derivations on Prime and Semi-prime Rings

Seda Oguz Unal, Hasret Durna

204

Weakly Invariant Subspaces for Multivalued Linear Operators on Banach Spaces

Gerald Wanjala

205

Speech Quality Analysis with Respect to Noise Corruption by a Kalman Filter to Estimation the Parameters

of the SWLP Method

Ervenila Xhaferraj (Musta)

206

S-Generalized Srivastava’s Triple Hypergeometric Functions

M. Baki Yagbasan, Aysegul Cetinkaya and I. Onur Kiymaz 207

xvii

Berezin Number Inequality for Convex Function in Reproducing Kernel Hilbert Space

Ulas Yamanci, Mehmet Gurdal and Mubariz T. Garayev

208

On Power Inequalities for Berezin Number of Operators and Convex Functions

Ulas Yamanci, Mehmet Gurdal and Ceren Celik

209

Spectral Properties of Discrete Klein-Gordon Equations

Nihal Yokus and Nimet Coskun

210

On the Inverse Problem on Graphs

Aysun Yurttas, Muge Togan and Ismail Naci Cangul

211

Summability of Subsequences of Divergent Sequences

Maria Zeltser and Johann Boss

212

Many to one Embedding Crossed Cube into Pancake Mohamed Faouzi Zerarka

213

______________________________________________________

1

INTERNATIONAL CONFERENCE on RECENT ADVANCES in

PURE AND APPLIED MATHEMATICS (ICRAPAM 2017)

May 11-15, 2017, Palm Wings Ephesus Resort Hotel,

Kusadasi - Aydin, TURKEY www.icrapam.org

The Sturm-Liouville Theory and Fourier Analysis

Mohammed Al-Gwaiz

Department of Mathematics,

King Saud University, Riyadh

[email protected]

Abstract: According to the Sturm-Liouville Theory, the eigenfunctions of a self

adjoint linear differential operator of second order form an infinite sequence

which is orthogonal and complete in L^2. Thus, depending on the choice of the

differential operator and the boundary conditions, we obtain an assortment of

bases for L^2. This provides a convenient approach for expanding any function

in L^2 in terms of these eigenfunctions. It turns out that the classical Fourier

series expansion on (-pi,pi) in terms of sin nx and cos nx is the result of choosing

the differential operator to be d^2 /dx^2, with appropriate boundary conditions.

For other choices we arrive at a more generalized theory of Fourier series based

on other orthogonal bases

https://www.researchgate.net/institution/King_Saud_University

mailto:[email protected]

______________________________________________________

2





Topological Spaces with an -base

Taras Banakh

Jan Kochanowski University in Kielce (Poland) and

Ivan Franko National University of Lviv (Ukraine),

Kielce-Lviv, Poland-Ukraine

[email protected]

Abstract: Given a partially ordered set P we shall discuss properties of

topological spaces X admitting a P-base, i.e., an indexed family (U)P of

subsets of XX such that U U for all in P and for every x X the

family (U[x])P of balls U[x]=yX:(x,y) U is a neighborhood base at x.

A P-base (U[x])P for X is called locally uniform if the family of entourages

(UU-1U)P remains a P-base for X. A topological space is first-countable if

and only if it has an -base. By Moore's Metrization Theorem, a T0-space is

metrizable if and only if it has a locally uniform -base.

In the talk we shall discuss topological spaces possessing a (locally uniform) -

base. Our results show that spaces with an -base share some common

properties with first countable spaces, in particular, many known upper bounds

on the cardinality of first-countable spaces remain true for countably tight -

based topological spaces. On the other hand, topological spaces with a locally

uniform -base have many properties, typical for generalized metric spaces.

Also we study Tychonoff spaces whose universal (pre- or quasi-) uniformity has

an -base and show that such spaces are close to being -compact.

More information can be found in the paper-book [1].

Keywords: generalized metric space, partially ordered set, neighborhood base.

References:

[1] T. Banakh, “Topological spaces with an -base”, 105 pp. preprint

(https://arxiv.org/abs/1607.07978).


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3





Schwarz Problem for Higher-order Equations in a Polydisc

A. Okay Celebi

Department of Mathematics, Yeditepe University

Istanbul, Turkey

[email protected]

Abstract: In this presentation, we discuss the Schwarz boundary value problem

for higher order linear complex differential equations in the unit polydisc. Firstly

we state the results obtained in ℂ (see for example [1]). Secondly the integral

representation for functions in ℂ𝑛[2,3,4] is improved. Then we give the solution

of the model equation with homogeneous Schwarz conditions posed in a

polydisc, which enables us to define an integral operator. Thus we can convert

the linear complex differential equations into an integral equation. The solution

is obtained via Fredholm theory.

Keywords: Schwarz problem, Polydisc,

P.S: This is a joint work with Umit Aksoy; Atilim University, Department of

Mathematics, Ankara, Turkey

References:

[1] U. Aksoy, A. O. Celebi; A survey on the boundary value problems for

complex partial differential equations, Adv. Dyn. Syst. Appl., 5(2010), 133-158.

[2] Begehr, H. and Dzhuraev, A., An Introduction to several complex variables

and partial differential equations, Pitman Monographs and Surveys1 in Pure and

Applied Mathematics, Addison Wesley Longman Limited

(1997).

[3] Begehr, H., Boundary value problems in C and C^n, Acta Mathematica

Vietnamica, 22(1997), 407-425.

[4] Begehr, H., Dai, D.-Q. and Li, X., Integral representation formulas in

polydomains, Comp. Var., 47(2002), 463-484


______________________________________________________

4





Gelfand Theory Unplugged

Robin Harte

Trinity College, Dublin, Ireland

[email protected]

Abstract: It was Norbert Wiener who observed that whenever a periodic

continuous function which never vanishes has an absolutely convergent Fourier

series, then so does its reciprocal. Pointwise multiplication generates

“convolution” of their coefficient sequences, with a homomorphism from

sequences to functions; according to Wiener, if the function is pointwise

invertible then also the sequence is “convolution invertible”. When Israel

Gelfand looked at these sequences he saw for the first time what would come to

be known as a commutative “Banach algebra”. He went on to extend Wiener’s

observation from absolutely summable sequences to these Banach algebras, with

a completely different and abstract proof. The electricity that powers this

“Gelfand theory” is Zorn’s lemma and “maximal ideals”, together with the

Gelfand-Mazur lemma, which says that maximal ideals are always generated by

bounded multiplicative linear functionals. The “unplugged” version bypasses

maximal ideals, and proceeds via the superficially more concrete spectral

mapping theorem for finite and infinite systems of Banach algebra elements.

Keywords: Fourier series, Banach algebra, maximals ideals, Gelfand characters,

several variable spectral mapping theorem.

References:

[1] Robin Harte, Invertibility and singularity, Dekker (New York) 1988.

[2] Robin Harte, Spectral mapping theorems - a bluffer’s guide, Springer Briefs

in Mathematics, 2014.

[3] R,E. Harte, Non-commutative Taylor invertibility, Operators and Matrices (to

appear).

[4] Vladimir Mu¨ller, Spectral theory of linear operators, Birkh¨auser Basel,

2007.


______________________________________________________

5





Decision Models for Autonomous Vehicles

Reza Langari

Engineering Technology and Industrial Distribution

Texas A&M University

[email protected]

Abstract: The market for autonomous vehicles (Level 4+ autonomy, or L4+) is

expected to reach $42B by 2025 (Bloomberg) and upwards of $85B by 2030.

The key issues in this context are i) localization, ii) perception, ii) decision logic,

iv) control execution as well as v) validation/verification. These are central to

effective functioning of autonomous vehicles and remain both research topics as

well as subjects of significant development effort by industry.

The presentation provides an overview of the issues listed above and the outlook

for future development in the relevant areas. In particular, we focus on decision

and control for autonomous vehicles where matters of expediency and safety

have to be balanced in a sensible manner in view of uncertainty in the behavior

of other vehicles. We present approaches based on classical optimization as well

as game theory, which offers a unique means of dealing with multi-player

decision processes. The benefits and drawbacks of this approach and future

outlook for its use in autonomous driving will also be discussed.


______________________________________________________

6





Summation and Quadrature Processes for Slowly Convergent

Series

Gradimir V. Milovanović

Serbian Academy of Sciences and Arts, Belgrade, Serbia

[email protected]

Abstract: An account on summation/integration methods for computation of

slowly convergent series and finite sums, as well as some new results on this

subject and new applications, are presented. Methods are based on Gaussian

quadrature formulas with respect to some non-classical weight functions over the

real line or the halfline. For constructing such quadrature rules we use recent

progress in symbolic compuation and variableprecision arithmetic, implemented

through our Mathematica package “OrthogonalPolynomials” [1], [2]. Some

details on these methods can be found in [3], [4], [5].

Keywords: Summation, Gaussian quadrature rules, weight function,

convergence, orthogonal polynomials.

References:

[1] A. S. Cvetković and G. V. Milovanović, “The Mathematica Package

OrthogonalPolynomials”, Facta Univ. Ser. Math. Inform. 19 (2004), 17-36.

[2] G. V. Milovanović and A. S. Cvetković, “Special classes of orthogonal

polynomials and corresponding quadratures of Gaussian type”, Math. Balkanica

26 (2012), 169-184.

[3] G. V. Milovanović, “Summation of series and Gaussian quadratures”, In:

Approximation and Computation (R.V.M. Zahar, ed.), ISNM Vol. 119, pp. 459-

475, Birkhäuser Verlag, Basel-Boston-Berlin, 1994.

[4] G. Mastroianni and G. V. Milovanović, Interpolation Processes - Basic

Theory and Applications, Springer Monographs in Mathematics, Springer

Verlag, Berlin - Heidelberg - New York, 2008.

[5] G. V. Milovanović, “Summation formulas of Euler-Maclaurin and Abel-

Plana: old and new results and applications”, In: Progress in Approximation

Theory and Applicable Complex Analysis – In the Memory of Q,I. Rahman

(N.K. Govil, R.N. Mohapatra, M.A. Qazi, G. Schmeisser, eds.), Springer, 2017

(to appear).


______________________________________________________

7





New Iterative Methods for Solving Non-Linear Equations

Osama Y. Ababneh

Department of Mathematics, Zarqa University, Zarqa, Jordan

[email protected]

Abstract: Solving the non-linear equation f(x) = 0 has nice applications in

various branches of physics and engineering. Sometimes the applications of the

numerical methods to solve non-linear equations depending on the second

derivatives are restricted in physics and engineering. The purpose of this paper is

to propose new modified Newton’s method for solving non-linear equations and

free from second derivative. Convergence results show that the order of

convergence of the proposed iterative methods is four. Finally, several numerical

examples are given to illustrate that the new iterative algorithms are effective.

Keywords: non-linear equations, Newton’s method.


______________________________________________________

8





Solution of Animplicit Complementarity Problem on Isotone

Projection Cones

Mujahid Abbas

Department of Mathematics, University of Management and Technology,

C-II Johar Town, Lahore, Pakistan,

and

Department of mathematics and applied mathematics,

University of Pretoria, South Africa

[email protected]

Abstract: In this talk an iterative algorithm is presented in connection with an

implicit complementarity problem. It is shown that if the sequence generated

through the defined algorithm is convergent, then its limit is a solution of the

coincidence point equation and thus solves the implicit complementarity

problem. Sufficient conditions are discussed for this sequence to be convergent

for implicit complementarity problems defined by isotone projection coneses.

https://scholar.google.com.pk/citations?view_op=view_org&hl=en&org=2820183501405604682


______________________________________________________

9





Analysis and Modeling the Drought Hydrologic by the Copulas

in North Algeria

Rassoul Abdelaziz

Department of Irrigation and Drainage, National High School of Hydraulics,

Blida, Algeria

[email protected]

Abstract: In this work, we use the three dimensional copula for modeling the

dependence of the drought variables, severity–duration–frequency (S–D–F).

Drought is a natural event, which has huge impact on both the society and the

natural environment. Drought events are mainly characterized by their severity,

duration and intensity. The study adopts standardized precipitation index (SPI)

for drought characterization, and copula method for multivariate risk analysis of

droughts. The Beni-Behdel River basin was selected as an example to illustrate

the copulas. Results indicates that the Student copula was more appropriate for

drought analysis in the selected area. Drought probabilities and return periods

were calculated and analyzed based on the three dimensional.

Keywords: Copula, Drought, SPI index, return period.

References:

[1] C. Genest, K. Ghoudi, L.P. Rivest (1995) A semiparametric estimation

procedure of dependence parameters in multivariate families of distributions.

Biometrika 82(3):543–552

[2] H. Joe (1997) Multivariate models and dependence concepts, vol 73.

Monographs on statistics and applied probability. Chapman and Hall, London, p

399

[3] W.C. Palmer WC (1965) Meteorological drought. Research paper no. 45, US

Weather Bureau, Washington, DC.

[4].A. Tawn (1988) Bivariate extreme value theory: models and estimation.

Biometrika 75(3):397–415

[5] A. Sklar (1959) Fonctions de répartition à n dimensions et leurs marges.

Publications de l’Institut de Statistique de l’Université´ de Paris 8:229–231


______________________________________________________

10





Rayleigh-Marangoni Convection in a Layer of Nanofluid

Abdullah A. Abdullah

Department of Mathematical Sciences, Umm Al-Qura University,

Makkah, Saudi Arabia

[email protected]

Abstract: A linear stability analysis for the onset of Rayleigh-Marangoni

convection in a horizontal layer of a nanofluid heated from below is investigated.

The model employed for the nanofluid incorporates the effects of Brownian

motion and thermophoresis. The lower boundary of the layer is assumed to be a

rigid surface at fixed temperature while the top boundary is assumed to be a non-

deformable free surface cooled by convection to an exterior region at a fixed

temperature. The boundaries of the layer are assumed to be impenetrable to

nanoparticles with their distribution being determined from a conservation

condition. The linear analysis uses spectral methods based on the expansion of

eigenfunctions as Chebyshev series. Stability boundaries for Rayleigh number

and temperature and nanofraction Marangoni numbers are obtained for several

nanofluids.

Keywords: Rayleigh-Marangoni convection, Nanofluid, Linear stability,

Brownian motion, Thermophoresis.


______________________________________________________

11





On the Properties of the Orthogonal Polynomials along a

Contour

Fahreddin.G.Abdullayev1, 2, Gülnara.A.Abdullayev²

¹Kyrgyz-Turkish Manas University, Bishkek, KYRGYZSTAN,

[email protected]; [email protected]

²Mersin University, Mersin, TURKEY

[email protected]

Abstract: Let be a complex plane; L be a closed rectifiable Jordan

curve: Let ( )h z be a non-negative, summable on L and non-zero except

possible on a set of measure zero function. The systems of polynomials

( )nK z ; ( ) ...n

n nK z z ; deg nK n ; n ; satisfying the

orthonormality condition:

,( ) ( ) ( )n m n m

L

h z K z K z dz ,

are called orthonormal polynomials for the pair ( , )L h . These polynomials are

determined uniquely if the major coeficient 0n . These polynomials were

first studied in [6]. Some properties of the polynomials ( )nK z under the various

conditions on the weight function ( )h z and contour L were investigated in [1]-

[5], [7]-[9] and others (also, references in therein).

In this work, we investigated the order of growth of the modulus of ( )nK z

polynomials in the weighted space, where the contour and the weight functions

have some singularities on the finite points on the contour. Exact estimations for

the growth of the modulus of orthogonal polynomials were obtained.

Keywords: Orthogonal Polynomial, Quasiconformal Curve, Coformal Mapping.


______________________________________________________

12





References:

[1] F.G. Abdullayev.,G.A. Abdullayev, On the Sharp Inequalities for

Orthonormal Polynomials Along a Contour, Complex Analysis and Operator

Theory, 1, 2017, DOI: 10.1007/s11785-017-0640-1.

[2] G. Fauth, Über die Approximation analytischer Funktionen durch

Teilsummenihrer Szegö-Entwicklung, Mitt. Mathem. Semin. Giessen, No:67,

(1966), pp.1-83.

[3] Ya.L. Geronimus, Polynomials Orthogonal on a Circle and Interval. IX + 210

S. m. 9 Tafeln. Oxford/London/New York/Paris 1960.

[4] P.P. Korovkin, Sur les polynomes orthogonaux le long d.un contour recti.able

dans le cas de la présence d.unpoids, Rec. Math. [Mat. Sbornik] N.S., (1941) ,

Vol. 9(51), No: 3, pp. 469.485.

[5] A.L Kuz.mina, Asymptotic representation of polynomials orthogonal on a

piecewise-analytic curves, Proc. "Functional Analysis and theory of Functions",

I,.Kazan., (1963), pp. 42-50.

[6] G. Szegö, Über orthogonale Polynome, die zu einer gegebenen Kurve der

komplexen Ebene gehören, Mathem. Zeitschr. 9 (1921), pp.218-270.

[7] G. Szegö, Orthogonal Polynomials, Fizmatgis,1962, (in Russian).

[8] P.K. Suetin, Main properties of the orthogonal polynomials along a circle.

Uspekhi Math. Nauk, Vol.21, No:2 (128), (1966), pp.41-88.

______________________________________________________

13





Modeling and Classifying by using Binary Logistic Regression

Analysis Application on Hepatitis Disease Data

Qais Mustafa Abdulqader

Department of Information Technology, Duhok Polytechnic University,

Dohuk, Zakho, Iraq

[email protected]

Abstract: Logistic Regression Analysis analyze the relationship between

multiple explanatory variables and a single binary response variable, a

categorical variable with two categories [1]. Many medical applications have

been done in this area such as [2,3,4 and 5]. In this paper, the binary logistic

regression analysis technique has been used and applied for building a suitable

model for hepatitis disease data using stepwise procedure and depending on

some laboratory tests which represents explanatory variables. Also, the technique

has used for classifying persons into two groups which are infected and

uninfected with viral hepatitis disease. The evaluation was depending on some

statistical criteria. The results of the analysis have been discussed and mentioned.

Keywords: Binary logistic regression, Hepatitis, Stepwise procedure, statistical

criteria.

References:

[1] S. Sweet, and K. Martin, "Data Analysis with SPSS: A First Course in

Applied Statistics," 4th ed., Pearson publisher, 2011.

[2] S. Javali, and P. Pandit, " Multiple logistic regression model to predict risk

factors of oral health diseases," Romanian statistical review journal, 5(2012), 73-

86.

[3] P. Reeda, and Y. Wub, " Logistic regression for risk factor modelling in

stuttering research," Journal of Fluency Disorders, 38 (2013), 88-101.

[4] M. T., Dev Mukherji, N. Padalia, and A. Naidu, " A heart disease prediction

model using SVM-decision trees-logistic regression (SDL)," International

Journal of Computer Applications, 68 (2013), 11-14.

[5] W. M. Amir et al., " Association of Hypertension with Risk Factors Using

Logistic Regression, " Applied Mathematical Sciences, 8(2014), 2563 – 2572.


______________________________________________________

14





Residual Power Series Approach to Handle a Class of

Fractional Differential Equations

Ayed H. Adamat

Department of Mathematics, Faculty of Science, Al-Hussein Bin Talal

University, P.O. Box 20, Ma'an, Jordan

[email protected]

Abstract: In this paper, we present a computational algorithm to find the

coefficients of the fractional power series solutions for linear and nonlinear

differential equations of fractional order. This approach provides the solution in

the form of a rapidly convergent series with easily computable components using

symbolic computation software [1-5]. The proposed method based on the

generalized Taylor's formula that involving Caputo fractional derivative which

constructs an analytical solution in the series form and reproduces the exact

solution when the solution is a finite series. This technique is applied to a few

test examples to illustrate the accuracy, efficiency and applicability of the

method. The results reveal that the method is very effective, straightforward, and

simple.

Keywords: Fractional differential equations; Fractional power series method;

Initial value problems; Generalized Taylor series approximation.

References:

[1] A. El-Ajou, O. Abu Arqub, M. Al-Smadi, A general form of the generalized

Taylor’s formula with some applications, Applied Mathematics and

Computation, 256 (2015), 851-859.

[2] Z. Odibat, N. Shawagfeh, Generalized Taylor’s formula. Appl. Math.

Comput., 186 (2007), 286-293.

[3] K. Moaddy, M. Al-Smadi, I. Hashim, A Novel representation of the exact

solution for differential algebraic equations system using residual power-series

method, Discrete Dynamics in Nature and Society, 2015 (2015), Article ID

205207, pp.1-12.

[4] I. Komashynska, M. Al-Smadi, A. Ateiwi, S. Al-Obaidy, Approximate

analytical solution by residual power series method for system of fredholm

integral equations. Applied Math. Inform. Sci., 10 (2016) 975-985.

[5] I. Komashynska, M. Al-Smadi, O. Abu Arqub, S. Momani, An efficient

analytical method for solving singular initial value problems of nonlinear

systems. Applied Math. Inform. Sci., 10 (2016), 647-656. DOI:

10.18576/amis/100224


______________________________________________________

15





On the Existence and Uniqeness of Positive Solution for a

Fractional Boundary Value Problem with New Fractional

Derivative

Asghar Ahmadkhanlu

Department of Mathematics, Azarbaijan Shahid Madani University,

Km 35 Tabriz-Maragheh rod, Tabriz, Iran

[email protected]

Abstract: We are concerned with the existence and uniqueness of positive

solutions for the following nonlinear fractional boundary value problem:

𝐷𝑡𝐴𝐵𝑅

0𝛼𝑢(𝑡) + 𝑓(𝑡, 𝑢(𝑡)) = 0 0 < 𝑡 < 1, 1 < 𝛼 < 2

𝐷𝑡𝐴𝐵𝑅

0𝛼−1𝑢(0) = 𝑢(1) = 0

where 𝐷𝑡𝐴𝐵𝑅

0𝛼 denotes the Atangana-Baleano fractional derivative in sense of

Reimman-liouville. Our analysis relies on a fixed point theorem in partially

ordered sets. Some examples are also given to illustrate the results

Keywords: Boundary value problem, Positive solution, fixed point theorems

References:

[1] A. Atangana, “On the new fractional derivative and application to nonlinear

Fisher’s reaction-diffusion equation”, App. Math. Comp., 273(2016) 948-956.

[2] N. Al-Salti, E. Karimov and S. Kerbal, “Boundary-value problems for

fractional heat equation involving Caputo-Fabrizio derivative”, NTMSCI, 4.4

(2016), 79-89.

[3] T. Salat, “Atangana-Baleanu derivative with fractional order applied to the

model of groundwater within an

unconfined aquifer”, J. Nonlinear Sci. Appl., 9 (2016), 3647-3654.

[4] D. Baleanu1, B. Agheli, M. M. Al Qurashi, “Fractional advection differential

equation within Caputo and Caputo–Fabrizio derivatives”, Advances in

Mechanical Engineering

8.12(2016), 1–8.


______________________________________________________

16





On Derivation of a Subclasses of Filiform Leibniz Algebras

AL-Nashri AL-hossain Ahmed

Department of Mathematics, AL-Qunfudhah University college, Umm

Al-Qura University, KSA.

[email protected]

Abstract: In this paper, dimension the derivations of a Third class of Leibniz

algebras are studied and discussed. For 𝐿 ∈ 𝑇𝐿𝑏𝑛 , we have 𝑛 + 1 ≤

dim 𝐷𝑒𝑟(𝐿) ≤ 2𝑛 + 1, are deduced.

Keywords: Filiform Leibniz algebra, numerical validation, gradation,

derivation..

References

[1] Albeverio, S.; Ayupov, Sh. A.; Omirov, B. A., On nilpotent and simple

Leibniz algebras, Comm. in Algebra Vol. 33(2005), 159-172.

[2] Albeverio, S., Omirov, B. A., Rakhimov, I. S., (2006), Classi_cation of 4-

dimensional nilpotent complex Leibniz algebras, Extracta Math., 3(2006), 197-

210.

[3] AL-hossain, A. A.; Khiyar, A. A.,Derivations of some Filiform Leibniz

algebras. Pure and Applied mathematics Journal.Vol. 3,No.6,(2014), 121-125.

[4] Alnashri. A. A., Derivations of one type of algebra of First class Filiform

Leibniz algebras of Dimension Derivation (n+1), International Journal of

Advanced Scienti_c and Technical Research,Vol. 1,No.5,(2015), 41-55.

[5] Alnashri. A. A., Derivations of Second type of algebra of _rst class Filiform

Leibniz algebras of Dimension Derivation (n+1), International Journal of

Advanced Scientific and Technical Research,Vol. 3,No.5,(2015), 29-43.

[6] Ayupov, Sh. A.; Omirov, B. A., On Leibniz algebra, Algebra and Operator

Theory. Proceeding of the Colloquium in Tashkent (1997), Kluwer (1998),

Doi 10.1007/978-94-011-5072-9-1 Springer, p 1-13.

[7] Ayupov, Sh. A.; Omirov, B. A., On 3-dimensional Leibniz algebra, Uzbek

Math. J. (1999), 9-14.

[8] Dixmier. J. and Lister. W. G. , Derivations of nilpotent Lie algebras, Proc.

Amer. Math. Soc. 8(1957), 155-158.

[9] Jacobson. N. , A note on automorphisms and derivations of Lie algebras,

Proc. Amer. Math. Soc. 6(1955), 281283.


______________________________________________________

17





Global Existence and Uniqueness of Weak Solution to a

Chemotaxis Model

N. Aïssa and A. Balehouane

Laboratoire AMNEDP, Faculté de Mathematiques

USTHB

BP 32, El Alia, Bab Ezzouar,

16111 Alger, Algeria.

Abstract: We prove global existence and uniqueness of weak solutions to a

chemotaxis model with nonlinear diffusion.

First, we use a fixed point theorem to prove local in time existence of a weak

solution.

In order to prove that the solution is global in time, we provide a priori estimates

of the solution in an appropriate Lebesgue space by adapting the method of [3].

Then, we obtain uniform bounds of the solution by using the result [1] based on

Moser's iterative method.

KeyWords: Quasilinear Parabolic Systems, Reaction-Diffusion Systems,

Chemotaxis.

References:

[1] N. D. Alikakos, Lp bounds of solutions of reaction-diffusion equations.

Comm. Partial Differential Equations 4, (1979), 827-868.

[2]R. Kowalczyk, Z. Szymanska, On the global existence of solutions to an

aggregation model, J. Math. Anal. Appl. 343 (2008), 379-398.

[3] L. Wang, C. Mu, P. Zheng, Q. Zhang, Global existence and boundedness of

classical solutions to a parabolic-parabolic chemotaxis system, Nonlinear Anal.

Real. World. Appl 14, 1634-1642 (2013).

______________________________________________________

18





A Generalization of Hereditary Noetherian Prime Rings

Evrim Akalan

Department of Mathematics, Hacettepe University,

Ankara, Turkey

[email protected]

Abstract: In this talk, we will introduce generalized hereditary noetherian prime

rings (G-HNP rings for short) which generalizes the class of hereditary

noetherian prime (HNP rings for short) rings. We will describe the structure of

projective ideals of G-HNP rings and some over rings of G-HNP rings.

Examples will be given to illustrate and delimit the theory.

Keywords: HNP Rings, projective ideals, invertible ideals.

References:

[1] D. Eisenbud, J. C. Robson, “Hereditary Noetherian Prime Rings”, J. Algebra

16 (1), (1970), 86-104.

[2] H. Marubaysahi, “A Krull type generalization of HNP rings with enough

invertible ideals”, Comm.

in Algebra 11 (5) (1983), 469-499.


______________________________________________________

19





On Some Inequalities of Analytic and Biunivalent

Functions Given by Subordination

Arzu Akgul

Department of Mathematics, Kocaeli University,

Kocaeli, Turkey

[email protected]

Abstract: In the present investigation, the subclass MΣ𝜑

(𝛾, 𝜆, 𝛿)_ of analytic

biunivalent functions is defined and established bounds for the coefficients for

this subclass. Also several related classes are considered and connections to

earlier known results are made.

Keywords: Analytic and bi-univalent functions, subordination, coefficient

estimate

References:

[1] R. M. Ali, S. K. Lee, V. Ravichandran and S. Supramaniam, Coefficient

estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math.

Lett., 25, (2012), 344-351.

[2] D.A. Brannan, T.S. Taha, On some classes of bi-univalent functions, in: S.M.

Mazhar, A. Hamoui, N.S. Faour (Eds.), Math. Anal. and Appl., Kuwait; February

18.21, 1985, in: KFAS Proceedings Series, vol. 3, Perg-

amon Press, Elsevier Science Limited, Oxford, 1988, pp. 53.60. see also Studia

Univ. Babe¸s-Bolyai Math. 31 (2) (1986) 70.77.

[3] D. A. Brannan and J. G. Clunie, Aspects of comtemporary complex analysis,

(Proceedings of the NATO Advanced Study Instute Held at University of

Durham:July 1-20, 1979). New York: Academic Press, (1980).

[4] S. Bulut, Faber polynomial coe¢ cient estimates for a subclass of analytic bi-

univalent functions, Filomat, Vol. 30, No. 6, (2016),1567-1575 .

[5] S. S. Ding, Y. Ling, and G. J. Bao, Some properties of a class of analytic

functions, Journal of Mathematical Analysis and Applications, vol. 195, no. 1,

pp. 71.81, 1995

[6] B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions,

Applied Mathematics Letters, 24, (2011), 1569-1573.

[7] E. Deniz, Certain subclasses of bi-univalent functions satisfying subordinate

conditions, Journal of Classical analysis, 2, 1, (2013), 40-60.

[8] J. M. Jahangiri and S. G. Hamidi, Coe¢ cient estimates for certain classes of

bi-univalent functions, Int. J. Math. Sci., ArticleID 190560, (2013), 4 pp.


______________________________________________________

20





Compact Finite Differences Method for Burgers-Huxley

Equation

Canan Akkoyunlu

Department of Mathematics and Computer Sciences, Istanbul Kultur University,

Bakırkoy, Istanbul, Turkey

[email protected]

Abstract: In this paper, a numerical solution for the Burgers-Huxley equation is

presented by using compact finite differences method. In the solution of the

problem, finite differences discretization along the time, and fifth-order compact

finite differences scheme along the spatial coodinate are applied. Dispersive

properties for the compact finite difference method are investigated for the

linearized equations to examine the nonlinear dynamics after discretization. The

result shows that the applied method in this study is an applicable tecnique and

approximates the exact solution very well.

Keywords: Burger-Huxley equation, compact finite differences method,

dispersion analysis.

References:

[1] AG. Bratsos, “A fourth order improved numerical scheme for the generalized

Burgers-Huxley equation’’, J. Comput Math, 1(2011), 152-158.

[2] B. Batiha, MSM. Noorani and I. Hashim, “Application of variational iteration

method to the generalized Burgers-Huxley equation’’, Chaos Solitons Fractals,

36(2008), 660-663.

[3] HNA, Ismail, K. Raslan, AAA. Rabboh, “Adomain decomposition method

for Burgers-Huxley and Burgers-Fisher equation’’, Appl Math Comput,

159(2004), 291-301.

[4] I. Hashim, MSM. Noorani and MRS. Al-Hadidi, “Solving the generalized

Burgers-Huxley equation using the adomain decomposition method’’, Math

Comput Model, 43(2006), 1404-1411.

[5] M. Javidi, “A numerical solution of the generalized Burgers-Huxley equation

by pseudospectral method and darvishi’s preconditioning’’, Appl Math Comput,

175(2006), 1619-1628.

[6] M. Javidi, “A numerical solution of the generalized Burgers-Huxley equation

by spectral collocation method’’, Appl Math Comput, 178(2006), 338-344.


______________________________________________________

21





Approximation Solution of System of Volterra Integro

Differential Using Finite Element Method

Adel Alamarashi*

*Department of Mathematics, College of Science

Jazan University, KSA.

*Department of Mathematics, College of Education,

Thamar University, Yemen.

[email protected] ; [email protected]

Abstract: In the present paper, we first obtain variational form of the problem,

and then, finite element method and basis functions will be used. Also, the error

analysis of the method is considered. Furthermore, we give numerical

computational example to test and validate the proposed method.

Keywords: System Of Volterra Integro-Differential; Finite element method-

error analysis.

References:

[1] Adel. Al-Marashi and Al-Faour.O.M. "Approximate solution for system of

multi- term initial value problem of Fractional Differential Equations by Spline

functions". Sana'a University Journal of Science & Technology, (2008), 1,

pp.251-264.

[2] Adel A. Al-Marashi ,” Approximate Solution of the System of Linear

Fractional Integro-Differential Equations of Volterra Using B- Spline Method”,

American Review of Mathematics and Statistics December 2015, Vol. 3, No. 2,

pp. 39-47

[3] Adel Al-Marashi. “Numerical Solution For Multi-term Fractional Orders

Differential Equations By Splin Functions”, Journal Focuses on Human

Knowledge and Applied Sciences, Issue no 9,June (2008),pp.170 – 187

[4] Z. Mahmoodi , J. Rashidinia & E. Babolian, B-Spline collocation method for

linear and nonlinear Fredholm and Volterra integro-differential equations, pp.

1787-1802, Journal Applicable Analysis An International Journal Volume 92,

2013 - Issue 9.

[5] Hermann Brunner, The numerical treatment of Volterra integro-differential

equations with unbounded delay, Journal of Computational and Applied

Mathematics, Volume 28, December 1989, Pages 5-23.



______________________________________________________

22





Fixed Point Theorem in FM-Spaces

Rateb AlBtoush

Department of Mathematics& Statistics

Faculty of Science P.O. Box (7)

Mu'tah University

Al-Karak-Jordan

[email protected]

Abstract: The goal of this section is to study the existence problems of fixed

points or common fixed points for some varieties of single-valued mappings in

non-Archimedean probabilistic fuzzy metric space.

Keywords: Fixed Point, Compatible mappings, Non-Archimedean Menger

probabilistic normed spaces.

References:

[1] Y. J. Cho, Fixed points in fuzzy metric spaces, J. Fuzzy Math. 5(1997), 949-

962.

[2] S. S. Chang, On the theory of probabilistic metric spaces with applications,

Acta Math. Sinica, New Series, 1(4) (1985), 366-377.

[3] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Set Syst. 27(1998),

385-390.

[4] V. Gregori, S. Morillas and A. Sapena, Examples of fuzzy metrics and

applications, Fuzzy Sets Syst. 170(2011), 95111.

[5] P.J. He, The variational principle in fuzzy metric spaces and its applications,

Fuzzy Sets and Systems, 45 (1992), 389394.

[6] M. Hegedus and T. Szilagyi, Equivalence conditions and a new _xed point

theorem in the theory of contraction mappings, Math. Japonica, 25 (1) (1980),

147-157.


______________________________________________________

23





Bounds for the Zeros of Polynomials by Using Similar Matrices

Mohammad. Al-Hawari

Department of Mathematics, Irbid National University,

Irbid, Jordan

[email protected]

Abstract: We apply several matrix inequalities to the similar Frobenius

companion matrices of monic polynomials to derive new bounds for the zeros of

these polynomials which are better than other bounds.

Keywords: Bounds for the zeros of polynomials; Companion matrix; Spectral

norm; Spectral radius

References:

[1] Horn, R.A. and Johnson, C.R., 1985, Matrix Analysis (Cambridge:

Cambridge University Press).

[2] Hou, J.C. and Du, H.K., 1995, Norm inequalities of positive operator

matrices. Integral Equations Operator Theory, 22, 281–294.

[3] Kittaneh, F. and Shebrawi, K .,2007,Bounds for the zeros of polynomials

from matrix inequalities – II, Linear and Multilinear Algebra., 55:2, 147-158.

[4] Kittaneh, F., 2003, Bounds for the zeros of polynomials from matrix

inequalities. Archiv des Mathematik, 81, 601–608.

[5] Kittaneh, F., 2003, A numerical radius inequality and an estimate for the

numerical radius of the Frobenius companion matrix. Studia Mathematica, 158,

11–17.

[6] Linden, H., 2000, Bounds for zeros of polynomials using traces and

determinants. Seminarberichte Fachbereich Mathematik FeU Hagen., 69, 127–

146.

[7] Mohammad H. Al-Hawari.,2016, ZEROS OF POLYNOMIALS BY USING

SOME INEQUALITIES. Far East Journal of Mathematical Sciences (FJMS).,

Volume 100, Number 10, 2016, Pages 1545-1550.


______________________________________________________

24





An Application of Decision Tree for Evaluating a Classroom

Teaching Practice

Sadri Alija and Halil Snopce

Faculty of Business and Economics,

South East European University,

Tetovo, Macedonia

[email protected]

Faculty of Contemporary Sciences and Technologies,

South East European University,

Tetovo, Macedonia

[email protected]

Abstract: The aim of this research is to use the decision-making tree in order to

give the meaning for the classification of some activities done during the

realization of the math subject lesson. Actually, the aim is to identify which

activity is more important in achieving the objective of the lesson and at the

same time, which one has bigger impact in achieving the final results on the

math course.

In total we have used 22 variables divided into three different groups: The first

one is about some activities concerning the beginning of the lesson, the second

groups are the variables about the continuation of the lesson and the third groups

are the variables concerning the exercises and assessment. For all of these three

activities we have chosen the averages of the answers for every group separately.

In this research are shown the results gathered from 48 randomly chosen students

of the Faculty of Business Economics at the SEE-University in Macedonia, who

have attended the math subject on the winter semester of the year 2016.

For the construction of the decision making tree, we have used the ID3 algorithm

by using the Weka software.

We have found that the root of the decision-making tree is the attribute

concerning the activities taken at the beginning of the lesson. This attribute at the

same time is the most important attribute from all 4 attributes.

Key words: Teaching practice, decision tree, ID3 algorithm, Weka software



______________________________________________________

25





Existence of Positive Solution of Boundary Value Fractional

Quadratic Differential Equations

Youssef Allaoui1, Khalid Hilai2 and Guida Karimi3

Laboratory of Applied Mathematics and Scientific Computing 1,2,3

Faculty Of Sciences and Technologies1,2,3

Sultan Moulay Slimane University, PO Box 523, 23000 Beni Mellal,

Morocco1,2,3

[email protected],[email protected],

[email protected]

Abstract: In this work, we prove the existence as well as approximate of the

positive solutions for boundary value problem of nonlinear fractional quadratic

differenrtial equations. We use some porprieties of the Mittag-Leffler functions

and its relationship with fractional calculus. Also we obain some results

regarding the existence of positive solutions using the Dhage iterative method

enbodied in a recent hybrid fixed point theorem of Dhage in partially ordered

normed lineair spaces.

Keywords: Fractional quadratic differential equation, Mittag-leffler equation,

Dhage iterative method, Approximate positive solution.

References:

[1] Bapurao C.Dhage, Lakshmikantham.V, Basic results on hybrid differential

equations, Nonlinear Anal. Hybrid syst. 4, 414-424 (2010).

[2] Bapurao C.Dhage, Lakshmikantham, Quadratic perturbations of periodic

boundary value problems of second order ordinary differential equations. Differ.

Equ. Appl. 2, 465-486 (2010).

[3] Bapurao C.Dhage and Shyam B. Dhage: Approximating positive solutions of

nonlinear first order ordinary quadratic differential equations: Applied and

Interdisciplinary Mathematics, Cogent Mathematics 2,1023671(2015).

[4]Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergi V. Rogostin:

Mittag-Leffler functions, Related Topics and Applications. Springer-Verlag

Berlin Heidelberg 2014.

[5]K.Hilal, A. Kajouni: Boundary value problems for hybrid differential

equations. Mathematical Theory and modeling. 2224-5804 (2015).


mailto:%[email protected]


______________________________________________________

26





z

Some Applications of Cozero Sets in Topological Spaces

Ahmad Al-Omari

Al al-Bayt University, Faculty of Sciences, Department of Mathematics

P.O. Box 130095, Mafraq 25113, Jordan

[email protected]

Abstract: An ideal on a set X is a nonempty collection of subsets of X with

heredity property which is also closed finite unions. The concept of ideal

topological spaces via cozero sets was introduced by Al-Omari [10]. In this

paper, we introduce and study some an operator via cozero sets and we construct

a topology τ∗ for X by using the cozero sets and an ideal I on X. Moreover, we

obtain characterizations and preserving theorems of quasi compact spaces.

Keywords: cozero set, zero set, quazi compact space, ideal topological space. References:

[1] S. Bayhan and I. L. Reilly, On some variants of compactness, Hacettepe

Journal of Mathematics and Statistics 43 (6) (2014), 891–898.

[2] S. Bayhan, A. Kanibir, A. McCluskey, and I. L. Reilly, On almost z-

supercontinuity, Filomat 27(6) (2013), 965–969.

[3] Z. Frolik, Generalizations of compact and Lindelof sppaces (Russian),

Czechoslovak Math. J. 9(84) (1959), 172–217.

[4] L. Gillman and M. Jerison, Rings of Continuous Functions, Van Nos- trand

Co., Inc., Princeton, N. J. 1960.

[5] J. K. Kohli and R. Kumar, Z-supercontinuous functions, Indian J. Pure Appl.

Math. 33 (7) (2002), 1097

[6] J. K. Kohli, D. Singh and R. Kumar, Generalizations of z-

supercontinuous functions and Dδ -supercontinuous functions, Appl. Gen.

Topology 9 (2008), 239-251.

[7] J. K. Kohli, D. Singh and J. Aggarwal, F-supercontinuous functions, Appl.

Gen. Topol. 10 (1) (2009)

[8] M. K. Singal and S. B. Niemse, z-continuous mappings, Math. Student 66

(1997), 193-210.

[9] W. T. Van Est and H. Freudenthal, Trennung durch stetige Funktionen in

topologischen Rau¨men, Indagationes Math. 15 (1951), 359-368.

[10] A. Al-Omari, On ideal topological spaces via cozero sets, Questions and

Answers in General Topology 34 (2) (2016), 83–91.

[11] D. Jankovic and T. R. Hamlett, New topologies from old via ideals, Amer.

Math. Monthly, 97 (4) (1990), 295-310.


______________________________________________________

27





An Efficient Analytical-Numerical Technique for Handling

Model of Fuzzy Differential Equations of Fractional-Order

Mohammad Aloroud1, Mohammed Al-Smadi2,*, Rokiah Rozita Ahmad1, Ummul

Khair Salma Din1

1School of Mathematical Sciences, Faculty of Science and Technology,

Universiti Kebangsaan Malaysia 2Department of Applied Science, Ajloun College, Al-Balqa Applied University,

Ajloun 26816, Jordan

[email protected]

Abstract: This paper proposes an efficient analytical numerical technique for

finding approximate solutions for a class of fuzzy fractional initial value

problems. The algorithm is based on the generalized Taylor series residual power

series (RPS), which is extended to handle such problems. The analytical solution

is calculated in the form of multiple fractional power series expansion of a

rabidly convergent series with easily computable components. In addition,

description of the RPS method is discussed [1-6]. In this sense, some numerical

examples are given to show the effectiveness and performance of the proposed

method. The results reveal that the method is quite accurate, simple,

straightforward, and convenient for exploring fuzzy fractional models.

Keywords: Generalized Taylor series, Residual power series method, Initial

value problem, Fuzzy fractional differential equations.

References:

[1] K. Moaddy, M. Al-Smadi and I. Hashim, A Novel Representation of the

Exact Solution for Differential Algebraic Equations System Using Residual

Power-series Method, Discrete Dynamics in Nature and Society, Vol. 2015

(2015), Article ID 205207, 1-12. http://dx.doi.org/10.1155/2015/205207

[2] M. Al-Smadi, Solving initial value problems by residual power series

method, Theoretical Mathematics & Applications 3(1), (2013) 199-210.

[3] I. Komashynska, M. Al-Smadi, O. Abu Arqub and S. Momani, An efficient


systems, Applied Mathematics & Information Sciences, 10(2), (2016) 647-656.


______________________________________________________

28





[4] I. Komashynska, M. Al-Smadi, A. Ateiwi and S. Al-Obaidy, Approximate

Analytical Solution by Residual Power Series Method for System of Fredholm

Integral Equations, Applied Mathematics & Information Sciences 10 (3), (2016)

975-985.

[5] I. Komashynska, M. Al-Smadi, A. Al-Habahbeh, A. Ateiwi, Analytical

approximate Solutions of Systems of Multi-pantograph Delay Differential

Equations Using Residual Power-series Method, Australian Journal of Basic and

Applied Sciences 8 (10), (2014) 664-675.

[6] O. Abu Arqub, Series solution of Fuzzy differential equations under strongly

generalized differentiability. J. Adv. Res. Appl. Math. 5, (2013) 31–52.

______________________________________________________

29





Adaptation of Fractional Power Series Method for Solving

Fuzzy BVPs

Mohammad Alaroud1, Rokiah Rozita Ahmad1, Mohammed Al-Smadi2,*,

Ummul Khair Salma Din1

1School of Mathematical Sciences, Faculty of Science and Technology,

Universiti Kebangsaan Malaysia 2Department of Applied Science, Ajloun College, Al-Balqa Applied University,


[email protected]

Abstract: In this paper, we propose a computational iterative technique, the

fractional power seies method (FPR) for finding numeric-analytic solutions for a

class of fuzzy BVPs. The approach constructs to express the solutions in form of

a series expansion in terms of elementary α-level representation [1-6]. By

linguistic of fuzzy terms, the fuzzy fractional equation is converted to system of

fractional equations in crisp case, whereas the crisp results are mapped to fuzzy

output using the membership functions. Further, numerical examples are

provided and discussed quantitatively and graphically to show the performance

features, generality and superiority of the FRP algorithm. The results reveal that

the method is quite accurate, simple, straightforward, and convenient for

exploring fuzzy fractional models.

Keywords: Generalized Taylor series, Residual power series method, Boundary

value problem, Fuzzy fractional differential equations.

References:

[1] K. Moaddy, M. Al-Smadi and I. Hashim, A Novel Representation of the

Exact Solution for Differential Algebraic Equations System Using Residual

Power-series Method, Discrete Dynamics in Nature and Society, Vol. 2015

(2015), Article ID 205207, 1-12. http://dx.doi.org/10.1155/2015/205207

[2] M. Al-Smadi, Solving initial value problems by residual power series

method, Theoretical Mathematics & Applications 3(1), (2013) 199-210.

[3] I. Komashynska, M. Al-Smadi, O. Abu Arqub and S. Momani, An efficient


systems, Applied Mathematics & Information Sciences, 10(2), (2016) 647-656.

doi:10.18576/amis/100224.

[4] I. Komashynska, M. Al-Smadi, A. Ateiwi and S. Al-Obaidy, Approximate

Analytical Solution by Residual Power Series Method for System of Fredholm

http://dx.doi.org/10.1155/2015/205207


______________________________________________________

30





Integral Equations, Applied Mathematics & Information Sciences 10 (3), (2016)

975-985. doi:10.18576/amis/100315

[5] I. Komashynska, M. Al-Smadi, A. Al-Habahbeh, A. Ateiwi, Analytical

approximate Solutions of Systems of Multi-pantograph Delay Differential

Equations Using Residual Power-series Method, Australian Journal of Basic and

Applied Sciences 8 (10), (2014) 664-675.

[6] O. Abu Arqub, Series solution of Fuzzy differential equations under strongly

generalized differentiability. J. Adv. Res. Appl. Math. 5, (2013) 31–52.

______________________________________________________

31





Solving Fuzzy Mixed Integral Equations of Second Kind in

Hilbert Spaces

Mohammed Al-Smadi

Department of Applied Science, Ajloun College, Al-Balqa Applied University,

Ajloun 26816, Jordan [email protected]

Abstract: In this paper, we propose a computational iterative technique for

finding numeric-analytic solutions for a class of fuzzy mixed integral equations

of the second kind based on orthonormal basis sets derived from Gram-Schmidt

process in reproducing-kernel Hilbert spaces [1-6]. The approach constructs to

express the solutions in form of a series expansion in terms of elementary 𝛼-level

representation in the Sobolev space 𝜔2[𝑎, 𝑏]. By linguistic of fuzzy terms, the

fuzzy integral equation is converted to system of integral equations in crisp case,

whereas the crisp results are mapped to fuzzy output using the membership

functions. Further, numerical examples are provided and discussed quantitatively

and graphically to show the performance features, generality and superiority of

the reproducing-kernel algorithm.

Keywords: Fuzzy calculus, Reproducing-kernel theory, Fredholm-Volterra

integral equations, Fourier series expansion.

References:

[1] O. Abu Arqub, M. Al-Smadi and N. Shawagfeh, “Solving Fredholm integro-

differential equations using reproducing kernel Hilbert space method”, Applied

Mathematics and Computation, 219 (2013), 8938-8948.

[2] M. Al-Smadi, O. Abu Arqub and S. Momani, “A Computational Method for

Two-Point Boundary Value Problems of Fourth-Order Mixed Integrodifferential

Equations”, Mathematical Problems in Engineering, 2013 (2013), Article ID

832074, 1-10. http://dx.doi.org/10.1155/2013/832074

[3] O. Abu Arqub and M. Al-Smadi, “Numerical algorithm for solving two-

point, second-order periodic boundary value problems for mixed integro

differential equations,Applied Mathematics and Computation,243(2014)911-922


______________________________________________________

32





[4] O. Abu Arqub, M. Al-Smadi, S. Momani and T. Hayat, “Numerical Solutions

of Fuzzy Differential Equations using Reproducing Kernel Hilbert Space

Method”, Soft Computing, (2015), 1-20. http://dx.doi.org/10.1007/s00500-015-

1707-4

[5] M. Al-Smadi, O. Abu Arqub, N. Shawagfeh and S. Momani, “Numerical

investigations for systems of second-order periodic boundary value problems

using reproducing kernel method”, Applied Mathematics and Computation, 291

(2016) 137-148.

[6] O. Abu Arqub, M. Al-Smadi, S. Momani and T. Hayat, “Application of

reproducing kernel algorithm for solving second-order, two-point fuzzy

boundary value problems”, Soft Computing, 2016 (2016), 1-16.

doi:10.1007/s00500-016-2262-3

______________________________________________________

33





Numerical Algorithm for Solving Time-Fractional Bvps in a

Simplified Reproducing Kernel Space

Mohammed Al-Smadi

Department of Applied Science, Ajloun College, Al-Balqa Applied University,


[email protected]

Abstract: In this paper, we propose a computational iterative technique for

finding numeric-analytic solutions for a class of of time-fractional boundary

value problem within favorable aspects of the reproducing kernel Hilbert space

in Caputo sense. The algorithm methodology is based on generating an

orthonormal basis sets derived from Gram-Schmidt process [1-6]. The approach

constructs to express the solutions in form of a series expansion in terms of

elementary representation in the Sobolev space. Error estimates are obtained as

well as numerical examples are provided and discussed quantitatively and

graphically to show the performance features, generality and superiority of the

reproducing-kernel algorithm. The numerical results indicate that the IRKA is a

significant development tool for handling such issues arising in computer,

physics and engineering fields.

Keywords: Fractional differential equations; Reproducing kernel theory; Inner

product spaces; Error estimation and error bound.

References:







832074, 1-10. http://dx.doi.org/10.1155/2013/832074


point, second-order periodic boundary value problems for mixed integro-

differential equations”, Applied Mathematics and Computation, 243 (2014), 911-

922.


______________________________________________________

34








1707-4




(2016) 137-148.




doi:10.1007/s00500-016-2262-3

______________________________________________________

35





Semiregularization of Almost Countably Compact Spaces

Zuhier Altawallbeh

Department of Mathematics, Tafila Technical University,

Tafila 66110, Jordan

[email protected]

Abstract: Among various covering properties of topological spaces a lot of

attention has been made to those covers. Weakly Lindelöf spaces were

introduced by Frolik [1] and nearly compact spaces were defined by Singal and

Mathur [2]. Other generalizations of Lindelöfness and compactness are given by

many authors as Balasubramanian [3], and Altawallbeh and Al-Momany in [4].

Bonanzinga, Matveev and Pareek [5] defined almost countably compact spaces

as a generalization of countably compact spaces. In this paper, we investigate

this new class of spaces, almost countably compact spaces, also we study some

other properties in the view of regular cover notion and semiregularization

topology relating to this class of spaces.

Keywords: regularly open sets, regularly closed sets, countably compact, nearly

countably compact, semiregularization topology.

References:

[1] Z. Frolik, “Generalizations of compact and Lindelöf spaces”, Czechoslovak

Math. J., 9.84(1959), 172-217.

[2] M.K Singal and A. Mathur, “On nearly compact spaces”, Boll. Un. Mat Ital.,

2.4(1969), 702-710.

[3] G. Balasubramanian, “On some generalizations of compact spaces”, Glas.

Mat. Ser. III, 17.37(1982), 357-380.

[4] Z. Altawallbeh and A. Al-Momany, “Nearly countably compact spaces”,

International Electronic Journal of Pure and Applied Mathematics, 8.4(2014),

59-56.

[5] M. Bonanzinga, M.V Matveev and M. Pareek, “Some remarks on

generalizations of countably compact spaces and Lindelöf spaces”,

Rend.Circ.Mat.palermo, 2.51.1(2002), 163-174.


______________________________________________________

36





Generalization on Countably Compact Spaces via Hereditary

Classes

Zuhier Altawallbeh

Department of Mathematics, Tafila Technical University,

Tafila 66110, Jordan

[email protected]

Abstract: A lot of work has been taken in account to generalize different

covering properties of spaces as compact and countably compact spaces in

different ways either by taking topologies with respect to an ideal as in [1] which

was presented by Hamlett and Jankovic or by giving weaker condition in the

definition as nearly countably compact spaces which is done by Altawallbeh and

Al-Momany in [2]. In this article, we use the notions of generalized topologies

and hereditary classes that was presented by Csa sza r in [3] and [4]. Here, we

define and characterize the countably compact spaces taking in account

generalized topologies in terms of hereditary classes. In particular, by setting a

generalized topology μ on a nonempty set X, we define new concept of

countably compactness, μԨ-countably compact space in generalized topology μ

in the sense of a hereditary class Ԩ, called ԨGTS. The space ԨGTS is μԨ-

countably compact if for every countable μ- covering of X there exists a finite

subset such that the complement, in X, of the union of sets of that subset belongs

to Ԩ.

Keywords: hereditary class, generalized topology.

References:

[1] T.R. Hamlett and D. Jankovic, “Ideals in general topology”, General

Topology and Applications, 1988, 115-125.

[2] Z. Altawallbeh and A. Al-Momany, “Nearly countably compact spaces”,

International Electronic Journal of Pure and Applied Mathematics, 8.4(2014),

59-56.

[3] Ả. Csẚszẚr, “Generalized topology, generalized continuity”, Acta Math.

Hungar, 96 (2002), 351-357.

[4] Ả. Csẚszẚr, “Modification of generalized topologies via hereditary classes”,

Acta Math. Hungar, 1-2. 115 (2007), 29-36.


______________________________________________________

37





Hybrid Master Equation of the Jump Diffusion Approximation

Derya Altintan* and Heinz Koeppl**

*Department of Mathematics, Selcuk University,

Konya, Turkey

**Department of Electrical Engineering and Information Technology,

Technische Universitat Darmstadt,

Darmstadt, Germany

[email protected]

Abstract: Most often biochemical reactions are multi-scale processes because

of the differences in the abundance of species and the reaction rates. To exploit

this multi-scale nature, hybrid models which combine the deterministic and

stochastic approaches are needed. In [1], we propose a jump diffusion

approximation to model and simulate these types of systems. The idea of the

method is to partition the reactions into fast and slow subgroups and model the

fast group by Langevin equation while slow group is modelled by continuous

time Markov chains. In this study, we define a new vector whose components

represents the number of occurrences of reactions in the hybrid model given in

[1]. Similar to the idea of splitting the reactions into two different groups, we

consider this vector as a combination of random vectors represent the continuous

and discrete random processes which count the occurrence of reactions in the fast

group and the slow group, respectively. Based on the studies in [4], we prove

that the time derivative of the probability distribution of this new vector which is

called hybrid master equation is a summation of the Fokker-Planck equation

(FPE) [2] which represents the time evolution of the conditional probability

distribution of the continuous random variable given discrete random variable

and chemical master equation (CME) [3] which is the time derivative of the

marginal distribution of the discrete variable.

Keywords: Multi-Scale Processes, Jump-Diffussion Approximation, Fokker-

Planck Equation (FPE), Chemical Master Equation (CME).








______________________________________________________

38





References:

[1] A. Ganguly, D. Altintan, H. Koeppl, “Jump-diffusion approximation of

stochastic reaction dynamics: Error bounds and algorithms”, SIAM journal of

Multiscale Modeling and Simulations, 13. 4 (2015), 1390-1419.

[2] D. T. Gillespie, “The Chemical Langevin and Fokker-Planck Equations for

the Reversible Isomerization Reaction”, The Journal of Physical Chemistry A,

106.20 (2002), 5063-5071.

[3] D. T. Gillespie, “A rigorous derivation of the chemical master equation,”

Physica A, 188 (1992), 404–425.

[4] R. F. Pawula. “Generalizations and extensions of the fokker-planck-

kolmogorov equations”, IEEE Transactions on Information Theory , 13.1, 1967,

33-41.

Acknowledgments

This work is supported by the Scientific and Technological Research Council of

Turkey (TÜBİTAK) Program no:3501 Grant, no. 115E252.

______________________________________________________

39





Coefficient Bounds for a Subclass of Analytic Functions with

Respect to Symmetric Points

Osman Altintas1, Oznur Ozkan Kilic2

1 Department of Mathematics Education, Baskent University,,

Ankara, Turkey

[email protected] 2 Department of Technology and Knowledge Management, Baskent University,,

Ankara, Turkey

[email protected]

Abstract: In this paper, we determine the coefficient bounds for a subclass of

analytic functions with respect to symmetric points which is introduced here

several corollaries are also considered.

Keywords: Analytic function, Close-to-convex function, Close-to-star function,

Symmetric points.

References:

[1] O. Altıntaş, “On a subclass of certain starlike functions with negative

coefficients”, Math. Japonica 36, No. 3, (1991), 489-495.

[2] O. Altıntaş, “Certain applications of subordination associated with

neighborhoods”, Hacettepe J.Math. Statist. 39, No. 4, (2010), 527-534.

[3] R. Bucur, D. Breaz and L. Georgescu, “Third hankel determinant for a class

of analytic functions with respect to symmetric points”, Acta Univer. Apulensis,

No.42, (2015), 79-86.

[4] R.N. Das, P. Sing, “On subclasses of schlicht mappings”, Indian. J. Pure

Appl. Math. 8 (1997), 864-872.

[5] K. Sakaguchi, “On certain univalent mappings”, J. Math. Soc. 11 (1959),

Japan, 72-75.

[6] C. Selveraj, N. Vasanthi, “Subclasses of analytic functions with respect to

symmetric and conjugate Points”, Tamkang J. Math. 42 (1) (2011), 87-94

[7] H. M. Srivastava, O. Altinta_s and S. K. Serenbay, “Coefficient bounds for

certain subclasses of starlike functions of complex order”, Appl. Math. Lett. 24

(2011), 1359-1363.



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40





On The Relationship Between A Family of Fibonacci And

Lucas Numbers

Ipek Altun2, Ali Aydogdu1, Engin Ozkan2

1Department of Mathematics and Computing, Beykent University 2Department of Mathematics. Erzincan University

[email protected], [email protected], [email protected]

Abstract: In this work, we prove some properties of a family of Fibonacci

numbers. Also some relationship between the family of Fibonacci and Lucas

numbers are given.

Keywords: Fibonacci Numbers, Generalized Fibonacci Numbers, Lucas

Numbers.

References:

[1] V.E. Hoggatt, “Fibonacci and Lucas numbers”, Houghton Mifflin, 1969

[2]. J. lvie , “A General Q-Matrix”, Fibonacci Quarterly, Vol. 10, No. 3, April,

1972, 255-261

[3] T. Koshy, “Fibonacci and Lucas numbers with applications”, John Wiley &

Sons, Inc.; 2001.




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41





Convergence, Consistency and Stability in Intuitionistic Fuzzy

Differential Equations

Bouchra Ben Amma1, Said Melliani2 and Lalla Saadia Chadli3

Laboratory of Applied Mathematics and Scientific Computing 1,2,3

Faculty Of Sciences and Technologies1,2,3

Sultan Moulay Slimane University, PO Box 523, 23000 Beni Mellal,

Morocco1,2,3

[email protected] , [email protected],

[email protected]

Abstract: In this work, we consider first-order intuitionistic fuzzy differential

equations with initial value conditions. The convergence, consistency and

stability of difference method for approximating the solution of intuitionistic

fuzzy differential equations are studied. Then the local truncation error is defined

and sufficient conditions for convergence, consistency and stability of difference

method are provided and some examples are presented to illustrate the accuracy

of our proposed concepts.

Keywords: Intuitionistic fuzzy differential equations, Convergence,

Consistence, Stability, Local truncation error

References:

[1] K. Atanassov, Intuitionistic fuzzy sets. VII ITKR’s session, Sofia (deposited

in Central Science and Technical Library of the Bulgarian Academy of Sciences

1697/84) (1983)

[2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986),

pp. 87-96.

[3] K. Atanassov, Operators over interval valued intuitionistic fuzzy sets, Fuzzy

Sets Syst. 64(2) (1994), pp. 159-174.

[4] S. Abbasbandy, T. Allahviranloo, Numerical Solution of fuzzy differential

equations by Taylor method, J.of Comp.Methods in Appl. Math. 2 (2002), 113-

124.

[5] S. Abbasbandy, T. Allahviranloo, O. Lopez-Pouso, J.J. Nieto, Numerical

methods for fuzzy differential inclusions, Journal of Computer and Mathematics

With Applications 48 (2004), pp. 1633–1641.




______________________________________________________

42





SQCQP Descent Scheme for Multi-objective Optimization

Problem

Md Abu Talhamainuddin Ansary 1, Geetanjali Panda2

Department of Mathematics, Indian Institute of Technology Kharagpur

Kharagpur, India 1 [email protected], 2 [email protected]

Abstract: Developing numerical approximation techniques for multi-objective

programming problem (MOP): (f1, f2,…fm) , f: is a

growing research area in recent time. Some of these techniques for unconstrained

MOP include steepest descent scheme by Fliege and Svaiter [1] in 2000, Newton

scheme by Fliege, Drummond, and Svaiter [2] in 2009, Quasi-Newton scheme

by Qu, Goh and Chan [3] in 2011 and for constrained MOP include SQP scheme

by Fliege and Vaz [4] in 2015. The SQP scheme due to Fliege and Vaz

considers the linear approximation of the constraint functions and quadratic

approximation of all objective functions. This paper has focused on nonlinear

MOP with inequality constraints and developed a descent converging sequence

considering quadratic approximation of both constraints and all objective

functions at every iterating point. This method is follows the idea of sequential

quadratically constrained quadratic program (SQCQP) technique. A non-

differentiable penalty function l∞ is used to restrict the constraint violations. It is

proved that the descent sequence generated in this process converges to a critical

point under Slater constraint qualifications. Global convergence of this scheme is

justified with some mild assumptions. This process is free from any kind of

priori chosen parameters and ordering information of objective functions as in

scalarization processes. The proposed scheme is verified and compared with

existing methods using a set of test problems.

Keywords: Sequential quadratically constrained quadratic programing; Slater

constraint qualification; Penalty function, Critical point.

References:

[1] J .Fliege and B.F. Svaiter, “Steepest descent scheme for multicriteria

optimization”, Math. Methods Oper. Res., 51.3(2000), 479-494.

[2] J. Fliege, L. M. G. Drummond, and B.F. Svaiter, “Newton's method for

multiobjective optimization”, SIAM J. Optim, 20.2(2009), 602-626.

[3] S. Qu and M. Goh and F. T. S. Chan , “Quasi-Newton methods for solving

multiobjective optimization”, Oper. Res. Lett., 39(2011), 139-150.

[4] J. Fliege and A. I. F. Vaz, “A method for constrained multiobjective

optimization based on SQP techniques”, SIAM J.Optim., 24.4(2015), 2091-2119.



______________________________________________________

43





On Gauss Balancing and Gauss Cobalancing Numbers

Mustafa Asci and Mustafa Yilmaz

Department of Mathematics, Pamukkale University, Kınıklı, Denizli, Turkey

[email protected]

Abstract: A. Behera and G.K. Panda [1] defined new number sequence

Balancing numbers as following: They call a natural number 𝑛 a balancing

number if

1 + 2 + ⋯ + (𝑛 − 1) = (𝑛 + 1) + (𝑛 + 2) + ⋯ + (𝑛 + 𝑟)

for some natural number 𝑟, while they call 𝑟 the balancer corresponding to the

balancing number 𝑛.

According to Panda and Ray [2] the values of 𝑛 satisfying the Diophantine

equation

1 + 2 + ⋯ + 𝑛 = (𝑛 + 1) + (𝑛 + 2) + ⋯ + (𝑛 + 𝑟)

for some natural number 𝑟 are known as cobalancing numbers while 𝑟 is the

cobalancer corresponding to the cobalancing number 𝑛. Many authors study the

interesting properties of Balancing and Cobalancing numbers. In this paper we

define and study the Gaussian Balancing and Gaussian Cobalancing numbers.

We give many properties of these numbers and we prove these properties by

matrix methods.

Keywords: Balancing Numbers, Cobalancing Numbers, Gauss Fibonacci

Numbers.

References:

[1] A. Behera and G.K. Panda. On the square roots of triangular numbers. The

Fib. Quart, 49 (1)28-33,

[2] G.K. Panda and P.K. Ray Cobalancing Numbers and Cobalancers. Int. J.

Math. Sci., 2005 (8): 1189-1200.

[3] Liptai, K.; Panda, G. K.; Szalay, L. A balancing problem on a binary

recurrence and its associate. Fibonacci Quart. 54 (2016), no. 3, 235–241.

[4] Rout, S. S.; Panda, G. K. k-gap balancing numbers. Period. Math. Hungar.

70 (2015), no. 1, 109–121.

[5] Davala, R. K.; Panda, G. K. On sum and ratio formulas for balancing

numbers. J. Indian Math. Soc. (N.S.) 82 (2015), no. 1-2, 23–32.

[6]Panda, G. K.; Panda, A. K. Balancing-like sequences associated with integral

standard deviations of consecutive natural numbers. Fibonacci Quart. 52 (2014),

no. 5, 187–192.

[7] Panda, G.K.; Rout, S. S. Gap balancing numbers. Fibonacci Quart. 51

(2013), no. 3, 239–248.

http://www.ams.org/mathscinet/search/author.html?mrauthid=328728

http://www.ams.org/mathscinet/search/publications.html?pg1=ISSI&s1=329193&sort=oldest


http://www.ams.org/mathscinet/search/journaldoc.html?id=1493






























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44





An Overview of Ordering Based on Nullnorms

Emel Asici

Department of Software Engineering, Faculty of Technology,

Karadeniz Technical University,

Trabzon, Turkey

[email protected]

Abstract: Nullnorms and t-operators were introduced by Calvo and et all [1] and

Mas and et all [2], respectively, which are also generalizations of the notions of

t-norms and t-conorms. In [3] Mas and et all it is pointed out that nullnorms and

t-operators are equivalent since they have the same block structures in [0,1]2. In

[4] Asici was define and discuss an order induced by nullnorms on bounded

lattices. In this paper, we investigate some properties an order induced by

nullnorms on bounded lattices. We determine with the examples the relationship

between the order induced by a nullnorm and the order on the lattice. So, 𝑆-

partial order and 𝑇-partial order are extended to a more general form.

Keywords: Nullnorm, Bounded Lattice, Partial order.

References:

[1] T. Calvo, B. De Baets and J. Fodor, “The functional equations of Frank and

Alsina for uninorms and nullnorms”, Fuzzy Sets Syst., 120(2001), 385-394.

[2] M. Mas, G. Mayor and J. Torrens, “t-operators”, Int. J. Uncertain. Fuzz.

Knowl.-Based Syst., 7(1999), 31-50.

[3] M. Mas, G. Mayor and J. Torrens, “The distributivity condition for uninorms

and t-operators”, Fuzzy Sets Syst., 7(1999), 31-50.

[4] E. Aşıcı, “An order induced by nullnorms and its properties”, Inf. Sci., 267

(2014), 323-333.

[5] E. Aşıcı and F. Karaçal, “On the T-partial order and properties”, Fuzzy Sets

Syst.,

[6] E. P. Klement, R. Mesiar and E. Pap, “Triangular Norms ”, Kluwer

Academic Publishers, Dordrecht 2000.

[7] J. Drewniak, P. Drygas and E. Rak, “Distributivity between uninorms and

nullnorms”, Fuzzy Sets Syst., 159(2008), 1646-1657.

[8] J. Casasnovas and G. Mayor, “Discrete t-norms and operations on extended

multisets”, Fuzzy Sets Syst., 159(2008), 1165-1177.


______________________________________________________

45





Analytical-Numerical Solutions for a class of Systems of

Differential Equations Using Reproducing Kernel Method

Ali Mahmud Ateiwi

Department of Mathematics, Faculty of Science, Al-Hussein Bin Talal

University, P.O. Box 20, Ma'an, Jordan

[email protected]

Abstract: This paper proposes an efficient numerical method to obtain

analytical-numerical solutions for a class of system of boundary value problems.

This new algorithm is based on a reproducing kernel Hilbert space method [1-6].

The analytical solution is calculated in the form of series in reproducing kernel

space with easily computable components. In addition, convergence analysis for

this method is discussed. In this sense, some numerical examples are given to

show the effectiveness and performance of the proposed method. The results

reveal that the method is quite accurate, simple, straightforward, and convenient

to handle a various range of differential equations.

Keywords: System of differential equations, Reproducing kernel method,

Boundary value problem, Gram-Schmidt process.

References:




doi:10.1007/s00500-016-2262-3




832074, 1-10. http://dx.doi.org/10.1155/2013/832074




(2016) 137-148.




______________________________________________________

46






1707-4


point, second-order periodic boundary value problems for mixed integro-

differential equations”, Applied Mathematics and Computation, 243 (2014), 911-

922.




______________________________________________________

47





A Fuzzy Project Scheduling with Constrained Resources

Lyazzat Atymtayeva, Ardakbek Kungaliyev, Daniyar Artykov

Department of Computer Engineering, Satbayev Kazakh National Research

Technical University, Almaty, Kazakhstan

[email protected]

Abstract: The problems of project scheduling optimization in the conditions of

constrained resources have been researched by many authors including Arvind

Sathi et al. [1], Xiaoqing (Frank) Liu et al. [2], Wang [3], Herroelen, W. et al.

[4], Javad Nematian et al. [5] and others. They have been focused on the using of

fuzzy logic and systems as an intelligent component in project management tools

for scheduling. The main purpose for their researches was the development of an

algorithm for solving Fuzzy Random Resource-Constrained Project Scheduling

problem. This problem concerned the using of linear programming approach that

was proposed by Alvarez-Valdes and Tamarit in 1993 [6]. In this paper we use

the mentioned concepts for development of intelligent tools and algorithms in

fuzzy project scheduling and discuss the ways how to make it enabled the

converting of original complex scheduling model to a mixed integer

programming model. Keywords: fuzzy project random resource-constrained scheduling, linear

programming, mixed interger programming.

References:

[1] Arvind Sathi, Thomas E. Morton, and Steven F. Roth.Callisto: An Intelligent

Project Management System, Journal AI Magazine. 7(5), 34-52 (1986)

[2] Xiaoqing (Frank) Liu, Gautam Kane, Monu Bambroo. An intelligent early

warning system for software quality improvement and project management,

Journal of Systems and Software. 79(11), 15521564 (2006)

[3] Wang, J. A fuzzy project scheduling approach to minimize schedule risk for

product development. Fuzzy Sets andSystems, 127, 99116 (2002).

[4] Herroelen W., and R. Leus. Project Scheduling under Uncertainty: Survey

and Research Potentials. European Journal of Operational Research 165, 289306

(2005).

[5] Javad Nematian, Kourosh Eshghi, Abdolhamid Eshragh- Jahromi. A

Resource-Constrained Project Scheduling Problem with Fuzzy Random

Duration. Journal of Uncertain Systems Vol.4, No.2, pp.123-132, 2010

[6] Alvarez-Valdes, R. and J. Tamarit. The project Scheduling Polyhedron:

Dimension, Facets and Lifting Theorems. European Journal of Operational

Research 67, 1993, pp. 204-220


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48





A Convergent Two-Level Linear Scheme for the Generalized

Rosenau-Kdv-RLW Eqution

Ayhan Aydin

Department of Mathematics, Atilim University,

Incek, Istanbul, Turkey

[email protected]

Abstract: A new convergent two-level finite difference scheme is proposed for

the numerical solution of initial value problem of generalized Rosenau-KdV-

RLW equation. The new scheme is linear and conservative. It contains one free

parameter. The impact of the parameter to error of the numerical solution is

studied. The prior estimate of the finite difference solution is obtained. The

existence, uniqueness and convergence of the scheme are proved. Accuracy and

reliability of the scheme is tested by simulating the solitary wave graph of the

equation. Numerical experiments indicate the efficiency of the method..

Keywords: conservative scheme, convergence, solitary wave.

References:

[1] Wongsaijai, B., Poochinapan, K., A tree-level average implicit finite

difference scheme to solve equation obtained by coupling the Rosenau-KdV

equation and the Rosenau-RLW equation, Applied Mathematics and

Computation, 245, (2014), 289-304.

[2] Pan, X., Wang, Y., Zhang, L., Numerical analysis of a pseudo-compact C-N

conservative scheme for the Rosenau-KdV equation coupling with the Rosenau-

RLW equation, Boundary Value Problem, (2015):65.

[3] Y.L. Zhou, Application of Discrete Functional Analysis to the Finite

Difference Methods, International Academic Publishers, Beijing, 1990


______________________________________________________

49





Fuzzy Soft Metric and Fuzzifying Soft Topology Induced by

Fuzzy Soft Metric

Ebru Aydogdu, Abdulkadir Aygunoglu, Halis Aygun

Department of Mathematics, Kocaeli University, Kocaeli, Turkey

[email protected] , [email protected] ,

[email protected]

Abstract: The aim of this study is to define fuzzy soft metric compatible to soft

theory and investigate fuzzifying soft topology induced by fuzzy soft metric. For

this, firstly we introduce a fuzzy soft metric on soft set and by using this we

construct a fuzzy metric on soft set. Then we investigate fuzzifying soft topology

characterized by this fuzzy metric and studied their properties.

Keywords: Soft metric, Fuzzy metric, Fuzzifying soft topology.

References:

[1] A. Aygünoğlu and H. Aygün, “Some notes on soft topological spaces”,

Neural Computing and Applications, 21.1(2012),113-119.

[2] A. Aygünoğlu, V. Cetkin and H. Aygün, “An introduction to fuzzy soft

topological spaces”, Hacettepe Journal of Mathematics and Statistics,

43.2(2014), 197-208.

[3] A. George and P. Veeramani, “On some results in fuzzy metric spaces”,

Fuzzy sets and systems, 64.3(1994), 395-399.

[4] A. Shostak, “Two decades of fuzzy topology: basic ideas, notions and

results”, Russ.Math.Surv., 44(1989), 125-186.

[5] B.P. Varol and H.Aygün, “Fuzzy soft topology”, Hacettepe Journal of

Mathematics and Statistics, 41.3(2012), 407-419.

[6] J.J. Minana and A. Šostak, "Fuzzifying topology induced by a strong fuzzy

metric." Fuzzy Sets and Systems 300 (2016), 24-39.

[7] M. Shabir and M. Naz, “On soft topological spaces” Comput. Math. Appl.”,

61(2011), 1786-1799.

[8] P.K. Maji, R. Biswas and A.R. Roy, “Soft set theory” Computers &

Mathematics with Applications, 45(2003), 555-562.

[9] S. Das and S.K. Samanta, “Soft real sets, soft real numbers and their

properties”, J. Fuzzy Math., 20.3(2012), 551-576.

[10] S. Das and S.K. Samanta, “Soft metric”, Annals of Fuzzy Mathematics and

Informatics, 6.1(2013), 77-94.

[11] S. Das and S.K. Samanta, “On soft metric spaces”, J. Fuzzy Math.,

21.3(2013), 707-734.




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50





Some Identities Associated With Hecke Operators

Aykut Ahmet Aygunes

Department of Software Engineering, Faculty of Engineering and Architecture,

Antalya Akev University,

Antalya, Turkey

[email protected]

Abstract: In this paper, we introduce the Hecke operators and we give some

properties of these operators. Then we deal with a new approach, based on

Hecke operators, to study a large class of special polynomials including

Bernoulli and Euler polynomials. From this new approach we obtain some

identities associated with Hecke operators.

Keywords: Hecke operators, partial Hecke operators, Bernoulli and Euler

polynomials.

References:

[1] L. Euler, Methodus generalis summandi progressiones, Comment. acad. sci.

Petrop., v.6 (1738) 68-97.

[2] Y. Hellegouarch, Invitation aux mathématiques de Fermat-Wiles, Dunod.

(2001).

[3] T. Kim, Symmetry identities for the twisted generalized Euler polynomials ,

Adv. Stud. Contemp. Math. Vol 19 ( 2009 ), 111-118.

[4] T. Kim, Some identities of symmetry for the generalized Bernoulli numbers

and polynomials , ( 2009) Arxiv, http://arxiv.org/pdf/0903.2955.

[5] J. L. Raabe, Zurückführung einiger Summen and bestimmten Integrale auf

die Jacob Bernoullische Function, Journal für die reine and angrew. math., 42

(1851) 348-376.

[6] J-P. Serre, Cours d'arithmétique, PUF, 1970.


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51





Some Rough Convergence Criteria for the Sequences of

Intervals of Fuzzy Numbers

Salih Aytar

Department of Mathematics, Süleyman Demirel University,

lsparta, Turkey

[email protected]

Abstract: An interval of fuzzy number is a set of fuzzy numbers with the

property that any fuzzy number that lies between two fuzzy numbers in the set is

also included in the set. In this talk, we examine the rough convergence relations

between a sequence of intervals of fuzzy numbers and a sequence of fuzzy

numbers included these intervals.

Keywords: Rough convergence; Fuzzy interval numbers

References:

[1] F.G. Akçay, S. Aytar (2015), Rough convergence of a sequence of fuzzy

numbers, Bulletin of Mathematical Analysis and Applications, 7(4): 17-23.

[2] S. Aytar (2008). Rough statistical convergence, Numer. Funct. Anal. and

Optimiz. 29(3-4):291-303.

[3] H.X. Phu (2001), Rough convergence in normed linear spaces, Numer. Funct.

Anal. and Optimiz., 22:201-224.


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52





Modified Simple Equation Method and its Applications to

Some Nonlinear Physical Equations

Gizel Bakicierler and Emine Misirli

Department of Mathematics, Ege University,

Bornova, İzmir, Turkey

[email protected] , [email protected]

Abstract: The model of many problems encountered in various fields of

engineering and science such as plasma physics, mathematical physics and fluid

mechanics is expressed by nonlinear partial differential equations. Therefore, it is

very important to investigate the solutions of these equations. In this paper, wave

solutions of some nonlinear physical equations are obtained by Modified Simple

Equation Method and wave types are determined. This method have been applied

(2+1) dimensional Calogero-Bogoyavlenskii-Schiff (CBS) equation and (3+1)

dimensional Jimbo-Miwa equation as a result we obtained exact solution

functions. The graphics of solution functions have been drawn using the

Mathematica program and these solutions of equations are interpreted.

Key Words: nonlinear partial differential equations, evolution equations,

modified simple equation method

References:

[1] Ayati, Zainab, "Exact Solutions of Nonlinear (2+ 1)-Dimension Nonlinear

Dispersive Long Wave and Coupled Boiti–Leon–Pempinelli Equations by using

the Modified Simple Equation Method." World Applied Programming, WAP

journal, Vol (3), Issue (12), December 2013. 565-571.

[2] Jawad, Anwar Ja’afar Mohamad, Marko D. Petković and Anjan Biswas,

"Modified simple equation method for nonlinear evolution equations." Applied

Mathematics and Computation 217 (2010): 869-877.

[3] Khan, M. Ashrafuzzaman and M. Ali Akbar, "Exact and Solitary Wave

Solutions to the Generalized Fifth-order KdV Equation by Using the Modified

Simple Equation Method." Applied and Computational Mathematics 4,3 (2015)

[4] Zayed, Elsayed ME, and Hoda Ibrahim SA, "Modified simple equation

method and its applications for some nonlinear evolution equations in

mathematical physics." International Journal of Computer Applications 67, 6

(2013).

mailto:emine.misirli@


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53





Jacobi Elliptic Function Solutions of the Space-Time Fractional

Symmetric Regularized Long Wave Equation

Dilek Varol Bayrama, Sevil Çulhab, Ayşegül Daşcıoğlua

aDepartment of Mathematics, Faculty of Science and Arts, Pamukkale

University, Denizli, 20070, Turkey bInstitute of Science, Pamukkale University, Denizli, 20070, Turkey


Abstract: In this work, new families of analytical exact solutions of the

fractional nonlinear symmetric regularized long wave (SRLW) equation are

presented by using the Jacobi elliptic function expansion method. By this

method, the solutions are found in general form containing the hyperbolic,

trigonometric, and rational functions. Also, the complex valued solutions and

soliton solutions are obtained.

Keywords: Jacobi elliptic function, fractional differential equation, SRLW

equation

References:

[1] S. Ahmadian, M.T. Darvishi, New exact traveling wave solutions for space-

time fractional (1+1)-dimensional SRLW equation, Optik 127 (2016)

10697–10704.

[2] R. Abazari, Application of 𝐺′ 𝐺⁄ -expansion method to traveling wave

solutions of three nonlinear evolution equations, Comput. Fluids 39

(2010)1957–1963.

[3] F. Xu, Application of exp-function method to symmetric regularized long

wave (SRLW) equation, Phys. Lett. A 372 (2008) 252–257.

[4] H. Jafari, N. Kadkhoda, C.M. Khalique, Travelling wave solutions of

nonlinear evolution equations using the simplest equation method,

Computers and Mathematics with Applications 64 (2012) 2084–2088.

[5] J.F.Alzaidy, The fractional sub-equation method and exact analytical

solutions for some nonlinear fractional PDEs, American Journal of

Mathematical Analysis, 1 (1) 2013 14-19.

[6] O. Guner, D. Eser, Exact Solutions of the Space Time Fractional

Symmetric Regularized Long Wave Equation Using Different Methods

Advances in Mathematical Physics, 2014 Article ID 456804.



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54





Functional Quadratic Integral Equations in the L1loc (R+) space

Latifa Benhamouche and Smail Djebali

Department of Mathematics, Faculty of Sciences, Saad Dahlab University

Blida, Algeria

[email protected]

Abstract : In this work we study the existence of solutions of functional

quadratic integral equations of Volterra type in the space L1loc (R+) consisting of

all real functions locally integrable on the positive real half axis. The main result

of this paper is obtained by using the new concept of family of measures of weak

noncompactness recenlty introduced by Olszowy in [1] a 2014 paper, which is

applied here in conjection with the Schawder- Tychonov fixed point theorem.

In fact many authors studied the solvability of different types of integral

equations on the Banach space BC (R+) consisting of all real functions defined,

bounded and continuous on the positive real half axis, while in some practical

situations integral equations are well understood in 𝐿1 settings see for example

Taoudi [3].

Recently in a 2015 paper [2], Wang and Zhou developed some fixed point

theorems in locally convex spaces with Krein-Smulian property. As an

application authors gave existence result in the space L1loc (R+) to a general

Volterra integral equation. Unfortunately the quadratic case is not covered by

their result. The quadratic case was followed with interest in [4] but only on

bounded intervals. In the present paper we focus on the question of existence of

solutions of functional quadratic integral equations on unbounded intervals.

References:

[1] L. Olszowy, A family of measures of noncompactness in the space L1loc (R+)

and its application to some nonlinear Volterra integral equation,Mediterr. J.

Math. 11, 2014, no. 2, 687--701.

[2] F. Wang, H. Zhou,Fixed point theorems and the Krein-Smulian property in

locally convex spaces, Fixed Point Theory Appl. 2015, 2015:154.

[3] N. Salhi and M.A Taoudi, Existence of integrable solutions of an integral

equation of Hammerstein type on unbounded interval, M. J of mathemathiques,

[4] A. Bellour, D. O'Regan, M.A. Taoudi, On the existence of integrable

solutions for a nonlinear quadratic integral equation, J. Appl. Math. Comput.

2014, 46:67-77.


______________________________________________________

55





Suborbital Graphs for a Non-Transitive Action of the

Normalizer

Murat Besenk, Bahadır Ozgur Guler, Abdurrahman Buyukkaya

Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey


Abstract: The notion of suborbital graphs was introduced by Sims[6]. We can

summarize Sims’theory as follows: a permutation group G act on a set H,

suborbital graphs formed by this action with vertex-set H on which G induces

automorphisms. After it was shown that this idea is also useful in the study of the

modular group whichis a finitely generated Fuchsian group[3], some other

finitely generated groups have been studied by suborbital graphs[1,2,4]. In most

of them, it has been emphasized the connection between elliptic elements in

group and circuits of the same order in graph closely related with the signature

problem. It is known that the graph of a group provides a method by which a

group can be visualized; in many cases it suggests an economical algebraic proof

for a result and it gives same information but in a much more efficient way [5].

In this view, the idea of suborbital graph has been used mainly by finite group

theorists. The aim of this paper is to examine the action of the normalizer which

produce some congruence equations with solutions. Actually, the suborbital

graphs of the normalizer were studied for some special cases[2]. In here, taking a

different case, we obtained new results.

Keywords: Normalizer, Imprimitive action, Suborbital graphs.

References:

[1] M. Beşenk, “Circuit lengths of graphs for the Picard group”. J Inequal Appl

(2013), 106:8.

[2] B.O. Güler et al., “Elliptic elements and circuits in suborbital graphs”, Hacet

J Math Stat 40(2) (2011), 203–210.

[3] G.A. Jones, D. Singerman, K. Wicks, “The modular group and generalized

Farey graphs”, Lond Math Soc Lect Note Ser 160(1991), 316–338.

[4] S. Kader, B.O. Güler (2013) “On suborbital graphs for the extended modular

group”, Gr Comb, 29(2013), 1813–1825.

[5] M. Magnus, A. Karrass, D. Solitar, “Combinatorial group theory”. Wiley,

New York, (1966).

[6] C.C. Sims, “Graphs and finite permutation groups”, Math. Z. 95(1967), 76–

86.




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56





On Spherically Symmetric Solutions of the Einstein-Maxwell

Field Equations

Rashida Bibi and Azad A. Siddiqui

Department of Mathematics, School of Natual Sciences, National University of

Science and Technology (NUST),

Islamabad, Pakistan

[email protected]

Abstract: In literature many solution of the Einstein-Maxwell equations have

been found [1-8]. We consider the spherically symmetric geometry and classify

the solutions of the Einstein-Maxwell equations by considering the null/non-null

electromagnetic field and isotropic/anisotropic mater with the help of Segre type

of the spacetime.

Keywords: Einstein-Maxwell Equations, null/non-null Electromagnetic Field,

Segre Type, and Isotropic/Anisotropic geometry.

References:

[1] H. Stephani, D. Kramer, M. MacCallum and C. Hoenselaers, Exact Solutions

to Einstein Field Equations, (2009).

[2] C. B. G. Mclntosh, J. M. Foyster and A. W. C. Lun, The classi_cation of the

Ricci and Plebanski Tensors in General Relativity using Newman-Penrose

Formalism, J. Math. Phys., 22 (1980).

[3] Tooba Feroze. Exact solutions of the Einstein-Maxwell equations with linear

equation of state, Can.J.Phys (2012). 90 1179-1183.

[4] G. S. Hall, and D. A. Negm, Physical structure of the energy-momentum

tensor in General Relativity, Int. J. Theo Phys. Volume 25, (1986).

[5] Rashida Bibi, Tooba Feroze, and Azad A. Siddiqui, Solution of the Einstein–

Maxwell equations with anisotropic negative pressure as a potential model of a

dark energy star, Canadian Journal of Physics 2016.

[6] S. Thirukkanesh and S. D. Maharaj, Charged Anisotropic Matter with Linear

Equation of State, Class. Quant. Grav., 25 (2008).

[7] M. K. Mak and T. Harko, Quark Stars Admitting a One Parameter Group of

Conformal Motions, Int. J. Mod. Phys. D, 13 (2004).

[8] J. M. Sunzu, S. D. Maharaj and S. Ray, Quark Star Model with Charged

Anisotropic Matter, Astrophysics and Space Science, 354 (2014).


______________________________________________________

57





A Numerical Approximation Based on Collocation Method for

the Solutions of Telegraph Equation

Kübra Erdem Bicer

Department of Mathematics, Manisa Celal Bayar University,

Manisa, Turkey

[email protected]

Abstract: In this paper, a numerical method based on Bernoulli polynomials is

developed to solve telegraph equations. By using Bernoulli polynomials and

collocation points, the main problem is reduced to the system of algebric

equations, after evaluating some matrix operations. By solving this system, we

obtain the coefficients of approximate solutions of the main problem. And also to

demonstrate the validity and applicability of this method, an error analysis based

on residual function is developed and this method is applied to some examples.

Keywords: Telegraph Equations, Partial Differential Equations, Numerical

Methods, Bernoulli Polynomials.

References:

[1] H. M Lieberstein, “Theory of Partial Differential Equations”, Academic

Press, New York (1972).

[2] G . Doetsch, “Introduction to the Theory and Application of the Laplace

Transformation”, Springer, Berlin (1974).

[3] D. R. Bland, “Wave Theory and Applications”, Oxford Clarendon press,

London (1988).

[4] V. H. Weston and S. He, “Wave splitting of the telegraph equation in R3 and

its application to inverse scattering”, InverseProblems, 9 (1993), 789–812.

[5] P. M. Jordan and A . Puri, “Digital signal propagation in dispersive media”,

Journal of Applied Physics, 85.3 (1999), 1273–1282.

[6] J. Banasiak and J. R. Mika, “Singular perturbed telegraph equations with

applications in the random walk theory” Journal of Applied Mathematics and

Stochastic Analysis, 11.1(1998), 9–28.

[7] P. R. Wallace, “Mathematical Analysis of Physical Problems”, Dover, New

York (1984).

[8] L. Debnath and P. Mikusinski, “Introduction to Hilbert Spaces with

Applications”, Elsevier Academic Press, London (2005).


______________________________________________________

58





Rotating Disk Cryptosystem: RDC

Sadek Bouroubi and Louiza Rezkallah

Department of Mathematics, USTHB University,

Bab Ezzoua, Algier, Algeria

[email protected]

Abstract: Cryptography is a hot and active topic, it plays a crucial role in many

aspects nowadays, from internet banking and e-commerce to email and

webbased business processes. An important area of research today is to test the

security of cryptosystems, a cryptographic system is safe as long as no one could

not break it. Modern cryptographic algorithms are based on mathematical

problems, known to be difficult, so breaking the security of a cryptosystem

requires the solution of a such problem, as in the case of RSA [1] which is based

on the factorization problem in number theory. This paper proposes a symmetric-

key cryptosystem named Rotating Disk Cryptosystem and is denoted as RDC

used for encryption and decryption of text as well as images which is based on

chaotic function and the factorization problem.

Keywords: Rotating Disk, Symmetric-key Cryptosystem, Chaotic function,

Linear Congruential Generator Modified, Factorization Problem.

References:

[1] R. Rivest, A. Shamir and L. Adleman, « A Method for Obtaining Digital

Signatures and Public-Key Cryptosystems », Communications of the ACM, vol.

21, no 2, 1978, p. 120-126.

[2] Arjen K. Lenstra and H. W. Lenstra, Jr. (eds.). "The development of the

number field sieve". Lecture Notes in Math. (1993) 1554. Springer-Verlag.

[3] Laurence T. Yang, Li Xu, Sang-Soo Yeo, Sajid Hussain, An integrated

parallel GNFS algorithm for integer factorization based on Linbox Montgomery

block Lanczos method over GF(2). Computers Mathematics with Applications,

Volume 60, Issue 2, July 2010, Pages 338–346.

[4] Delfs, Hans Knebl, Helmut (2007). "Symmetric-key encryption".

Introduction to cryptography: principles and applications. Springer. ISBN

9783540492436


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59





Free Convection inside a Porous Enclosure

Canan Bozkaya

Department of Mathematics, Middle East Technical University,

Ankara, Turkey

[email protected]

Abstract: The steady free convection in a rectangular enclosure filled with a

fluid-saturated porous medium is numerically investigated in the present study.

The left vertical wall of the enclosure is maintained at a temperature greater than

the temperature of the right vertical wall. The top and bottom horizontal walls of

the enclosure are adiabatic. The incompressible, laminar flow inside the

homogeneous and isotropic porous medium is assumed to obey Darcy law. The

fluid physical properties are constant except the density in the body force term

which is treated according to Boussinesq approximation. The fluid and porous

medium are in thermal equilibrium, and the thermal radiation flux in y-direction

is considered negligible compared to that in x-direction. Thus, the temperature

gradient in x-direction is higher than that in y-direction. For this reason, the

thermo-diffusion velocity only in the x-direction is considered. The governing

equations, obtained under these assumptions, in non-dimensional stream function

and temperature formulation are solved using the dual reciprocity boundary

element method (DRBEM). Dual reciprocity BEM aims to transform the

differential equations into equivalent integral equations only on the boundary of

computational domain by treating the nonhomogeneity through a radial basis

function approximation. The stream function equation is solved by DRBEM in

the usual way, that is by using the fundamental solution of the Laplace equation.

On the other hand, the fundamental solution to the modified diffusion

(Laplacian) term in the energy equation (that is, the coefficients of the second

order derivatives in x- and y-directions are not equal due to higher thermal

radiation in x-direction) is used, and moreover the corresponding radial basis

functions for the modified diffusion equation are derived. The results of the

present numerical model is compared with previously published works. The

validated model is employed to investigate the effect of the physical parameters,

namely Rayleigh number and radiation parameter, on the flow and heat transfer

characteristics.

Keywords: Free convection, porous medium, thermal radiation, DRBEM.


______________________________________________________

60





Tauberian Theorems for the Cesáro Second Order Operators

for Sequences of Fuzzy Numbers

Naim L. Braha

Department of Mathematics and Computer Sciences

University of Prishtina, Avenue Mother Teresa, No-4, Prishtine, 10000, Kosova

[email protected]

Abstract: In this paper we define the Cesáro second order summability method

for fuzzy numbers and prove some theorems dealing with weighted statistical

converge of fuzzy numbers and their behaviors. In second section we prove

Tauberian theorems for this kind of summability method and in the end of the

paper we prove Tauberian theorems, related to the Cesáro second order mean-

level convergence.

Keywords: Cesáro second order summability method, Tauberian theorems.

References:

[1] Y. Altin; M. Mursaleen, H. Altinok, Statistical summability $(C,1)$ for

sequences of fuzzy real numbers and a Tauberian theorem, Journal of Intelligent

and Fuzzy Systems 21 (2010) 379-384.

[2]S. Aytar; M. A. Mammadov and S. Pehlivan, Statistical limit inferior and

limit superior for sequences of fuzzy numbers, Fuzzy Sets and Systems 157(7)

(2006), 976-985.

[3] B. Bede and S. G. Gal, Almost periodic fuzzy number valued functions,

Fuzzy Sets and Systems 147 (2004), 385-403.

[4] Braha, Naim L. Geometric properties of the second-order Ces\'aro spaces.

Banach J. Math. Anal. 10 (2016), no. 1, 1-14.

[5] N. L. Braha, Tauberian conditions under which $\lambda -$statistical

convergence follows from statistical summability $(V,\lambda ),$ Miskolc Math.

Notes 16(2) (2015), 695-703.

[6] N.L. Braha and Mikail Et, Tauberian theorems for the Euler-N\"orlund mean-

convergent sequences of fuzzy numbers, to appear in Iranian Journal of Fuzzy

Systems.

[7N.L. Braha, Tauberian Theorems under N\"orlund-Ces\'aro summability

methods (357-411), Current Topics in Summability Theory and Applications,

editors, Hemen Dutta and Billy E. Rhoades, Springer, 2016.


______________________________________________________

61





Estimating the Distortion Parameter of the Proportional

Hazards Premium for Heavy-Tailed Losses

Brahimi Brahim

Laboratory of Applied Mathematics, Mohamed Khider University, Biskra,

Algeria.

[email protected]

Abstract: Estimating the distorted parameter in the case of non negative heavy-

tailed losses has been treated in [1]. In this paper, we extend this work to the case

of the real heavy-tailed losses. We derive an asymptotic distribution of the

estimator. We construct a practically implemented confidence interval for the

distortion parameter and illustrate the performance of the interval in a simulation

study with application to real data.

Keywords: Proportional-hazard premium; Distortion risk measure; Distortion

parameter; Extreme value; Heavy tail; Risk aversion index; Lévy-stable

distribution.

References:

[1] Brahimi, B., Meraghni, D., Necir, A. and Zitikis, R., (2011). Estimating the

distortion parameter of the proportional-hazard premium for heavy-tailed losses.

Insurance Math. Econom. 49, 325-334.

[2] Brahimi, B; Abdelli, J., (2016). Estimating the distortion parameter of the

proportional hazards premium for heavy-tailed losses under Lévy-stable

regime.Insurance Math. Econom. 70 (2016), 135--143.

[3] Hill, B.M., (1975). A simple approach to inference about the tail of a

distribution. Ann. Statist. 3, 1136-1174.

[4] Necir, A. and Meraghni, D., (2010). Estimating L-functionals for Heavy-

tailed Distributions and Applications. Journal of Probability and Statistics.

Volume 2010, ID 707146.

[5] Necir, A., Rassoul, A., Zitikis, R., (2010). Estimating the conditional tail

expectation in the case of heavy-tailed losses. Journal of Probability and

Statistics 2010, ID 596839.


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62





On Some Fixed Point Results Related to Almost Generalized

(𝜶, 𝜷) − (𝝍, 𝝓) −Weakly Contractive Mappings in 𝑺 Metric

Spaces

Abdurrahman Buyukkaya1, Mahpeyker Ozturk2

1Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey 2Department of Mathematics, Sakarya University, Sakarya, Turkey

[email protected], [email protected]

Abstract: In this paper, we establish some fixed and common fixed point

theorems by using almost generalized (𝛼, 𝛽) − (𝜓, 𝜙) −weakly contractive

mappings in the settings of 𝑆 metric spaces, which given results are

generalizations of some existing literature.

Keywords: Fixed Point, Almost Contraction, Admissible Mappings, S Metric

Spaces.

References:

[1] L. Ciric, M. Abbas, R. Saadati and N. Hussain, Common fixed points of

almost generalized contractive mappings in ordered matric spaces , Appı. Math.

Comput. 217(2011), 5784-5789.

[2] M. Abbas, G. V. R. Babu, and G. N. Alemayehu, On common fixed of

weakly compatible mappings satisfying generalized condition (B), Filomat,

25(2) (2011), 9-19.

[3] S. Alizadeh, F. Moradlou, P. Salimi, Some fixed point results for

(Alpha,Beta)-(Psi,Phi)-conrtactive mappings, Filomat, 28(3) (2014) 635-647.

[4] S. Sedghi, N. Shobe, S. Aliouche, A generalization of fixed point theorems S

metric spaces, Matematicki Vesnik, 64(3) (2012), 258-266.

[5]O. Yamaod, W. Sintunavarat, Some Fixed Point Results for Generalized

Contraction with Cyclic (Alpha,Beta)-admissible Mapping in Multiplicative

Metric Spaces, Journal of Inequalities and Applications, 488 (2014), 1-15.

[6]S. Sedghi, N. V. Dung, Fixed point theorems on S metric spaces, Matematicki

Vesnik, 66(1) (2014), 113-124

mailto:[email protected],%[email protected]

______________________________________________________

63





Beyond Statistical Quasi Cauchy Sequences

Huseyin Cakalli

Maltepe University, Graduate School of Science and Engineering, Marmara

Egitim Koyu, TR 34857,Maltepe, Istanbul, Turkey

[email protected]

Abstract: A sequence (αk) is called -statistically downward quasi-Cauchy if

limn (1/n)|k≤n: k+1-k|=0 for every >0, where (n) is a non-decreasing

sequence of positive real numbers tending to such that limsupn (n) /n )<,

n =O(1), and αk =αk+1 – αk for each positive integer k. A real valued function

defined on a subset of the set of real numbers is -statistically downward

continuous if it preserves -statistically downward quasi-Cauchy sequences, i.e.

(f(k)) is -statistically downward quasi-Cauchy whenever (k) is. It turns out

that the set of -statistical downward continuous functions defined on an above

bounded set is a proper subset of the set of uniformly continuous fonctions.

Keywords: statistical convergence, -statistical downward quasi Cauchy

sequence,.

References:

[1] D. Burton, J. Coleman, “Quasi-Cauchy sequences”, Amer. Math. Monthly,

117 (2010), 328-333.

[2] H.Cakalli, “Forward continuity”,J. Comput. Anal. Appl.,13 2(2011),225-230.

[3] H. Cakalli, “Statistical ward continuity”, Appl. Math. Lett., 24 10 (2011),

1724-1728.

[4] H. Cakalli, “Statistical quasi-Cauchy sequences”, Math. Comput. Modelling,

54 (2011), 1620-1624.

[5] H. Cakalli, “A Variation on Statistical Ward Continuity”, Bull. Malays.

Math. Sci. Soc., DOI 10.1007/s40840-015-0195-0

[6] H.Cakalli,”Upward and downward statistical continuities”, Filomat, 29 10

(2015), 2265-2273.

[7] H.Cakalli, and H. Kaplan, “A study on N-theta-quasi-Cauchy sequences”,

Abstr. Appl. Anal, 2013 (2013), Article ID 836970, 4 pages.

[8] H. Cakalli, and H. Kaplan, “A variation on lacunary statistical quasi cauchy

sequences”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 66 2 (2017),1-9

[9] H. Cakalli, and M.K. Khan, “Summability in topological spaces”, Appl.

Math. Lett., 24 (2011), 348-352.


______________________________________________________

64





A Study on Strongly Lacunary Ward Continuity

Huseyin Cakalli*, Huseyin Kaplan**

* Maltepe University, GraduateSchool of Science and Engineering,

Marmara Egitim Koyu, Maltepe, Istanbul, Turkey

[email protected]

** Niğde University, Faculty of Science and Letters, Niğde, Turkey

[email protected]

Abstract: In this paper, the concept of a strongly lacunary 2-quasi-Cauchy

sequence is investigated. In this investigation, we proved interesting theorems

related to strongly lacunary 2-ward continuity, and some other kinds of

continuities, introducing strongly lacunary 2 ward continuity in the sense that a

real valued function f defined on a subset A of IR, the set of real numbers, is

strongly lacunary 2 ward continuous on A if it preserves strongly lacunary 2

quasi-Cauchy sequences of points in A, i.e. (f(αk)) is a strongly lacunary 2

quasi-Cauchy sequence whenever (αk) is a strongly lacunary 2 quasi-Cauchy

sequences of points in A, where a sequence (αk) is called strongly lacunary 2

quasi-Cauchy if (2 αk) is a strongly lacunary quasi-Cauchy sequence where 2

αk= αk+2 -2 αk+1 + αk for each positive integer k.

Keywords: Summability; series and sequences; continuity and related questions.

References: [1] D. Burton, and J. Coleman, “Quasi-Cauchy Sequences”, Amer. Math.

Monthly, 117 4 (2010), 328-333.

[2] Naim L. Braha, H. Cakalli, “A new type continuity for real functions”, J

Math. Analysis.7 6 (2016), 54-62.

[3] H. Cakalli, “On G-continuity”, Comput. Math. Appl., 61 (2011), 313-318.

[4] H. Cakalli, “N-theta-Ward continuity”, Abstr. Appl. Anal,. 2012 Article ID

680456 (2012), 8 pp.

[5] H. Cakalli, “A variation on arithmetic continuity”, Bol. Soc. Paran. Mat., 35

3 (2017), 195-202.

[6] H. Cakalli, C. Gunduz Aras and A. Sonmez, “Lacunary statistical ward

continuity”, AIP Conf. Proc. 1676, 020042 (2015)



______________________________________________________

65





A Study on Abel Statistical Quasi Cauchy Sequences

Huseyin Cakalli*, Iffet Taylan**

* Maltepe University, Graduate School of Science and Engineering, Marmara

Egitim Koyu, Maltepe, Istanbul, Turkey

[email protected]

** Maltepe University, Education Faculty, Maltepe, Istanbul, Turkey

[email protected]

Abstract: In this paper, we investigate the concepts of Abel statistical

convergence and Abel statistical quasi Cauchy sequences. We also study Abel

statistical continuity and Abel statistical ward continuity. A real valued function f

is Abel statistically continuous on a subset E of IR, the set of real numbers, if it

preserves Abel statistical convergent sequences, i.e. (f (pk)) is Abel statistically

convergent whenever (pk) is an Abel statistical convergent sequence of points in

E. Some other types of continuities are also studied and interesting results are

obtained.

Keywords: Statistical Convergence; Abel series method; continuity.

References:

[1] D. Burton, J. Coleman, “Quasi-Cauchy sequences”, Amer. Math. Monthly,

117 (2010), 328-333.

[2] H. Cakalli, “A study on statistical convergence”, Funct. Anal. Approx.

Comput.1 2 (2009) , 19–24.

[3] H. Cakalli, “Forward continuity”, J. Comput. Anal. Appl., 13 2 (2011), 225-

230.

[4] H. Cakalli, “Statistical ward continuity”, Appl. Math. Lett., 24 10 (2011),

1724-1728.

[5] H. Cakalli, “Statistical quasi-Cauchy sequences”, Math. Comput. Modelling,

54 (2011), 1620-1624.

[6] H. Cakalli, “On G-continuity”, Comput. Math. Appl. 61 (2011), 313-318.

[7] H. Cakalli, “A variation on arithmetic continuity”, Bol. Soc. Paran. Mat. 35 3

(2017), 195-202.

[8]H. Çakallı and M. Albayrak, “New Type Continuities via Abel Convergence”,

Scientific World Journal, 2014 (2014), Article ID 398379, 6 pages.



______________________________________________________

66





Graph Theoretical Applications of Molecular Graphs

Ismail Naci Cangul

Department of Mathematics, Uludag University,

Bursa, Turkey

Joint work with Aysun YURTTAS, Muge TOGAN, Ahmet Sinan CEVIK

Abstract: Most of the papers on graph theory published recently deal with

molecular graphs due to their intensive applications in chemistry and

pharmacology. In this paper we give some applications of topological graph

indices in these two areas.

Keywords: Molecular graph, topological graph index.

References:

[1] K. Ch. Das, N. Akgunes, M. Togan, A. Yurttas, I. N. Cangul, A. S. Cevik, On

the first Zagreb index and multiplicative Zagreb coindices of graphs, Analele

Stiintifice ale Universitatii Ovidius Constanta 24 (1) (2016)

[2] K. C. Das, K., Xu, I. N., Cangul, A. S., Cevik, A., Graovac, On the Harary

Index of Graph Operations, Journal of Inequalities and Applications, SI: Recent

Advances in General Inequalities, DOI: 10.1186/1029-242X-2013-339, 2013,

[3] K. Ch. Das, A. Yurttas, M. Togan, I. N. Cangul, A. S. Cevik, The

multiplicative Zagreb indices of graph operations, Journal of Inequalities and

Applications, (2013), 1-14.

[4] I. Gutman, N. Trinajstic, Graph theory and molecular orbitals III, Total $\pi$-

electron energy of alternant hydrocarbons, \textitChem. Phys. Lett.,

\textbf17 (1972), 535-538.

[5] H. Hosoya, K. Kawasaki, K. Mizutani, 1972, Topological index and

thermodynamic properties: Empirical rules on the boiling point of saturated

hydrocarbons, Bull. of the Chem. Soc. of Japan, 45, 3415.

[6] H. Wiener, 1947, Correlation of heats of isomerization and differences in

heats of paraffin hydrocarbons, J. of the American Chemical Society, 69, 2636

[7] H. Wiener, 1947, Structural determination of parafin boiling points, J. of the

American Chemical Society, 69, 17

[8] N. Trinajsti?, Chemical graph theory, vols. I and II, CRC, Boca Raton, FL,

1983

______________________________________________________

67





A Study on Public Transit Users’ Route Choice and

Assignment Function

Buket Capali1, Halim Ceylan2

1Department of Civil Engineering, Faculty of Engineering, Süleyman Demirel

University, Isparta, Turkey 2Department of Civil Engineering, Faculty of Engineering, Pamukkale

University, Denizli, Turkey

[email protected]

Abstract: Many passengers wants to travel between two points from point A to

point B, the next step is to determine the routes to reach their destination. This

determination relies on passenger behavior. When there are more than two routes

to travel, a rate representing the amount of interest in the travel assignment

process for the different transit routes is determined. In this study; a new formula

for transit users’ route choice and assignment, which includes travel demand and

waiting time, has been developed.

Keywords: Public transportation, route choice, transit assignment.


______________________________________________________

68





A New Developed Semi–Empirical Formula for Nuclear

Reaction Cross–Section Calculations

Veli Capali1, Mert Sekerci1, Hasan Ozdogan2, Abdullah Kaplan1

1Department of Physics, Süleyman Demirel University, Isparta, Turkey

2Department of Biophysics, Akdeniz University, Antalya, Turkey

[email protected]

Abstract: In this study; a new semi–empirical formula for reaction cross–section

calculations, which includes inelastic scattering and Coulomb effects, has been

developed. The cross–sections and asymmetry parameters are dependent on

target nuclei and the selected energies which are 10-11, 18-19 and 22-23 MeV.

The reaction cross–section calculations have been performed for (p,n) reaction

for sample materials. The cross–section values calculated from developed semi–

empirical formula have been compared with the experimental values exist in the

literature and nuclear reaction models’ computation results.

Keywords: Semi–Empirical Formula, Nuclear Cross–Section, Asymmetry

Parameter.


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69





On Uninorms on Bounded Lattices

Gül Deniz Cayli and Funda Karacal

Department of Mathematics, Faculty of Sciences, Karadeniz Technical

University, 61080, Trabzon, Turkey

[email protected]

[email protected]

Abstract: The triangular norms (t-norms) with 1 as neutral element and

triangular conorms (t-conorms) with 0 as neutral element were introduced by

Schweizer and Sklar in [14]. Uninorms that were introduced by Yager and

Rybalov in [15] are generalization t-norms and t-conorms. These operators allow

the freedom for the neutral element e (sometimes called identity) to be an

arbitrary element from unit interval [0,1], which is 1 for t-norms and 0 for t-

conorms. In [11] the existence of uninorms on an arbitrary bounded lattice 𝐿 for

the neutral element e to be an arbitrary element from 𝐿 ∖ 0,1 has been shown.

As a by-product, it has been demonstrated that the existence of the smallest

uninorm and of the greatest uninorm on L with a fixed neutral element 𝑒 ∈ 𝐿 ∖

0,1. In [6] the existence of idempotent uninorms on given bounded lattice L for

any element 𝑒 ∈ 𝐿 ∖ 0,1 playing the role of a neutral element has been proved.

By this construction method, the smallest idempotent uninorm and the greatest

idempotent uninorm with the neutral element 𝑒 ∈ 𝐿 ∖ 0,1 is obtained. In this

paper, we study uninorms on bounded lattices and investigate some properties of

these operators. By considering the existence of t-norms and t-conorms on an

arbitrary bounded lattice L, we give methods of constructing uninorms with

given neutral element 𝑒 ∈ 𝐿 ∖ 0,1. And we consider some special classes of t-

norms and t-conorms by using the presence of uninorms on arbitrary bounded

lattice L with a fixed neutral element 𝑒 ∈ 𝐿 ∖ 0,1.

Keywords: Uninorm, Bounded lattice, T-norm, T-conorm.

References:

[1] E. Aşıcı, F. Karaçal, “On the T -partial order and properties”, Inf. Sci.

267(2014), 323-333.



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70





[2] E. Aşıcı, F. Karaçal, “Incomparability with respect to the triangular order”,

Kybernetika 52(2016), 15-27.

[3] G. Birkhoff, “Lattice Theory”, American Mathematical Society Colloquium

Publishers, Providence, RI, 1967.

[4] B. De Baets, “Uninorms: the known classes”, Third Internat FLINS

Workshop in Fuzzy Logic and Intelligent Technologic, 1998.

[5] S. Bodjanova, M. Kalina, “Construction of uninorms on bounded lattices”,

IEEE 12th International Symposium on Intelligent Systems and Informatics,

SISY 2014, September 1113, 2014, Subotica, Serbia.

[6] G.D. Çaylı, F. Karaçal, R. Mesiar, “On a new classes of uninorms on

bounded lattices”, Inf. Sci. 367–368(2016), 221-231.

[7] G. Deschrijver, “Uninorms which are neither conjunctive nor disjunctive in

interval-valued fuzzy set theory”, Inf. Sci. 244(2013), 48-59.

[8] P. Drygaś, “On properties of uninorms with underlying t-norm and t-conorm

given as ordinal sums”, Fuzzy Sets Syst. 161(2010), 149-157.

[9] P. Drygaś, D. Ruiz-Aguilera, J. Torrens, “A characterization of uninorms

locally internal in A(e) with continuous underlying operators”, Fuzzy Sets Syst.

287 (2016), 137-153.

[10] J.Fodor, R.R. Yager, A. Rybalov, “Structure of uninorms,” Internat J.

Uncertain Fuzziness Knowledge-Based Systems, 5(1997), .411-427.

[11] F. Karaçal, R. Mesiar, “Uninorms on bounded lattices”, Fuzzy Sets Syst.

261(2015), 33-43.

[12] J. Martin, G. Mayor, J. Torrens, “On locally internal monotonic operations”,

Fuzzy Sets Syst. 137(2003), 27-42

[13] R. Mesiar, E. Pap, “Different interpretations of triangular norms and related

operations”, Fuzzy Sets Syst. 96(1998), 183-189.

[14] B.Schweizer, A.Sklar, “Statistical metric spaces”, Pacific J. Math, 10(1960),

313-334.

[15] R.R. Yager, A. Rybalov, “Uninorms aggregation operators”, Fuzzy Sets

Syst. 80(1996), 111-120.

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71





On Statistical Dunford and Pettis Integration

Anita Caushi

Department of Mathematical Engineering, Polytechnic University of Tirana

Mother Teresa Square nr.4, Tirana, Albania

[email protected]

Abstract: Pettis and Dunford integrals are more important concepts with respect

to modern theory of probabilities. We can find them in the definitions of

mathematical expectation as well as dispersion. Some random probailitary

funktions take the value on vectorial spaces.In this paper we extend the usual

concept of Dunford and Pettis integration to a statistical form. We give some

essential properties of them and give an example where we find one function that

is statistical Dunford integrable but not Pettis integrable. We obtain some special

properties of statistical Pettis integration which are well known for usual the

Pettis integration.

References:

[1] Bhardwaj V., Balai., On Ëeakly Statistical Convergence, international

Journal of Mathematics and Mathematical Sciences, 2007, Article iD 38530, 9p

[2] Çakalli H., A study on statistical convergence. Functional analysis,

approximation and computation 1:2(2009), 19-24

[3] Caushi, A., Tato, A., A statistical integral of Bohner type on Banach space,

Hikari Ltd Appl. Math. Sci., Vol. 6, 2012, no. 137-140, 6857-6870.

[4] Connor J., Ganichev M., and Kadets V., “A characterization of Banach

spaces ëith separable duals via weakly statistical convergence,” Journal of

Mathematical Analysis and Applications, vol. 244, no. 1, pp. 251–261, 1989.

[5] Fast H., “Sur la convergence statistique,” ColloquiumMathematicum, 2,1951.

[6] Fridy J. A., “On statistical convergence,”Analysis, 5-4, 301-313, 1985.

[7] Fridy J. A., “Statistical limit points,” Proceedings of the American

Mathematical Society, vol. 118, no. 4, pp. 1187–1192, 1993.

[8] Schoenberg i. J., “The integrability of certain functions and related

summability methods,” The American Mathematical Monthly, 66, 5, 1959.

[9] Schëabik S., Guoju Y., Topics in Banach space integration, Series in

Analysis vol. 10. Ëorld Scientific Publishing Co. Singapore 2005.

[10] Steinhaus H., “Sur la convergence ordinaire et la convergence

asymptotique,” Colloquium Mathematicum, vol. 2, pp. 73–74, 1951.

[11] Zygmund A., Trigonometric Series, Cambridge University Press,

Cambridge, UK, 1979


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72





On The Cardinality of Category Spaces

Bahaettin Cengiz1, Banu Gunturk2

1Faculty of Engineering, Baskent University,

Ankara, Turkey

[email protected]

2Faculty of Engineering, Baskent University,

Ankara, Turkey

[email protected]

Abstract: We call a compact Hausdorff space Ω a category space if C(Ω), the

space of all scalar-valued continuous functions, is a dual space. Category spaces

are necessarily extremally disconnected, and on such a space there always exists

an essentially unique category (or perfect) Borel measure. If one of the category

measures on a category space is σ-finite, then so are the rest. These measures

play a crucial role in determining the greatest lower bound for the cardinalities of

infinite category spaces. In this paper, among other things, it is proved that for

any infinite category space Ω, card(Ω) ≥ 2c if the category measure is σ-finite,

and 22ℵ1 otherwise, where c is the cardinality of the continuum, ℵ1 is the first

uncountable cardinal number, and for any infinite cardinal number ℵ, 2ℵ denotes

the cardinality of the power set of a set of cardinality ℵ. Both of the above

mentioned cardinal numbers are actually attained.

Keywords: Category space, cardinality, dual space.



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73





Remarks and Observations on Some Special Arithmetical Sums

1Elif Cetin and 2Yilmaz Simsek

1Department of Mathematics, Faculty of Art and Science, University of Manisa

Celal Bayar, Manisa, Turkey, 2Department of Mathematics, Faculty of Science University of Akdeniz TR-

07058,

Antalya, Turkey. [email protected] , [email protected]

Abstract: In this talk, we investigate some properties of the Dedekind sums and

Hardy sums. These sums are used commonly not only in analytic number theory,

but also in other areas of mathematics. The Dedekind sums arise in the

behaviour of the Dedekind eta functions under the modular groups. On the other

hand, the Hardy sums arise in the behaviour of the Theta functions under the

subgroups of the modular groups. Recently, many authors give relation between

the Dedekind sums and geometry (lattice point enumeration in polytopes,

topology (signature defects of manifolds), algorithmic complexity (pseudo

random number generators), character theory, the family of zeta functions, the

Bernoulli and Euler functions. Moreover, we give some applications of the

special arithmetic sums related to the Hardy sums, the Dedekind sums and the

other special arithmetical sums.

Keywords: Dedekind sums, Hardy-Berndt sums, Generating functions,

Bernoulli numbers and polynomials.

References:

[1] T. M. Apostol, “Introduction to Analytic Number Theory”, Springer-Verlag,

New York, USA (1976), 340pp.

[2] B.C. Berndt, “Analytic Eisenstein series, Theta-functions, and series relations

in the spirit of Ramanujan”, J. Reine Angew. Math. 303/304(1978), 332-365.

[3] E. Cetin, Y. Simsek and I.N. Cangul, “Some special finite sums related to the

three-term polynomial relations and their applications”, Adv. Difference. Equ.,

283(2014), 1-18.

[4] E. Cetin, “A Note on Hardy type Sums and Dedekind Sums”, FILOMAT,

30.4(2016), 977-983.



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74





S-Generalized Mittag-Leffler Function

Aysegul Cetinkaya, I. Onur Kiymaz, M. Baki Yagbasan

Department of Mathematics, Ahi Evran University,

Kırşehir, Turkey

[email protected]

Abstract: In this study, we introduced a new generalization of Mittag-Leffler

function by using S-generalized beta function. Furthermore, we investigated some

of its properties such as integral representations, recurrence formulas, derivative

formulas and Mellin transform.

Keywords: S-Generalized Beta function, Mittag-Leffler function, Mellin

transform.

Acknowledgement: This work was supported by Ahi Evran University Scientific

Research Projects Coordination Unit. Project Number: FEF.A3.16.035

References:

[1] Agarwal, P.,Choi, J.,Paris,R.B.“Extended Riemann-Liouville fractional

derivative operator and its applications”,J.Nonlinear Sci.Appl,8,(2015): 451-466.

[2]Chaudhry M. A., Qadir A., Rafique M., Zubair S. M., “Extension of Euler's

beta function”, J. Comput.Appl. Math., 78, (1997): 19-32.

[3] Luo, Min-Jie, Milovanovic, G. V., Agarwal, P., “Some results on the

extended beta and extended hypergeometric functions”, Applied Mathematics

and Computation, 248, (2014): 631-651.

[4] Prabhakar, T. R. “A singular integral equation with a generalized Mittag

Leffler function in the kernel”, Yokohama Math. J., 19, (1971): 7-15.

[5] Srivastava, H. M., Agarwal, P., Jain S., “Generating functions for the

generalized Gauss hypergeometric functions”, Applied Mathematics and

Computation, 247, (2014): 348-352.

[6] Srivastava, H. M., Jain, R., Bansal, M. K. “A Study of the S-Generalized

Gauss Hypergeometric Function and Its Associated Integral Transforms”,

Turkish Journal of Analysis and Number Theory, 3.5, (2015): 116-119.

[7] Srivastava, H. M., Manocha, H.L., “A Treatise on Generating Functions”,

Halsted, New York (Ellis Horwood, Chichester), (1984).

[8] Özergin, E., Özarslan, M. A., Altın, A., “Extension of gamma, beta and

hypergeometric functions”, Journal of computational and applied mathematics,

235.16 (2011): 4601-4610.

[9] Özarslan, M. A., Yılmaz, B. “The extended Mittag-Leffler function and its

properties”, Journal of Inequalities and Applications, 2014.1, (2014): 85.


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75





Jacobi Elliptic Function Solutions of Time-Fractional Kdv-

Zakharov-Kuznetsov Equation

Sevil Culha, Dilek Varol Bayram, Aysegul Dascioglu

Department of Mathematics, Faculty of Science and Arts, Pamukkale University

Denizli, Turkey [email protected]

Abstract: In this study, new analytical exact solutions of the nonlinear evolution

equation in mathematical physics, namely the conformable time-fractional KdV–

Zakharov–Kuznetsov (KdV–ZK) equation are presented by using the Jacobi

elliptic function expansion method.

Keywords: Jacobi elliptic function, fractional differential equation, KdV- ZK

equation.

References:

[1] R.L. Mace, M.A. Hellberg, The Korteweg–de Vries–Zakharov–Kuznetsov

equation for electron-acoustic waves, Phys. Plasmas 8 (6) (2001) 2649–

2656.

[2] M.H. Islam, K. Khan, M.A. Akbar, M.A. Salam, Exact traveling wave

solutions of modified KdV–Zakharov–Kuznetsov equation and viscous

Burgers equation, Springer Plus 3 (105) (2014) 1–9.

[3] T. Abdeljawad, On conformable fractional calculus, Journal of

Computational and Applied Mathematics 279 (2015) 57–66.

[4] H. Naher, F.A. Abdullah, M.A. Akbar, Generalized and improved (𝐺’/𝐺)-

expansion method for (3+1)-dimensional modified KdV–Zakharov–

Kuznetsov equation, PLoS One 8(5) (2013) 1–7.

[5] K. Khan, M. A. Akbar, Exact and solitary wave solutions for the Tzitzeica–

Dodd–Bullough and the modified KdV–Zakharov–Kuznetsov equations

using the modified simple equation method, Ain Shams Engr J 4(4) (2013)

903–909.

[6] S. T. Mohyud-Din, A. Irshad, On exact solutions of modified KdV-ZK

equation, Alexandria Engineering Journal (55) (2016) 3253-3265.

[7] E. M. E. Zayed, New traveling wave solutions for higher dimensional

nonlinear evolution equations using a generalized (𝐺′ 𝐺⁄ )-expansion

method Journal of Physics A: Mathematical and Theoretical (42) (2009).


______________________________________________________

76





A Fix-And-Optimize Heuristic for the Integrated Fleet Sizing

and Replenishment Planning Problem with Predetermined

Delivery Frequencies

Niousha Karimi Dastjerd, Kadir Ertogral

Department of Industrial Engineering, TOBB University of Economics and

Technology,

Sogutozu, Ankara, Turkey


Abstract: We tackled an integrated fleet sizing and replenishment planning

problem in a vendor managed inventory system. There is a set of customers

which must be replenished based on a given set of predetermined frequencies.

The vehicle fleet consists of multiple types of heterogeneous vehicles which

differ in carrying capacity, cost per kilometer, and ownership costs. Customer

demands are taken as deterministic values. The main decision we make in this

problem is the triple asignment of vehicle-frequency-customer. As a result of

these assignment decisions, we obtain an annual costs consisting of vehichle

ownership cost, routing cost, inventory holding and fixed replenishment costs. A

key simplification in the model is the use of linear approxiamation for the

routing cost based on the number of customers visited in a tour. The developed

model, which is new in the literature, integrates fleet sizing and replenishment

planning decisions.

Our problem is NP-hard since it can be shown that a special case of our problem

is a bin packing problem. In order to solve large problems efficiently, we

suggested and applied a fix and optimize heuristic as a solution procedure. This

fix and optimize heuristic divides the problem into smaller problems in which

some variables are binaries and the others are linearly relaxed, and it fixes the

linear decision variable iteratively. We also showed the effectiveness of the

suggested heuristic solution procedure on a large set of randomly generated

problems.

Keywords: Fleet sizing, Replenishment planning, Predetermined frequencies,

Fix and Optimize



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77





Catalogue of Degree Sequences of Molecular Graphs

Sadik Delen, Ismail Naci Cangul


Bursa, Turkey


Abstract: Molecular graphs are those graphs which are trees with vertex degrees

at most 4. They have applications in chemistry and pharmacology. In this paper

we give the catalogue of all molecular graphs and give results on their

classification.

Keywords: Molecular graph, degree sequences.

References:

[1] B. Bollobas, Degree sequences of random graphs, Discrete Mathematics 33

(1981), 1-19.

[2] Delen, S., Cangul, I. N., Algebraic Properties of Some Graph Operations in

Terms of Degree Sequences, (preprint)

[3] Delen, S., Cangul, I. N., Degree Sequences of Join and Corona Products of

Graphs, (preprint)



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78





Streamline Topology of Vortex Breakdown Bubbles near the

Re-Entrant Corner

Ali Deliceoglu 1 and Ebutalib Celik 2

1Erciyes University, Kayseri, Turkey,

[email protected] 2Erciyes University, Kayseri, Turkey,

[email protected]

Abstract: In this paper, topological bahavior of a viscous flow near a re-entrant

corner is studied. The method derived in this paper is intended to clarify the

understanding flow structures near the re-entrant corner. A numerical-asymptotic

matching solution for computing the local singular behavior of a viscous flow

around a re-entrant corner is developed. The theory is applied to the vortex

brakdown bubbles found numerically in an L-shaped cavity.

Keywords: Vortex Breakdown, Flow structure, Bifurcations.

Research supported by the TUBITAK under Grant No: 114F525

References:

[1] Deliceoğlu, A. and Aydın, S.H., “ Flow bifurcation and eddy genesis in an L-

shaped cavity” . Computers and Fluids, Vol. 73, pp. 24-46, 2013.

[2] Deliceoğlu, A. and Aydın, S.H., “Topological flow structures in an L-shaped

cavity with the vertical motion of the upper lid” . Journal of Computational and

Applied Mathematics, Vol. 259, pp. 937-943, 2014.

[3] Hawa T. And Rusak Z., Numerical-Asymptotic expansion matching for

computing a viscous flow around a sharp expansion corner, Theoret. and Comp.

Fluid Dyn., Vol. 15, pp. 265-281, 2002.



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79





Optimality Conditions for a Linear Differential System with

Two Delays

Hanna Demchenko

Department of Mathematics, Faculty of Electrical Engineering and

Communication, Brno University of Technology,

Brno,Czech Republic

[email protected]

Abstract: In the contribution, for linear differential system with two delays

𝑑𝑥(𝑡)

𝑑𝑡= 𝐴0𝑥(𝑡) + 𝐴1𝑥(𝑡 − 𝜏) + 𝐴2𝑥(𝑡 − 𝛿) + 𝑏𝑢(𝑡), (1)

where 𝐴0, 𝐴1 and 𝐴2are 𝑛 × 𝑛 constant matrices, 𝑏 ∈ 𝑅𝑛, 𝜏 > 0, 𝛿 > 0,

𝑢(𝑡) ∈ 𝑅 and 𝑢(𝑡) is a control function, a problem of minimizing a functional

𝐼 = ∫ (𝑥𝑇(𝑡)𝐶11𝑥(𝑡) + 𝑥𝑇(𝑡)𝐶12𝑥(𝑡 − 𝜏) + 𝑥𝑇(𝑡)𝐶13𝑥(𝑡 − 𝛿) + 𝑥𝑇(𝑡 −∞

𝑡0

𝜏)𝐶21𝑥(𝑡) + 𝑥𝑇(𝑡 − 𝜏)𝐶22𝑥(𝑡 − 𝜏) + 𝑥𝑇(𝑡 − 𝛿)𝐶31𝑥(𝑡) + 𝑥𝑇(𝑡 − 𝛿)𝐶33𝑥(𝑡 −𝛿) + 𝑑𝑢2(𝑡))𝑑𝑡 (2)

where integrand is a positive-definite quadratic form, is considered. To solve the

problem, Malkin’s approach and Lyapunov’s second method are utilized.

Theorem. Assume that there exists a positive-definite matrix 𝐻 satisfying the

matrix equation

𝐴0𝑇𝐻 + 𝐻𝐴0 + 𝐶11 + 𝐶22+𝐶33 −

1

𝑑𝐻𝑏𝑏𝑇𝐻 = 𝜃.

If, moreover, 𝐻𝐴1 = −𝐶12 and 𝐻𝐴2 = −𝐶13, then for problem (1)-(2) the

optimal stabilization control function exists and equals

𝑢0(𝑡) = −1

𝑑𝑏𝑇𝐻𝑢(𝑡).

Keywords: optimal control, delayed differential system, Lyapunov-Krasovskii

functional, integral quality criterion.

References:

[1] G.A. Dolenko, D.Ya Khusainov, “A partial inverse linear-quadratic

optimization problem”, Cybernetics and System Analysis, Vol.41, No.3 (2005),

473-478.

[2] F. R. Gantmacher, “The Theory of Matrices”, AMS Chelsea Publishing,

Providence, RI, USA (2002).

[3] I.G. Malkin, “Theory of Stability of Motion, Second revised edition”,

Moscow, Nauka Publisher (1966), 530.


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80





α-Convexity of Some Struve and Lommel Functions

1Erhan Deniz,

2Halit Orhan,

1Murat Caglar

1Department of Mathematics, Kafkas University, Kars, Turkey

2Department of Mathematics, Atatürk University, Erzurum, Turkey

[email protected] (E.Deniz)

[email protected] (H.Orhan)

[email protected] (M. Çağlar)

Abstract: In this paper our first aim is to determine the radii of α-convexity of

some normalized Struve and Lommel different of the first kind. Moreover,

necessary and sufficient conditions are also given for the parameters such that

the these functions are α-convex in the open unit disk. The key tools in the proof

of our main results are the Mittag-Leffler expansion for Struve and Lommel

functions, properties of zeros of the Struve and Lommel functions and their

derivatives and some inequalities for complex and real numbers.

Keywords: Sruve function, Lommel function, convex functions, starlike

functions, α-convex functions, radii of α-convexity, zeros of Stuve and Lommel

functions.

Acknowledgements: The research of E. Deniz and M. Çağlar was supported by

the Commission for the Scientific Research Projects of Kafkas University,

project number 2016-FM-67.

References:

[1] Á. Baricz, P. A. Kupán, R. Szász, The radius of starlikeness of normalized

Bessel functions of the first kind. Proc. Amer. Math. Soc. 142(5) (2014), 2019-

2025.

[2] Á. Baricz, R. Szász, The radius of convexity of normalized Bessel functions

of the first kind. Anal. Appl. 12(5) (2014), 485-509.

[3] A. Baricz, D.K. Dimitrov, H. Orhan, N. Yağmur, Radii of starlikeness of

some special functions, Proc. Amer. Math. Soc. (in press)

doi:10.1090/proc/13120.

[4] A. Baricz, N. Yağmur, Geometric properties of some Lommel and Struve

functions, Ramanujan J. (in press) doi:10.1007/s11139-015-9724-6.




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81





Fuzzy Soft Topolical Spaces and the Related Category FST

Tugbahan Simsekler Dizman, Naime Tozlu

Department of Science and Mathematics Education, Gaziantep University

Sehitkamil, Gaziantep, Turkey

[email protected]

Abstract: Fuzzy set theory defined by Zadeh in 1968 as a new method for

vagueness. Certainly this theory became the most succesful theory for unprecise

concepts. Both in mathematics and in engineering a lot of papers based on this

theory were published. In 2001, Molodtsov defined soft set theory as a different

approach for vague concepts. Molodtsov searched the relations between this

theory with the fuzzy set theory and showed that soft set is more general than

fuzzy set. In a short time the researchers worked on soft set theory and its

applications. Also the hybrid models as fuzzy soft set were defined and studied

by several researchers.

In this paper we consider fuzzy soft sets with a different approach. We inspire of

Sostak’s fuzzy sets and generalize this idea for fuzzy soft sets. This allows us to

grade the openness and closedness of a fuzzy soft set in a fuzzy soft topological

space. The degree may range from 1 to 0 for each parameter. We define fuzzy

soft continuous mappings between two fuzzy soft topological spaces also we

define the category FST of fuzzy soft topological spaces and give some

properties of this category. Moreover we define the initial and the final fuzzy soft

topological spaces.

Keywords: fuzzy soft set, fuzzy soft topology, category FST

References:

[1] A.Aygunoğlu and H.Aygun, Some notes on soft topological spaces, Neural

Computing and Applications, doi: 10.1007/s00521-011-0722-3, 2011.

[2] A. Kharal and B.Ahmad, Mappings on fuzzy soft classes, Advances in Fuzzy

Systems, doi:10.1155/2009/407890, 2009.

[3] P. K. Maji, A. R. Roy, R. Biswas, Fuzzy soft sets, J. Fuzzy Math.9.3 (2001),

589-602.

[4] D. Molodtsov, Soft set theory-First results, Comput. Math. Appl. 37.45

(1999),19-31.

[5] T. Simsekler, S.Yuksel, Fuzzy soft topological spaces, Ann. Fuzzy Math.

Inform.,5.1(2013),87-96.

[6] A. Sostak, On a fuzzy topological structure, Proceedings of the 13thˇ Winter

School on Abstract Analysis, Section of Topology,11 (1985), 89103.


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82





Fuzzy Soft Ditopological Spaces

Tugbahan Simsekler Dizman, Naime Tozlu, Şaziye Yüksel

Department of Science and Mathematics Education, Gaziantep University,

Sehitkamil, Gaziantep, Turkey

[email protected]

Abstract: Fuzzy and soft sets are two different approaches for vague concepts.

Both of these theories took attention of researchers and were applied several

branches of mathematics. Also the hybrid models as fuzzy soft sets were defined

and searched by the mathematicians. The concept of a ditopology was introduced

by L.M. Brown and studied in a series of papers by L.M. Brown and co-authors.

Ditopologies are related to the concept of a bitopology introduced by J.L. Kelly.

In this paper we consider the case when two independent fuzzy soft structures on

a given set are defined – one of them is realizing the property of openness, and

the other is interpreting the property of closedness. Hence we define the concept

of a fuzzy soft ditopological space. Some properties of such spaces are studied.

Keywords: Fuzzy set, soft set, ditopology

References:

[1] L. M. Brown and M. Diker, Ditopological texture spaces and intuitionistic

sets, Fuzzy Sets and Systems 98 (1998), 217–224.

[2] L. M. Brown, R. Erturk, ¨ Fuzzy sets as texture spaces, I. Representation

theorems, Fuzzy Sets and Systems 110 (2) (2000), 227–236.

[3] J.L. Kelly, Bitopological spaces , Proc. Lond. Math.Soc., III Ser. 13 (1963),

71–89 .

[4] D. Molodtsov, Soft set theory-First results, Comput. Math. Appl. 37(4-5)

(1999), 19-31.

[5] A. Sostak, ˇ On a fuzzy topological structure, Suppl. Rend. Circ. Matem.

Palermo, Ser II 11 (1985), 89–103.

[6] A. Sostak, ˇ Two decades of fuzzy topology: basic ideas, notions and results,

Russian Math. Surveys 44:6 (1989), 125–186.

[7] S. Roy and T. K. Samanta, A note on fuzzy soft topological spaces, Ann.

Fuzzy Math. Inform. 3 (2012) 305–311

[8] L. A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965) 338–353.


______________________________________________________

83





On the Difference Method for Approximating of Second Order

Derivatives of a Solution of Laplace's Equation in a

Rectangular Parallelepiped

Adiguzel A. Dosiyev and Hediye Sarıkaya

Department of Mathematics, Near East University,

Nicosia, KKTC, Mersin 10, Turkey

[email protected]

Abstract: A 14-point averaging operator is used to construct finite difference

problems for the approximation on a cubic grid with step size h, of the pure and

mixed second order derivatives of a solution of the Dirichlet problem of

Laplace's equation on a rectangular parallelepiped. The boundary functions 𝜑𝑗 on

the faces 𝛤𝑗 , 𝑗 = 1,2, . . . ,6 belong to the Hölder classes 𝐶𝑝,𝜆, 0 < 𝜆 < 1, 𝑝 ∈

4,5, and on the edges their second and fourth order derivatives satisfy the

compatibility conditions.

It is proved that the solutions of the constructed difference problems converge of

orders 𝑂(ℎ𝑝−2+𝜆) and O(ℎ𝑝−2+𝜆) to the exact value of the second pure and

mixed derivatives, respectively.

Numerical experiments are illustrated to support the theoretical results.

Keywords: finite difference method, approximation of the derivatives, error

estimations, Laplace's equation on parallelepiped


______________________________________________________

84





Kolmogorov Inequality on Variable Exponent Lebesgue Spaces

Ismail Ekincioglu, Esra Kaya

Dumlupinar University, Department of Mathematics, Kutahya, Turkey,

[email protected]

Dumlupinar University, Department of Mathematics, Kutahya, Turkey,

[email protected]

Abstract: In this study, it is considered the Riesz-Bessel transforms, The Riesz-

Bessel transforms are bounded on variable exponent Lebesgue

spaces for , but these operators are not bounded on variable exponent

Lebesgue spaces for . For this reason, it is necessary to work in

variable exponent Hardy spaces to get the boundedness of such operators for

. The most important method to show the boundedness of the Riesz-

Bessel transforms in variable exponent Hardy spaces is atomic

decomposition. The most important inequality used when atomic decomposition

is applied is Bessel type Kolmogorov inequality. Therefore, in this paper, Bessel

type Kolmogorov inequalities, which is necessary to demonstrate the

boundedness of Riesz-Bessel transforms in the variable exponent Hardy spaces,

will be proved in variable exponent Lebesgue spaces. We say that

is a convolution-type singular integral operator with regularity of order if the

distribution coincides with a function on and has the properties that

are hold and, for all multi-indices

and . Therefore, singular integrals that satisfy above

conditions are bounded on , . More importantly, the

pointwise smoothness conditions guarantee that they satisfy weighted norm

inequalities. In this work, we will obtain weighted Kolmogorov inequality.

Keywords: Generalized Shift Operator, Laplace-Bessel Operator, Kolmogorov

Inequality, Variable Exponent Lebesgue Spaces.

References:

[1] A. Osexkowski, “Sharp Inequalities for Riesz Transforms”, Stud. Math.,

222, (2014), 1-18.

[2] B. M. Levitan, “Generalized Shift Operators”, Moskow Nauva (1973).



______________________________________________________

85





An Application of Functional Variable Method For Semi-

Analytical Solutions of Nonlinear Evolution Equations

Berfin Elma and Emine Misirli

Department of Mathematics, Ege University

Bornova, İzmir, Turkey


Abstract: In recent years, many powerful methods have been developed to

obtain exact solutions of partial differential equations. In this paper, we obtained

some semi-analytical solutions of the nonlinear Modified Benjamin-Bona

equation and nonlinear Coupled Klein-Gordon system which seems in the

various scientific and engineering fields such as fluid mechanics, chemical

kinematics, by using Functional Variable method. We specified wave types of

these equations. Also the physical behaviors of the obtained solution functions

are examined and three dimensional graphics are drawn using the Mathematica

program. It is shown that this method is used to solve the equations of evolution

in mathematical physics and engineering.

Key Words: evolution equations, nonlinear partial differential equations,

functional variable method.

References:

[1] Kamruzzaman K.H.A.N., and M. Ali AKBAR," Study of functional variable

method for finding exact solutions of nonlinear evolution equations." Walailak

Journal of Science and Technology (WJST) 12,11 (2014): 1031-1042.

[2] Zayed, Elsayed ME and S.A. Hoda Ibrahim, " The functional variable

method and its applications for finding the exact solutions of nonlinear PDEs in

mathematical physics." AIP Conference Proceedings. Eds. Theodore E. Simos, et

al.Vol.1479.No.1.AIP,2012.

[3] Zayed, Elsayed ME, Yaser A. Amer, and Ahmed H. Arnous, " Functional

variable method and its applications for finding exact solutions of nonlinear

PDEs in mathematical physics." Scientific Research and Essays 8,42 (2013):

2068-2074.

[4] Zerarka, A.S.Ouamane, and A. Attaf, " On the functional variable method

for finding exact solutions to a class of wave equations." Applied Mathematics

and Computation 217,7 (2010): 2897-2904.


______________________________________________________

86





New Types of Soft Separation Axioms and Soft

Compactness in Soft Topological Spaces

M. E. El-Shafei1, M. Abo-Elhamayel1 and T. M. Al-shami2

1Department of Mathematics, Mansoura University, Egypt 2Department of Mathematics, Sana'a University

[email protected]

Abstract: In the present article, we define partial belong and total non belong

relations which are more e_ective to theoretical and application studies in soft

topological spaces. Many properties related to these two relations are studied and

discussed. We then introduce new soft separation axioms namely p-soft Ti-

spaces (i = 0; 1; 3; 4), depending on a totally non belong relation, and study their

characterizations in detail. with the help of examples, we illustrate the

relationships among these soft separation axioms and point out that p-soft Ti-

spaces are stronger than soft Ti-spaces, for i = 0; 1; 4. Also, we definedne a p-

soft regular space, which is weaker than a soft regular space ([1], Def.31), by

utilizing a total non belong relation instead of non belong relation (2.2) and

verify the equivalent between soft T2-spaces and p-soft T3-spaces when the

universe set is _nite. In the last section, we initiate a concept of soft locally

compact spaces and study main properties. We investigate under what conditions

a soft subset of a soft T2-space is soft compact. Moreover, we derive some

important results such that every soft compact T2-space is soft T3-space and a

_nite product of soft locally compact spaces is soft locally compact. we

illuminate that some _ndings obtained in general topology are not true

concerning softitopological spaces such as a _nite soft topological space need not

be soft compact.

Keywords: Partial belong (Total non belong) relation, Soft regular, p-soft Ti-

space (i = 0; 1; 3; 4), Soft T2-space, Soft compactness, Soft locally compactness

and soft topological spaces.

References:

[1] M. Shabir and M. Naz, On soft topological spaces, Computers and

Mathematics with Applications 61 (2011) 1786-1799.


______________________________________________________

87





On Quaternion n-Spaces

Fatma Ozen Erdogan, Atilla Akpinar


Bursa, Turkey


Abstract: In this presentation, we introduce some combinatorial results related

to points and lines of the quaternion n space P(J') defined by the special

Jordan matrix algebra ( , )n

J' H Α J , the set of n by n matrices, with

entries in an local ring :A Q Q (an quaternion division ring Q , Q

and 2 0 ), that are symmetric with respect to the canonical involution J .

Keywords: local ring, special Jordan matrix algebra; quaternion; quaternion 3-

space; quaternion n-space, projective Klingenberg plane, projective plane.

References:

[1] Akpinar, A. and Erdogan, F.O., “On Special Jordan Algebras of Dimension

2n²-n”, 2017 (under review)

[2] Akpinar, A. and Erdogan, F.O., “Collineations and Cross-Ratios in Octonion

Planes”, 2017 (under review)

[3] Baker C.A., Lane N.D., Lorimer J.W., “A coordinatization for Moufang-

Klingenberg Planes”, Simon Stevin, 65(1991), 3-22.

[4] Bix, R., “Octonion Planes over Local Rings”, Trans. Amer. Math. Soc.,

261(2), (1980), 417-438.

[5] Faulkner, J.R., “Octonion Planes Defined by Quadratic Jordan Algebras”,

Mem. Amer. Math. Soc., 104(1970), 1-71.

[6] Faulkner, J.R., “The Role of Nonassociative Algebra in Projective

Geometry”, Graduate Studies in Mathematics, Amer. Math. Soc., Providence,

R.I., 159(2014).

[7] Jacobson, N., “Structure and Representations of Jordan Algebras”, Colloq.

Publ., Amer. Math. Soc., Providence, R.I., 39(1968).

[8] Jacobson, N., “Basic Algebra I”, W. H. Freeman and Company, New York,

1985.

[9]McCrimmon,K., “The Freudenthal-Springer-Tits Constructions of

Exceptional Jordan Algebras”, Trans. of the Amer. Math. Soc.,139(1969), 495-

510.



______________________________________________________

88





Decomposition of Soft Continuity via Soft Locally b-Closed Set

Zehra Guzel Ergul, Naime Tozlu, Saziye Yuksel

Department of Mathematics, Ahi Evran University, Kırsehir, Turkey

[email protected]

Department of Mathematics, Omer Halisdemir University, Nigde, Turkey

[email protected]

Department of Mathematics, Selcuk University, Konya, Turkey

[email protected]

Abstract: In this paper, we introduce soft locally b-closed sets in soft

topological spaces, which are defined over an initial universe with a fixed set of

parameters, and study some of their properties. We investigate their relationships

with different types of subsets of soft topological spaces with the help of

counterexamples. Also, the concept of soft locally b-closed continuous functions

is presented. Finally, some decompositions of soft continuity are obtained.

Keywords: Soft set, Soft topological space, Soft locally b-closed set, Soft

locally b-closed continuous function.

Acknowledgements: This work is supported by Ahi Evran University Scientific

Research Projects Coordination Unit. (Project Number: FEF. A3.16.020).

References:

[1] Acikgoz A. and Arabacioglu Tas N., “Some new soft sets and

decompositions of some soft continuities”, Annals of Fuzzy Mathematics and

Informatics, 9.1(2015), 23-35.

[2] Akdag M. and Ozkan A., “Soft α-open sets and soft α-continuous functions”,

Abstract and Applied Analysis, http://dx.doi.org/10.1155/2014/891341, (2014).

[3] Akdag M. and Ozkan A., “Soft b-open sets and soft b-continuous functions”,

Math. Sci., 8.124(2014).

[4] Akdag M. and Ozkan A., “On Soft preopen sets and soft pre separation

axioms”, Gazi University Journal of Science, 27.4(2014), 1077-1083.

[5] Akdag M. and Ozkan A., “On soft β-open sets and soft β-continuous

functions”,The Scientific World Journal, http://dx.doi.org/10.1155/2014/843456,

(2014).

[6] Ali M.I., Feng F., Liu X., Min W.K. and Shabir M., “On some new

operations in soft set theory”, Computers and Mathematics with Applications,

57(2009), 1547-1553.




______________________________________________________

89





Periodic Solutions for a Third-Order Delay Differential

Equation

Nouioua Farid and A. Ardjuoni

Department of Mathematics, Souk-Ahras University,

Souk-Ahras, Algeria

[email protected]

Abstract: In this paper, the following third order nonlinear delay differential

equation with periodic coefficient

))(()()))((),(,()()()(')()('')()(''' ttxtcttxtxtftxtrtxtqtxtptx

is considered. By employing Green’s function, Krasnoselskii’s …fixed point

theorem and the contraction mapping principle, we state and prove the existence

and uniqueness of periodic solutions to the third-order delay differential

equation. Finally, an example is given to illustrate our results.

A. Ardjouni and A. Djoudi, Existence of periodic soluxions for a second-order

non-linear neuxral dixerentixl equation with variable delay, Palesx. J. Math.,

x(x014),191-197.

Keywords: Fixed point , positive periodic solutions, third-order delay

differential equations.

References:

[1] A. Ardjouni and A. Djoudi, Existence of periodic solutions for a second-

order nonlinear neutral differential equation with variable delay,Palesx. J. Math ,

3(2014), 191-197 .

[2] A. Ardjouni, A. Djoudi, and A. Rezaiguia, Existence of positive periodic

solutions for two types of third-order nonlinear neutral differential equation with

variable delay, Appl. Math. E-Notes, 14(2014), 86-96

[3] A. Ardjouni and A. Djoudi, Existence of positive periodic solutions for a

nonlinear neutral differential equation with variable delay, Appl. Math. E-Notes,

12(2012), 94-101 .

[4] A. Ardjouni and A. Djoudi, Existence of periodic solutions for a second-

order nonlinear neutral differential equation with functional delay, Electronic. J.

Qual. Theory Diff. Eq, 2012, No. 31,9 pp.

[5] T. A. Burton, Liapunov functionals, fixed point and stability by

Krasnoselskii’s theorem nonlinear stud, 9(2002), 181-190


______________________________________________________

90





Copula Conditional Tail Expectation for Multivariate Financial

Risks

Benatia Fatah and Brahim Brahimi

Laboratory of Applied Mathematics,

Mohamed Khider University, Biskra, Algeria,

[email protected]

Abstract: Our goal in this paper is to propose an alternative risk measure which

takes into account the fluctuations of losses and possible correlations between

random variables. This new notion of risk measures, that we call Copula

Conditional Tail Expectation describes the expected amount of risk that can be

experienced given that a potential bivariate risk exceeds a bivariate threshold

value, and provides an important measure for right-tail risk. An application to

real financial data is given.

Keywords: Conditional Tail Expectation; Positive Quadrant Dependence;

Copulas; Dependence measure; Risk Management; Market Models.

References:

[1] Artzner, P. H., Delbaen, F., Eber, J. M., Heath, D., 1997. Thinking

Coherently, RISK 10, 68-71.

[2] Brahimi, B., Meraghni, D., Necir, A., 2010. Distortion risk measures for

sums of dependent losses. J. Afr. Stat. 5, 260-267.

[3] Joe, H., 1997. Multivariate Models and Dependence Concepts. Monographs

on Statistics and Applied Probability 73. Chapman and Hall, London.

[4] Nelsen, R. B., 2006. An Introduction to Copulas. second ed. Springer, New

York.

[5] Sklar, A., 1959. Fonctions de répartition à n dimensions et leurs marges,

Publ. Inst. Statist. Univ. Paris 8, 229-231.th. Econom. 21(2), 173-183.


______________________________________________________

91





New Properties of Fractional Derivatives Defined Using Mittag

Leffler Kernel

Arran Fernandez 1, Dumitru Baleanu 2,3

1 Department of Applied Mathematics & Theoretical Physics, University of

Cambridge, Wilberforce Road, Cambridge, United Kingdom 2 Department of Mathematics, Cankaya University, 06530 Balgat, Ankara,

Turkey 3 Institute of Space Sciences, Magurele-Bucharest, Romania

[email protected]

Abstract: Recent developments in the theory of fractional calculus have

included a new definition introduced by Atangana and Baleanu [1] for fractional

derivatives in terms of a Mittag-Leffler kernel function; the theory of such

derivatives has been further extended in other papers such as [2]. In this

presentation we prove a new formula for such fractional derivatives, in terms of

an infinite convergent series of standard Riemann-Liouville or Caputo fractional

derivatives. This enables us to extend various results from classical calculus,

such as the product rule and chain rule, much more easily than otherwise. We

also consider the semigroup property for derivatives and integrals and how it

applies to these new fractional differintegrals, and we show how to solve certain

fractional ODEs using the new definition.

Keywords: Fractional Derivatives, Fractional Integrals, Laplace Transforms,

Ordinary Differential Equations

References:

[1] A. Atangana and D. Baleanu, “New fractional derivatives with nonlocal and

non-singular kernel: theory and application to heat transfer model”, Therm. Sci.

20(2) (2016), 763–769.

[2] T. Abdeljawad and D. Baleanu, “Integration by parts and its applications of a

new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel”, J.

Nonlinear Sci. Appl. 10(3) (2017), 1098-1107.


______________________________________________________

92





Nodal Solutions for Indefinite Robin Problems

Michael Filippakis

Department of Digital Systems

Univeristy of Piraeus

Piraeus 18536, Greece

[email protected]

Abstract: We consider a semilinear Robin problem driven by the negative

Laplacian plus an indefinite, unbounded potential. The reaction term is a

Caratheodory function of arbitrary structure outside an interval [−c, c] (c > 0),

odd on [−c, c] and concave near zero. Using a variant of the symmetric mountain

pass theorem, together with truncation, perturbation and comparison techniques,

we show that the problem has a whole sequence unn≥ 1 of distinct nodal

solutions converging to zero in C1 (Ω).

Keywords: Indefinite potential, Robin boundary condition, sequence of nodal

solution, regularity theory, strong maximum principle


______________________________________________________

93





On Slowly Oscillating Double Sequences

Goksen Findik, Ibrahim Canak, Umit Totur

Department of Mathematics, Ege University, Bornova, Izmir, Turkey


Department of Mathematics, Adnan Menderes University, Aydin, Turkey

[email protected]; [email protected] ;

[email protected]

Abstract: In this paper, we first examine the relationships between a double

sequence and its arithmetic means in different senses (i.e. (C,1,0), (C,0,1) and

(C,1,1) means) in terms of slow oscillation in certain senses and investigate

some properties of oscillatory behaviors of the difference sequence between the

double sequence and its arithmetic means in different senses. Next, we give an

alternative proof of the generalized Littlewood Tauberian theorem for Cesaro

summability method as an application of the results obtained in the first part.

Keywords: Tauberian conditions and theorems, convergence in Pringsheim's

Sense, slow oscillation, double sequences, summability (C, 1, 0), (C, 0, 1) and

(C, 1,1)

References:

[1] R. Schmidt, “Über divergente Folgen und lineare Mittelbildungen”, Math. Z.,

22 (1925), 89-152.

[2] E. Landau, “Über einen Satz des Herrn Littlewood”, Palermo Rend., 35

(1913), 265-276.

[3] T. Vijayaraghavan, “A Tauberian theorem”, J. Lond. Math. Soc., 1 (1926),

113-120.

[4] F. Móricz, “Tauberian theorems for Cesaro summable double sequences”,

Studia Math., 110 (1) (1994), 83-96.




______________________________________________________

94





A Bayes Minimax Result for a Large Class of Distributions

Dominique Fourdrinier, Fatiha Mezoued and William E. Strawderman

Université de Rouen, France,

Ecole Nationale de Statistique et d'Economie Appliquée, Algiers, Algeria

Rudgers University, USA

[email protected], [email protected],

[email protected]

Abstract: We consider Bayesian estimation of the location parameter of a

random vector X having a unimodal spherically symmetric density (‖𝑥−𝜃‖2) for a

spherically symmetric superharmonic prior density ((‖𝜃‖2)). We consider

minimaxity of the Bayes estimator 𝛿𝜋(𝑋) = 𝑋 + 𝛻𝑀(∥𝑋∥2)/ 𝑚(∥𝑋∥2) under

quadratic loss, where m is the marginal associated to 𝑓(∥𝑥−𝜃 ∥2) and M is the

marginal with respect to 𝐹(∥𝑥−𝜃 ∥2)=1/2∫𝑓(𝑡)∞‖𝑥−𝜃‖2𝑑𝑡 . In this paper we

extend the results given by Fourdrinier, Strawderman in 2008 [3], and

Fourdrinier, Mezoued strawderman in 2012 [2].

Keywords: Bayesian estimation, Spherically symmetric density, Minimaxity,

Superharmonicity, proper and improper estimators.

References:

[1]J.O. Berger, “Minimax estimation of location vectors for a wide class of

densities”, Annals of Statistics, 3:13181328, (1975).

[2]D. Fourdrinier, F. Mezoued, and W. E. Strawderman, “Bayes minimax

estimators in the Berger class”, EJS, 6: 783-809, (2012).

[3]D. Fourdrinier and W. E. Strawderman, “Generalized bayes minimax

estimators of location vector for spherically symmetric distributions”, Journal of

Multivariate Analysis, 99(4): 735-750, (2008).




______________________________________________________

95





A Search for Designs with the Same Parameters as 2-

(256,64,21) Design with 2-Rank 25

Mustafa Gezek

Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, USA [email protected]

Abstract: Let D be a t − (v, k, λ) design with b blocks. One of the important

results in theory of combinatorial designs is that the number of blocks of a design

≥ the number of points, named as the Fisher inequality. This implies that the p-

rank of D is not greater than v. The researchers working in this area are

interested about the lower bound on the p-ranks of some certain designs and a

great amount of research is done on this problem. Let D_1 be a geometric design

having as blocks the d -subspaces of P G(n, q) or AG(n, q), and let m be the p-

rank of D_1 . Hamada [3] conjectured that if D_2 is a design with the same

parameters as D_1 , then the p-rank of D_2 is greater or equal m, and the

equality holds if and only if D_2 is isomorphic to D_1 . In [1, 2, 4, 5, 6], there

are some proven cases and as well as some counterexamples to the this

conjecture. Our work here is using the connection of known 2-(64,16,5) designs

with 2-rank 16 to find non-geometric designs with the same parameters as AG 3

(4, 4).

References:

[1] Clark D., Jungnickel D., Tonchev V.D., Affine geometry designs, polarities,

and Hamada’s conjecture, Journal of Combinatorial Theory, Series A 118 231-

239 (2011).

[2] Doyen J., Hubaut X., Vandensavel M., Ranks of incidence matrices of

Steiner Triple Systems, Math Z., Vol.163 (1978) 251 - 259.

[3] Hamada N., On the p-rank of the incidence matrix of a balanced of partially

balanced incomplete block design and its applications to error correcting codes,

Hiroshima Math J. 3, 153-226 (1973).

[4] Hamada N., Ohmori H., On the BIB design having the minimum p-rank,

J.Combin Theory Ser. A Vol 18 (1975) 131 - 140.

[5] Harada M., Lam C., Tonchev V.D., Symmetric (4,4)-nets and generalized

Hadamard matrices over groups of order 4. Des. Codes Cryptogr. 34, 71-87

(2005).

[6] Teirlinck T., On the projective and affine hyperplanes, J. Combin. Theory

Ser. A, Vol. 28 (1980) 290 - 306.


______________________________________________________

96





Compact and Matrix Mappings on the Space |𝑨𝒇𝛉|𝒌

Fadime Gokce, G.Canan Hazar Gulec

Department of Mathematics, Pamukkale University,

Denizli, Turkey


Abstract: In this study, we characterize compact and matrix operator in the

class (|𝐴𝑓θ|𝑘, |𝐵𝑓| ) for k≥1, and give some topological and algebraic properties

of the space |𝐴𝑓θ|𝑘, where A and B are factorable matrices, θ = (θ𝑛) is

nonnegative sequence. Also we determine norms and Hausdorff measure of

noncompactness of matrix operators in these classes. Thus we extend some

recent results of Sarıgöl [8,9] and some well known results.

Keywords: Matrix Transformations; Factorable Matrices; Sequence Spaces;

Measure Hausdorff Noncompactness; Norms; Compact Operators.

References:

[1] Bor, Hüseyin. "On two summability methods." Math. Proc. Cambridge

Philos. Soc. 97 (1985), 147-149.

[2] Maddox, I.J., Elements of functinal analysis, Cambridge University Press,

London, New York, 1970.

[3] Malkowsky E., Rakocevic, V., On matrix domains of triangles, Appl. Math.

Comp. 189 (2007), 1146-1163.

[4] Malkowsky E., Rakocevic, V. An introduction into the theory of sequence

space and measures of noncompactness, Zb. Rad.(Beogr) 9 (2000), 143-234.

[5] Orhan, C. and Sarıgöl, M.A., On absolute weighted mean summability ,

Rocky Moun. J. Math. 23 (3) (1993), 1091-1097.

[6] Rakocevic, V., Measures of noncompactness and some applications, Filomat

12 (1998), 87-120.

[7] Sarıgöl, M.A., Extension of Mazhar's theorem on summability factors,

Kuwait J. Sci. 42 (2015), 1-8.

[8] Sarıgöl, M., A., Characterization of general summability factors and

applications, Comp. Math. Appl. 62 (2011), 2665-2670.

[9] Sarıgöl, M.A., Matrix transformations on fields of absolute weighted mean

summability, Studia Sci. Math. Hungar. 48 (3) (2011), 331-341



______________________________________________________

97





On Some Classes of Fractional Differential Equations of

Parabolic Type

Dilovar Guljonov

A.Juraev Insitute of Mathematics, Academy of Sciences of the Republic of

Tajikistan

Dushanbe, Tajikistan

[email protected]

Abstract: The present paper is devoted to studying the equations of parabolic

type in which instead of Laplaсe operator considered the differential operator

with fractional orders of derivatives by spatial variables. Instead of classical

equation of normal diffusion of form 𝝏𝒖

𝝏𝒕= ∆𝒖 (𝟏)

is consider a fractional equation of isotropic anomaly diffusion 𝝏𝒖

𝝏𝒕= ∆𝜶/𝟐𝒖, 𝟏 ≤ 𝜶 ≤ 𝟐 (𝟐)

or an equation of anisotropic anomaly diffusion 𝝏𝒖

𝝏𝒕= 𝛁 ∙ (𝓙𝑴

𝟏−𝜷𝛁𝐮), (𝟑)

where 𝛁 − gradient operator and operator 𝓙𝑴𝟏−𝜷[𝒗] is defined for vector-valued

function 𝒗 and has form

𝓙𝑴𝟏−𝜷[𝒗] = 𝑭−𝟏 [ ∫ 𝒎(𝒊𝒎 ∙ 𝝃)𝜷−𝟏𝒎 ∙ (𝝃)𝑴(𝒅𝒎)

|𝒎|=𝟏

].

Here 𝑴 − probability measure in unit sphere ℝ𝒏 described an anisotropic

diffusion, 𝑭−𝟏[𝒗] − an inverse Fourier transform of function 𝒗 ∈ 𝑳𝟐 ⊂ ℝ𝒏.

Equation (1) is correspond to the random walk model and equations (2) and (3)

are correspond to the continuous in time random walk and Levi flights models

(see, e.g., [1]).

Initial-boundary problem for the equations (2) and (3) are invistiges by method

of Fourier fractional analysis.

References:

[1] V.V. Uchaykin, “Self-similar anomaly diffusion and stable laws”, Uspekhi

Physic.Nauk, 173.8(2003), 847-876.


______________________________________________________

98





Some Results about ΔI-Statistically Pre-Cauchy Sequences with

an Orlicz Function

Hafize Gumus, Omer Kisi and Ekrem Savas

Abstract: In this study, we define the concept of I-statistically convergence for

difference sequences and we use an Orlicz function to obtain more general

results. We also show that an ΔI-statistically convergent sequence with an Orlicz

function is ΔI -statistically pre-cauchy.

References:

[1] Das, P. and Sava¸s, E., On I-statistically pre-cauchy.sequences, Taiwanese

Journal of Mathematics, Vol.18, No.1, 115-126, (2014).

[2] Khan, V.A., Ebadullah, K., Ahmad, A., I-Pre-Cauchy sequences and Orlicz

functions, Journal of Mathematical Analysis, 3(1), 21-26, (2012).

[3] Dutta, A. J. and Tripathy, B.C., Statistically pre-cauchy fuzzy real-valued

sequences deÖned by an Orlicz function, Proyecciones Jour. of Mathematics,

33(3), 235-243, (2014).

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99





A Numerical Analysis of FLMM for Semilinear Time

Fractional Schrödinger Equations

Betul Hicdurmaz

Department of Mathematics, Istanbul Medeniyet University,

Uskudar, Istanbul, Turkey

[email protected]

Abstract: In this study, semi linear time fractional Schrödinger differential

equations are solved approximately with three types of difference schemes.

Semi-discretization in time variable is provided by an iterated Lubich

approximation and two different iterated Fractional linear multi step method

(FLMM) methods. Numerical analysis of the obtained theoretical results are

presented with a discussion on some particular problems.

Keywords: Semi linear time fractional Schrödinger equation, Fractional linear

multi step method, Lubich approximation.

References:

[1] R. Garrappa, I. Moret, M. Popolizio, “On the time-fractional Schrödinger

equation: Theoretical analysis and numerical solution by matrix Mittag-Leffler

functions", Computers & Mathematics with Applications, 2016, In press.

[2] M. Naber, "Time fractional Schrodinger equation", J. Math. Phys. Vol 45,

No. 8 pages 3339-3352, Aug. 2004.

[3] A. H. Bhrawy, M. A. Zaky, "An improved collocation method for multi-

dimensional space–time variable-order fractional Schrödinger equations",

Applied Numerical Mathematics, 111, 2017, 197–218.


http://www.sciencedirect.com/science/journal/01689274/111/supp/C

http://www.sciencedirect.com/science/journal/08981221

http://www.sciencedirect.com/science/journal/01689274

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100





On Modified FLMM Methods for Fractional Population

Equations

Betül Hicdurmaz and Emine Can*

Department of Mathematics, Istanbul Medeniyet University

*Department of Physics Engineering, Istanbul Medeniyet University


Abstract: In the present paper, a new modified Fractional Linear Multistep

Method (FLMM) is presented for the numerical solution of linear and semi linear

differential equations. Constructed methods are implemented on the generalized

time fractional-order biological population model (GTFBPM) with one or two

dimensions which arise in population dynamics. Selected problems are equations

which are applied to population growth in species in biology.

Keywords: Population dynamics, Fractional Linear Multistep Method.

References:

[1] V. K. Srivastava, S. Kumar, M. K. Awasthi, B. K. Singh, “Two-dimensional

time fractional-order biological population model and its analytical solution”,

Egyptian Journal of Basic and Applied Sciences, 1 (2014), 71-76.

[2] N. V. Mantzaris, P. Daoutidis, F. Srienc, “Numerical solution of multi-

variable cell population balance models. II. Spectral methods”, Computers and

Chemical Engineering 25 (2001) 1441–1462.

[3] S. Allaart-Bruin, J. ter Maten, S. Verduyn Lunel, Modified Extended BDF

time-integration methods, applied to circuit equations, RANA Report 02-25,

Eindhoven University of Technology, Presented at SCEE-2002, Eindhoven, June

2002.

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101





Coincidence Best Proximity Points for Geraghty Type

Proximal Cyclic Contractions

Azhar Hussain

Department of Mathematics, University of Sargodha

Sargodha, Pakistan

[email protected]

Abstract: In this talk we introduce the notions of generalized Geraghty proximal

cyclic contractions for non-self mapping and obtain coincidence best proximity

point theorems in the setting of complete metric space. Some examples are given

to show the validity of our results. Our results extended and unify many existing

results in the literature.

Keywords: α-Geraghty proximal contraction of first and second kind, α-

proximal cyclic contraction, α-proximal admissible maps.

References:

[1] Abbas, M, Hussain, A, Kummam, P: A Coincidence Best Proximity Point

Problem in G-Metric Spaces. Abst. and Appl. Anal. 2015, Article ID 243753, 12

pages (2015).

[2] Akbar, A, Gabeleh, M: Global optimal solutions of noncyclic mappings in

metric spaces. J. Optim. Theory Appl. 153, 298-305 (2012).

[3] Basha, S.S. (2011). Best proximity point theorems generalizing the

contraction principle. Nonlinear Anal., 74:5844-5850, (2011).

[4] Basha, SS, Shahzad, N, Jeyaraj, R: Best proximity points: approximation and

optimization. Optim. Lett. (2011).

[5] Shahzad, N, Basha, SS, Jeyaraj, R: Common best proximity points: global

optimal solutions. J. Optim. Theory Appl. 148, 69-78 (2011).


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102





Estimation of a Loss Function for Spherically Symmetric

Distribution with Constraints on the Norm

Ouassou Idir

Cadi Ayyad University, National School of Applied Sciences

Marrakesh, Morocco

[email protected]

Abstract: In this paper we consider the problem of estimating the quadratic loss

of point estimators of a location parameter θ for family of symmetric distribution

with known scale parameter, when its norm satisfies different constraints and

when a residual vector U is available. We compare the robust and non robust

estimators and condition on the distribution for the domination of competing

estimators are given. In particular we show that it occurs for t-distributions when

the dimension of the residual vector is sufficiently large. The main tools in the

development are upper and lower bounds on the risk are exact at θ = 0.


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103





An overview on Fuzzy AHP and Its Priority Derivation

1Iftikhar, 2Musheer Ahmad

1,2Department of Applied Sciences and Humanities

Faculty of Engineering and Technology

Jamia Millia Islamia, New Delhi-110025, India


Abstract: Fuzzy AHP is a mathematical technique for multicriteria decision

making (MCDM) in fuzzy environments. Priority derivation is one of the pivotal

steps in Fuzzy AHP methods. In this work, we are introducing various methods

for determining the priority vectors, 𝑤 = (𝑤1 , 𝑤2 … , 𝑤𝑛 ) 𝑇 . Each method is

defined by a function, 𝜏: 𝑅 𝑛×𝑛 → , which synthesize pairwise comparisons

into a rating. Several examples are solved for illustrating the working of each

method.

Keywords: Fuzzy AHP; priority vectors; pairwise comparison matrices;

multicriteria decision making.

References:

[1] Saaty T.L., Scaling method for priorities in hierarchical structures, J. Math.

Psychol. 1977, 15, 3, 234-28.

[2] Basak I., Comparison of statistical procedures in analytic hierarchy process

using a ranking test, Math. Comp. Model. 1998, 28, 105-118.

[3] Budescu D.V., Zwick R., Rapoport A., Comparison of the analytic hierarchy

process and the geometric mean procedure for ratio scaling, Appl. Psychol.

Meas. 1986, 10, 69-78.

4] Saaty T.L., Vargas L.G. Comparison of eigenvalue, logarithmic least square

and least square methods in estimating ratio, J. Math. Model. 1984, 5, 309-324.

[5] Koczkodaj W.W., A new definition of consistency of pairwise comparisons,

Mathematical and Computer Modeling 1993, 18(7), 79-84.



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104





Solutions of (n) (n 1)od od When n 1 Has Three Distinct

Odd Primes

Nazli Yildiz Ikikardes, Daeyeoul Kim and Lianrong Ma

Balikesir University, Turkey, National Institute for Mathematical Sciences, South

Korea, Tsinghua University, China


Abstract: In this study, we define |n,2 |

(n)od dd

d. We investigate solutions of

the equation (n) (n 1)od od . We find all solutions of the equation

(n) (n 1)od od up to 402n . Also, we obtain the equation

(n) (n 1) (n 2) 1(mod2)od od od has no solution.

Keywords: Congruence, Divisor Functions, Odd Divisor Functions

First author was supported by The Research Fund of Balikesir University,

Project No: 2016/44.

References:

[1] V. Annapurna, “Inequalities for (n) and (n) ”, Math. Mag. 45(1972),

187-190.

[2] B. Cho, D. Kim and H. Park, “The multinomial convolution sums of certain

divisor functions”, J. Math. Anal. Appl, 448(2017), 1163-1174.

[3] P. Erdös, “Some remarks on Eulers function and some related problems”,

Bull. Amer. Math. Soc., 51(1945), 540-544.

[4] J. W. L. Glaisher, “On certain sums of products of quantities depending upon

the divisors of a number”, Mess. Math., 15(1885), 1-20.

[5] R. K. Guy, “Unsolved problems in number theory”, Springer, 2004.

[6] D. Kim and A. Bayad, “Convolution identities for twisted Eisenstein Series

and twisted divisor functions”, Fixed Point Theory and App., (2013), 2013:81.

[7] Y. Li, L. Ma and J. Zhang “Odd solutions of (n) 2 2n have at least six

distinct prime factors”, Publicationes Mathematicae Debrecen, 82(2012), 1-12.

[8] K. S. Williams, “Number theory in the spirit of Liouville”, Cambridge

University Press, 2011




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105





Hypersurfaces of a Kenmotsu Space Form

Mohammad Ilmakchi


Tabriz, Iran

[email protected]

Abstract: The purpose of this paper to introduce of hypersurfaces in Kenmotsu

space form and study with some special conditions. In general, we have some

relations about locally symmetric condition, recurrent and D -recurrent structure

Jacobi operator, weakly constant holomorphic curvature and another inequality

condition.

Keywords: Kenmotsu space form, locally symmetric, recurrent, Jacobi operator.

References:

[1] A. Bejancu, CR-submanifolds of Kaeher Manifold $I$, Proc. Amer.Math.

Soc. 69, no.1, (1978) , 135-142.

[2] A. Bejancu, Geometry of CR-submanifolds, D. Reidel Publishing Company,

Dordrecht, Boston, Lancaster, Tokyo, (1986).

[3] D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in

Mathematics, Vol. 509, Springer-Verlag, Berlin, (1976).

[4] M. Djoric, M. Okumura, Certain CR submanifolds of maximal CR dimension

of complex space forms, Differential Geometry and its Applications, 26(2), 208-

217, (2008).

[5] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku

Math. J.24, (1972) , 93-103.


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106





On Some Classes of Fractional Integrodifferential Equations in

Hilbert Space

Mamadsho Ilolov

Center of Innovative Development of Science and New Technologies, Academy

of Science of Republic of Tajikistan


[email protected]

Abstract: Let 𝑓 ∈ 𝐿1(𝑅+, 𝐻), 𝐻 − separable Hillbert space and 0 ≤ 𝛼 < 1. The

expression

(𝒥𝑡𝛼𝑓)(𝑡) =

1

Γ(𝛼)∫(𝑡 − 1)𝛼−1𝑓(𝑠)𝑑𝑠, 𝑡 > 0, 𝛼 > 0

𝑡

0

with 𝒥𝑡0𝑓(𝑡) = 𝑓(𝑡) is called Riemann-Liouville integral of order 𝛼 of 𝑓. For

𝑓(𝑡) ∈ 𝐶𝑚−1(𝑅+𝐻) the Caputo fractional derivalive of order 𝛼 of 𝑓 defined by

( 𝐷𝑡𝛼

𝐶 )(𝑡) = 𝐷𝑡𝑚𝒥𝑡

𝑚−𝛼 [𝑓(𝑡) − ∑𝑡𝑖

𝑖!

𝑑𝑖𝑓(0)

𝑑𝑡𝑘

𝑚−1

𝑖=0

] (𝑡), 𝐷𝑡𝑚 =

𝑑𝑚

𝑑𝑡𝑚.

We are interested in studying the Cauchy problem for fractional

integrodifferential equation in 𝐻 of the type

( 𝐷𝑡𝛼𝑢𝐶 )(𝑡) + 𝐴𝑢(𝑡) + ∑ ∫ 𝑒−𝛾𝑘(𝑡−𝑠)𝐴𝑘𝑢(𝑠)𝑑𝑠

𝑡

0

𝑛

𝑘=0

= 𝑓(𝑡),

𝑢(0) = 𝑢0, (1)

where 𝐴0, 𝐴1, … , 𝐴𝑛 –unbounded linear self-adjoint operators with 𝐷(𝐴𝑘) ⊃

𝐷(𝐴0), 0 < 𝐴𝑘−1 ∈ ℒ(𝐻), 𝛾𝑘 –positive constants, 0 < 𝛾1 < ⋯ < 𝛾𝑛 < ∞, 𝑓 =

𝑓(𝑡): 𝑅+ → 𝐻 given function, 𝑢0 ∈ 𝐻.

Let 𝑢(𝑡) – strong solution of (1). We introduce new desired functions 𝑢𝑘(𝑡), 𝑘 =

0, … , 𝑛 with accordance with formulas

𝑢0(𝑡) = 𝑢(𝑡), 𝑢𝑘(𝑡) = ∫ 𝑒−𝛾𝑘(𝑡−𝑠)𝐴𝑘

12⁄

𝑢0(𝑠)𝑡

0

𝑑𝑠, 𝑘 = 1,2, … , 𝑛

and then we come to fractional differential equations


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107





( 𝐷𝛼𝑐 )(𝑡) + 0 = 𝑓(𝑡), (0) = 𝐻0, (2)

in Hilbert space

𝐻 = 𝐻0 + 𝐻1, 𝐻0 = 𝐻, 𝐻1 = ⨁𝑘=1𝑛 𝐻𝑘 , 𝐻𝑘 = 𝐻,

𝑘 = 1,2, … , 𝑛, (3)

where

(𝑡) = (𝑢0(𝑡), 𝑢1(𝑡))𝑇 , 𝑢1(𝑡) = (𝑢1(𝑡), … , 𝑢𝑛(𝑡))𝑇 , 𝑓(𝑡) = (𝑓(𝑡), 0),

(0) = (𝑢0, 0)𝑇

and operator 0 have a following matrix presentation

0 = (𝐴𝑖𝑗)1𝑖𝑗

1= 0, 𝐴00 = 𝐴0, 𝐴01 = (𝐴1

1/2, … , 𝐴𝑛

1/2)

𝑇,

𝐴10 = − (𝐴1

12, … , 𝐴𝑛

12 )

𝑇

, 𝐴11 = 𝑑𝑖𝑎𝑔(𝛾𝑘𝐼)𝑘=1𝑛 .

Integer order of equation (1) was studied in [1].

References:

[1] M. Ilolov, Kh. Kuchakshoev. “The classification of abstract

integrodifferential equation of higher order”, 7th European Congress of

Mathematics, (2016), 483.

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108





The Generators of Regular, Quasi-regular Representations and

Casimir Operator

Yasemin Isik 1, Mehmet Sezgin 2

Department of Mathematics, Trakya University,

Edirne, Turkey 1 [email protected]

2 [email protected]

Abstract: Special pseudo-orthogonal group is

𝑆𝑂(𝑝, 𝑞) = 𝐴 ∈ 𝑂(𝑝, 𝑞) | det 𝐴 = 1 .

Dealing with regular and quasi-regular representstion of the group, infinitesimal

operators 𝐽0, 𝐽1, 𝐽2 can be found and Casimir operator of the group can be

obtained using these operators. In this paper we shall obtain generators of

regular, quasi-regular representations and the Casimir operator 𝐶 of 𝑆𝑂(1,2)

group. We also shall analyzed the solutions of

𝐶 𝑓(𝑥) = 𝜎(𝜎 + 1) 𝑓(𝑥),

where 𝜎(𝜎 + 1) is eigenvalue, 𝑓(𝑥) is eigenfunction.

Keywords: Lie group, Casimir operator, regular and quasi-regular

representation.

References:

[1] Y. A. Verdiyev, “Harmonic Analysis on Homogeneous Spaces of SO(1,2)”,

Hadronic Press. (1988)

[2] A. Kirillov, Jr, “Introduction to Lie Groups and Lie Algebras”, Suny at Stony

Brook.

[3] A. M. Perelomov, V. S. Popov, “Casimir Operator for Semisimple Lie

Groups”, Math USSR-Izvestija, 2(1968).

[4] R. da Rocha, E. Capelas de Oliveria “The casimir Operator of SO(1,2) and

the Pöschl-Teller Potential: an AdS Approach”, Analysis, 5(1985), 301-313.

[5] S.A. Mohiuddine and Q.M. Danish Lohani, “On generalized statistical

convergence in intuitionistic fuzzy normed space”, Rev. Mex. Fis., 51 (1) (2005),

1-4.



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109





Some Properties of Cartan Null Curves in Semi-Euclidean

4-space with index 2

Esen Iyigün


Görükle, Bursa, Turkey

[email protected]

Abstract: In this paper, we give some properties by using Frenet equations

which are given in [2] of Cartan null curves in Semi-Euclidean 4-space with

index 2. Also, we discuss the conditions for Cartan null curves lying on some

subspaces of these space. Finally, we obtain that the image of the curve lying on

the pseudohyperbolic space H31 in the same space.

Keywords: Semi-Euclidean 4-space with index 2, Frenet frame, Cartan null

curve.

References:

[1]

B. O'Neill, "Semi-Riemannian geometry with applications to relativity",

Academic Press, New York,1983.

[2] A. Uçum, O. Keçilioğlu and K. İlarslan, "Generalized pseudo null Bertrand

curves in Semi-Euclidean 4-space with index 2", Rend. Circ. Mat. Palermo, DOI

10.1007/s12215-016-0246-x, (2016), 1-14,

[3] M.A. Akgün and A.I. Sivridağ, "On the null Cartan curves of R41", Global

Journal of Mathematics, 1. January 26(2015), 41-50.

[4] M.A. Akgün and A.I. Sivridağ, "On the characterizations of null Cartan

curves in R41", International Journal of Mathematics, 1.June1(2015), 1-13.

[5] K.L. Duggal and D.H. Jin, "Null curves and hypersurfaces of Semi-

Riemannian manifolds" World Scientific, London, 2007.

[6] M. Petrovic-Torgasev and E. Sucurovic, "Some characterizations of the

spacelike, the timelike and the null curves on the pseudohyperbolic space H²0 in

E30”, Kragujevac J. Math., 22(2000), 71-82.

[7]

Z. Şanlı and Y. Yaylı, "On indicatrices of null Cartan curves in R41",

International Journal of Engineering Research & Technology (IJERT),

10.2(2013), 2567-2570.

[8] M. Sakaki, "Null Cartan curves in R4

2 ", Toyama Math., 32 (2009), 31-39.


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110





Proximal Point Algorithms Involving Cesaro Type Mean of

Total Asymptotically Nonexpansive Mappings in CAT(0)

Spaces

Amna Kalsoom and Hafiz Futhar ud Din

Department of Mathematics& Statistics, International Islamic University,

Islamabad, Paksitan

[email protected]

Abstract: Fixed point theory in a CAT(0) space was first studied by Kirk [1].

Since then, fixed point theory for various types of mappings in CAT(0) spaces

has been investigated rapidly. In 2008, Dhompongsa-Panyanak[2] studied the

strong and ∆-convergence for the Mann Iteration process and Ishikawa iteration

process for nonexpansive mappings in CAT(0) spaces.

Alber et al. [3] introduced a unified and generalized notion of a class of nonlinear

mappings in Banach spaces which can be introduced in CAT(0) spaces. A

modified proximal point algorithm involving fixed point of Cesaro type mean

of total asymptotically nonexpansive mappings in CAT(0) spaces is proposed.

Under suitable conditions, the ∆-convergence and the strong convergence to

a common element of the set of minimizers of a convex function and the

set of fixed points of the Cesaro type mean of total asymptotically

nonexpansive mapping in CAT(0) space are proved.

Keywords: CAT (0) space, Cesaro type mean, Proximal point algorithm, Total

asymptotically nonexpansive mapping.

References:

[1] W. A. Kirk, “Geodesic geometry and fixed point theory, Seminar

of Mathematical Analysis (Malaga/Seville, 2002/2003)”, Univ. Sevilla Secr.

Publ., Seville, (2003), 195–225.

[2] S. Dhompongsa, B. Panyanak, “On ∆-convergence theorems in CAT (0)

spaces”, Comput. Math. Appl., 56 (2008), 2572–2579.

[3] C.E. Chidume, E.U. Ofoedu, “Approximation of common fixed points for

finite families of total asymptotically nonexpansive mappings” J. Math. Anal.

Appl., 333(2007), 128-141


______________________________________________________

111





Semi–Empirical Systematic Development for Photon Induced

Nuclear Reaction Cross–Section Calculations

Abdullah Kaplan2, Hasan Ozdogan1,2, Mert Sekerci2, Veli Capali2

1Department of Biophysics, Akdeniz University, Antalya, Turkey

2Department of Physics, Süleyman Demirel University, Isparta, Turkey

[email protected]

Abstract: In this study, photon-neutron cross-section calculations have been

performed using pre-equilibrium nuclear reaction models. For pre-equilibrium

model calculation comparisons, some computation codes have been employed

that include theoretical nuclear reaction models. In addition, by obtaining giant

dipole resonance parameters in standard Lorentzian mode, semi-empirical cross

sections have been calculated. Obtained results have been compared with the

experimental values exist in the literature and nuclear reaction models’

computation results.

Keywords: Semi–Empirical Formula, Nuclear Cross–Section, Asymmetry

Parameter.


______________________________________________________

112





Positive Solutions for Fractional-Order Boundary Value

Problems

Ilkay Yaslan Karaca


35100 Bornova, Izmir, Turkey

[email protected] [email protected]

Abstract: In this study, six functionals fixed point theorem is used to research

the existence of positive solutions for fractional-order nonlinear boundary value

problems. As an applications, examples are presented to illustrate the main

results.

Keywords: Four functionals fixed point theorems, impulsive dynamic

equations, positive solutions, boundary value problems, time scale.

References:

[1] Avery, R. Henderson, J. and O’Regan, D., 2008, Six functional fixed point

theorem, Communications in Applied Mathematics, 12(1):69-81p.

[2] Dalir, M. and Bashour, M., 2010, Applications of fractional calculus,

Mathematical Sciences, Vol. 4, 1021-1032.

[3] Guo D., Lakshmikkantham V., Ames W. F., Nonlinear Problems in Abstract

Cones, Academic Press, New York, 1988.

[4] Kilbas, A.A. Srivastava, H.M., Trujillo, J.J., Theory and Applications of

Fractional Differential Equations, North-Holland Mathematics Studies 204, 69-

79p.

[5] Liu, X., Jia,M., Ge, W., 2013, Multiple Solutions of a p- Laplacian Model

Involving a Fractional Derivatives, Advances in Difference Equations.



______________________________________________________

113





The Existence of Positive Solutions of Boundary Value

Problems with P-Laplacian on the Half-Line

Ilkay Yaslan Karaca and Aycan Sinanoglu


35100 Bornova, Izmir, Turkey


Abstract: In this study, four functionals fixed point theorem is used to

investigate the existence of positive solutions for second-order time-scale

boundary value problem of dynamic equations on the half-line.

Keywords: Four functionals fixed point theorems, impulsive dynamic equation,

positive solutions, boundary value problems, time scale. References:

[1] G. Chai, Existence of positive solutions of boundary value problem for

second-order functional differential equations on infinite intervals, Fixed Point

Theory, 13 (2012), 423-437.

[2] X. Chen, X. Zhang, Existence of positive solutions for nonlinear systems of

second-order differential equations with inregral boundary conditions on an

infinite interval in Banach Space, Electron. J. Differential Equations, 2011

(2011), no. 154 19 pp.

[3] X. Chen, X. Zhang, Existence of positive solutions for singular impulsive

differential equations with integral boundary conditions on an infinite interval in

Banach Space, Electron. J. Qual.Differ. Equ., 2011 (2011), no. 28 18 pp.

[4] Y. Guo, C. Yu, J. Wang, Existence of three positive solutions for m-point

boundary value problem in infinite intervals , Nonlinear Anal., 71 (2009),717-

722.

[5] Z. Hao, L. Ma, Existence of positive solutions for multi-point boundary value

problem on infinite intervals in Banach Space, Abstr. Appl. Anal., 2012 (2012),

Art. ID 107276, 18pp.

[6] I. Y. Karaca, F. Tokmak, Existence of three positive solutions for m-point

time scale boundary value problem on infinite intervals, Dynam. Systems Appl.,

20 (2011), 355-367.

[7] X. Zhao, W. Ge, Multiple positive solutions for time scale boundary value

problem on infinite interval, Acta Appl. Math., 106 (2009), 265-273.

[8] X. Zhao, W. Ge, Unbounded positive solutions for m-point time-scale

boundary value problem on infinite intervals, J. Appl. Math. Comput., 33 (2010),

103-123.



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114





The Dimension of Digital Khalimsky Manifolds

Ismet Karaca1, Gokhan Temizel2

1Ege University

Faculty of Science, Department of Mathematics, Izmir,Turkey

[email protected] 2Ege University

Graduate School of Natural and Applied Sciences, Izmir, Turkey

[email protected]

Abstract: The digital counterpart of Euclidean topology which is defined on the

real line, has been studied by Efim Khalimsky. Khalimsky has defined this

topology on the integers and it is called Khalimsky’s topology. Digital

Khalimsky manifolds, digital manifolds with respect to Khalimsky topology, is a

digital response of real manifolds. These manifolds are used in order to

identifying to digital counterpart of the images on the Euclidean geometry and

they play an important role in image processing and computer graphics. In this

poster, we will explain the dimension of digital Khalimsky manifolds.

Keywords: Khalimsky Topology, Digital Manifold, Join Operator, Topological

Embedding

References:

[1] L. Boxer, “A classical construction for the digital fundamental group”,

Journal of Mathematical Imaging and Vision, 10:51-62, 1999.

[2] E. Melin, “How the find a Khalimsky-continuous approximation of a real-

valued function”, IWCIA 2004, LNSC 3322:351-365, 2004.

[3] E. Melin, “Extension of continuous function in digital spaces with the

Khalimsky topology”, Topology and Its Applications, 153:52-65, 2005.

[4] E. Melin, “Continuous Extension in topological digital spaces”, Applied

General Topology, 9:51-61, 2008.

[5] E. Melin, “Digital Khalimsky Manifolds”, Journal of Mathematical Imaging

and Vision, 33:267-280

[6]L.W. Tu, “An introduction to manifolds”, Springer Science+ Business Media,

LLC, 2008.



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Some Properties of Persistent Homology Groups

Ismet Karaca and Hatice Sevde Denizalti


Bornova, Izmir, Turkey


Abstract: Simplicial homology is a corner stone of algebraic topology in terms

of extracting topological features of spaces and persistent homology is occured

as an extension to simplicial homology. Persistence is investigated in [6] and

then generalized in [4]. Persistent homology is generally used for solving the

problem of unveiling global topological informations obtained from a sample of

a high-dimensional data sets of the space. To find the persistent homology of a

space, the space must be represented as a simplicial complex filtrations. In this

poster, we give some information about history of persistent homology and offer

its fundamental notions.

Keywords: Simplicial homology, simplicial complex filtration, persistent

homology.

References:

[1] A. Hatcher, “Algebraic Topology”, cambridge University Press, (2002).

[2] G. Carlsson, T. Ishkhanov, V. de Silva and A. Zomorodian “On the local

behaviour of spaces of natural images”, International Journal of Computer

Vision, 76.1(2008), 1-12.

[3] H. Edelsbrunner and E. P. Mcke, “Three-dimensional alpha shapes”, ACM

Transactions on Graphics, 13.1(1994), 43-72.

[4] H. Edelsbrunner, D. Letscher and A. Zomorodian “Topological persistence

and simplification”, Discrete Computational Geometry, 33(2005), 249-274.

[5] R. Ghrist, “Barcodes: the persistent topology of data”, Bulletin of the

American Mathematical Society, 45.1(2008), 61-75.

[6] A. Zomorodian and G. Carlsson, “Computing persistent homology”, Discrete

Computational Geometry, 28.4(2002), 511-533



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On Digital Cohomology Groups

Ismet Karaca1, Ozgur Ege2

1Department of Mathematics, Ege University, Bornova, Izmir, Turkey

[email protected] 2Department of Mathematics, Manisa Celal Bayar University, Yunusemre,

Manisa, Turkey

[email protected]

Abstract: Digital topology, introduced by Rosenfeld [8], is an area of great

theoretical interest having the additional bonus of significant applications in

imaging science and related areas. It continues to rise in many fields of science

and engineering such as mathematics, image processing, biology, information

system and computer science with a great number of applications. Important

developments have been made in this area after the works of Boxer[1,2]. Some

results on digital simplicial homology groups were introduced in [4] and [5]. In

[6], simplicial cohomology theory is given for digital images. Digital

cohomology operations were introduced in [7]. In this paper, we compute

simplicial cohomology groups of connected sum of certain minimal simple

surfaces by using the Universal Coefficient Theorem for digital cohomology

groups. We also prove some theorems related to degree properties of a map on

digital spheres.

Keywords: Digital image, Universal Coefficient Theorem, digital cohomology

group.

References:

[1] L. Boxer, “Digital continuous functions”, Pattern Recognition Letters,

15(1994), 833-839.

[2] L. Boxer, “A classical construction for the digital fundamental group”,

Journal of Mathematical Imaging and Vision, 10(1999), 51-62.

[3] L. Boxer, I. Karaca and A. Oztel, “Topological invariants in digital images”,

Journal of Mathematical Sciences: Advances and Applications, 11.2(2011), 109-

140.



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[4] O. Ege and I. Karaca, “Some results on simplicial homology groups of 2D

digital images”, International Journal of Information and Computer Science,

1.8(2012), 198-203.

[5] O. Ege and I. Karaca, “Fundamental properties of simplicial homology

groups for digital images”, American Journal of Computer Technology and

Application, 1.2(2013), 25-42.

[6] O. Ege and I. Karaca, “Cohomology theory for digital images”, Romanian

Journal of Information Science and Technology, 16.1(2013), 10-28.

[7] O. Ege and I. Karaca, “Digital cohomology operations”, Applied

Mathematics and Information Sciences, 9.4(2015), 1953-1960.

[8] A. Rosenfeld, “Digital topology”, American Mathematical Monthly,

86(1979), 76-87.

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118





Some Common Fixed Point Theorems on Complex Valued

Gb-Metric Spaces

Ismet Karaca1, Ozgur Ege2

1Department of Mathematics, Ege University, Bornova, Izmir, Turkey

[email protected] 2Department of Mathematics, Manisa Celal Bayar University, Yunusemre,

Manisa, Turkey

[email protected]

Abstract: Fixed point theory is very active area with various applications in

mathematics, biology, image processing [2] and computer science. In this theory,

the Banach contraction principle plays a key role to solve many problems. After

the Banach’s work [1], researchers have obtained important results in various

metric spaces. The notion of complex valued Gb-metric space was introduced in

[3]. Then some new fixed point results have been given by several authors [4,5]

in this space. The concept of the common fixed point of mappings satisfying

contractive type condition has generally been used to prove existence problems.

In this study, we prove some common fixed point theorems in complex valued

Gb-metric spaces.

Keywords: Fixed point, common fixed point theorem.

References:

[1] S. Banach, “Sur les operations dans les ensembles abstraits et leurs

applications aux equations integrales”, Fundamenta Mathematicae, 3(1922), 133-

181.

[2] O. Ege and I. Karaca, “Banach fixed point theorem for digital images”,

Journal of Nonlinear Science and Applications, 8.6(2015), 1014-1021.

[3] O. Ege, “Complex valued Gb--metric spaces”, Journal of Computational

Analysis and Applications, 21.2(2016), 363-368.[4] O. Ege, “Some fixed point

theorems in complex valued Gb--metric spaces”, to appear in Journal of

Nonlinear and Convex Analysis, (2017).

[5] A.H. Ansari, O. Ege and S. Radenovic, “Some fixed point results on complex

valued Gb-metric spaces”, to appear in Revista de la Real Academia de Ciencias

Exactas, Fisicas y Naturales, Seria A. Matematicas, Doi: 10.1007/s13398-017-

0391-x, (2017), 1-10



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On Some Deddens Subspaces of Banach Algebras

Mubariz Karaev 1, Mehmet Gurdal2, Havva Tilki2

1Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

2Department of Mathematics, Süleyman Demirel University, Isparta, Turkey

[email protected]; [email protected]; [email protected]

Abstract: Let A be a Banach algebra with a unit e , and let Aa be an

invertible element. We define the following algebra:

.0 and 0 somefor :: x

xx

nnloca cxncxaax

AB

In this article we study some properties of this algebra; in particular, we prove

that 0: pepxxlocpe AB , where p is an idempotent in A . We also

investigate the following Deddens subspace. Let Aba, be two elements. Fix

any number , 10 , and consider the following subspace of :A

. as ::, nnOxbaxD nnba

A

Here we study some properties of the subspaces baD , and .,

abD

Keywords: Banach algebra, Deddens subspace, Deddens algebra, Idempotent

element, Nilpotent element

Acknowledgement. This work is supported by Suleyman Demirel University

with Project 4799-YL1-16.

References:

[1] W.Arveson, Interpolation problems in nest algebras, J.Funct. Anal.,

20(1975), 208-233.

[2] J.A.Deddens, Another description of nest algebras, Lecture Notes in Math.,

693(1978), 77-86.

[3] D.Drissi and M.Mbekhta, Operators with bounded conjugation orbits, Proc.

Amer. Math. Soc., 128(2000), 2687-2691.

[4] J.A.Erdos, Unitary invariants for nests, Pacific J. Math., 23(1967), 229-256.

[5] M.Gürdal, Description of extended eigenvalues and extended eigenvectors of

integration operators on the Wiener algebra, Expo. Math., 27(2009), 153-160.




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Duhamel Operator and Existence of Invariant Subspace

Mubariz Karaev 1, Mehmet Gurdal2, Mualla Birgul Huban2

1Department of Mathematics, King Saud University, Riyadh, Saudi Arabia 2Department of Mathematics, Süleyman Demirel University, Isparta, Turkey


Abstract: In this work, we gives some sufficient conditions in terms of

reproducing kernels and Duhamel operators for the existence of nontrivial

invariant subspace in Hardy-Hilbert Space.

Keywords: Reproducing kernel, Berezin symbol, Invariant subspace, Duhamel

operator, Hardy space

Acknowledgement This work is supported by the Scientific and Technological

Research Council of Turkey (TÜBİTAK) with Project 115F265.

References:

[1] P. Ahern, M. Flores and W. Rudin, “An invariant volume-mean-value

property”, J. Funct. Anal., 111 (2) (1993), 380-397.

[2] M. Engliš, “Functions invariant under the Berezin transform”, J. Funct.

Anal., 121 (1) (1994), 233-254.

[3] M. Lacruz, “Invariant subspaces and Deddens algebras”, Expo. Math., (33)

(1) (2015), 116-120.

[4] A. Lambert, “Hyperinvariant subspaces and extended eigenvalues”, New

York J. Math., 10 (2004), 83-88.

[5] M.M. Malamud, “Invariant and hyperinvariant subspaces of direct sums of

simple Volterra operators”, Oper. Theory Adv. Appl., 102 (1998), 143-167.

[6] N. M. Wigley, “The Duhamel product of analytic functions”, Duke Math. J.,

41 (1974), 211-217.

[7] N.M. Wigley, “A Banach algebra structure for pH ”, Canad. Math. Bull., 18

(4) (1975), 597-603.

[8] K. Zhu, “Operator Theory in Function Spaces”, Marcel Dekker, New York,

1990.




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On Extended Eigenvalues and Extended Eigenvectors of

Toeplitz Operators

Mubariz Karaev 1, Mehmet Gurdal2, Mualla Birgul Huban2

1Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

2Department of Mathematics, Süleyman Demirel University, Isparta, Turkey


Abstract: In this paper, we consider the operators from Englis algebras, in

particular, the Toeplitz operators on the Hardy space, and give some results on

the commutant, extended eigenvalues and extended eigenvectors of operators.

Keywords: English algebra, Hardy space, Toeplitz operator, extended

eigenvalue

Acknowledgement: This work is supported by TUBA through Young Scientist

Award Program (TUBA-GEBIP/2015).

References:

[1] H. Alkanjo, “On extended eigenvalues and extended eigenvectors of

truncated shift”, Concrete Operators, 1 (2013), 19-27.

[2] A. Biswas, A. Lambert and S. Petrovic, “Extended eigenvalues and the

Volterra operator”, Glasgow Math. J., 44 (2002), 521-534.

[3] M. Gürdal, “On the extended eigenvalues and extended eigenvectors of shift

operator on the Wiener algebra”, Appl. Math. Lett., 22 (2009), 1727-1729.

[4] M. T. Karaev, “On extended eigenvalues and extended eigenvectors of some

operator classes”, Proc. Amer. Math. Soc., 134 (2006), 2383-2392.




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A Generalization on the Incidence Energy and Laplacian-

Energy-Like Invariant

Ezgi Kaya and A. Dilek Maden

Department of Mathematics-Computer, Igdir University,

Igdir, Turkey

[email protected]

Department of Mathematics, Selcuk University,

Konya, Turkey

[email protected]

Abstract: For a graph G and a real number α, the graph invariant 𝑠𝛼(𝐺) is the

sum of the powers of signless Laplacian eigenvalues and 𝜎𝛼(𝐺) is equal to the

sum of powers of Laplacian eigenvalues of G. In this study, considering these

sum for some special cases of α, we give some bounds for incidence energy and

Laplacian-energy-like invariant of graphs.

Keywords: Laplacian matrix, signless Laplacian matrix, Incidence energy,

Laplacian-Energy-Like invariant

References:

[1] S. Akbari, E. Ghorbani, J. H. Koolen and M. R. Oboudi, “On sum of powers

of the Laplacian and signless Laplacian eigenvalues of graphs”, Electron. J.

Combin. 17 (2010), R115.

[2] S. Furuichi, “On refined Young inequalities and reverse inequalities”, J.

Math. Inequal., 5(2011), 21-31.

[3] I. Gutman, The energy of a graph, Ber. Math. Statist. Sekt. Forschungsz.

Graz 103 (1978), 1-22.

[4] I. Gutman, D. Kiani, M. Mirzakhah, On incidence energy of graphs, MATCH

Commun. Math. Comput. Chem. 62 (2009), 573-580.

[5] M. Jooyandeh, D. Kiani, M. Mirzakhah, “Incidence energy of a graph”,

MATCH Commun. Math. Comput. Chem. 62 (2009), 561-572.

[6] H. Kober, “On the arithmetic and geometric means and the Hölder

inequality”, Proc. Amer. Math. Soc., 59(1958), 452-459.

[7] J. Liu, B. Liu, A Laplacian-energy like invariant of a graph, MATCH

Commun. Math. Comput. Chem. 59 (2008), 355-372.

[8] B. Liu, Y. Huang, Z. You, A survey on the Laplacian–energy like invariant,

MATCH Commun. Math. Comput. Chem. 66 (2011), 713–730.

[9] B. Zhou, “On sum of powers of the Laplacian eigenvalues of graphs”, Linear

Algebra Appl. 429(2008), 2239–2246.


mailto:ezgi.kaya@igdir.

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123





A Data Mining Approach: Application to the Extraction of the

Characteristics of IARD Products in the Insurance Sector

Sadi Khadidja1,2, Lounici Mosbah Nora1,2

1. Higher National School of Statistics and Applied Economics

2. Laboratory of Applied Statistics

ENSSEA, University of Kolea, Algeriers, Algeria


Abstract: In this study, we are interested in IARD property and Multi-risk

insurance products, which covers fire, accidents and various risks [1] of an

Algerian insurance company. We want to know the variables that best

characterize each of the two products. To solve this problem, we have combined

three methods borrowed from Data Mining and decisional statistics [2][3]. The

use of data mining tools to realize a classification and to bring out the most

informative variables is usual tasks of this discipline. The aim of this work is to

extract knowledge from an actuarial database by adopting an approach to data

mining [4] and to compare the results obtained by querying tools and techniques,

implemented in data mining software.

Keywords: Insurance IARD, data mining approach, classification, machine

Learning

References :

[1] F. Noël. La gestion des sinistres IARD incendies et risques divers,

édition séfi, Canada 2014.

[2] S. Tuffery. Data mining et statistique décisionnelle 4ième ed, Broché – 21

août 2012.

[3] C. Wesphal & T. Blaxton. "Data Mining Solutions ", John Wiley, New

York, 1998.

[4] M. Boullé. Recherche d’une représentation des données efficace pour la

fouille des grandes bases de données. Ph. D. thesis, ENST. 2007.



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124





The Le Corbusier Approach in the Relationship between

Architecture and Mathematics

Murat Kilic and Melih Kurnali

Faculty of Fine Arts, Deparment of Interior Architechure & Environment

Design,

Kırıkkale University, Kırıkkale, Turkey

[email protected]

Abstract: In defining the relationship between architecture and mathematics,

dealing with and evaluating different points of view is important and necessary

in terms of both creating new horizons and a new perception for these two

disciplines. In general, architecture and mathematics are dealt with according to

their technical characteristics. Architecture makes use of mathematics as a

technique and a tool. However, these two disciplines should be used together to

create art and allow art reach top level aesthetic values as well. In the period of

Modernism, Le Corbusier who has been in search of this purpose and

mathematical systems which could meet all conditions for architecture is in fact

an important architect who has internalized mathematics to reach artistic

aesthetics. In Le Corbusier’s and contemporary mathematicians’ point of view

on mathematics, it can be seen that there is a deep opposition. This is caused by

the contradictive comparisons made between scientistd and artists. Although

architecture is regarded as an art, it is actually a discipline which is formed by

the perfect synthesis of science and art [1]. Le Corbusier can be considered as

being closer to the artistic side of this synthesis. Although his modular system

seems mathematical, or scientific, we can say that his artistic side gains more

importance due to the fact that he has not been educated on building construction

techniques and the technical complaints he has received about his structures from

his clients. In particular, the Ronchamp Chapel embodies a sculptural artistry and

he is firstly a painter. Although Le Corbusier’s architectural and mathematical

approach has been criticized, it is apparent that he had an intellectual foundation

which gave inspiration. So much so that, the proportional system called modulor

which he developed for architecture has inspired the composition of a piece


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called “Metastassis” [2]. Le Corbusier is at a critical point in the art, mathematics

and architecture triangle and this study is in search of knowledge about Le

Corbusier and his mathematical understanding to allow these disciplines to be

evaluated with new approaches.

Keywords: Architecture, Mathematics, Le Corbusier, Modulor.

References:

[1] J. Loach, “Le Corbusier and the Creative Use of Mathematics”, The British

Society for the History of Science, (1998), 185-215.

[2] Le Corbusier. “Modulor 2”, Yem Press (2011), 328-329.

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126





The Absolute Möbius Divisor Function and Euler function

Daeyeoul Kim1, Umit Sarp2 and Sebahattin Ikikardes2

1National Institute for Mathematical Sciences, Yuseong-daero 1689-gil,

Yuseong-gu, Daejeon 305-811, South Korea

[email protected] 2Department of Mathematics, Balikesir University, 10100 Balikesir, Turkey

[email protected]

[email protected]

Abstract: In this study,we introduce the absolute Mobius divisor function ( )U n .

Also we investigate the sequences m mU n , which concerns the iteration of

the absolute Mobius divisor function ( )U n . According to some numerical

computational evidence, we consider integer pairs ; 1n n satisfying;

1 1 .n n U n U n

Furthermore, we give some examples and proofs for our results.

Keywords: Mobius divisor function, Fermat pirmes, Euler function, n-gonal

number.

References:

[1] A. Bayad and D. Kim, Polygon Numbers Associated with the Sum of Odd

Divisors Function, to appear of Exp. Math.

http://dx.doi.org/10.1080/10586458.2016.1162231.

[2] V. Annapurna, Inequalities for (n) and '(n), Math. Mag. 45 (1972), 187-190.

[3] L. E. Dickson, History of the theory of numbers. Vol I: Divisibility and

Primality. Chelsea Publishing Co., New York 1966.

[4] P. Erdös, Some remarks on Eulers function and some related problems,

Bull. Amer. Math. Soc. 51 (1945), 540-544.

[5] R. K. Guy, Unsolved Problems in Number Theory, Springer, 2004.




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S-Generalized Lauricella’s Hypergeometric Functions

I. Onur Kiymaz, M. Baki Yagbasan, Aysegul Cetinkaya


Kırşehir, Turkey

[email protected]

Abstract: In this study, we introduced new generalizations of Lauricella’s

hypergeometric functions by using S- generalized beta function. Furthermore, we

investigated some of their properties such as integral representations and

transformation formulas.

Keywords: S-Generalized Beta function, Lauricella’s hypergeometric functions.

Acknowledgement: This work was supported by Ahi Evran University

Scientific Research Projects Coordination Unit. Project Number: FEF.D1.16.001

References:

[1]Bailey W.N., “Generalized Hypergeometric Series”, Cambridge Tracts in

Mathematics and Mathematical Physics, vol. 32, Cambridge University Press,

Cambridge, (1935).


beta function”, J. Comput.Appl. Math., 78, (1997): 19-32.

[3]Hasanov, A., Srivastava, H. M., “Some decomposition formulas associated

with the Lauricella function and other multiple hypergeometric functions”, Appl.

Math. Lett., 19.2, (2006): 113-121.

[4]Luo, Min-Jie, Milovanovic, G. V., Agarwal, P., “Some results on the

extended beta and extended hypergeometric functions”, Applied Mathematics

and Computation, 248, (2014): 631-651.

[5]Padmanabham, P. A., Srivastava, H. M., “Summation formulas associated

with the Lauricella function Appl. Math. Lett., 13.1, (2000): 65-70.

[6] Srivastava H. M., Karlsson P. W., “Multiple Gaussian Hypergeometric

Series”, Ellis Horwood Limited, (1985).

[7] Srivastava, H. M., Agarwal, P., Jain, S., “Generating functions for the


Computation, 247, (2014): 348-352.

[8]Srivastava, H. M., Jain, R., Bansal, M. K., “A Study of the S-Generalized

Gauss Hypergeometric Function and Its Associated Integral Transforms”,Turkish

Journal of Analysis and Number Theory, 3.5, (2015): 116-119.


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128





Some Remarks on Fuzzy Anti-Normed Spaces

Ljubiša D.R. Kočinac

Faculty of Sciences and Mathematics, University of Niš, Serbia

[email protected]

Abstract: Let E be a real linear space with a fuzzy anti-norm with respect to a

t-conorm. We discuss some (statistical) convergence and covering properties of

such spaces. We also consider norms on E generated by .

Keywords: Statistical convergence, fuzzy anti-normed space, boundedness.


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129





On Asymptotically f-Statistical Equivalent Sequences

Sukran Konca and Mehmet Kucukaslan

Department of Mathematics, Bitlis Eren University, 13000, Bitlis, Turkey

Department of Mathematics, Mersin University, 33343, Mersin, Turkey


Abstract: By using modulus functions, we have obtained a generalization of

statistical convergence of asymptotically equivalent sequences, a new non-matrix

convergence method, which is intermediate between the ordinary convergence

and the statistical convergence. Further, we have examined some inclusion

relations related to asymptotically f-statistical equivalence of real sequences in

the light of a partial order.

Keywords: Statistical Convergence, strong Cesaro summability; f-

asymptotically equivalent sequences.

References:

[1] M. Marouf, “Asymptotic equivalence and summability”, Internat. J. Math.

Math. Sci. 16 (4) (1993), 755-762.

[2] R. F. Patterson, “On asymptotically statistically equivalent sequences”,

Demonstratio Math, 36 (1) (2003), 149-153.

[3] A. Aizpuru, M. C. Listan-Garcia and F. Rambla-Barreno, “Density by moduli

and statistical convergence”, Quaestiones Mathematicae., 37 (4) (2014), 525–-

530.

[4] V. K. Bhardwaj, S. Dhawan, and S. Gupta, “Density by moduli and statistical

boundedness”, Abst. Appl. Analysis, 2016(2016), 6 pages.

[5] H. Nakano, “Concave modulars”, J. Math. Soc. Japan, 5(1953), 29–-49.


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Some Permanents of Hessenberg Matrices

Sibel Koparal, Nese Omur and Cemile Duygu Sener

Department of Mathematics, Kocaeli University,

Kocaeli, Turkey

[email protected] ,[email protected],

[email protected]

Abstract: In this study, we define a sequence 𝑅𝑛(𝑎, 𝑏, 𝑐) and represent

relationships between this sequence and permanents of certain matrices. Some

special cases for permanents are given.

Keywords: Hessenberg matrix, Relation recurrence, Permanent.

References:

[1]R.A. Brualdi and P.M. Gibson, “Convex Polyhedra of Doubly Stochastic

Matrices: Applications of the permanents Function”, J.Combin Theory A,

22(1977), 194-230.

[2]E. Kılıç and D.Taşcı, “On the permanents of some tridiagonal matrices with

applications to the Fibonacci and Lucas numbers”, Rocky Mountain Journal of

Mathematics, 37.6(2007), 203-219.

[3]E. Kılıç, Tribonacci sequences with certain indices and their sums”, Ars

Combinatoria, 86(2008), 31-40.

[4]E.Kılıç and D. Taşcı, “Negatively subscripted Fibonacci and Lucas numbers

and their complex factorizations”, Ars Combinatoria, 96(2010), 275-288.

[5] H. Mine, “Permanents of (0,1)-circulants”, Canad. Math. Bull., 7(1964), 253-

263.

[6]J.L. Ramnrez, “Hessenberh matrices and the generalized Fibonacci-Narayana

sequence”, Filomat, 29.7(2015), 1557-1563.




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Best Proximity Points for Generalized Geraghty

Proximal Contraction Mapping in Elliptic Valued Metric Space

Isil Arda Kosal1, Hidayet Huda Kosal2, Mahpeyker Ozturk3

1,2,3 Department of Mathematics,

Sakarya Universitesi, Sakarya, TURKEY


Abstract: In this study, we introduce the concept of best proximity points for the

generalized Geraghty proximal contraction mappings between two

subsets of elliptic valued metric space. Elliptic numbers are generalized form of

complex and so real numbers. Thus, the obtained results extend, generalize and

complement some known fixed and best proximity point results from the

literature.

Keywords: Contraction mapping, Best proximity, Ellipitc valued metric spaces.

References:

[1] A. Harkin and J. Harkin, “Geometry of generalized complex numbers”,

Mathematics Magazine, 77.2(2004), 118–129.

[2] A. Azam, B. Fisher and M Khan, “Common fixed point theorems in complex

valued metrik spaces”, Numerical Functional Analysis and Optimization. An

International Journal, 32.3(2011), 243–253.

[3] M. Ozturk and N. Kaplan,” Common fixed points of f-contraction mappings

in complex valued metric spaces”, Mathematical Sciences, 8.129(2014).

[4] M. Ozturk, “Common fixed points theorems satisfying contractive type

conditions in complex valued metrik spaces”, Abstract and Applied Analysis,

7(2014).

[5] J. Hamzehnejadi and R. Lashkaripour, “Best proximity points for generalized

Geraghty proximal contraction mapping and its applications”, Fixed

Point Theory and Applications, 72.1(2016), 1-13.

[6] E. Karapinar, “A Discussion on Geraghty contraction type mapping”,

Filomat, 28.4(2014), 761-766.

[7] N. Bilgili, E. Karapinar and K. Sadarangani, “A generalization for the best

proximity point of Geraghty contraction”, Journal of Inequalities and

Applications, 286(2013), 1-9




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Characterizations of , ,p q - Convex Sequences

Xhevat Z. Krasniqi

Faculty of Education, University of Prishtina “Hasan Prishtina”,

10000 Prishtina, Republic of Kosovo

[email protected]

Abstract: The class of convex sequences has important applications in several

branches of mathematics as well as their generalizations. In this paper, we have

introduced a new class of convex sequences, the so-called , ,p q -convex

sequences. Moreover, the characterizations of such sequences belonging to this

class has been shown.

Keywords: Sequence, Convexity,$(p;r)-$monotonicity, $(p,q;r)-$convexity,

$p$-starshaped sequence, $(p,q;\alpha )$-convexity.

References:

[1] H. Bor, A new application of convex sequences. J. Class. Anal. 1 (2012), no.

1, 31--34.

[2] H. Bor, Xh. Z. Krasniqi, A note on absolute Cesàro summability factors.

Adv. Pure Appl. Math. 3 (2012), no. 3, 259--264.

[3] Xh. Z. Krasniqi, Some properties of $(p,q;r)$-convex sequences. Appl. Math.

E-Notes 15 (2015), 38--45.

[4] Xh. Z. Krasniqi, Characterizations of $(p,\alpha )$-convex sequences. Appl.

Math. E-Notes, accepted.

[5] L. M. Koci\'c, I. Z. Milovanovi\'c, A property of $(p,q)$-convex sequences,

Period. Math. Hungar. Vol. 17 (1) (1986), pp. 25--26.

[6] I. B. Lackovi\'c, M. R. Jovanovi\'c, On a class of real sequences which satisfy

a difference inequality, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. No. 678

(1980), 99--104.

[7] B. Makarov, A. Podkorytov, Real Analysis: Measures, Integrals and

Applications, Springer--Verlag London, 2013.

[8] J. E. Pe\ucari\'c, On some inequalities for convex sequences. Publ. Inst.

Math. (Beograd) (N.S.) 33(47) (1983), 173--178.

[9] F. Qi, B.-N. Guo, Monotonicity of sequences involving convex function and

sequence. Math. Inequal. Appl. 9 (2006), no. 2, 247--254.


______________________________________________________

133





A Note on the Numbers Yn(Λ) and the Polynomials Yn(X;Λ)

and Their Generating Functions

Irem Kucukoglu1,a and Yilmaz Simsek2,b

1Department of Software Engineering, Faculty of Engineering and Architecture,

Antalya AKEV University Antalya, Turkey. 2Department of Mathematics, Faculty of Science University of Akdeniz TR-

07058, Antalya, Turkey.


Abstract: In this talk, we study on the numbers Yn(λ) and the polynomials

Yn(x;λ) which have been recently introduced by Simsek in [7]. We give partial

derivative formulas including the generating functions of these numbers and

polynomials. By using these formulas and functional equations for the generating

functions, we give some recurrrence relations and identities for these numbers

and polynomials related to some special numbers such as the Apostol-Bernoulli

numbers, the Apostol-Euler numbers, the Stirling numbers of the first kind, the

Cauchy numbers.

Keywords: Generating functions, Functional equations, Partial differential

equations, Daehee numbers, Changhee numbers, Stirling numbers.

References:

[1] T. M. Apostol, On the Lerch zeta function, Pacific J. Math. 1 (1951), pp. 161-

167.

[2] N. P. Cakic and G. V. Milovanovic, On generalized Stirling numbers and

polynomials, Mathematica Balkanica 2004; 18: 241-248.

[3] G. B. Djordjevic and G. V. Milovanovic, Special classes of polynomials,

University of Nis, Faculty of Technology Leskovac, 2014.

[4] D. S. Kim, T. Kim and J. Seo, A note on Changhee numbers and

polynomials, Adv. Stud. Theor. Phys. 7 (2013), 993-1003.

[5] D. S. Kim and T. Kim, Daehee numbers and polynomials, Appl. Math. Sci.

(Ruse) 7 (120) (2013), 5969-5976.

[6] T. Kim, D. V. Dolgy, D. S. Kim and J. J. Seo, Differential equations for

Changhee polynomials and their applications, J. Nonlinear Sci. Appl. 9 (2016),

2857-2864.

[7] Y. Simsek, Generating Functions for family of (q-) generalized Apostol-type

Numbers And Polynomials: Analysis of the p-adic q-integrals, (preprint).



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134





Modelling Worldwide CO2 Emissions and Oil Consumption

based on the 𝑳𝟏, 𝑳𝟐 𝐚𝐧𝐝 𝑳∞-norm Regressions

1Pranesh Kumar and 2Mohamadtaghi Rahimi

1Department of Mathematics and Statistics,

University Northern British Columbia, Prince George, BC V2N 4Z9, Canada

[email protected] 2Department of Mathematics,

Iran University of Science and Technology, Narmak, Tehran, Iran.

[email protected]

Abstract. Regression models are commonly used to model the relationship

among random variables in statistical data analysis with an aim to use them to

make future predictions. The regression model estimated by the method of least

squares is known to be optimal and perform relatively well under certain

assumptions such as when the errors: follow normal distributions, are free of

large size outliers and satisfy the Gauss-Markov assumptions. However, in

practice, the least squares error linear regression models may fail to provide best

results in non-Gaussian situations especially when the errors follow distributions

with fat tails and error terms possess a finite variance. Historically, in the

eighteenth century, mathematicians, notably, Mayer, Boscovich, Laplace,

Legendre, Simpson, Gauss, and Euler did pioneering work to develop procedures

for fitting functions. The most significant research was the development of

methods of least absolute deviations, least squares deviations and minimax

absolute deviations. The theory of function fitting methods of least squares is

credited to the published works of Legendre (1805) and Gauss (1809).

Alternatively, we may use 𝐿𝑝-norm to estimate the linear regression model

parameters to search for an appropriate regression model. In this paper, we

provide a perspective on the 𝐿1, 𝐿2 and 𝐿∞-norm based regression models.

Worldwide oil consumption and CO2 emissions are an on-going environmental

worldwide concern and often result in both immediate and long-term

environmental damage. We discuss the results on modeling of worldwide CO2

emissions and oil production from these models. We conclude the paper with

relevant concerns in the applications of regression-model methodology and

further research of interest.



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135





Some Symmerty Identities for Modified Degenerate Apostol-

Bernoulli and Modified Degenerate Apostol-Euler Polynomials

Related to Multiplier Sums

Burak Kurt

Department of Mathematics, Faculty of Educations

University of Akdeniz

TR-07058 Antalya, Turkey

[email protected]

Abstract: Dogly et. al. in [2] defined and investigated modified degenerate

Bernoulli polynomials and numbers. They proved some identities and recurrence

relations for these polynomials. H.-In Known et. al. in [3] defined the modified

degenerate Euler polynomials and numbers. They investigated some properties

for these polynomials. Also, they gave some identities arising from the fermonic

p-adic integral on ℤ _p.

In this article, we define the modified degenerate Apostol-Bernoulli polynomials

and numbers. Also, we give modified degenerate Euler-polynomials and

numbers. We give some symmetric relations between for these polynomials.

Also, we generalize to Srivastava-Pintér summation formulea for the modified

degenerate Apostol-Bernoulli polynomials and the modified degenerate Apostol-

Euler polynomials

Keywords: Bernoulli polynomials and numbers, Euler polynomials and

numbers, Apostol-Bernoulli polynomials and numbers, Apostol-Euler

polynomials and numbers, Degenerate Bernoulli polynomials and numbers,

Degenerate Euler polynomials and numbers, Modified Degenerate Apostol-

Bernoulli polynomials, Modified Degenerate Apostol-Euler polynomials.

References:

[1] L. Carlitz, “Degenerate Stirling Bernoulli and Eulerian numbers”, Utilitas

Math., 15 (1979), 51-88.

[2] D. V. Dolgy, T. Kim, Known H.-In and J. J. Seo, “On the modified

degenerate Bernoulli polynomials”, Adv. Stu. In Comtep. Math., 26(2016), 203-

209.

[3] Q.-M. Luo, “Multiplication formulas for the Apostol-Bernoulli and Apostol-

Euler polynomials of higher order”, Integral Transforms, Spec. Func., 20(2009),

377-391.


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136





Univalency Conditions of a General Nonlinear Integral

Operator of Analytic Functions with Different Domains

Shuhai Li, Huo Tang

School of Mathematics and Statistics, Chifeng University,

Chifeng 024000, Inner Mongolia, China


Abstract: In this paper, we give some new univalence conditions of a general

nonlinear integral operator of analytic functions defined by subordination with

different domains. The results present here improve and generalize some known

results.

Keywords: Analytic function, Univalent functions, Nonlinear integral operator,

Subordination.

References:

[1] P. L. Duren. Univalent functions. Grundlehren der Mathematischen

Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and

Tokyo, 1983.

[2] W. Janowski. Some extremal problems for certain families of analytic

functions,I, Ann. Polon. Math. 28(1973), 297-326.

[3] J. Stankiewicz and J. Waniurski. Some classes of functions subordinate to

linear transformation and their applications, Ann. Univ, Mariae Curie-

Sklodowska, Section A. 28(1974), 85-94.

[4] B. A. Frasin. Univalency of a nonlinear integral operator of analytic

functions, Journal of Mathematical Inequalities. 9(2015), 763-771.

[5] Adriana Oprea, Daniel Breaz and H. M. Srivastava, Univalence conditions

for a new family of integral operators, Filomat. 30(2016), 1243-1251.

[6] Liangpeng Xiong, Properties of certain nonlinear integral operator associated

with Janowski Starlike and convex functions, Journal of Mathematical Research

with Applications. 36(2016), 432-440.

[7] Sh. Najafzadeh, A. Ebadian and H. Rahmatan, Univalency conditions for a

new integral operator, Journal of Computer Science and Applied Mathematics.

1(2015), 35-37.



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137





Certain Subclasses of Harmonic Univalent Functions Defined

By Convolution and Subordination

Shuhai Li, Huo Tang

School of Mathematics and Statistics, Chifeng University,

Chifeng , Inner Mongolia, China


Abstract: Let HS be the class of functions ghf that are harmonic

univalent and sense-preserving in the open unit disk 1: zzU for which

01)0()0( ' ff . In the present paper, we introduce some new subclasses of

HS consisting of univalent and sense-preserving functions defined by

convolution and subordination. Sufficient coefficient conditions, distortion

bounds, extreme points and convolution properties for functions of these classes

are obtained. Also, we discuss the radius of starlikeness and convexity.

Keywords: Harmonic univalent functions, subordination, convolution, sufficient

coefficient condition, radius.

References:

[1] J. Clunie and T. Sheil Small, Harmonic univalent functions, Ann. Acad. Sci.

Fenn. Ser. A I Math. 39(1) (1984), 3–25.

[2] J. M. Jahangiri, Coefficient bounds and univalent criteria for harmonic

functions with negative coefficients,Ann. Univ. Marie-Curie Sklodowska Sect.

A. 52 (1998), 57–66.

[3] J. M. Jahangiri, Harmonic functions starlike in the unit disc, J. Math. Anal.

Appl. 235 (1999), 470–477.

[4] H. Silverman and E. M. Silvia, Subclasses of harmonic univalent functions,

New Zealand J. Math. 28(1999), 275–284.

[5] S. Nagpal and V. Ravichandran, A comprehensive class of harmonic

functions defined by convolution and its connection with integral transforms and

hypergeometric functions, Stud. Univ. Babes Bolyai-Math. 59(1) (2014), 41–55.

[6] S. Nagpal and V. Ravichandran, Fully starlike and fully convex harmonic

mappings of order α, Ann. Polon.Math. 108 (2013), 85–107.

[7] R. M. El-Ashwah and B. A. Frasin, Hadamard product of certain harmonic

univalent meromorphic functions, Theory and Applications of Mathematics

Computer Science. 5 (2) (2015), 126–131.



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138





Refinement of Some Inequalities Concerning to Bn-Operator of

Polynomials with Restricted Zeros

A. Liman

Department of Mathematics, National Institute of Technology Srinagar

Jammu and Kashmir, India

[email protected]

Abstract: Let Pn be the class of polynomials of degree at most n. Rahman

introduced the class Bn of operators B that map Pn into itself. We present the

correct proof of the result of Rather and Gulzar (Adv Inequal Appl 2:16–30,

2013). Moreover our result improves many prior results involving Bn operators

and a number of polynomial inequalities can also be deduced by a uniform

procedure.

Keywords: Polynomials, B-operator, inequalities.

References:

[1] Abdul Aziz, A refinement of an inequality of S. Bernstein, J. Math. Anal.

Appl., 142(1989), 1-10.

[2] N. A. Rather, S. Gulzar, On an operator preserving inequalities between

polynomials. Adv. Inequal. Appl. 2, 16–30 (2013)

[3] S. Bernstein, Sur la limitation des derivees des polynomes, C. R. Acad. Sci.

Paris., 190(1930), 338-340.


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139





Gaussian Approximation to the Estimator of the Mean of a

Heavy-Tailed Distribution under Random Censoring

Djamel Mearghni

Department of Mathematics, Mohamed Khider University,

Biskra, Algeria

[email protected]

Abstract: In many real life applications, the observations may not be available

in their entirety: they are usually randomly censored. This happens quite often

with, for instance, lifetime, reliability or insurance data. We model this situation

by introducing a non-negative random variable (rv), called censoring rv,

independent of the rv of interest. Then, we focus on minimum of the two rv's and

an indicator rv which determines whether or not there has been censorship. In

this work, we first apply the extreme value theory results to define an estimator

for the mean of a heavy-tailed distribution under random censoring. Then, we

make use of the empirical process theory to provide a Gaussian approximation to

the proposed estimator, which would lead to its asymptotic normality.

Keywords: Empirical process; Gaussian approximation; Heavy-tailed

distribution; Mean estimator; Order statistics; Random censoring.


______________________________________________________

140





Industrial Application of Fuzzy Logic Control for

Torque-ripple Minimization in Electricals Machines

Zineb Mekrini, Seddik Bri

Materials and Instrumentation (MIM), Electrical Engineering Department, High

School of Technology, Moulay Ismail University Meknes-Morocco

[email protected]

Abstract: This paper deals with fuzzy system application in the industry. Fuzzy

logic use linguistic descriptions of variable and linguistic for the input and output

behavior.Numerical input quantities are mapped to numerical output quatities by

using, fuzzification,inference ,and defuzzification procedures.As a

consequence,fuzzy systems can be based as nonlinear systems .The

asynchronous machine constitute a theoretically interesting and practically

important class of nonlinear systems. They are described by nonlinear

differential equation.The major problem that is usually associated with control of

this machine is the high torque ripple as it is not directly controlled. The high

torque ripple causes vibrations to the motor which may lead to component lose,

bearing failure or resonance. The fuzzy logic controller is applied to reduce

electromagnetic torque ripple.

Keywords: Fuzzy logic, Asynchronous machine ,Torque –Electromagnetic flux .

References:

[1] F.Korkmaz, I.Topaloğlu, H.Mamur,“Fuzzy Logic Based Direct Torque

Control Of Induction Motor With Space Vector Modulation ”, International

Journal on Soft Computing, Artificial Intelligence and Applications

(IJSCAI),Vol.2, No. 5/6, pp.32–40, December 2013.

[2]Rajendra .S. Soni, S. Dhamal, “ Direct Torque Control Of Three Phase

Induction Motor Using Fuzzy Logic”, International Conference on Electrical,

Electronics and Computer Engineering , pp.34–38, 25th August 2013,

[3] F.Korkmaz, I.Topaloğlu, H.Mamur,“ Direct Torque Control of Induction

Motor With Fuzzy Logic for Minimization of Torque Ripples”, International

Journal of Engineering Research and General Science , Vol 3, Issue 1, pp.361–

367, January-February, 2015.

[4] D. SUN, HE ,Yikang, I.Topaloğlu, H.Mamur. Fuzzy Logic Direct Torque

Control for Permanent Magnet Synchronous Motors”, IEEE Transactions, the

5Ih World Congress on Intelligent Control and Automation, pp.4401-4405, June

15-19,2004,Hangzhou.


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141





On Optimal Control of Stochastic Mean Field Systems

Brahim Mezerdi

Laboratory of Applied Mathematics, Mohamed Khider University,

Biskra, Algeria

[email protected]

Abstract: In this talk, we deal with optimal control of systems driven by mean-

field stochastic differential equations. These equations are obtained as limits of

interacting particle systems, as the number of particle tends to infinity. This kind

of approximation result is called "propagation of chaos", which says that when

the number of particles (players) tends to infinity, the equations defining the

evolution of the particles could be replaced by a single equation, called the

McKean-Vlasov equation. This mean-field equation, represents in some sense

the average behavior of the infinite number of particles. Since the earlier papers

by Lasry-Lions and Huang-Malhamé-Caines, mean-field control theory and

mean-field game theory has raised a lot of interest, motivated by applications to

various fields such as game theory, mathematical finance, communications

networks, management of oil ressources. Mean-field control problems occur in

many applications, such as in a continuous-time Markowitz's mean--variance

portfolio selection model where the variance term involves a quadratic function

of the expectation. We are interested in relaxed controls which are measure

valued processes. We prove that the strict and relaxed control problems have the

same value function and that an optimal relaxed control exists. In a second step,

we establish necessary conditions for optimality in the form of a relaxed

stochastic maximum principle, obtained via the first and second order adjoint

processes, see [1,2].

Keywords: Mean-field stochastic differential equation; relaxed control;

martingale measure; adjoint process; stochastic maximum principle; variational

principle.

References:

[1] K. Bahlali, M. Mezerdi, B. Mezerdi, Existence of optimal controls for

systems governed by mean-field stochastic differential equations, Afrika

Statistika, Vol. 9 (2014), No 1, 627-645.

[2] K. Bahlali, M. Mezerdi, B. Mezerdi, Existence and optimality conditions for

relaxed mean-field stochastic control problems, Systems and Control Letters,

Issue in progress 2017 http://dx.doi.org/10.1016/j.sysconle.2016.12.009.

http://dx.doi.org/10.1016/j.sysconle.2016.12.009


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142





Ring Theory Approaches to Solve Cauchy-Euler Differential

Equations of Several Variables

Assal Miloud

Department of Mathematics, university of Jeddah,

Jeddah, KSA

Department of Mathematics, Carthage University,

Tunisia

Abstract: In this paper we introduce a new ring R of ponderation functions and

we study a class of modules over R and prove that Laplace transform and

Fourier transform generate some free modules over the ring R. Moreover we

characterize the projective modules and simple modules and we prove that the

socle of this ring is not an injective module. As an application we use the ring

properies to give a new methode to solve equations of the form

Div(Xf)= g

in several variables. Furthermore, we give a general solution of the Cauchy-Euler

Equations in high dimensions.

Keywords: Ring, Cauchy-Euler differential Equations.

References:

[1] Assal M., Zeyada N, “New ring of a class of Bessel integral operators.

Integral Transforms Spec Funct. 2016;27(8):611-619..

[2] Atiyah, MF, Macdonald, IG. “Introduction to Commutative Algebra”.

Westview Press: New York; 1969.

[3] T. Pierce RS. “Associative Algebras”. Graduate Texts in Mathematics

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143





Subgradient Method of Solving the Problem of Linear

Stochastic Programming with Bifurcation Effect

Fakhriddin Mirzoahmedov

Center of Innovative Development of Science and New Technologies,

Academy of Science of Republic of Tajikistan


[email protected]

Abstract: In modern conditions from innovation point of view necessarily of the

mathematical modeling is the presence of uncertainty, nonlinearity, ambiguities,

critical points, branching processes, etc.

Hereinafter, the bifurcation theory has become a source and a part of the

mathematical theory of catastrophes and description of the various systems

associated with the presence of nonlinearity or piecewise linearity.

Examples of bifurcation may be a split in the experiments and processes, when

after the critical point, can be observed in case either one way or the other.

One of the sections developed by mathematical modeling is a linear

programming problem, which is widely used in technological processes of

production systems, where the main objective is to optimize the costs.

However, products manufactured with such a criterion in this period cannot be

implemented (in the case of proficiently) or insufficient to meet the demand

(deficiency case), which by nature is random and creates the effect of

bifurcation.

This report will explore the stochastic analogue of the general problem of linear

programming considering bifurcation effect and subgradient algorithm to solve

it. We give also the results for numerical experiments.

References:

1. Mirzoahmedov F. Conflicting models of linear programming in production

and economic systems. -Dushanbe: Tajik State National University, 2002.

2. Ermoliev YM Methods of stochastic programming. - M .: Nauka, 1976.

3. Mirzoahmedov F. Mathematical models and methods of production

management, taking into account the random faktorov. Kiev, "Naukova Dumka,"

1991.


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144





Modelling Asymmetric Magnetic Recording Heads with an

Underlayer Using Superposition

Ammar Edress Mohamed

Duhok Polytechnic University, Zakho Technical Institute, Kurdistan Region -

Iraq

[email protected]

Abstract: This paper analyses and calculates the head fields of asymmetrical 2D

magnetic recording heads when the soft-underlayer is present using the

appropriate Green's function to derive the surface potential/field by utilising the

surface potential for asymmetrical head without underlayer. The results follow

closely the corners, while the gap region shows a linear behaviour for d/g < 0.5

compared with the calculated fields from finite-element.

Keywords: Magnetic recording heads, Laplace’s equation, Karlqvis head,

Finite-element.

References:

[1] G. Fan, “A study of the playback process of a magnetic ring head,” IBM

J. Res. Dev., vol. 5, pp. 321–325, 1961.

[2] 0. Karlqvist, “Calculation of the magnetic field in the ferromagnetic

layer of a magnetic drum,” Trans. Roy. Inst. Technol. Stock. Sweden, vol.

86, no. 1, pp. 1–27, 1954.

[3] N. Curland and J. Judy, “Calculation of exact ring head fields using

conformal mapping,” Magnetics, IEEE Transactions on, vol. 22, no. 6.

pp. 1901–1903, 1986.

[4] J. S. Yang and H. L. Huang, “Calculation of exact head and image fields

of recording heads by conformal mapping,” IEEE Trans. Magn., vol. 25,

no. 3, pp. 2761–2768, 1989.

[5] T. J. Szczech, D. M. Perry, and K. E. Palmquist, “Improved Field

Equations For Ring Heads,” IEEE Trans. Magn., vol. M, no. 5, pp. 5–9,

1983.

[6] S. Iwasaki, “Perpendicular Magnetic Recording,” IEEE Trans. Magn.,

vol. 16, no. 1, pp. 71–76, 1980.


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145





G-compactness for Topological Groups with Operations

1Osman Mucuk and 2Huseyin Cakalli

1Department of Mathematics, Erciyes University, Kayseri, Turkey

[email protected] 2Maltepe University, Graduate School of Science and Engineering, Maltepe,

Istanbul-Turkey

[email protected]

It is well known that for a Hausdorff topological group X, the limits of

convergent sequences in X define a function denoted by lim from the set of all

convergent sequences in X to X. This notion has been modified by Connor and

Grosse-Erdmann in [7] for real functions by replacing lim with an arbitrary

linear functional G defined on a linear subspace of the vector space of all real

sequences. Some authors have recently extended the concept to the topological

group setting and introduced the concepts of G-sequential continuity [2], [10],

G-sequential connectedness [3], [5] and G-sequential compactness [4].

On the other hand in [12] Orzech introduced a certain algebraic category C

called category of groups with operations including groups, rings without

identity, R-modules, Lie algebras, Jordan algebras, and many others. Mucuk and

Çakallı in [6] extended the connectedness of topological groups to more general

topological groups with operations. In this paper we prove some results on the

different types of G- compactness for topological group with operations.

Keywords: Sequences, G-continuity, G-conpactness, topological group with

operations

References:

[1] H. F. Akız, N. Alemdar, O. Mucuk, T. Şahan, Coverings of internal

groupoids and crossed modules in the category of groups with operations,

Georgian Math. J., 20-2 (2013) 223-238.

[2] H. Çakallı, On G-continuity, Comput. Math. Appl. , Vol. 61, No.2, (2011)

313-318.

[3] H. Çakallı, Sequential definitions of connectedness, Appl. Math. Lett., Vol.

25, No.3, , (2012) 461-465.



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[4] H. Çakallı Sequential definitions of compactness, Appl. Math. Lett., 21 , 6,

(2008) 594-598.

[5] H. Çakallı, O. Mucuk, On connectedness via a sequential method, Revista

de la Uniòn Matemática Argentina, Vol.54, No.2, (2013) 101-109.

[6] O. Mucuk, H. Cakalli, G-connectedness for topological groups with

operations, Filomat (ICAAM 2016).

[7] J.Connor, K.-G. Grosse-Erdmann,Sequential definitions of continuity for real

functions, Rocky Mountain J. Math. , Vol. 33, No.1, (2003)93-121.

[8] S. Lin and L. Liu, G-methods, G-sequential spaces and G-continuity in

topological spaces, Top. App.212 (2016) 29-48.

[9] G. D. Maio, L.D.R. Kocinac, Statistical convergence in topology, Topology

Appl. 156 (2008) 28-45.

[10] O. Mucuk, T. Şahan, On G-sequential Continuity, Filomat Vol.28, No.6,

(2014) 1181-1189.

[11] O. Mucuk, T. Şahan, N. Alemdar, Normality and quotients in crossed

modules and group-groupoids, Appl. Categ. Structures, 23-3 (2015) 415-428.

[12] G. Orzech, Obstruction theory in algebraic categories I and II, J. Pure.

Appl. Algebra, Vol.2, (1972) 287-314 and 315-340.

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147





Topological Aspects of Monodromy Groupoids for Group-

Groupoids

1Osman Mucuk and 2Serap Demir

1Department of Mathematics, Erciyes University, Kayseri, Turkey

[email protected] 2Department of Mathematics, Erciyes University, Kayseri, Turkey

[email protected]

Abstract: One form of the monodromy principle was enunciated by Chevalley

in [4]. The general idea is that of extending a local morphism f on a topological

structure G, or extending a restriction of f, not to G itself but to some simply

connected cover of G. A different approach was indicated by J. Pradines in [8] to

generalise the standard construction of a simply connected Lie group from a Lie

algebra to a corresponding construction of a Lie groupoid from a Lie algebroid.

Let G be a topological groupoid such that the stars G_x the fibres of initial

point map of the groupoid are path connected and have universal covers. Let

Mon(G) be the disjoint union of the universal covers of the stars G_x's at the

base points identities of the groupoid G. Then there is a groupoid structure on

Mon(G) defined by the concatenation composition of the paths in the stars G_x.

We call Mon(G) as the monodromy groupoid of G. In [3] Brown and Mucuk in

the smooth groupoid case including topological groupoids, the star topological

groupoid and topological groupoid structures of Mon(G) were studied under

some suitable local conditions. Then the group-groupoid structure of Mon(G)

was recently developed in [7] and internal groupoid structure of Mon(G) was

given in [1] . In this paper we will develop the topological aspect of Mon(G) and

prove that if G is a topological group-groupoid, then Mon(G) becomes a

topological group-groupoid; and give a monodromy principle for topological

group-groupoids.

Keywords: Group-groupoid, monodromy groupoid, topological group-

grouppoid



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148





References:

[1] H. F. Akız, N. Alemdar, O. Mucuk, T. Şahan, Coverings of internal

groupoids and crossed modules in the category of groups with operations,

Georgian Math. J., 20-2 (2013) 223-238.

[2] M.E.-S.A.-F., R. Brown, The holonomy groupoid of a locally topological

groupoid, Top. Appl., 47 (1992)7-113.

[3] R. Brown, O. Mucuk, The monodromy groupoid of a Lie groupoid, Cah.

Top. Géom.Diff. Cat. 36 (1995) 345-370.

[4] C. Chevalley, Theory of Lie groups, Princeton University Press, 1946.

[5] L. Douady, M. Lazard, Espaces fibrés en algébres de Lie et en groupes,

Invent. Math. 1 (1966) 133-151.

[6] K.C.H Mackenzie, Lie groupoids and Lie algebroids in differential

geometry, London Math. Soc.Lecture Note Series 124, Cambridge University

Press, 1987.

[7] O. Mucuk, B. Kılıçarslan, T. Şahan, N. Alemdar, Group-groupoid and

monodromy groupoid, Topology Appl. 158 (2011) 2034-2042.

[8] J. Pradines, J., Théorie de Lie pour les groupoïdes différentiables, relation

entre propriétés locales et globales, Comptes Rendus Acad. Sci. Paris, Sér A,

263 (1966), 907-910.

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149





A Characterization of the Two-Weight Inequality for Riesz

Potentials on Cones of Radially Decreasing Functions

Ghulam Murtaza

Department of Mathematics, GC University, Faisalabad, Pakistan.

[email protected]

Abstract: We establish necessary and sufficient conditions on a weight pair

(v,w) governing the boundedness of the Riesz potential operator Iα defined on a

homogeneous group G from Lpdec,r(w,G) to Lq(v,G), where Lp

dec,r(w,G) is the

Lebesgue space defined for non-negative radially decreasing functions on G. The

same problem is also studied for the potential operator with product kernels Iα1,α2

defined on a product of two homogeneous groups G1 × G2. In the latter case

weights, in general, are not of product type. The derived results are new even for

Euclidean spaces. To get the main results we use Sawyer-type duality theorems

(which are also discussed in this paper) and two-weight Hardy-type inequalities

on G and G1 × G2, respectively.

Keywords: Riesz potential; multiple Riesz potential; homogeneous group; cone

of decreasing functions; two-weight inequality; Sawyer’s duality theorem


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150





On The Fourth Geometric-Arithmetic Index of Graphs

Y. Nacaroglu and A. Dilek Maden

Department of Mathematics, Selcuk University,

Konya, Istanbul, Turkey

[email protected] and [email protected]

Abstract: Topological indices are the numerical value associated with chemical

constitution professes for correlation of chemical structure with various physical

properties, chemical and biological activity [1]. In 2010, M. Ghorbani and A.

Khaki defined the eccentricity based geometric arithmetic index named as

eccentric version of Geometric arithmetic index [2]. In this paper, we present

some upper and lower bounds on the fourth geometric arithmetic index.

. Keywords: Topological index, Eccentricity, Geometric-arithmetic index, Fourth

geometric arithmetic index

References:

[1] M.K. Jamil, M.R. Farahani, M.R.R. Kanna, “Fourth Geometric Arithmetic

Index of Polycyclic Aromatic Hydrocarbons (PAHk)”, Pharm. and Chem. J.

3(2016), 94-99.

[2] M. Ghorbani and A. Khaki, “A note on the fourth version of Geometric –

Arithmetic index”, Optoelectron. Adv. Mater-Rapid Commun., 4(2010), 2212-

2215.

[3] K. Ch. Das, I. Gutman, B. Furtula, “Survey on Geometric – Arithmetic

indices of graphs”, Match. Commun. Math. Comput. Chem., 65(2011), 595-644.

[4] J. M. Rodríguez, J. M. Sigarreta, “On the Geometric- Arithmetic Index”,

Match. Commun. Math. Comput. Chem., 74(2015), 103-120.

[5] I. Gutman, N. Trinajstić, “Graph theory and molecular orbitals. Total φ-

electron energy of alternant hydrocarbons”, Chemical Physics Letters, 17(4)

(1972), 535-538.



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151





Laplace Transform of Fractional Differential Equations

Khaled I. Nawafleh

Physics Department, Mu,tah University,

Al-Karak, Jordan;

[email protected]

Abstract: The aim of this work is to study the possible extension of applying the

Laplace transform for solving fractional differential equations. The Laplace

transform allow us to transform fractional differential equations into algebraic

equations and then by solving this algebraic equations, we can obtain the unknown

function by using the inverse Laplace transform. Two illustrative examples are

included to demonstrate the validity and applicability of the presented technique, the

first one is the LC circuit as a conservative system, and the second one is the RC

circuit as a non-conservative system.

Keywords: Fractional Differential Equations, Laplace Transform, LC Circuit,

RC Circuit.

References:

[1] Om P. Agrawal (2001), Formulation of Euler-Lagrange Equations for

Fractional Variational Problems, J. Math. Anal. Appl. 272(2002) 386-379.

[2] Eltayeb. A. M. Yousif and Fatima. A. Alawad. Laplace Transform Method

Solution of Fractional Ordinary Differential Equations, University of Africa

Journal of Sciences. (2012) 2, 139-160.

[3] Saeed Kazem. Exact Solution of Some Linear Fractional Differential

Equations by Laplace Transform, International Journal of.Nonlinear Science,

(2013) 16 (1) 3-11.

[4] Shy-Der Lin and Chia-Hunglu. Laplace transform for solving some families

of fractional differential equations and its applications, a springer open journal,

(2013) 137.

[5] Joseph M. Kimeu (2009), Fractional Calculus: Definitions and Applications,

Masters Theses & Specialist Projects.

[6] Arfken, G., & Weber, H. J. Mathematical Method for Physicists Academic.

New York, (1985) 309.

[7] Saxena R. K., and Nishimoto, K. On a fractional integral formula of .Saigo

operator, J. Fract. Calc., (2002) 22, 57-58.


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152





Gaussian Approximation of a New Tail Index Estimator for

Right-Censored Pareto-Type Distributions

Abdelhakim Necir

Laboratory of Applied Mathematics, Mohamed Khider University,

Biskra, Algeria [email protected]

Abstract: A new consistent and an asymptotically normal estimator for the

positive tail index of right-censored data is proposed. In this context, a tail

empirical process is introduced and its Gaussian approximation is established. A

simulation study is carried out to compare the proposed estimator with the

existing ones in terms of bias and mean squared error. An application to survival

time of Australian male Aids patients are provided.

Keywords: Extreme value index; Gaussian approximation; Random censoring,

Tail empirical process.

References:

[1] Einmahl, J.H.J., Fils-Villetard, A. and Guillou, A., 2008. Statistics of

extremes under random censoring. Bernoulli 14, 207-227.

[2] de Haan, L. and Ferreira, A., 2006. Extreme Value Theory: An Introduction.

Springer.

[3] Hill, B.M., 1975. A simple general approach to inference about the tail of a

distribution. Ann. Statist. 3, 1163-1174.

[4] Stupfler, G., 2016. Estimating the conditional extreme-value index under

random right-censoring. J. Multivariate Anal. 144, 1-24.

[5] Worms, J. and Worms, R., 2014. New estimators of the extreme value index

under random right censoring, for heavy-tailed distributions. Extremes 17, 337-

358.


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153





On Residual Algebraic Free Extensions of Valuations

Figen Oke

Trakya University Department of Mathematics

Edirne,Turkey

[email protected]

Abstract: If v is a valuaton on a field K with rankv=2 then there exist three kind

residual algebraic free extensions of v to the rational function field K(x) with

one variable over K. In this study the first kind residual algebraic free extension

of v to K(x) is studied.

Keywords: extensions of valuations, residual algebraic free extensions, valued

fields

References:

[1] V. Alexandru - N. Popescu - A. Zaharescu, A theorem of characterization of

residual transcendental extension of a valuation, J. Math. Kyoto Univ., 28

(1988), 579-592.

[2] V. Alexandru - N. Popescu - A. Zaharescu, Minimal pair of definition of a

residual transcendental extension of a valuation, J. Math. Kyoto Univ. 30 (1990),

no. 2, 207-225

[3] V. Alexandru - N. Popescu - A. Zaharescu, All valuations on K(X), J. Math.

Kyoto

Univ. 30 (1990), no. 2, 281-296.

[4] N. Bourbaki, Algebre Commutative, Ch. V: Entiers, Ch. VI: Valuations,

Hermann, Paris (1964).

[5] O. Endler, Valuation Theory, Springer, Berlin -Heidelberg-New York (1972).

[6] N. Popescu, C. Vraciu, On the extension of valuations on a field K to K(x)-I,

Ren. Sem. Mat. Univ. Padova, 87 (1992), 151-168

[7] N. Popescu, C. Vraciu, On the extension of valuations on a field K to K(x)-II,

Ren. Sem. Mat. Univ. Padova, 96(1996), 1-14

[8] O.F.G. Schilling, The Theory of Valuations, A.M.S. Surveys, no. 4,

Providence, Rhode Island (1950).


______________________________________________________

154





Statistically (C,1,1) Summable Double Sequences of Fuzzy

Numbers and a Tauberian Theorem

Zerrin Onder, Ibrahim Canak, Umit Totur

Department of Mathematics, Ege University, İzmir, Turkey

Department of Mathematics, Ege University, İzmir, Turkey

Department of Mathematics, Adnan Menderes University, Aydın, Turkey


Abstract: Developed based on the concept of fuzzy sets which was discovered

and introduced by Zadeh, fuzzy set theory have received more and more

attention from researchers who have intended to apply the concept of fuzziness

to individual works with different aspects from theoretical to practical in almost

all scientific areas. One of the areas which the concept of fuzziness was practised

is the summability theory, as well. In this talk, we recall some notations, basic

definitions and theorems with respect to fuzzy numbers and its double sequences

and define the concepts of slow oscillation for the double sequences of fuzzy

numbers in certain senses. In the sequel, we prove that a bounded double

sequence of fuzzy numbers which is statistically convergent is also statistically

(C, 1, 1) summable to the same number. We construct an example that the

converse of this statement is not true in general. Finally, we indicate that the

statistically (C, 1, 1) summable double sequence of fuzzy numbers is convergent

and statistically convergent to the same fuzzy number in Pringsheim's sense

under the slowly oscillating and statistically slowly oscillating conditions in

certain senses, respectively.

Keywords: Double sequences of fuzzy numbers, ,Slowly oscillating sequences,

(C,1,1) summability, Statistical convergence, Tauberian theorems.

References:

[1] H. Fast, “Sur la convergence statistique”, Colloq. Math. 2(1951), 241-244.

[2] I. J. Schoenberg, “The integrability of certain functions and related

summability methods”, Am. Math. Mon. 66(1959), 361-375.

[3] B. C. Tripathy and A. J. Dutta, “On fuzzy real-valued double sequence

spaces”, Soochow J. Math. 32(2006), 509-520.

[4] B. C. Tripathy and A. J. Dutta, “Statistically convergent and Cesaro

summable double sequences of fuzzy real numbers ”, Soochow J. Math.

33(2007), 835-848.

[5] L. A. Zadeh, “ Fuzzy sets”, Inform. Control 8(1965), 338-353.




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155





The Sheffer Stroke Basic Algebras on the Intervals

Tahsin Oner1, Tugce Katican2

Department of Mathematics, Ege University1,2,



Abstract: The axiom system of Sheffer Stroke operation was introduced by

Henry Sheffer in 1913 [6], and the improvements of this operation have beeen

given in [2] and [7]. The notions about basic algebras were mentioned in [1], [3]

and [4]. Afterwards, Oner and Senturk introduce some definitions and notions

about the Sheffer Stroke basic algebras in [5]. In this work, giving basic concepts

about the Sheffer Stroke operation and Sheffer stroke basic algebras 𝒜 = (𝐴; ∣),

we define the operations ∣𝑎, ∣𝑏 and ∣𝑎𝑏 for any elements 𝑎, 𝑏 ∈ 𝐴 such that

([𝑎, 1]; ∣𝑎), ([0, 𝑏]; ∣𝑏) and ([𝑎, 𝑏]; ∣𝑎𝑏) are Sheffer Stroke basic algebras,

respectively. We also show that these interval Sheffer Stroke basic algebras on a

given Sheffer Stroke basic algebra 𝒜 = (𝐴; ∣) verify the patchwork condition.

Keywords: Sheffer Stroke basic algebra, interval sheffer stroke basic algebra,

patchwork condition.

References:

[1] Chajda, Ivan. "Basic algebras, logics, trends and applications." Asian-

European Journal of Mathematics, Vol.8, No 31550040, (2015).

[2] Chajda, Ivan. "Sheffer operation in ortholattices." Acta Universitatis

Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica Vol. 44,

no.1, pp. 19-23, (2005).

[3] Chajda I, Kolařík M. “Independence of the axiomatic system of basic

algebras.” Soft Computing, Vol. 13, pp. 41-43, (2009).

[4] Chajda I, Kolařík M. "Interval Basic Algebras." NOVI SAD J. MATH., Vol.

39, 2, (2009).

[5] Oner, T., Senturk I. "The Sheffer Stroke Operation Reducts of Basic

Algebras", submitted, (2017).

[6] Sheffer, H. M.. “A set of five independent postulates for Boolean algebras,

with application to logical constants.” Transactions of the American

Mathematical Society, 14(4), 481-488, (1913).

[7] Whitehead, A. N., Russell, B. Principia Mathematica. New York, Cambridge

University Press, (1927).



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156





A Reduction of Basic Algebras: Sheffer Stroke Basic Algebras

Tahsin Oner1, Ibrahım Senturk2




Abstract: The concept of basic algebras was introduced in Chajda and

Emanovský [1], see also Chajda [2] and Chajda et al.[3] for the further

information. Basic algebras are an important notions of algebras used in diff erent

non-classical logics since they not only contain orthomodular lattices 𝐿 = (L; ∨,

∧, ⊥, 0, 1), where x ⊕ y = (x ∧ 𝑦⊥) ∨ y and ¬ x = 𝑦⊥, but they also constitute

an axiomatization of the logic of quantum mechanics along with MV-algebras

[4], which get an axiomatization of many-valued Łukasiewicz logics; see Chajda

[5] and Chajda et al. [6]. In this study, we present a term operation Sheffer stroke

in a given basic algebra A and examine properties of the Sheffer stroke reduct of

A. In addition, we qualify such Sheffer stroke basic algebras. Finally, we

construct a bridge between basic algebras and Boolean algebras.

Keywords: Basic algebras, Sheffer Sroke operation, Reduction

References:

[1] I. Chajda and P. Emanovský, “Bounded lattices with antitone involutions

and properties of MV-algebras”, Discussiones Mathematicae, General Algebra

and Applications, 24.1 (2004), 32-42.

[2] I. Chajda, “Lattices and semilattices having an antitone involution in every

upper interval”, Comment. Math. Univ. Carolin, 44.4 (2003), 577-585.

[3] I. Chajda, “Basic algebras”, Clone Theory and Discrete MathematicsAlgebra

and Logic Related to Computer Science, (2013).

[4] R. L. Cignoli, I. M. d’Ottaviano and D. Munduci, Algebraic foundations of

many valued reasoning (Vol. 7), Springer Science & Business Media.

[5] I. Chajda, “Basic algebras and their applications”, an overview. Contr Gen

Algebra, 20, (2011).

[6] I. Chajda, R. Halaš and J. Kühr, “Many-valued quantum algebras”,

AlgebraUniversalis,60.1(2009),63-90.



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157





Applications on Weak and Strong Forms of Fuzzy α-Open

(Closed) Sets

Hakeem A. Othman*

*Department of Mathematics, AL-Qunfudhah University college, Umm

Al-Qura University, KSA.

*Department of Mathematics, Rada'a College of Education and Science,

Albaydaa University, Albaydaa, Yemen.


Abstract: The present paper tries to introduce some applications on fuzzy

(supra-) infra- α -open (closed) sets, likely, fuzzy (supra-) infra- α –continuous

mappings, fuzzy (supra-) infra- α -open (closed) mappings, fuzzy supra- α -

irresolute mapping and fuzzy supra- α -connected space. Moreover, The relations

and converse relations between these mappings are highlighted. Important results

about these mappings and fuzzy supra- α –connected space are investigated and

presented.

Keywords: fuzzy infra- α -open set; fuzzy infra- α -closed set; fuzzy supra- α -

continuous mapping; fuzzy infra- α -continuous mapping; Fuzzy supra- α -

irresolute mapping; Fuzzy infra- α - irresolute mapping; Fuzzy infra- α -

connected space.

References

[1] K. K. Azad, "On fuzzy semi continuity, fuzzy almost continuity and weakly

continuity", J. Math. Anal. Appl., 82 (1981), pp.14-32.

[2] A. S. Bin Shahna, "On fuzzy strongly semi continuity and fuzzy

precontinuity", Fuzzy Sets and Systems, 44 (1991), pp.330-308.

[3] M. H. Ghanim, E. E. Kerre and A. S. Mashhour, "Separation Axioms,

Subspace and Sums in Fuzzy Topology ", J. Math. Anal Appl, 102(1984), pp.

189-202.

[4] Hakeem A. Othman, "On fuzzy sp-open sets", Hindawi Publishing

Corporation, Advances in Fuzzy Systems Volume 2011, Article ID 768028, 5

pages,doi:10.1155/2011/768028.

[5] Hakeem A. Othman and Md.Hanif.Page, "ON An Infra-_-Open Sets ",

Global Journal of Mathematical Analysis, 4(3) (2016) pp. 12-16.



______________________________________________________

158





Code Verification Using Method of Manufactured Solutions for

CFD Problems

Hatice Ozcan


Kırsehir, Turkey

[email protected]

Abstract: To find numerical solutions of non-linear hyperbolic, parabolic

systems of partial differential equations (PDEs), which predominantly appear in

computational fluid dynamics (CFD) field, are fundamental parts of discovering

the physical properties of flows [1]. The essential aim of CFD is to utilize

numerical methods and algorithms to solve and analyze fluid dynamic problems.

To this end, the motivation of this work is to ensure that the computer code

designed to solve a set of PDEs is accurate; in another words, it is bug free.

Therefore, Method of Manufactured Solutions (MMS) is used to check the

accuracy of existing code and to estimate order of accuracy of the developed

numerical method [2,3,4]. An example for Euler equations of gas dynamics is

provided to demonstrate the effective use of this method.

Keywords: manufactured solution, code verification, order of accuracy, Euler

equations of gas dynamics.

Acknowledgement : This work is supported by Ahi Evran University Scientific

Research Projects Coordination Unit (Project Number : FEF.E2.17.029).

References:

[1] C. B. Laney, “Computational gas dynamics”, Cambridge University Press

(1998).

[2] B. W. Boehm, “Verifying and validating software requirements and design

specifications”, IEEE Software 1.1(1984), 75-88.

[3] P. J. Roache, “Fundamentals of computational fluid dynamics”, Albuquerque,

NM, Hermosa Publishers (1999). [4] P. J. Roache, “Verification and validation

in computational science and engineering”, Albuquerque, NM, Hermosa

Publishers (1998).


______________________________________________________

159





On the Existence of Einstein Weyl Manifold with a Special

Metric Connection

F. Ozdemir, M. D. Turkoglu

Faculty of Science and Letters, Department of Mathematics, İstanbul Technical

University

Maslak-Istanbul,Turkey


Abstract: On a Weyl manifold, the existence of a semi-symmetric recurrent

metric connection is proved and curvature invariants and their characteristics of

manifolds having this connection are studied. Also it is introduced and examined

the necessary and sufficient condition for an Einstein Weyl (E𝑊𝑛) manifold to be

an Einstein Weyl manifold with semi-symmetric special metric connection

(EW𝑆𝑛).

Keywords: Einstein Weyl manifold, metric connection, semi-symmetric

recurrent metric connection.

References:

[1] L. P. Eisenhart, “Non-Riemannian Geometry” , New York: The American

Mathematical Society Publishing (1927).

[2] V. Hlavaty, “Theorie d'immersion d'une W_m dans W_n“, Ann. Soc. Polon.

Math., 21 (1949), 196-206.

[3] K. Yano, “On semi-symmetric metric connection”, Rev. Roumaine Math.

Pures Appl., 15(1970), 1579-1586.

[4] Y. X. Liang, “On semi-symmetric recurrent-metric connection”, Tensor

(N.S.), 55 (1994), 107-112.

[5] N. Rosen, “Weyl's geometry and physics”, Foundations Of Physics, 12/3

(1982), 213-248.

[6] E. Scholz, “Weyl geometric gravity and breaking of electroweak symmetry”,

Annalen De Physik, 523(2011), 507-530.

[7] J. T. Wheeler, “Weyl gravity as general relativity”, Phys. Rev. D 90 (2014),

025027.


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160





Repeat Codes, Even Codes, Odd Codes and Their Equivalence

Mustafa Ozkan and Figen Oke

Department of Mathematics, Trakya University,

Edirne, Turkey

[email protected]

Abstract: Codes over the chain ring are obtained by writting special matrices.

Gray images of these codes are binary codes. It is shown that first repeat code,

second repeat code, even code and odd code are either equivalent or equal to

these codes. The definitions of direct sum and direct product of these codes were

given. Moreover dual codes were classed. Self dual codes and self orthogonal

codes were established.

Keywords: Codes over rings, Lee distance, Even codes, Odd codes, Dual codes.

References:

[1] M. Ozkan and F. Oke, “A relation between Hadamard codes and some

special codes over 2 2u ”, App.Mathematics and Inf. Sci, 10.2 (2016), 701-

704.

[2] M. Ozkan and F. Oke, “ Results On Hadamard Codes and Codes Over

Rings”, 3rd International Conference On Recent Advances In Pure and Applied

Mathematics (2016)

[3] S. Zhu, Y. Wang, M. Shi, Some Result On Cylic Codes Over 2 2v ,

IEEE Trans. Inf. Theory, 56. 4 (2010),1680-1684.

[4] A. Bonnecaze and P. Udaya, Cyclic codes and self dual codes 2 2u ,

IEEE Trans. Inf. Theory, 45, (1999),1250-1255.

[5] Krotov, D. S. Z4-linear perfect codes ,Diskretn. Anal. Issled. Oper.7.4

(2000), 78–90.

[6] J.Wolfmann, Negacyclic and cyclic codes over 𝑍4, IEEE Trans. Inf. Theory,

45, (1999),2527-2532.


______________________________________________________

161





Tauberian Theorems for the Weighted Mean Summability

Methods of Integrals

Firat Ozsarac, Ibrahim Canak



Abstract: Let 0p x be a nondecreasing real-valued differentiable function

on 0, such that 0 0p

and p x

as x . Given a real-

valued function f x which is continuous on 0,

and

0

x

s x f t dt

We define the weighted mean of s x as

0

1x

p x p t s t dtp x

,

where p t is the derivative of p t .

We give some classical type Tauberian theorems to retrieve convergence of

s x out of the weighted mean integrability of p x

under some Tauberian

conditions.

Key words: Tauberian theorem, Tauberian condition, Weighted mean method of

integrals, slow decrease, slow oscillation.

References:

[1]F. Moricz, ‘‘Ordinary convergence follows from statistical summability (C,1)

in the case of slowly decreasing or oscillating sequences’’, Colloq. Math. , 99(2),

(2004), 207-219.

[2] İ. Çanak and Ü.Totur, ‘‘A Tauberian theorem for Cesaro summability of

integrals’’, Appl. Math. Lett. , 24(3), (2011), 391-395.

[3] İ. Çanak and Ü.Totur, ‘‘Tauberian conditions for Cesaro summability of

integrals’’, Appl. Math. Lett. , 24(6), (2011), 891-896.

[4] İ. Çanak and Ü.Totur, ‘‘Altenative proofs of some classical type Tauberian

theorems for Cesaro summability of integrals’’, Math. Comput. Modell. , 55(3),

(2012), 1558-1561.

[5] A. Fekete and F. Moricz, ‘‘ Necessary and sufficient Tauberian conditions in

the case of weighted mean summable integrals over R+’’ , II. Publ. Math. , 67(1-

2), (2005) , 65-78.



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162





On Lifting Polynomials and Distinguished Pairs

Burcu Ozturk, Figen Oke

Department of Mathematics,TrakyaUniversity,

Edirne, Turkey


Abstract: Let𝑣 be a valuation of a field 𝐾 and 𝑢 be a residual algebraic free

extension of 𝑣 to the rational function field 𝐾(𝑥). So𝑢 can be defined by using a

residual transcendental extension of 𝑣 to 𝐾(𝑥) and a lifting polynomial. In this

study relations between lifting polynomials and distinguihed pairs are given

bykeeping in view of valuation 𝑢.

Keywords:Valuations, Lifting Polynomials, Distinguished Pairs, Transcendental

Extensions

References:

[1] N. Popescu, A. Zaharescu, “ On the Structure of Irreducible Polynomials over

Local Fields”, J. Number Theory, 52, (1995), 98-118.

[2] V. Alexandru, N. Popescu, A. Zaharescu, “ A Theorem of Characterization of

Residual Transcendental extensions of a Valuation”, J. Math. Kyoto Univ., 28,

(1988), 579-592

[3] S. Bhatia, S.K. Khanduja, “On Extensions Generated by Roots of Lifting

Polynomials”, Mathematika, 49 (1-2), (2002), 107-118

[4] A. Zaharescu, “Lifting Polynomials over a Local Field”, Bol. Soc. Mat.

Mexicana (3) vol.10 (2004), 15-27

[5] S.K. Khanduja, U. Grag, “Rank 2 Valuations of K(x)”, Mathematika, 37,

(1990), 97-105

[6] K. Aghigh, S.K. Khanduja, “ On Chains Associated wirh Elements Algebraic

over a Henselian Valued Field”, Algebra Colloquium 12:4 (2005), 607-616

[7] K. Aghigh, S.K. Khanduja, “ On The Main Invariant of Elements Algebraic

over a Henselian Valued Field”, Proceedings of the Edinburgh Mathematical

Society, 45, (2002), 219-227

[8] P. J. McCarthy, “Algebraic Extensions of Fields” (Blaisdell Publishing

Company, Waltham, Massachusetts, Toronto, London), (1966)



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163





On Some Fixed Point and Common Fixed Theorems in b-

Metric-Like Spaces

Mahpeyker Ozturk

Department of Mathematics,

Sakarya University, Sakarya, TURKEY

[email protected]

Abstract: In this study, we establish some existence and uniqueness theorems

for mappings via the concept of admissibility in the settings of b-metric-like and

generalized b-metric-like spaces.

Keywords: b-metric-like spaces, fixed point, admissible mappings.

References:

[1] H. Aydi, E. Karapınar, B.Samet, Fixed points for generalized alpha, psi-

contractions on generalized metric spaces., J. Inequal. Appl., (2014), 16 pages.

[2] E. Karapınar, P.Kumam, P. Salimi, On alpha-psi-Meir-Keeler contractive

mappings, Fixed Point Theory and Appl., 2013, (2013), 12 pages.

[3] A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points,

Fixed Point Theory and Appl., 2012, (2012), 10 pages.

[4] H. Aydi, A. Felhi, S. Sahmim, Common fixed points via implicit

contractions on b-metric-like spaces, J. Nonlinear Sci. Appl., 10,1524--1537,

(2017).

[5] M.A.Alghamdi, N. Hussain, P. Salimi, Fixed point and coupled fixed point

theorems on b-metric-like spaces, J. Inequal. Appl., 2013, (2013), 25 pages.


______________________________________________________

164





Experimental Evidence of Landau Damping in a Fluid at a

Macroscopic Scale

Eric Padilla, William Cody Wilson, Andrei Ludu

Department of Mathematics, Embry-Riddle Aeronautical University,

Daytona Beach, Florida, USA

[email protected] , [email protected] , [email protected]

Abstract: The Landau damping effect occurs mainly in collisionless plasmas [1-

3] as a microscopic resonant mechanism of the excitation of collective modes of

oscillations. In our paper, we demonstrate the occurrence of this effect at the

macroscopic scale in a fluid populated by a system of freely moving repelling

probes (magnetic buoys) which simulate the free electrons in a plasma. The

electrons’ Coulombian interaction is replaced by magnetic dipole repulsion, and

instead of the electromagnetic wave we use a free, nonlinear, liquid surface wave

traveling through the fluid. We couple the Green-Naghdi Hamiltonian for the

incompressible fluid with the kinetic and magnetic potential of the buoys. The

dynamical resulting equation is a Vlasov-Poisson type equation which includes

at the same time the Benjamin-Feir instability and the Landau damping

phenomenon. We derive analytically and numerically the values of the Phillips’

constant and of the enhancement factor, and we compare the results with

experimental analysis of the dynamics of buoys and waves. We find that the

effect of Landau damping is present in our system, and manifests by suppressing

the formation of coherent structures. In addition, we will study the phase

transitions of the buoy network under nonlinear wave perturbations.

Keywords: Landau Damping, resonance, damping, Benjamin-Feir instability,

Green-Naghdi Hamiltonian, Vlasov-Poisson equation, nonlinear waves, fluid

dynamics, magnetic dipole, collective modes.

References:

[1] L. D. Landau, J. Physics USSR, 10 (1946) 26.

[2] I. Langmuir and L. Tonks, Phys. Rev., 33 (1929) 195.

[3] D. D. Ryutov, “Landau damping: half a century with the great discovery”,

Plasma Phys. Control Fusion, 41 (1999) A1-A12.




______________________________________________________

165





A Boundary Value Problem for an Irrational Order Partial

Equation

A.A. Pashavand, N.A. Aliyev, A.Y. Delshad Gharegheshlaghi

Institute of Mathematics and Mechanics of NAS of Azerbaijan

9, B.Vahabzade str., AZ 1141, Baku, Azerbaijan

[email protected]

Abstract: It is known that as the investigation of the solutions of problems stated

for partial equations is difficult than the investigation of problems stated for

ordinary equations, the solution of problems stated for fractional order equations

is more difficult than the investigation of the solutions of problems stated for

irrational order equations. Here we will be engaged in finding the solution of a

boundary value problem for a partial equation whose order is an irrational

number

Keywords irrational order partial discrete equation, a boundary value problem

for such an equation, finding of the solution in the form of unknown coefficient

series corresponding to Mittag-Loffler functions.

References:

[1] Tricomi F.G. Differential Equations. Blackie & Son Limited 1961, pp. 349.

[2]Petrovsky L.G. Lectures on theory of ordinary differented equations.

Gostichizdat. M.-L, 1952, 232 p. (Russian).

[3]Petrovsky I.G., Lectures on partial equations, “Nauka” Moscow, 1974

(Russian)

[4]Aliyev N. Jahanshahi M. Investiqation of BVP and IVP including Differential

Equations with real orders. Second Joint Seminar On Applied Mathematics.

Zanjan University and Baku State University, 2000, p. 92.


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166





Generalized Close to Convex Functions with q-Properties

Yasar Polatoglu 1, Oya Mert 2, 3 and Asena Cetinkaya 1

1Department of Mathematics and Computer Sciences, Istanbul Kultur University,

Turkey 2Department of Mathematics Duzce University, Turkey

3Department of Mechanical Engineering, Istanbul Kemerburgaz University,

Turkey 1 [email protected],

2, 3 [email protected] 1 [email protected]

Abstract: q-property of analytic functions can be described as a property of any

class of these functions which use methods of quantum calculus.The main idea

of the present work is inspired on the R.J.Libera [3]. This study uniquely aims to

obtain a generalized close to convex functions that include q-properties.

Keywords: Growth theorem, distortion theorem.

References:

[1] G.E.Andrews, Application of basic Hypergeometric Functions, SIAM

Rew,(16) 1974, 441-484.

[2] M.K. Aouf and M.A.Nasr, On convex functions of complex order,

Bull.Fac.Sci.Univ.Mansoura, (9), 1982, 566-581

[3] V. Paatero, Uber Gebiete von beschrankter randdrehung Ann. Acad. Sci.

Fenn. Ser. A, 37(1933), 1-20.

[4] K. Padmanabhan and R. Parvatham, Properties of a class of functions with

bounded boundary rotation, Ann. Polon. Math., 31(1975), 311-323.

[5] B. Pinchuk, Functions with bounded boundary rotation, Isr. J. Math.,

10(1971), 7-16.

[6] M. S. Roberston, On the theory of univalent functions, Ann. Math., 37(1936),

374-408. 02010 Mathematics Subject Classification: 30C45 Key words and

phrases: Growth theorem, distortion theorem.



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167





Steady-State Modeling of the Biological Network via

Long-tailed Symetric Distribution

Vilda Purutcuoglu1 and Melih Agraz2

1, 2Department of Statistics, Middle East Technical University,

Ankara, Turkey [email protected] ; [email protected]

Abstract: The steady-state modeling of the biological systems presents the

acivation of the systems’ elements without the randomness. This model is the

most common modeling approach of the complex systems since the majority of

the available data is more suitable in this type of description. In the mathematical

representation of the underlying activation, the Gaussian graphical model (GGM)

is the most well-known probabilistic model which is depedent on the conditional

independence of the nodes (i.e., proteins, genes or other species of the system in

this context), under the multivariate normality assumption of the measurements

[1]. Althougt GGM is successful in the description of the small and moderately

large systems, its inference is computationally demanding particularly for large

networks and it is powerful under the strick normality assumption [2]. Hereby, in

this study, we extend this model by denoting the measurements via the long-

tailed symmetric distribution family which covers a wide range of densities from

Cauchy, student-t to normal. By this way, we can obtain a new graphical

explaination of the system having more realistic assumption abou the data and

we call it the long-tailed graphical model (LTGM). Then, we derive the explicit

form of the model parameteres via the modified maximum likelihood estimators

(MMLE) [3] which is obtained from the order statistics and is the asymptotic

equivalence of the maximum likelihood estimator. From our simulation studies,

we show that LTGM with MMLE is computationally more efficient and accurate

than GGM with its inference algorithms. Hence, we believe that our suggested

approach can be a promising alternative of the steady-state description of the

biological systems.

Keywords: Gaussian graphical model, modified maximum likelihood

estimators, biological networks.



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168





Acknowledgement: The authors thank the BAP project (no: BAP-01-09-2017-

002) at Middle East Technical University for its support.

References:

[1] J. Whittaker, “Graphical models in applied multivariate statistics”, John

Wiley and Sons, (1990).

[2]E. Ayyıldız, M. Ağraz and V. Purutçuoğlu, “MARS as an alternative approach

of Gaussian graphical model for biochemical networks”, Journal of Applied

Statistics, (2016), 1-19.

[3] M.L. Tiku, “Estimating the mean and standard deviation from a censored

normal sample”, Biometrika, 54 (1967), 155-165.

______________________________________________________

169





Quadrature Formula with High Degree of Exactness

Abedallah Rababah

Department of Mathematics and Statistics, Jordan University of Science andTechnology,

22110 Irbid, Jordan

[email protected]

Abstract: In this article, a quadrature formula of degree 2 is given that has

degree of accuracy 3 and order 5. The formula is valid for any planar curve given

in parametric form unlike existing Gaussian quadrature formulas that are valid

only for functions.

Key words: quadrature formula; quadratic formula; parametric curves; degree of

accuracy three; fifth order.

References:

1. G. Farin, Curves and Surfaces for Computer Aided Geometric Design,

Academic Press, Boston (1988).

2. K. Hollig, J. Horner, Approximation and Modeling with B-Splines, SIAM,

Titles in Applied Mathematics 132, (2013).

3. A. Rababah, Taylor theorem for planar curves, Proc. Amer. Math. Soc. Vol

119 No. 3, (1993), 803-810.

4. A. Rababah, Approximation von Kurven mit Polynomen und Splines, Ph.

Dissertation, Stuttgart Universitat, (1992).

5. A. Rababah, High accuracy Hermite approximation for space curves in <d, J.

Math. Anal. Appl. 325, Iss. 2, (2007), 920-93

6. A. Rababah, The Best Uniform Quadratic Approximation of Circular Arcs

with High Accuracy, Open Mathematics 14, (2016), 118-127.

7. A. Rababah, Quartic approximation of circular arcs using equioscillating error

function, International Journal of Advanced Computer Science and Applications,

7(7), (2016), 590-595.

8. A. Rababah, The best uniform cubic approximation of circular arcs with high

accuracy, Communications in Mathematics and Applications 7(1), (2016), 37-46.


______________________________________________________

170





Best Cubic Spline Interpolation Based on Minimizing the Error

Abedallah Rababah, Mohammed Bani Khalid

Department of Mathematics and Statistics

Jordan University of Science and Technology

Irbid, Jordan


Abstract: In this talk, a modified cubic spline is introduced. The proposed spline

can be obtained by considering some flexible boundary conditions that involve

some additional parameters. These parameters are incorporated to improve the

accuracy of the classical cubic spline. Moreover, these parameters are estimated

by minimizing the error function in L1 - norm. The boundary conditions are

adjusted to get new parameters that are used to get better approximation. Some

numerical examples are given to demonstrate the advantages in accuracy and

efficiency of the proposed method over traditional cubic methods.

Keywords: cubic spline; minimizing the error; best cubic approximation

References:

K. Hӧllig, J. Hӧrner: Approximation and Modeling with B-Splines, SIAM, Titles

in Applied Mathematics 132, 2013.

I. J. Schoenberg, On equidistant cubic spline interpolation. Bull. Amer. Math.

Soc. 77 (1971), no. 6, 1039-1044.

Rababah, High accuracy Hermite approximation for space curves in Rd, J. Math.

Anal. Appl. 325, Iss. 2 (2007), 920-931.

J. Rice, The approximation of functions, Vol. 1: linear theory. Addison-Wesley,

(1964).



______________________________________________________

171





On Chebyshev Collocation Method and Applications to

Nonlinear Integral Equations

Abdalah Rababah1, Benferhat Leila2, Hichem Ramoul3, Nora Mahloul4

1Department of Mathematics and Statistics, Jordan University of Science and

Technology

Irbid, Jordantage

[email protected] 2Department of Algebra and Numbers Theory, University of Science and

Technology Houari Boumediene, Algiers, Algeria

[email protected] 3ICOSI laboratory, Abbes Laghrour University-Khenchela,

Khenchela, Algérie

[email protected] 4Department of Algebra and Numbers Theory, University of Science and

Technology Houari Boumediene,

Algiers, Algeria

[email protected]

Abstract: This paper is devoted to solve some classes of one-dimensional non-

linear Volterra-Hammerstein integral equations with singular kernels. The key

ingredient is to transform integral equation to algebraic equation with unknown

Chebyshev coefficients. We use here a suitable weighted Chebyshev polynomial

to approximate the solution of the non-linear integral equation.

Keywords: Chebyshev polynomials, integral equations, collocation method.

References:

[1] Dardery, S. M., & Allan, M. M. “Chebyshev polynomials for solving a class

of singular integral equations”, Applied Mathematics, 5.04 (2014), 753.

[2] Mason, John C., and David C. Handscomb. “Chebyshev polynomials”. CRC

Press, 2002.

[3] Danaei, R., Molaei, H., & Khazili, M. “Solving Fredholm integral equations

using with Chebyshev polynomials”, International Journal of Innovative Science,

Engineering & Technology, 2.5(2015), 297-300.



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172





The Treatment of Fractional Singular Lagrangian

Eqab Rabei

Al al-Bayt University

[email protected]

Abstract: The singular Lagrangian with fractional derivative will be

investigated. The Euler-Lagrangian will be derived and some example will be

given.


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173





MHD Convective Flow due to a Curved Surface with Thermal

Radiation and Chemical Reaction

Madiha Rashid

Quaid-i-azam University, Islamabad

[email protected]

Abstract: Present work is devoted to the convection flow of viscous fluid by a

curved stretching sheet. Fluid is electrically conducting with the presence of

uniform magnetic field. Heat and mass transfer characteristics are studied by

using heat and mass convective conditions. Thermal radiation and chemical

reaction are also taken into consideration. With the help of allocated

transformations the presented nonlinear partial differential systems are reduced

into the nonlinear ordinary differential system. Impact of pertinent parameters on

physical quantities like fluid velocity, temperature and concentrations fields are

observed. Computations for surface shear stress and heat and mass transfer rates

are carried out. It is observed that pressure inside the boundary layer flow due to

curved stretching plate cannot be neglected


______________________________________________________

174





On The Isolated Points of the Spectrum of M-Paranormal

Operators

Mohammad Rashid

Department of Mathematics, Alkarak, Mutah University

Alkarak, Jordan

[email protected]

Abstract: For 𝑀 −paranormal operator 𝑇 on a separable complex Hilbert space

𝐻 we show that (1) If 𝜎𝑤 = 0, then 𝑇 is compact and normal and (2) every

Riesz idempotent 𝐸 with respect to a non-zero isolated point 𝜆 of 𝜎(𝑇) is self-

adjoint (i.e., it is an orthogonal projection) and satisfies that 𝑅(𝑇) =

ker(𝑇 − 𝜆) = ker(𝑇∗ − 𝜆).

Keywords: paranormal operators, M-paranormal operators, Riesz idempotent.

References:

[1] P. Aiena, Fredholm and local spectral theory with applications to multipliers,

Kluwer, 2004.

[2] S.C. Arora, Ramesh Kumar, M-Paranormal operators, Publ. Inst. Math.,

Nouvelle serie 29 (43) (1981), 5-13.

[3] M. Ch_o and S. ^ Ota, On n-paranormal operators, J. Math. Research 5

(2013), no. 2, 107-114.

[4] R.E. Harte, Invertibility and singularity for bounded linear operators, Dekker,

New York, 1988.

[5] P.R. Halmos, A Hilbert Space Problem Book, Van Nostrand, Princeton,1967.

[6] J.K. Han, H.Y Lee, W.Y Lee, Invertible completions of 2 _ 2 upper triangular

operator matrices, Proc. Am. Math. Soc. 128(2000),no.1, 119-123.

[7] H. Heuser, Functional Analysis, Dekker, New York, 1982.


______________________________________________________

175





Existence of Homoclinic Orbit in Generalized Planar System of

Lienard Type

Vahid Roomi


Tabriz, Iran

[email protected]

Abstract: The object of this paper is to study the orbit structure of a generalized

Li_enard type system in a neighborhood of a trajectory which is doubly

asymptotic to an equilibrium solution, i.e., an orbit which lies in the intersection

of the stable and unstable manifolds of a critical point. Such an orbit is called a

homoclinic orbit.

Keywords: Lienard System, Homoclinic orbit.

Consider the planar system

x = P(Q(y) − F(x)

y = −g(x) (1)

which is a generalized Lienard type system, where P, Q, F and g are continuous

functions which ensure the existence of a unique solution to the initial value

problem.

System (1.1) includes the classical Lienard system as a special case, which is of

great importance in various applications (see [1-15] and the references cited

therein). In system (1), a trajectory is said to be a homoclinic orbit if its α − and

ω −limit sets are the origin. The purpose of this paper is to give an implicit

necessary and sufficient condition and some explicit sufficient conditions on

F(x), g(x), P(u) and Q(y) under which system (1) has homoclinic orbits.

References:

[1] R. P. Agarwal, A. Aghajani, V. Roomi, Existence of homoclinic orbits for

generalized planar Dynamical System of Lienard Type”, Dynamic of

Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

81 (2012), 271-284.

[2] A. Aghajani, A. Moradifam, “”Some sufficient Conditions for the

Intersection with the Vertical Isocline”, Appl. Math. Lett, 19(2006), 491-497.


______________________________________________________

176





Some Results of the Picard-Krasnoselskii Hybrid Iterative

Process

Aynur Sahin and Metin Basarir

Department of Mathematics, Sakarya University,

Sakarya, 54050, Turkey


Abstract: In this study, we establish the strong convergence and stability results

of Picard-Krasnoselskii hybrid iterative process for a general class of

contractive-like operators in hyperbolic spaces. Furthermore, we give an

example to support our results. Finally, we apply this iterative process to obtain

the solution of a functional equation in a Banach space.

Keywords: Fixed point, Picard-Krasnoselskii hybrid iterative process, Stability,

Functional equations, Contractive-like operators.

References:

[1] V. Berinde, Iterative Approximation of Fixed Points, Springer, Berlin, 2007.

[2] V. Berinde and A. R. Khan, “On a functional equation arising in

mathematical biology and theory of learning”, Creath. Math. Inform. 24.1(2015),

9-16.

[3] A. O. Bosede and B. E. Rhoades, “Stability of Picard and Mann iteration for

a general class of functions”, J. Adv. Math. Stud. 3.2(2010), 23-25.

[4] C. O. Imoru and M. O. Olatinwo, “On the stability of Picard and Mann

iteration processes”, Carpath. J. Math. 19(2003), 155-160.

[5] G. A. Okeke and M. Abbas, “A solution of delay differential equations via

Picard-Krasnoselskii hybrid iterative process”, Arab. J. Math. 6(2017), 21-29.

[6] M. O. Osilike, “Stability results for Ishikawa fixed point iteration procedure”,

Indian J. Pure Appl. Math. 26.10(1995), 937-941.

[7] I. Timiş, “On the weak stability of Picard iteration for some contractive type

mapping”, Annal. Uni. Craiova, Math. Comput. Sci. Series, 37.2(2010), 106-

114.



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177





Optimal Coincidence Best Proximity Point Results in Fuzzy

Metric Spaces

Naeem Saleem

Department of Mathematics, University of Management and Technology,

C-II Johar Town, Lahore,Pakistan

[email protected]

Abstract: In this paper, we disscused some sufficient conditions for existence

and uniqueness of the best proximity points and optimal coincidence point

results for non-self mapping in fuzzy metric space. We also mentioned some

interesting aspects of best proximity point theory in the setup of fuzzy metric

spaces. We provided some examples to explain the obtained results, which also

shows that obtained results are generalization of already existing results in

literature. This article could be viewed as a discussion on extension of recent

development on proximal contraction mappings in such spaces.

Keywords: Fuzzy metric Space, Best Proximity point, Optimal Coincidence best

proximity point

References:

[1] K. Fan, “Extensions of two fixed point theorems of F. E. Browder”. Math. Z.

112, 234-240 (1969).

[2] S. Sadiq Basha, N. Shahzad, R. Jeyaraj.“Optimal approximate solutions of

fixed point equations”. Abstr. Appl. Anal. 2011, 174560 (2011).

[3] N. Saleem, B. Ali,M. Abbas, Z. Raza.“Fixed points of Suzuki type

generalized multivalued mappings in fuzzy metric spaces with applications”.

Fixed Point Theory Appl. 2015, 36 (2015).

[4] LA. Zadeh. “Fuzzy sets”. Inf. Control 8, 103-112 (1965).

[5] M. Abbas, N. Saleem and M. De la Sen, “Optimal coincidence point results

in partially ordered non-Archimedean fuzzy metric spaces”, Fixed Point Theory

and Applications, 2016 (1), 1-18.

[6] N. Saleem, M. Abbas and Z. Raza, “Optimal coincidence best approximation

solution in non-Archimedean Fuzzy Metric Spaces”, Iranian Journal of Fuzzy

Systems, 13(3), 113-124, 2016.

[7] Z. Raza, N. Saleem and M. Abbas, “Optimal coincidence points of proximal

quasi-contraction mappings in non-Archimedean fuzzy metric spaces”, Journal

of nonlinear science and application, 9 (2016), 3787- 3801


______________________________________________________

178





New Concept of Determinants with Three Indexes (3D

Determinants) and Possibilities of Use

Armend Salihu

Department of Computer Science, University for Business and Technology

Prishtine, Kosovo

[email protected]

Abstract: In this paper will will present a new concept of determinants with

three indexes (3D Determinants), we will present how we will try to solve the 3D

determinants and what are possibilities of usage of those determinants.

Keywords: Determinants, 3D, Determinants Calculation.

References:

[1] Cramer, Gabriel (1750). "Introduction à l'Analyse des lignes Courbes

algébriques" (in French). Geneva: Europeana. pp. 656–659. Retrieved 2012-05-

18

[2] Thomas S. Shores (2007). Applied Linear Algebra and Matrix Analysis.

Springer Science & Business Media. p. 132. ISBN 978-0-387-48947-6.

[3] Leon, Steven J. (2006), Linear Algebra with Applications (7th ed.), Pearson

Prentice Hall

[4] Hedman, Bruce A. (1999). "An Earlier Date for "Cramer's Rule"". Historia

Mathematica 26 (1999), 365–368


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179





Boundedness Properties of Some Operators on dM P,Q

Ayse Sandikci

Department of Mathematics, Ondokuz Mayis University,

Samsun, Turkey

[email protected]

Abstract: The Lorentz mixed normed modulation space dM P,Q is the

set of all tempered distributions df S such that the short-time Fourier

transform gV f of f is in the Lorentz mixed norm space 2dL P,Q , where

dg S is a non-zero window function, 1 21 P p ,p and

1 21 Q q ,q . In this work we investigate the boundedness properties

of Wigner distribution and time-frequency localization operator on

dM P,Q . Some key references are given below.

Keywords: Lorentz mixed normed modulation space, Wigner distribution, time-

frequency localization operator.

References:

[1] P. Boggiatto, Localization operators with L^p symbols on the modulation

spaces, In Advances in Pseudo-Differential Operators, vol. 155 of Oper. Theory

Adv. Appl., 149--163, Birkhäuser, Basel, 2004.

[2] E. Cordero, K. Gröchenig, Time-frequency analysis of localization operators,

J. Funct. Anal., 205(1) (2003), 107-131.

[3] D.L. Fernandez, Lorentz spaces, with mixed norms, J. Funct. Anal., 25

(1977), 128-146.

[4] K. Gröchenig, Foundation of Time-Frequency Analysis. Birkhäuser, Boston

2001, ISBN 0-8176-4022-3.

[5] R.A. Hunt, On L(p,q) spaces, Extrait de L'Enseignement Mathematique,

T.XII, fasc.4 (1966), 249-276.

[6] A. Sandıkçı, On Lorentz mixed normed modulation spaces, J. Pseudo-Differ.

Oper. Appl., 3 (2012), 263-281.

[7] A. Sandıkçı, Continuity of Wigner-type operators on Lorentz spaces and

Lorentz mixed normed modulation spaces, Turk J. Math., 38 (2014), 728-745.


______________________________________________________

180





On Approximate Biprojectivity of Banach Algebras

M. H. Sattari

Department of Mathematics Azarbaijan Shahid Madani University,

Tabriz, Iran

[email protected]

Abstract: The notion of approximate biprojectivity of Banach algebras was

introduced by Pourmahmood-Aghababa [4], O. Yu. Aristov [1] and Y. Zhang

[5] in different ways. Here some hereditary properties of this concept is

investigated, according to definaion of Pourmahmood-Aghababa. Among other

things is shown that approximate biprojectivity of the second dual of A implies

approximate biprojectivity of A , where **A is equipped with the first Arens

product [2].

Keywords: Approximate biprojective, Banach Algebra, Second dual.

References:

[1] O. Yu. Aristov, “On approximation of flat Banach modules by free modules”,

Sbornik. Math. 196(11) (2005), 1553–1583.

[2] H. G. DALES. Banach Algebras and Automatic Continuity (Oxford, 2000).

[3] F. Ghahramani and Y. Zhang, “Pseudo-amenable and pseudo-contractible

Banach algebras”, Math. Proc. Cambridge Philos. Soc. 142 (2007), 111–123.

[4] H. Pourmahmood-Aghababa, “Approximately biprojective Banach algebras

and nilpotent ideals”, Bull. Aust. Math. Soc. 87 (2013) 158-173.

[5] Y. Zhang, “Nilpotent ideals in a class of Banach algebras”, Proc. Amer.

Math. Soc. 127(11) (1999), 3237–3242.



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181





On Some New Sequence Spaces Defined By Almost Lacunary

Bounded Variation

Ekrem Savas

Department of Mathematics, Istanbul Ticaret University,

Sütlüce, Istanbul, Turkey

[email protected]

Abstract: In this paper we introduce and examine a new sequence space by

using Orlicz function and almost lacunary bounded variation. We also study

some basic topological and algebraic properties for these spaces. Furthermore we

shall established inclusion theorems between these sequence spaces.

Keywords: almost convergence, almost lacunary convergence, lacunary

sequence; bounded variation ; Orlicz function .

References:

[1] S. Banach, Theorie des Operations linearies, Warszawa, 1932.

[2] G. Das and S. K. Mishra, Banach limits and lacunary

strong almost convergence, J. Orissa Math. Soc. 2(2) (1983),

[3] V. Karakaya and E. Savas, On almost p-bounded variation of lacunary

sequences , Computer and Math. with Appl., 61(2011), 1502-1506

[4] S. D. Parashar, and B. Choudhury, Sequence space defined by Orlicz

functions, Indian J. Pure Appl. Math., 25(14) (1994)419-428.

[5] E. Savas, and V. Karakaya, Some new sequence spaces defined by lacunary

sequences ,Math. Slovaca, 57(2007), 393-399.


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182





On Filter Convergence of Nets in Uniform Spaces

Ekrem Savas1 and Ulas Yamanci2

1Department of Mathematics, Istanbul Ticaret University, İstanbul, Turkey 2Department of Statistics, Süleyman Demirel University, Isparta, Turkey

[email protected]; [email protected];

Abstract: In this paper, we introduce F -convergence and stF -fundamental of

nets in uniform space and study some of its consequences

Keywords: Ideal, filter, net, filter-convergence.

References:

[1] B.T. Bilalov, T.Y. Nazarova, “On statistical type convergence in uniform

spaces”, Bull. Iranian Math. Soc., 42(2016), 975-986.

[2] J.A. Fridy, On statistical convergence, Analysis, 5 (1985) 301-313.

[3] P. Das, E. Savaş, “On I -convergence of nets in locally solid Riesz spaces”,

Filomat, 27(2013), 89-94.

[4] B.K. Lahiri, P. Das, “I and I -convergence of nets”, Real Anal. Exchange,

33 (2007-2008), 431-442.

[5] E. Savaş, P. Das, “A generalized statistical convergence via ideals”, Appl.

Math. Lett., 24 (2011), 826-830.



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183





On E-J Hausdorff Transformations for Double Sequences

Rabia Savas and Hamdullah Sevli

Sakarya University, Sakarya, Turkey

[email protected]

Istanbul Commerce University, Istanbul, Turkey

[email protected]

Abstract: In 1933, Adams [1] developed Hausdorff transformations for double

sequences. Şevli and Savaş [2] proved some result for double Endl- Jakimovski

(E-J) generalization. In this study, we consider some further results for E-J

Hausdorff transformations for double sequences.

Keywords: Hausdorff matrices, double series, absolute summability.

References:

[1] Adams, C. R., Hausdorff transformations for double sequences, Bull. Amer.

Math. Soc. 39, 303-312, 1933.

[2] Şevli, H. and Savaş, R., On double Hausdorff summability method, Journal

of Inequalities and Applications, 240, 1-10, 2014.



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184





Double Lacunary Statistical Boundedness of Order α

Rabia Savas and Mahpeyker Ozturk

Department of Mathematics, Sakarya University, Sakarya, Turkey


Abstract: In this paper we introduce and the study the concept of the double

lacunary statistical boundedness of order α and also give a general descriptions

of inclusion between double statistical boundedness and double lacunary

boundedness of order α.

Keywords: Double lacunary sequences, double statistical boundedness, double

lacunary statistical boundedness

References:

[1] V. K. Bhardwaj, S. Gupta, S. A. Mohiuddine and A. Kılıçman, On Lacunary

Statistical Boundedness, J.Ineq. Applications, 2014, 2014:311.

[2] M. Et, S.A. Mohiuddine and H. Şengul, On Lacunary Statistical

Boundedness of order α, Facta Universitatis, Ser. Math. Inform. Vol. 31, No 3,

2016, 707-716.

[3] R. F. Patterson and E. Savas, Lacunary Statistical Convergence of Double

Sequences, Mathematical Com. 10, 2005, 55-61.



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185





Statistıcal Convergent Functions Via Ideals With Respect To

The Intuitionistic Fuzzy 2-Normed Spaces

Rahmet Savas

Department of Mathematics, Istanbul Medeniyet University, Istanbul, Turkey

[email protected]

Abstract: The main objective of this paper is to introduce and study the notion

of ideal -statistical convergence of a non-negative real-valued Lebesque-

measurable function in the interval (1, ) with respect to the intuitionistic fuzzy

2-normed ( , ) . Investigate their relationship, and make some observations

about these classes. Further, we prove some inclusion theorems.

Keywords: Ideal, filter, I-Statistical convergence of function, I - statistical

convergence of functions, intuitionistic fuzzy normed space, intuitionistic fuzzy

2− normed space.

References:

[1] K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1986)

87–96.

[2] K. Atanassov, G. Pasi, R. Yager, Intuitionistic fuzzy interpretations of multi-

person multicriteria decision making, in: Proceedings of 2002 First International

IEEE Symposium Intelligent Systems, 1(200) ,115–119.

[3] R. Colak, Statistical convergence of order α, Modern methods in Analysis

and its Applications, New Delhi, India, Anamaya Pub., (2010), 121-129.

[4] R. Colak, C. A. Bektas, λ-statistical convergence of order α, Acta Math.

Scientia, 31B (3) (2011), 953-959. [5] J. Connor, The statistical and strong p -

Cesaro convergence of sequences, Analysis, 8(1988), 47-63.

[6] H. Fast, Sur la convergence statistique, Colloq. Math. 2, 1951, 241-244.

[7] J.A. Fridy, On statistical convergence, Analysis 5 (1985) 301-313.

[8] S. G¨ahler, Linear 2-normietre Raume, Math. Nachr. 28(1965).

[9] P. Kostyrko, T. ˇSal´at, W. Wilczynki, I-convergence, Real Anal. Exchange

26 (2) (2000-2001) 669-685.

[10] Mohiuddine, S. A., Lohani, Q. M. D. On generalized statistical convergence

in intuitionistic fuzzy normed space, Chaos, Solitons and Fractals, 42, 3, 2009

[11] M. Mursaleen, λ-statistical convergence, Math. Slovaca 50 (2000) 111–115.

[12] M. Mursaleen and Q. M. Danish Lohani, Intuitionistic fuzzy 2- normed

space and some relates concepts Chaos, Solitons and Fractals, 42,(2009), 224-

234.


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186





Submanifolds in 1

2H ( 1)m with Finite Type Pseudo-

Hyperbolic Gauss Map

Ruya Yegin Sen* and Ugur Dursun**

* Department of Mathematics, Istanbul Medeniyet University,


[email protected]

** Department of Mathematics, Isik University,

Sile, Istanbul, Turkey

[email protected]

Abstract: The notion of finite type submanifold of a Euclidean space has been

introduced in late seventies. Since then the finite type submanifolds of Euclidean

or pseudo-Euclidean spaces have been studied extensively. In this work, we

mention the pseudo-hyperbolic Gauss map in the Obata’s sense. We study

pseudo-Riemannian submanifolds of 1

2H ( 1)m with finite pseudo-hyperbolic

Gauss map. We classify the pseudo-Riemmanian submanifolds of 1

2H ( 1)m

with 1-type pseudo-hyperbolic Gauss map. Then, we investigate the maximal

surface fully lying in 4 1

2 2H ( 1) H ( 1)m with 2-type pseudo-hyperbolic

Gauss map.

Keywords: Finite type map, pseudo-hyperbolic Gauss map, pseudo-hyperbolic

space.

References:

[1] Chen, B.-Y., Finite type submanifolds in pseudo-Euclidean spaces and

applications, Kodai Math. J., 8 (1985), 358-374.

[2] Chen, B.-Y., Finite-type pseudo-Riemannian submanifolds, Tamkang Journal

[3] Dursun, U. and Yeğin, R., Hyperbolic submanifolds with finite type

Hyperbolic Gauss map, Int. J. Math., 26(2015).

[4] Ishihara, T., Maximal spacelike submanifolds of a pseudo-Riemannian space

of constant curvature, Michigan Math. J., 35 (1988), 345-352.

[5] Sakaki, M., Spacelike maximal surfaces in 4-dimensional space form of

index 2, Tokyo J. Math , 25(2002), 295-306.



______________________________________________________

187





On the Determination of Validity of Categorical Syllogisms by

Using a Mathematical Model

Ibrahım Senturk1, Tahsin Oner2




Abstract: The earliest systematic approachment for determination of validity of

syllogisms was introduced by Aristotle [1] . In the 19th. and 20th. centuries,

Lewis Caroll [2] and Jan Łukasiewicz [3] made a significant contribution to

convert categorical syllogisms into modern logical structures. In this work, we

examine the validity of categorical syllogisms with the help of Caroll

Diagrammatic Method (SLCD) by constructing a logical calculus system [4] . In

the sequel, we indicate that any categorical syllogism is valid if and only if it is

provable in this system. In addition to these, we tackle with sorites validity

problems in categorical syllogisms. This enables us to construct a more general

solution technique for determination of their conclusions and validity.

Keywords: Categorical Syllogisms, Syllogistic systems, Carrolls' Diagrammatic

Method

References:

[1] Aristotle, “Prior Analytics” translation and commentary by Robin Smith,

Hackett Publishing, (1989).

[2] L. Carroll, “Symbolic Logic”, Clarkson N. Potter, (1896).

[3] J. Łukasiewicz, “Aristotle's Syllogistic From the Standpoint of Modern

Formal Logic”, Oxford University Press (1957).

[4] I. Senturk and T. Oner, “A Construction of Heyting Algebra on Categorical

Syllogisms”, Matematichki Bilten, 40.4 (2016), 5-12.

mailto:[email protected]%20%20%20%[email protected]

______________________________________________________

188





Converse Theorems for Statistical Convergence

Sefa Anil Sezer 1, Rahmet Savas 1, Ibrahim Canak 2

1 Department of Mathematics, Istanbul Medeniyet University, Istanbul, Turkey 2 Department of Mathematics, Ege University, Izmir, Turkey

[email protected]; [email protected];

[email protected]

Abstract: A real or complex sequence ( )ns is said to be statistically convergent

to a finite if for all 0 ,

1

lim : 0,1

nn

n N sN

where the vertical bars indicate the cardinality of the enclosed set. It is known

that the statistical convergence can be studied as a regular summability method,

and also it is not included by any matrix method. In this study we investigate

relations between statistical convergence and a certain class of matrix

summability methods. Besides, we establish conditions needed for a statistically

convergent sequence to be ordinary convergent.

Keywords: Statistical convergence, converse theorems, Tauberian theorems,

matrix summability methods.

References:

[1] H. Fast, “Sur la convergence statistique”, Colloq. Math. 2(1951), 241-244.

[2] I. J. Schoenberg, “The integrability of certain functions and related

summability methods”, Amer. Math. Monthly, 66(1959), 361-375.

[3] J. A. Fridy, “On statistical convergence”, Analysis, 5(1985), 301-313.

[4] J. A. Fridy, H. I. Miller, “A matrix characterization of statistical

convergence”, Analysis, 11(1991), 59-66.

[5] F. Mòricz, “Theorems relating to statistical harmonic summability and

ordinary convergence of slowly decreasing or oscillating sequences”, Analysis,

24(2004), 127–145.

[6] S. A. Sezer, İ. Çanak, “Tauberian theorems for the summability methods of

logarithmic type”, Bull. Malays. Math. Sci. Soc. (2016), doi:10.1007/s40840-

016-0437-9

[7] S. A. Sezer, İ. Çanak, “Power series methods of summability for series of

fuzzy numbers and related Tauberian Theorems”, Soft Comput. 21(2017), 1057–

1064




______________________________________________________

189





Cesàro Summability of Sequences in 2-Normed Spaces

Sefa Anil Sezer, Rahmet Savas

Department of Mathematics, Istanbul Medeniyet University,

Istanbul, Turkey


Abstract. The concept of 2-normed spaces was introduced by Gähler [7] in

1964. This notion recieved the attention of a wider audience after the study of

White [1] in 1969. He defined convergent sequences and Cauchy sequences in 2-

normed spaces which lead the birth of theory of 2-Banach spaces. In the last

decade, 2-normed spaces has attained noticeable importance and popularity from

the researchers working on summability theory. Firstly, Gürdal and Pehlivan

[4,5] presented the statistical convergence of sequences in 2-normed spaces.

Meanwhile, Şahiner et al. [2] defined the ideal convergence of sequences in such

spaces. Later, Savaş [3] and Das et al. [6] determined certain new sequence

spaces using ideal convergence and Orlicz functions in 2-normed spaces and

examined some of their properties.

In this study we have introduced the concept of Cesàro summability for

sequences in 2-normed spaces and obtained necessary and sufficient conditions

under which convergence follows from Cesàro summability.

Keywords: Tauberian conditions, 2-normed spaces, Cesàro summability.

References:

[1] A. G. White Jr., “2-Banach spaces”, Math. Nachr. 42(1969), 43–60.

[2] A. Şahiner, M. Gürdal, S. Saltan, H. Gunawan, “Ideal convergence in 2-

normed spaces”, Taiwanese J. Math., 11(2007), 1477-1484.

[3] E. Savaş, “Δm-strongly summable sequences spaces in 2-normed spaces

defined by ideal convergence and an Orlicz function”, Appl. Math. Comput.,

217(2010), 271-276.

[4] M. Gürdal, S. Pehlivan, “The statistical convergence in 2-Banach spaces”,

Thai J. Math., 2(2004), 107-113.

[5] M. Gürdal, S. Pehlivan, “Statistical convergence in 2-normed spaces”,

Southeast Asian Bull. Math., 33(2009), 257-264.

[6] P. Das, E. Savaş, S. Bhunia, “Two valued measure and some new double

sequence spaces in 2-normed spaces”, Czechoslovak Math. J., 61(2011), 809-

825.

[7] S. Gähler, “Lineare 2-normierte Räume”, Math. Nachr., 28(1964), 1–43.



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190





Applications of the Schwarz Lemma to Inequalities for

Polynomials with Restricted Zeros

Lubna Wali Shah

Department of Mathematics, National Institute of Technology,

Srinagar, Jammu and Kashmir India

[email protected]

Abstract: By using a boundary refinement of the classical Schwarz Lemma

some results for the polynomial inequalities with restricted zeros have been

proved.The estimates obtained strengthen some known results earlier proved by

Lax, Turan, Aziz and others.

Keywords: Schwarz Lemma, Inequalities in the complex domain, s-fold zeros

References:

[1] Abdul Aziz, A refinement of an inequality of S. Bernstein, J. Math. Anal.

Appl., 142(1989), 1-10.

[2] A. Aziz and W. M. Shah, Inequalities for a polynomial and its derivative,

Math. Inequal. Appl., 7(3) (2004), 379-391.

[3] S. Bernstein, Sur la limitation des derivees des polynomes, C. R. Acad.

Sci.Paris., 190(1930), 338-340.

[4] V. N. Dubinin, Applications of the Schwarz Lemma to inequalities for entire

functions with constraints on zeros. J. Math. Sci.,(N.Y) 143(3)(2007), 3069-

3076.

[5] S. G. Krantz, The Schwarz Lemma at the Boundary, Complex Var.

EllipticEqu., 56(5)(2011), 455-468.


______________________________________________________

191





Growth of Maximum Modulus of Polynomials and Rational

Functions in the Complex Domain

Wali Mohammad Shah

Department of Higher Education

University of Kashmir, Srinagar, India.

[email protected]

Abstract: In this talk we discuss the latest developments concerning the

extremal properties and growth of maximum modulus of polynomials and

rational functions. Our main objective will be to discuss Bernstein [4] type of

inequalities for rational functions with prescribed poles and the use of a

boundary refinement of Schwarz lemma [2,3] and a lemma due to Dubinin [1].

We [5] also show how the inequalities for the derivative and polar derivative

besides the growth of polynomials can be deduced as special cases from these

inequalities concerning the rational functions.

Key words : Polynomials, Rational functions, Inequalities , zeros

References:

[1] V.N. Dubinin, Distortion theorems for polynomials on the circle, Sb. Math.,

191(12) (2000) 1797-1807.

[2] S. G. Krantz, The Schwarz lemma at the boundary, Complex Var. Elliptic

Equ., 56 (5) (2011), 455-468.

[3] R. Osserman, A sharp Schwarz inequality on the boundary for functions

regular in the disk, Proc. Amer . Math. Soc., 12(2000), 3513-3517 .

[4] Q. I. Rahman and G Schmeisser, Analytic Theory of Polynomials, Oxford

University Press, New York, 2002.

[5] S. L. Wali and W. M. Shah, Some applications of Dubinin's lemma to

rational functions with prescribed poles., J. Math. Anal. Appl., 450(2017), 769-

779.


______________________________________________________

192





Trace Formula for Witt Vector Rings

Mokhfi Siham

Department of Mathematics, Saad DahlabUniversity,

Blida, Algérie

[email protected]

Abstract: We commence by giving a generalisation of Pulita exponential series.

We thenuse series to establish an analog of the trace formula for Witt vector

rings.

Keywords: Trace formula, Pulita series, Witt vector rings.

References:

[1] E. Artin, “Algebraic Numbers and Algebraic Functions”, Gordon and Breach,

New York. Math (1967).

[2] D. Barsky, “On Morita's p-adic gamma Functions”, Math. Proc.Camb.phil.

Soc, 89, Fasc 1(1981), 23-27.

[3] B. Benzaghou, “Algèbres de Hadamard ”, Soc. Math. France Slovaca,

98(1970), 209-252.

[4] R. Blache, “Stickelberger Theorem for p-adic Gauss sums”, Acta

Arithmetica, vol 18 n°1(2005), 11-26.

[5] B. Dwork , “The Rationality of the zeta Function of an Algebraic Variety ”,

Amer. Math 82 (1960) 631-648.

[6] M. Hazewinkel, “Witt vectors ”, Part 1 . Handbook of Algebra , Vol 6

section 4H, 319-472. Elsiever , North Holland. (1960) 631-648

[7] J. Lubin and J.Tate , “Formal Complex Multiplication in Local Fields ”, Ann

of Math (2) 81 (1965) 380-387.

[8]B. Benzaghou and S. Mokhfi , “Trace formula for Witt Vector Rings”,

Comptes Rendus Mthématiques (2016)

[9] A. Pulita , “Rank one solvable p-adic Differential Equations and Finite

Abelian Characters via Lubin-Tate groups ”, Math. Ann. 337 (2007) n°03 489-

555.


______________________________________________________

193





On Parametrization of the q-Bernstein Basis Functions

Yilmaz Simsek

Department of Mathematics, Faculty of Science University of Akdeniz TR-07058,

Antalya, Turkey

[email protected]

Abstract: In this talk, we study main properties of the q-Bernstein basis

functions with their generating functions. We show that these q-Bernstein basis

functions are parametrizations of the standard Bernstein basis functions. We

define q-Bezier type curves. Moreover, we plot graphs of these basis functions,

their generating funtions and q-Bezier type curves. Finally, we give remarks and

observations on the q-Bezier type curves related to parametrizations of the q-

Bernstein basis functions.

Keywords: q-Bernstein basis functions, Bezier curves, Generating function.

References:

[1] S. N. Bernstein, “Démonstration du théorème de Weierstrass fondée sur la

calcul des probabilités”, Comm. Soc. Math. Charkow Sér. 2 t. 13, 1-2 (1912-

1913).

[2] R. Goldman, “Identities for the Univariate and Bivariate Bernstein Basis

Functions”, Graphics Gems V, edited by Alan Paeth, Academic Press, (1995),

149-162.

[3] T. Kim, L.-C. Jang, and H. Yi, “A note on the modified q-Bernstein

polynomials”, Discrete Dyn. Nat. Soc. 2010, Article ID 706483, 12 pages, 2010.

[4] T. Kim, “Some identities on the q-integral representation of product of

several q-Bernstein-type polynomials”, Abst. Appl. Anal., 2011, Article ID:

634675, 1-11.

[5] M.-S. Kim, D. Kim, T. Kim, “On q-Euler numbers related to the modified q-

Bernstein polynomials”, Abst. Appl. Anal. 2010, Article ID 952384, 15 pages.

[6] G. M.Phillips, “Bernstein polynomials based on the q-integers”, The heritage

of P. L. Chebyshev: a Festschrift in honor of the 70th birthday of T. J. Rivlin,

Annals of Numerical Math. 1-4 (1997), 511-518.

[7] Y. Simsek, “Interpolation function of generalized q-Bernstein type

polynomials and their application, Curve and Surface”, Springer Verlag Berlin

Heidelberg 2011, LNCS 6920, (2011), 647-662.


______________________________________________________

194





Control of the Performance of the Panel of Judge in Sensory

Analysis by a Functinal Principal Component Analysis of

Probability Densities Function

Yousfi Smail

Mouloud Mammeri University

[email protected]

Abstract: In this work, the Functional Principal Component Analysis (FPCA) of

a set of probability density functions is used to study the performance of a panel

of 14 judges in sensory analysis context. For this, we integrate the FPCA of

densities in the context of Multiblock data analysis where, each block contain the

scores assigned by judges for 10 rosebushes according two sensory variables at

three different occasions. The planes of representations of densities gives a firt

global appreciation of variations contained in the data, one part of these

variations summarizes the repetability of the scores assigned by the judges and

another part, the discrimination of products tested.


______________________________________________________

195





Optimization of an Execution Time for Parallel Matrix

Multiplication by adding a New Set of Processors on the Array

1Halil Snopce, 2Sadri Alija, 3Azir Aliu and 4Artan Luma

1,3,4 Faculty of Contemporary Sciences and Technologies, SEE-University Tetovo,

Macedonia 2Faculty of Business and Economics, SEEU, Ilindenska n.335, Tetovo,

Macedonia [email protected], , [email protected], [email protected],

[email protected]

Abstract: In this paper we investigate the possible methods of optimization of

the execution time of some parallel algorithms for matrix-matrix multiplication.

Actually, there is known that the time complexity of execution the algorithm of

matrix multiplication by using just one processor element is O(n3). If one uses

the hexagonal array of n2 processor the optimized execution time is proved to be

3n-2. In this research, among others we show that if the array of processors is

increased by n new processors (putting new column of processors), the execution

time will be shortened for one unit of time. If we continue adding new columns

of processors, the execution time of the algorithm is shortened consecutively per

one unit of time after each new step.

Assuming that there are put k columns of n processors, then we show that the

time complexity of an algorithm is optimized to the order of O(N). Actually, we

show that this value at the worst case is equal to 2n-k where n is the number of

processors per column and k is the number of new added columns of processors

to the hexagonal array of processors.

For confirmation of obtained results, there are used some methods of linear

algebra.

.

Keywords: Matrix multiplication, optimization, execution time of algorithm,

time complexity, hexagonal array of processors, linear methods.



______________________________________________________

196





From Dido to Morrey: Variational Problems and

Regularity Theory!

Lubomira G. Softova

Second University of Naples

Department of Civil Engineering, Design, Construction and Environment, Italy

[email protected]

Abstract: Although ancient Greek and Roman sources report that Dido, the

founder and first queen of Carthage was the first person who formulated a

problem in Calculus of Variations (CV), the classical existence theory is

connected mainly with the names of Euler, Lagrange and Ostrogradskij. The

notorious Euler-Lagrange equation is a second order Partial Differential

Equation (PDE), the solvability of which ensures the existence of a minimizer of

a given functional. The question of regularity for the solutions of this PDE was

firstly posed by David Hilbert in his 19th and 20th problem, presented during a

celebrated lecture at the International Congress of Mathematics (ICM) 1900 in

Paris. During the last century, these two problems gave a strong impulse to the

development of the regularity theory for problems from CV and PDE. Our goal

is to present some classical and new results concerning regularity properties of

the solutions to the Dirichlet problem for elliptic equations and systems. We

obtain essential boundedness of the solution to a class of nonlinear elliptic

systems. In addition, we establish estimates in


______________________________________________________

197





A Publicly Verifiable Authenticated Encryption Scheme Based

on Chaotic Maps and Factoring Problems

Nedal Tahat

Department of Mathematics, Faculty of Sciences

The Hashemite University, Zarqa 13133, Jordan

[email protected]

Abstract: In this study, an authenticated encryption scheme with public

verifiability based on chaotic maps and factoring problems is proposed. The

main aim of deploying a chaos-based cryptosystem is to provide encryption with

several advantages over traditional encryption algorithms such as high security,

speed, and reasonable computational overheads and computational power

requirements. Therefore, to enhance system security, we explore the

implementation of a cryptosystem algorithm based on both cryptographic and

chaotic system characteristics. We also provide security against known

cryptographic attacks and discuss the performance analysis of the developed

system.

Keywords: Authenticated encryption scheme, chaotic maps, factoring problem.

References: [1] C. Tsai, C. Liu, S. Tsaur and M. Hwang, A publicly verifiable authenticated

encryption scheme based on factoring and discrete logarithms. International

Journal of Network Security, 2017, 19(3): 443-4480

[2] P. Horster, M. Michel and H. Peterson, “Authenticated encryption schemes

with low communication costs,” Electronics letters, 1994, 30(15): 1212-1213.

[3] W.-B. Lee and C.-C. Chang, “Authenticated Encryption without Using a

One Way Function,” Electronics Letters,1995,31(19):1656-1657.

[4] Y. Zheng, “Digital Signcryption or How to Achieve Cost (Signature &

Encryption) << Cost (Signature) + Cost (Encryption),” Proc. CRYPTO’97,

LNCS 1294, Springer Verlag,1997: 165-179.

[5] Y. Zheng, “Signcryption and Its Application in Efficient Public Key

Solution,” Proc. Information Security Workshop (ISW’97), LNCS 1397,

1998.Springer-Verlad: 291-312.

[6] C. Ma and K. Chen, “Publicly Verifiable Authenticated Encryption,”

Electronics Letters, 2003. 39(3): 281-282.

[7] S. F. Tzeng, Y. L. Tang, and M. S. Hwang, \A new convertible authenticated

encryption scheme with message linkages," Computers and Electrical

Engineering, vol. 33, no. 2, pp. 133-138, 2007.


______________________________________________________

198





Third-Order Differential Sandwich-type Results Involving the

Liu-Owa Operator

Huo Tang1

, M. K. Aouf2

, Shigeyoshi Owa3

and Shu-Hai Li1

1. School of Mathematics and Statistics, Chifeng University, Chifeng 024000,

Inner Mongolia, People's Republic of China


2. Department of Mathematics, Faculty of Science, Mansoura University,

Mansoura 35516, Egypt

[email protected]

3. Department of Mathematics, Faculty of Education, Yamato University,

[email protected]

Abstract: In this paper, we derive some third-order differential subordination

and superordination results for multivalent analytic functions in the open unit

disk, which are defined by using the Liu-Owa operator. The results are obtained

by investigating appropriate classes of admissible functions. New third-order

differential sandwich-type results for the Liu-Owa operator are also obtained.

Keywords: Differential subordination; Differential superordination; Multivalent

analytic functions; Sandwich-type results; Liu-Owa operator.

References:

[1] R. M. Ali, V. Ravichandran and N. Seenivasagan, Differential subordination

and superordination of analytic functions defined by the Dziok-Srivastava

operator, J. Franklin Inst. 347 (2010), 1762-1781.

[2] R. M. Ali, V. Ravichandran and N. Seenivasagan, On subordination and

superordination of the multiplier transformation for meromorphic functions,

Bull. Malaysian Math. Sci. Soc. 33 (2010), 311-324.

[3] J. A. Antonino and S. S. Miller, Third-order differential inequalities and

subordinations in the complex plane, Complex Var. Elliptic Equ. 56 (2011),

439-454.

[4] I. B. Jung, Y. C. Kim and H. M. Srivastava, The Hardy space of analytic

functions associated with certain one-parameter families of integral operators, J.

Math. Anal. Appl. 176 (1993), 138-147.


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199





Second-Order Differential Superordination for Analytic

Functions in the Upper Half-Plane

Huo Tang1

, H. M. Srivastava2,3

, Guan-Tie Deng4

and Shu-Hai Li1

1. School of Mathematics and Statistics, Chifeng University, Chifeng 024000,

Inner Mongolia, People's Republic of China


2. Department of Mathematics and Statistics, University of Victoria,

Victoria, British Columbia V8W 3R4, Canada

3. Department of Medical Research, China Medical University Hospital,

China Medical University, Taichung 40402, Taiwan, Republic of China

[email protected]

4. School of Mathematical Sciences, Beijing Normal University, Beijing 100875,

People's Republic of China

[email protected]

Abstract: There are many articles in the literature dealing with the second-order

differential subordination and differential superordination problems for analytic

functions in the unit disk : 1U z z C and z , but there are only a few

articles dealing with the above problems in the upper half-plane

: Im( ) 0z z C and z . The concept of second-order differential

subordination in the upper half-plane was introduced by Raducanu and Pascu in

[1], and studied recently by Tang et al. in [2]. Let be a set in the complex

plane C . Also let ( )p z be analytic in the upper half-plane and suppose that

3:C C . In this paper, we investigete the problem of determining

properties of functions ( )p z that satisfy the following second-order differential

superordination:

( ( ), ( ), ( ); ) :p z p z p z z z C .

Applications of these results to second-order differential superordination for

analytic functions in are also presented.




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200





Keywords: Differential subordination; Differential superordination; Analytic

functions; Admissible functions; Upper half-plane.

References:

[1] D. Raducanu and N. N. Pascu, Differential subordinations for holomorphic

functions in the upper half-plane, Mathematica (Cluj). 36(1994), 215-217.

[2] H. Tang, M. K. Aouf, G.-T. Deng and S.-H. Li, Differential subordination

results for analytic functions in the upper half-plane, Abstr. Appl. Anal. 2014

(2014), Article ID 565727, 1-6.

______________________________________________________

201





Capacity Sizing and Pricing with Heterogeneous Products and

Flexible Resources

Salih Tekin

Industrial Engineering Department, TOBB University of Economics and

Technology,

Ankara, Turkey

[email protected]

Abstract: We consider the capacity and pricing decisions made by a

monopolistic firm producing three heterogeneous products under demand

uncertainty. The objective is to maximize profit. Our model includes dedicated

and flexible resources, product substitutability, and processing rates that may

depend on the product and on the resource type. We provide the optimum prices

and production quantities as functions of resource capacities and demand

intercepts. We also show that investment in flexible capacity is only desirable

when it is optimal to invest in dedicated capacities for both products, and obtain

upper bounds for the costs of the dedicated capacities that need to be satisfied for

investment in the flexible resource. We conclude with numerical examples that

illustrate the points discussed and provide insights into how the optimal

capacities and expected production quantities, prices, and profit depend on

various model parameters.

Keywords: Revenue Management, Stochastic Programming, Pricing.


______________________________________________________

202





A New Class of the r-Stirling Numbers and the Generalized

Bernoulli Polynomials

Meriem Tiachachat

Faculty of Mathematics, RECITS's laboratory, USTHB

Algiers, Algeria.

[email protected]

Abstract: The r-Stirling number of the second kind, counts the number of

partitions of an n-set into k non-empty subsets such that the r-first elements are

in different subsets [3]. In [11], the authors expressed the n-th high order

polynomial [7, 14] in terms of the r-Stirling numbers of both kinds by some

formulas. In 2010, Kurt [6] introduced an extension of the generalized Bernoulli

polynomials. The main object of this paper is to express the values at non

negative integers of the generalized Bernoulli polynomials on using a new class

of the Stirling numbers of the second kind.

Keywords: The r-stirling numbers, the quasi associated r-Stirling numbers, the

generalized Bernoulli polynomials

References:

[1] E. T. Bell, Exponential polynomials, Ann. Math., 35 (1934) 258-277.

[2] G. Bretti, P. Natalini, P. E. Ricci, Generalizations of the Bernoulli and Appell

polynomials, Abst. Appl. Anal., 7 (2004) 613–623.

[3] A. Z. Broder, The r-Stirling numbers, Discrete Math., 49 (1984) 241-259.

[4] L. Comtet, Advanced Combinatorics, D. Reidel Publishing Company,

Dordrecht-Holland / Boston-U.S.A, (1974).

[5] H. W. Gould, Higher order extensions of Melzaks formula, Util. Math., 72

(2007) 23-32.

[6] B. Kurt, A further generalization of the Bernoulli polynomials and on the 2D-

Bernoulli polynomials B 2

n (x; y); Appl. Math. Sci., 4 (2010) 2315-2322.

[7] Y. L. Luke, The special functions and their approximations, vol. I, Academic

Press, New York, London, 1969.


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203





Degree Sequences and Inverse Problem on Graphs

Muge Togan, Aysun Yurttas, Ismail Naci Cangul


Bursa, Turkey


Abstract: Degree sequence of a graph is the set of all vertex degrees of the given

graph in non-decreasing order. There are algorithms to determine which sets of

positive integers can be the degree sequence of a graph, but yet no complete

solution is given. Topological graph indices are getting more and more interest

every day due to their applications in Chemistry and Pharmacology and most of

them are calculated for many graph types. Molecular graphs are the graphs with

vertex degree at most 4. A recent problem in graph theory is called inverse

problem. This problem deals with what integer values can be taken by these

topological graph indices. In this talk, by means of degree sequences, we give the

answer for several topological indices.

Keywords: Degree sequence, inverse problem, topological graph index

References:

[1] H. Wang, G. Yu, All but 49 numbers are Wiener indices of trees, Acta Appl

Math 92 (2006) 15-20

[2] I. Gutman, Y.-N. Yeh, The sum of all distances in bipartite graphs, Math.

Slovaca 45 (4) (1995) 327-334

[3] S. M. Cioaba, Sums of powers of the degrees of a graph, Discrete

Mathematics 306 (2006) 1959-1964




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204





Notes on Permuting tri-derivations on Prime and Semi-prime

Rings

Seda Oguz Unal, Hasret Durna

Cumhuriyet University,

Sivas, Turkey


Abstract: Derivations in prime rings firstly initiated by Posner [1] and it

is considered a fundamental construction in the theory of centralizing maps on

prime rings.. A great deal of work in this context are available in the literature

(see, for example [2] and [3]). In this sense, in [4], Ozturk presented permuting

tri-derivations in prime and semi-prime rings.The aim of this talk is to show that

a ring is a prime and semiprime ring admitting the trace satisfying several

conditions of permuting tri-derivation.

Keywords: Permuting tri-derivations, traces, prime rings, semi-prime rings, Lie

ideals.

References:

[1] E. C. Posner,"Derivations in prime rings", Proc. Amer. Math. Soc., 8(1957),

1093–1100.

[2] N. Argac and M. S. Yenigul,"Lie ideals and symmetric bi-derivation on

prime and semi-prime rings", Pure and Applied Mat. Sci., 44(1996), 17–21.

[3]M. A. Ozturk, D. Ozden and Y. B. Jun,"Permuting tri-derivations in prime

and semi-prime gamma rings",Kyungpook Math. J., 46(2011), 153–167.

[4] M. A. Ozturk, " Permuting tri-derivations in prime and semi-prime rings",

East Asian Math. J., 15(1999), 177–190.



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205





Weakly Invariant Subspaces for Multivalued Linear Operators

on Banach Spaces

Gerald Wanjala

Department of Mathematics and Statistics, Sultan Qaboos University,

Muscat, Oman

[email protected]

Abstract: Losomonov [1] showed that if a bounded linear operator T on a

Banach space X commutes with a non-zero compact operator, then T has a

nontrivial invariant subspace. This result was generalized by Peter Saveliev [2]

to the case of multivalued linear operators by applying fixed point techniques. In

particular, he proved that if S and K are multilivalued linear operators defined on

a Banach space X and having finite dimensional multivalued parts, and if K is

compact and right commutes with S, that is SK ⊂ KS, then S has a nontrivial

weakly invariant subspace. However, the case of left commutativity remained

open. In this talk, we address the case of left commutativity. We apply the

operator representation techniques developed in [3] to acheive the desired result.

Keywords: Multivalued linear operator, Weakly invariant subspace.

References:

[1] V. I. Lomonosov, “Invariant subspaces for the family of operators which

commute with a completely continuous operator”, Func. Anal. Appl., 7(1973),

213-214.

[2] P. Savelieve, “Lomonosov’s invariant subspace theorem for multivalued

linear operators”, Proc. AMS, 131(2002), 825-8344.

[3] G. Wanjala, “Operator representation of sectorial linear relations and

applications”, J. Ineq. Appl., (2015), 2015:60.


______________________________________________________

206





Speech Quality Analysis with Respect to Noise Corruption by a

Kalman Filter to Estimation the Parameters of the SWLP

Method

Ervenila Xhaferraj (Musta)

Department of Mathematics, Faculty of Mathematics and Physics

Engineering, Polytechnic University of Tirana

Tirane, Albania

[email protected]

Abstract: Revolutions Applications such as telecommunications, hands-free

communications, recording, etc. which need at least one microphone, the signal

is usually infected by noise and echo. The important application is the speech

enhancement, which is done to remove suppressed noises and echoes taken by a

microphone, beside preferred speech. Accordingly, the microphone signal has to

be cleaned using digital signal processing DSP tools before it is played out,

transmitted, or stored. Engineers have so far tried different approaches to

improving the speech by get back the desired speech signal from the noisy

observations. Especially Mobile communication, so in this paper will do

reconstruction of the speech signal, observed in additive background noise, using

the Kalman filter technique to estimate the parameters of the Autoregressive

Process (AR) in the state space model and the output speech signal obtained by

the MATLAB. The accurate estimation by Kalman filter on speech would

enhance and reduce the noise then compare and discuss the results between

actual values and estimated values which produce the reconstructed signals.

References:

[1]. J. R. Deller, J. H. L. Hanson and J. G.Proakis. Diccrere-The Processing of

Speech Signal, EEE PRESS, NewYork 2000.

[2]. K. K. Paliwal and A.Basu, “A speech enhancement method based on Kahan

filtering, Proceedings of ICASSP’87,pp.177-180. Dallas, TX, USA, 1987.

[3]. T.K.Mmn, “The Expectation-Maxlmizaion Algorithm”,IEEE Signof

Processing Magazine, pp. 47-60, Nov. 1996.

[4] Shumway, Robert H., Stoffer, David S., Time Series Analysis and Its

Applications with R Examples, second edtition, Springer Texts in Statistics

Series, 2006.


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207





S-Generalized Srivastava’s Triple Hypergeometric Functions

M. Baki Yagbasan, Aysegul Cetinkaya, I. Onur Kiymaz


Kırşehir, Turkey

[email protected]

Abstract: In this study, we introduced new generalizations of Srivastava's triple

hypergeometric functions by using S-generalized beta function. Furthermore, we

investigated some properties of these new functions.

Keywords: S-Generalized Beta function, Srivastava's triple hypergeometric

functions.

Acknowledgement: This work was supported by Ahi Evran University

Scientific Research Projects Coordination Unit. Project Number: FEF.A4.17.002

References:

[1] Çetinkaya, A., Yagbasan, M. B., Kıymaz İ. O., “The extended Srivastava’s

triple hypergeometric functions and their integral representations”, Journal of

Nonlinear Sciences and Applications, 9.6, (2016): 4860-4866.

[2] Bailey W.N., “Generalized Hypergeometric Series”, Cambridge Tracts in

Mathematics and Mathematical Physics, vol. 32, Cambridge University Press,

Cambridge, (1935).


beta function”, J. Comput.

Appl. Math., 78, (1997): 19-32.

[4] Luo, Min-Jie, Milovanovic, G. V., Agarwal, P. “Some results on the extended

beta and extended hypergeometric functions”, Applied Mathematics and

Computation, 248, (2014): 631-651.

[5] Srivastava H. M., Karlsson P. W., “Multiple Gaussian Hypergeometric

Series”, Ellis Horwood Limited, (1985).

[6] Srivastava, H. M., Agarwal, P., Jain, S. “Generating functions for the


Computation, 247, (2014): 348-352.

[7] Srivastava, H. M., Jain, R., Bansal, M. K., “A Study of the S-Generalized

Gauss Hypergeometric Function and Its Associated Integral Transforms”,

Turkish Journal of Analysis and Number Theory, 3.5, (2015): 116-119.


______________________________________________________

208





Berezin Number Inequality for Convex Function in

Reproducing Kernel Hilbert Space

Ulas Yamanci1, Mehmet Gurdal2, Mubariz T. Garayev3

1Department of Statistics, Süleyman Demirel University, Isparta, Turkey

2Department of Mathematics, Süleyman Demirel University, Isparta, Turkey 3Department of Mathematics, King Saud University, Riyadh, Saudi Arabia


Abstract: By using Hardy-Hilbert's inequality, some power inequalities for the

Berezin number of a self-adjoint operators in Reproducing Kernel Hilbert Spaces

(RKHSs) with applications for convex functions are given.

Acknowledgement: The second author is supported by TUBA through Young

Scientist Award Program (TUBA-GEBIP/2015).

Keywords: Berezin number, Hardy-Hilbert’s inequality, convex function, self-

adjoint operator.

References:

[1] G. Hardy, J.E. Littlewood, G., Polya, “Inequalities”, 2 nd ed. Cambridge

University Press, Cambridge, 1967.

[2] F.A. Berezin, “Covariant and contravariant symbols for operators”, Math.

USSR-Izv., 6 (1972), 1117-1151.

[3] M. Kian, “Hardy-Hilbert type inequalities for Hilbert space operators”, Ann.

Funct. Anal., 3(2)(2012), 128-134.

[4] M.T. Garayev, M. Gürdal, M., A. Okudan, “Hardy-Hilbert's inequality and a

power inequality for Berezin numbers for operators”, Math. Inequal. Appl.,

(3)(19)(2016), 883-891.

[5] B. Yang, “Discrete Hilbert-type inequalities”, Bentham Science Publishers

Ltd., 2011.




______________________________________________________

209





On Power Inequalities for Berezin Number of Operators and

Convex Functions

Ulas Yamanci1, Mehmet Gurdal2, Ceren Celik2

1Department of Statistics, Süleyman Demirel University,

2Department of Mathematics, Süleyman Demirel University,

Isparta, Turkey


Abstract: In this paper, some power inequalities are given for Berezin numbers,

defined by reproducing kernel, on reproducing kernel Hilbert spaces.

Acknowledgement. This work is supported by Suleyman Demirel University

with Project 4903-YL1-17.

Keywords: Berezin number, Hardy-Hilbert’s inequality, convex function,

reproducing kernel Hilbert space.

References:

[1] G. Hardy, J.E. Littlewood, G., Polya, “Inequalities”, 2 nd ed. Cambridge

University Press, Cambridge, 1967.

[2] F.A. Berezin, “Covariant and contravariant symbols for operators”, Math.

USSR-Izv., 6 (1972), 1117-1151.

[3] M. Kian, “Hardy-Hilbert type inequalities for Hilbert space operators”, Ann.

Funct. Anal., 3(2)(2012), 128-134.

[4 M.T. Karaev, “Berezin symbol and invertibility of operators on the functional

Hilbert spaces”, J. Funct. Anal., 238(2006), 181-192.

[5] S. Saitoh, Y. Sawano, “Theory of reproducing kernels and applications”,

Springer, 2016.




______________________________________________________

210





Spectral Properties of Discrete Klein-Gordon Equations

Nihal Yokus, Nimet Coskun

Department of Mathematics, Karamanoglu Mehmetbey University,

Karaman, Turkey


Abstract: Spectral analysis of Sturm-Liouville boundary value problem was

investigated by Naimark[1]. Bairamov and Celebi[2] studied the Klein-Gordon s-

wave equation which includes the Sturm-Liouville equation as a special case in

their paper. As a result of developments in discrete calculus, discrete analogues

of the Sturm-Liouville and Klein-Gordon equation have gained a prominent

attention. Spectral theory of discrete Klein-Gordon equation has been treated by

Adivar[3]. In this study, we shall present Jost solution, discrete spectrum and

spectral singularities of the discrete Klein-Gordon equation under certain

conditions.

Keywords: Discrete equations, spectral analysis, Klein-Gordon equation.

References:

[1] M.A. Naimark, ‘‘Investigation of the spectrum and the expansion in

eigenfunctions of a non-selfadjoint operator of second order on a semi-axis’’,

AMS Transl. 2(1960), 103-193.

[2] E. Bairamov and A.O. Celebi, ‘‘Spectral properties of the Klein-Gordon s-

wave equation with complex potential’’, Indian J. Pure Appl. Math. 28(1997),

813-824.

[3] M.

Adivar, ‘‘Quadratic pencil of difference equations: Jost solutions,

spectrum, and principal vectors’’, Quaestiones Mathematicae, 33(2010), 305-

323.



______________________________________________________

211





On the Inverse Problem on Graphs

Aysun Yurttas, Muge Togan, Ismail Naci Cangul


Bursa, Turkey


Abstract: Topological graph indices are getting more and more interest every

day due to their applications in Chemistry and Pharmacology. Their values are

calculated for many graph types and relations with molecular graphs are

established. Molecular graphs are the graphs with vertex degree at most 4. A

recent problem in graph theory is called inverse problem. This problem deals

with what integer values can be taken by these topological graph indices. In this

talk, we give the answer for several topological indices.

Keywords: Molecular graph, inverse problem, topological graph index

References:

[1] H. Wang, G. Yu, All but 49 numbers are Wiener indices of trees, Acta Appl

Math 92 (2006) 15-20

[2] I. Gutman, Y.-N. Yeh, The sum of all distances in bipartite graphs, Math.

Slovaca 45 (4) (1995) 327-334

[3] S. M. Cioaba, Sums of powers of the degrees of a graph, Discrete

Mathematics 306 (2006) 1959-1964




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212





Summability of Subsequences of Divergent Sequences

Maria Zeltser with Johann Boss

School of Digital Technologies, Mathematics and Didactics of Mathematics,

Tallinn University,

Tallinn, Estonia

[email protected]

Abstract: C. Stuart proved in [1] that the Cesàro matrix 𝐶1 cannot sum almost

every subsequence of a bounded divergent sequence 𝑥. At the end of the paper

he stated the problem whether this proposition could be generalized for any

regular matrix. We confirm Stuart's conjecture, and even we extend it to the

more general case of divergent sequences x. Moreover we determine a class 𝑄 of

subsequences (𝑥𝑛𝑖) of 𝑥 such that a given regular matrix does not sum sum all

elements of Q.

Keywords: Regular matrices, summability of subsequences.

References:

[1] C. Stuart. Summability of subsequences of a divergent sequence. Rocky

Mountain J. Math., 44(1): 289-295, 2014.


______________________________________________________

213





Many to one Embedding Crossed Cube into Pancake

Mohamed Faouzi Zerarka

Abstract: Among Cayley graphs on the symmetric group, the pancake graph is

one as a viable interconnection scheme for parallel computers, which has been

examined by a number of researchers. The pancake was proposed as alternatives

to the hypercube for interconnecting processors in parallel computers. Some

good and attractive properties of this interconnection network include: Small

degree, a sub-logarithmic diameter, extendability, and high connectivity

(robustness), easy routing, and regularity of topology, fault tolerance,

extensibility and embeddability of other topologies. A graph embedding has been

known as a powerful tool for implementation of parallel algorithms and

simulation of interconnection networks. In this paper, we present the many-to-

one model of mapping nodes and edges of crossed cubes into nodes and paths of

pancake respectively and to minimize the dilation and the expansion costs.

Keywords: Embedding; dilation, expansion, crossed cubes, pancake.

References:

1. X. Yang, Q. Dong and Y.Y. Tan, Embedding meshes/tori in faulty crossed

cubes, Information Processing Letters, Vol. 110, no. 14-15, 559 - 564, 2010.

2. P.-L. Lai and C.-H. Tsai, Embedding of tori and grids into twisted cubes,

Theoretical Computer Science, Vol. 411, no. 40-42, 3763 - 3773, 2010. 11.

3. Y. Han, J. Fan, S. Zhang, J. Yang and P. Qian, Embedding meshes into locally

twisted cubes, Information Sciences, Vol. 180, no. 19, 3794 - 3805, 2010. 12.

4. J. Fan and X. Jia, Embedding meshes into crossed cubes, Information

Sciences, Vol. 177, no. 15, 3151 - 3160, 2007.

5. Y. Saad and M.H. Schultz, Topological properties of hypercubes, IEEE

Transactions on Computers,Vol. 37, no. 7, 867 - 872, 1988.

6. K. Efe, The crossed cube architecture for parallel computing,IEEE

Transactions Parallel and Distruibuted Systems, Vol. 3, no. 5, 513 -524, 1992

8. Akers S. and Krishnamurthy B., “A Group Theoretic Model for Symmetric

Interconnection Networks,” IEEE Transactions on Computers, vol. 38, no. 4, pp.

555-566, 1989.

9. Asai S., Kounoike Y., Shinano Y., and Kaneko K., “Computing the Diameter

of 17-Pancake Graph Using a PC Cluster,” Euro-Par 2006 Parallel Processing,

Dresden, Germany, pp. 1114-1124, 2006

10. Christian Lavault. Embeddings into the Pancake Interconnection Network.

Parallel Processing Letters, World Scientific Publishing, 2002, 12 (3-4), pp.297-

310

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