6th international conference on recent advances in … · 6th international conference on recent...

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6th INTERNATIONAL CONFERENCE ON RECENT

ADVANCES IN PURE AND APPLIED

MATHEMATICS,

ISTANBUL MEDENIYET UNIVERSITY,

ISTANBUL, TURKEY

JUNE 12-15, 2019

Abstract Book

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Honorary Chair

• Prof. Dr. Gülfettin ÇELİK Rector of Medeniyet University, Turkey

• Prof. Dr. Ekrem SAVAŞ Rector of Usak University, Turkey

Organizing Committee

• Prof. Dr. Ekrem Savas, Usak University, Turkey • Prof. Dr. Richard Patterson, North Florida University, USA • Prof. Dr. Mehmet Gurdal, Suleyman Demirel University • Prof. Dr. Martin Bohner, Missouri S&T, USA • Prof. Dr. Ram Mohapatra, Uni. of Central Florida, USA • Prof. Dr. Fairouz Tchier, King Saud University, Saudi Arabia • Prof. Dr. Mehmet Dik, Rockford University, USA • Prof. Dr. Lubomira Softova, Second University of Naples, Italy • Prof. Dr. Agron Tato, Polytechnic Uni. of Tirana, Albania • Prof. Dr. Debasis Giri, Haldia Institute of Technology, India • Prof. Dr. Naim Braha, • Assoc. Prof. Dr. Rahmet Savas, Istanbul Medeniyet University, Turkey • Assoc. Prof. Dr. Erhan Deniz, Kafkas University, Turkey • Assoc. Prof. Dr. Mahpeyker Ozturk, Sakarya University, Turkey • Assoc. Prof. Dr. Emel Kalın, Karadeniz Technical University, Turkey • Assist. Prof. Dr. Arzu Akgun, Kocaeli University, Turkey • Assist. Prof. Dr. Veli Capali, Usak University, Turkey • Assist. Prof. Dr. Rabia Naz, Department of Mathematics Fccollege university,

Pakistan • Assist. Prof. Dr. Betül Hicdurmaz, Istanbul Mediniyet university, Turkey • Dr. Lakhdar Ragoub, Alyammah university, Saudi Arabia

Local Organizing Committee

• Abdurrahman Büyükkaya • Melek Eriş Büyükkaya • Rabia Savaş • S. Anıl Sezer • Tuğba Yıldırım • Neslihan Kaplan

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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. Mehmet Akbaş, Turkey • Prof. Dr. Erhan Coskun, Turkey • Prof. Dr. Funda Karacal, Turkey • Prof. Dr. Haskız Coskun, Turkey • Prof. Dr. Sultan Yamak, Turkey • Prof. Dr. Selcuk Han Aydin, Turkey • 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. 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

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• Prof. Dr. Ismail N. Cangul, Turkey • Prof. Dr. Lejla Miller Van-Wieren, Bosnia • Prof. Dr. Murat Tosun, 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. Srivastava, India • Prof. Dr. Azhar Hussain, Pakistan • Prof. Dr. Ayhan Aydın, Turkey • Prof. Dr. Hanya Kherchi Medjden, France • Assoc. Prof. Dr. Yasemin Sağıroğlu, Turkey • Assoc. Prof. Dr. Tülay Kesemen, Turkey • Assist. Prof.Dr. Hafize Gök, Turkey • Assist. Prof.Dr. Stuti Borgahain, India • Assist. Prof.Dr. Sukran Konca, Turkey • Assist. Prof.Dr. Rabia Naz, Pakistan • Dr. Mayssa Alqurashi, Saudi Arabia • Dr. Fardous Taoufic, Saudi Arabia

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Dear Collogues;

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

Advances in Pure and Applied Mathematics (ICRAPAM 2019).

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.

The conference was organized by Istanbul Medeniyet University in Istanbul and supported by

Turkish Cooperation and Coordination Agency (TIKA), Ziraat Bank, and Kanyon College.

We would like to thank Istanbul Medeniyet University (Host University) for providing the

excellent facility for this conference. And also Turkish Cooperation and Coordination Agency

(TIKA), Ziraat Bank, and Kanyon College. We also 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. Rahmet SAVAS

Chair of the Conference

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6th INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN PURE AND APPLIED

MATHEMATICS, ISTANBUL MEDENIYET UNIVERSITY, ISTANBUL, TURKEY

JUNE 12-15, 2019

INVITED TALKS

A discussion on attractive points of further generalized mappings Prof. Dr. Mujahid Abbas

1

Recent Results on Absorbing Ideals of Commutative Rings Prof. Dr. Ayman Badawi

2

Indices in Cubic Number Fields and Thue Equations Prof. Dr. Abdelmejid Bayad

3

Modeling and simulation of a spatio-temporal pattern with nonsingular order fractional derivatives Prof. Dr. Zakia Hammouch

4

Methods for Numerical Construction of s-Orthogonal Polynomials Prof. Dr. Gradimir V. Milovanović

5

Solvability of Infinite System of a Class of Boundary Value Problems Prof. Dr. M. Mursaleen

7

Two parametric kinds of Apostol type numbers and polynomials related to Eisenstein series and Dedekind sums Prof. Dr. Yilmaz Simsek

8

vii

6th INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN PURE AND APPLIED

MATHEMATICS, ISTANBUL MEDENIYET UNIVERSITY, ISTANBUL, TURKEY JUNE 12-15, 2019

LIST OF TALKS

E-duality results for E-differentiable E-convex vector optimization problems

Najeeb Abdulaleem

9

E-duality results for E-differentiable vector optimization problems under (generalized) E-convexity

Najeeb Abdulaleem

10

Mathematical analysis of cochlear pressure in micromechanical model

Fatima-Ezzahra Aboulkhouatem

11

Mathematical study of the wind speed influence of on the annual profit of purse seiners

I. Agmour

12

Approximation Properties of Multivariate Szasz-Gamma Type Operators Based on Dunkl Analogue

P. N. Agrawal

13

On (P,Q)-Lucas Polynomial coefficients for a New Class of Bi-Univalent Functions Given by Subordination

Arzu Akgül

14

The Arithmetic–Geometric Mean Inequalities

Mohammad Al-Hawari

15

Characterization of rough weighted Norlund-Euler statistical limit set

Ekrem Aljimi

16

Generalized Monotone Iterative Techniques for Dynamic Equations with the Initial Value Problem on Time

Scales

Nour Alsharif

17

Chain level proof for the isomorphism between Lie and Hochschild homologies

Zuhier Altawallbeh

18

Approximate Solutions for Nonlinear Second order Differential Equation by using Reprodusing Kernel Hilbert

Space Method

Ali Ateiwi

19

Notes on nullnorms on an arbitrary bounded lattice

Emel Aşıcı

20

Predation of aristeus antennatus in protected and unprotected fishing area

Nossaiba Baba

21

Parametric generalization of α-Bernstein Operators

Behar Baxhaku

22

Approximation of functions by Generalized Lototsky-Bernstein type Operators

Erdem Baytunç

23

Behavior of new models of hybrid conjugate gradient algorithm

Mohammed Belloufi 24

viii

Extremal Graphs for a Bound on the Roman Domination Number

Ahmed Bouchou

25

Some properties of Baskakov-Schurer-Szasz operators via power summability methods

Naim Braha

26

Complex and Real Optical soliton Solution of the Time Fractional Resonant Davey-Stewartson Equations

Hasan Bulut

27

Some Fixed Point and Best Proximity Point Results on −Admissible Mappings via Simulation Functions

Abdurrahman Büyükkaya

28

Comparison for Covariance Matrices of Predictors in General Linear Mixed Model

Melek Eriş Büyükkaya

29

Approximation of Nuclear Reaction Cross Section Data Using Machine Learning Algorithm

Veli Capali

30

A Study on Utilization of 2 Analysis in Text Analytics Studies

Elif Cesur

31

Fixed Point Results For f -Contraction Mappings Satisfying B -Contractions in Modular Spaces

Şeyda Çakar

32

Developing a route choice model based on fuzzy logic in public transport system

Buket Çapalı

33

Second Order Optimality Conditions for a Semilinear Elliptic Control Problem of Infinite Order with Pointwise

Control Constraints

S. A. El-Zahaby

34

On the location bl-domatic number

Noureddine Ikhlef-Eschouf

35

Oscillation of Fourth-order Differential Equations with Noncanonical Operators

Nagehan Kılınç Geçer

36

Generalized Lototsky and Jayasri matrices with Generelazied Bernstein Operators

Halil Gezer

37

Some fixed point results in non-Archimedean quasi modular metric spaces

Ekber Girgin

38

Stability of Reduced Functional Differential Inclusions

Nurgül Gökgöz

39

L∞ as a Dual Space

Banu Güntürk

40

On Numerical Analysis of General Coupled Systems of Time-Space Fractional Schrödinger Equations

Betul Hicdurmaz

41

On (n,k)-quasi class Q* Operators

Ilmi Hoxha

42

On the Fractional Resolvent Families and Fractional Integro-differential Equations

Mamadsho Ilolov 43

ix

Orthogonal Lie Groups and Their Lie Algebras

Yasemin Işık

44

Fixed Point Theorem for Generalized Hybird Mapping in Hyperbolic Metric Spaces

Amna Kalsoom

45

Permanent Displacements in the Vicinity of a Cylindrical Canyon Covered with an Anisotropic Layer

Hasan Faik Kara

46

Bn -Maximal Operator and High Order Riesz-Bessel Transforms on variable exponent Lebesgue spaces

Esra Kaya

47

A Note on Two Parametric Apostol Type Polynomials

Neslihan Kilar

48

Set-Star Menger and Related Spaces

Sukran Konca

49

Numerical Solution of Two Dimensional Brusselator Model by Time Splitting Method

Sıla Övgü Korkut

50

The effect of basilar membrane stiffness on the displacement of cochlear partition

Fatiha Kouilily

51

L1-convergence of the sine series whose coefficients belong to some generalized classes of sequences

Xhevat Krasniqi

52

Lebesgue constants on the real projective spaces

Alexander Kushpel

53

Packing chromatic number in some graphs

Rachid Lemdani

54

θ-type contraction mappings in complete b-metric spaces and applications to polynomial approximations

Nora Mahloul

55

Unsupervised classification of superficial waters quality of l’Oued Moulouya (North East Morocco).

Application of Self Organizing Maps

Imad Manssouri

56

Direct Torque Control using Neural Networks and Fuzzy Logic

Zineb Mekrini

57

New Approach to q-Fractional Derivative

S. Norozpour

58

Full cycle extendability of triangulary connected partly claw-free graphs

Abdelkader Sahraoui

59

A new sequence space and invariant mean

Ekrem Savaş

60

- mean and uniform (A, φ)- statistically convergent sequences

Rahmet Savaş

61

Biharmonic Hypersurfaces in a Pseudo-Euclidean Space

Rüya Yeğin Şen

61

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Bade-property, Extremally rich JB*-triples and λ-property

Haifa M. Tahlawi

63

Fixed point on modified semi-linear uniform spaces

A. Tallafha

64

Fuzzy Relational Graphs

Fairouz Tchier

65

On Some Properties of a Normed Intersection Space

Cihan Unal

66

Some Conditions over a Strongly Regular Graph in The Environement of Euclidean Jordan algebras

Luís Vieira

67

Spectral Theory and Stability of Index for Multivalued Linear Operators

Gerald Wanjala

68

Mixture of two Methods for Solving Some Differential Equations

Ervenila Xhaferraj

69

Inverse Berezin number inequality and related problems

Ulas Yamanci

70

I-statistical convergence in n-normed spaces

Ulas Yamanci

71

Degenerate maximal hyponormal differential operators for the first order

Fatih Yılmaz

72

IFRS 17: Impact to the life insurance companies in Albania

Oriana Zacaj

73

Characterizations of extremal graphs for some bounds on k-domination number

Mohamed Zemir

74

Common Fixed Points of Semigroup Actions

Yong Zhang 75

On the Analytical and Numerical Solutions of Chemotaxis Model

Kholiknazar Kuchakshoev 76

Intelligent Control Using Fuzzy Logic

Saih Mohammed 77

INTERNATIONAL CONFERENCE on RECENT ADVANCES in

PURE AND APPLIED MATHEMATICS (ICRAPAM 2019)

JUNE 12-15 2019, Istanbul Medeniyet University, Istanbul, TURKEY

www.icrapam.org

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1

A discussion on attractive points of further generalized mappings

Mujahid Abbas

Department of Mathematics,

GCU-54000 Lahore Pakistan [email protected]

Abstract: Attractive point theory is attracting the attention of nonlinear annalists. The aim of

this talk is discuss attractive points of monotone further generalized mappings. Some strong and

weak convergence results of attractive point are considered for monotone further generalized

mappings.

mailto:[email protected]




www.icrapam.org

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2

Recent Results on Absorbing Ideals of Commutative Rings

Ayman Badawi

Department of Mathematics & Statistics, The American University of Sharjah, P.O. Box 26666,

Sharjah, United Arab Emirates

[email protected]

Abstract: Let R be a commutative ring with 1 0. Recall that a proper ideal I of R is

called a 2-absorbing ideal of R if a, b, c ∈ R and abc ∈ I, then ab ∈ I or ac ∈ I or bc

∈ I . A more general concept than 2-absorbing ideals is the concept of n-absorbing ideals. Let

n ≥ 1 be a positive integer. A proper ideal I of R is called an n-absorbing ideal of R if a1, a2,

..., an+1 ∈ R and a1a2 · · · an+1 ∈ I, then there are n of the ai’s whose product is in I. The concept

of n-absorbing ideals is a generalization of the concept of prime ideals (note that a prime ideal

of R is a 1-absorbing ideal of R). In this talk, we will state recent developments on the study of

absorbing ideals of commutative rings.

Key words: Prime, primary, weakly prime, weakly primary, 2-absorbing, n- absorbing, weakly

2-absorbing, weakly n-absorbing, 2-absorbing primary, weakly 2-absorbing primary.

References:

[1] D. F. Anderson and A. Badawi, On (m, n)-closed ideals of commutative rings. To appear in

Journal of Algebra and Its Applications. DOI: 10.1142/ S021949881750013X

[2] D. F. Anderson and A. Badawi, On n-absorbing ideals of commutative rings. Comm. Algebra

39, 1646–1672(2011)

[3] D. F. Anderson and A. Badawi, On (m,n)-closed ideals of commutative rings. J. Algebra

Appl. 16 (2017), no. 1, 1750013, 21

[4] Badawi, On 2-absorbing ideals of commutative rings. Bull. Austral. Math. Soc. 75, 417– 429

(2007)

[5] Badawi,n-absorbing ideals of commutative rings and recent progress on three conjectures: a

survey. Rings, polynomials, and modules, 33-–52, Springer, Cham, 2017.

[6] Badawi, M. Issoual and N. Mahdou, On n-absorbing ideals and (m,n)-closed ideals in trivial

ring extensions of commutative rings, (Available on Line), to appear in Journal of Algebra and

Its Applications.

[7] D. Bennis and B. Fahid, Rings in which every 2-absorbing ideal is prime, Beitr

Algebra Geom 59, 391–396(2018)

[8] P. J. Cahen, M. Fontana, S. Frisch, and S. Glaz, Open problems in commutative ring theory,

Commutative Algebra. Springer, 353–375(2014)

[9] H. Seung Choi and A. Walker, The radical of an n-absorbing ideal. arXiv:1610.10077

[math.AC] (2016) (to appear in Journal of Commutative Algebra).

[10] Yousefian Darani and E.R. Puczy-lowski, On 2-absorbing commutative semigroups and their

applications to rings. Semigroup Forum 86, 83–91(2013)

[11] Issoual and N. Mahdou, Najib Trivial extensions defined by 2-absorbing-like conditions. J.

Algebra Appl. 17 (2018), no. 11, 1850208, 10 pp.

[12] H. Fazaeli Moghimi and S. Rahimi Naghani, On n-absorbing ideals and the n-Krull dimen-

sion of a commutative ring. J. Korean Math. Soc. 53, 1225-1236(2016)




www.icrapam.org

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3

Indices in Cubic Number Fields and Thue Equations

Abdelmejid Bayad

Universite´ D’e´ Vry Val D’essonne, Universite´ Paris-Saclay, Labora- Toire De Mathe´ Matiques Et

Mode´ Lisation D’e´ Vry (Umr 8071), I.B.G.B.I., 23 Bd. De France, 91037 E´ Vry Cedex, France

[email protected], [email protected]

Abstract: Let ,f X Y be a homogeneous irreducible polynomial of degree 3n and

k be an integer. In 1909 Thue proved that the diophantine equation

f (x, y)= k

has only finitely many solutions in integers x and y.

His method does not give explicitly the solutions. In this talk, first we review old and new results

on this direction.

We investigate the theory of indices in cubic number fields. We then obtain new method to study

Thue Equations. We obtain precise results when f is irreducible binary cubic form.

As a consequence of our study we will be able to obtain information on the number of integers

and also of the number of rational points of the Mordell’s elliptic curves:

Ed : dy2 = x3 + Ax + B. These families are extremely studied in the literature and are sources of intensive research at

present in the field of elliptic curves.

In particular, there is:

• Connection between the number of integers points on the curves Ed and the rank of Ed.

• Connection with Birch-Swinnerton-dyer conjecture and special values at integers of the

L-function associated to Ed.

References:

[1] S. Alaca, K. S. Williams, Introductory Algebraic Number Theory, Cambridge University

Press. (2004).

[2] E. T. Avanesov, Solution in integers of the indeterminate equation x3-2x2y-5xy2-y3=1,

Ivanov. Gos. Ped. Inst. Ucen. Zap. 61 (1969), 61-83.

[3] E. T. Avanesov, A bound for the number of representations by a special class of binary cubic

forms of positive discriminant, Acta Arith. 20 (1972), 17-31.

[4] M. Ayad and O. Kihel Common divisors of values of polynomials and common factors of

indices in a number field, Int. J. Number Theory. 7 (2011), 1173-1194.

[5] A. Bayad and M. Seddik, On cubic Thue equations and the common index divisors of cyclic

cubic fields, this paper appear in Acta Arithmetica.

[6] A. Baily, On the density of dsicriminants of quartic fields, J. reine angew. Math. 315 (1980),

190-210.

[7] A. Baker, Contribution to the theory of Diophantine equations, Phil. Trans. Roy. Soc.

London, Ser. A. 167 (1967/68), 717-208.




www.icrapam.org

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4

Modeling and simulation of a spatio-temporal pattern with nonsingular

order fractional derivatives

Zakia Hammouch Faculty of Sciences and Techniques Errachidia Moulay Ismail University,

Morocco

[email protected]

Abstract: This talk concerns a robust numerical method based on the fractional Adams-

Bashforth and the Fourier spectral methods to explore some spatiotemporal patterns in a range

of Belousov-Zhabotinskii reaction systems. The standard integer-order time-derivative is

replaced with the Atangana-Baleanu fractional order derivative in the sense of Caputo. Details

of existence and stability of positive solution are given. Numerical experiments are carried out

at some instances of fractional power to demonstrate the suitability of the methods, and to

explore the dynamic richness in some chemical species when modelled with non-integer-order

derivatives.

Keywords: Fourier spectral method; Existence of solution; Fractional reaction-diffusion;

Spatiotemporal oscillations; Stability analysis.

References: [1] A. Atangana and K.M. Owolabi, New numerical approach for fractional differential

equations, Mathematical Modelling of Natural Phenomena, 13 (2018) 3. [2] A. Atangana, Non validity of index law in fractional calculus: a fractional differential

operator with Markovian and non-Markovian properties, Physica A 505 (2018) 688-706.

[3] A. Atangana, Blind in a commutative world: Simple illustrations with functions

and chaotic attractors, Chaos, Solitons and Fractals 114 (2018) 347-363. [4] K.M. Owolabi and K.C. Patidar, Higher-order time-stepping methods for time dependent

reaction-diffusion equations arising in biology, Applied Mathematics and Computation, 240

(2014) 30-50.





www.icrapam.org

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5

Methods for Numerical Construction of s-Orthogonal Polynomials

Gradimir V. Milovanović

Serbian Academy of Sciences and Arts

Belgrade, Serbia

[email protected]

Abstract: Let ( )d t be a positive measure on with finite or unbounded support, for which

all moments ( ), 0k

k t d t k = , exist and are finite, and 0 > 0. For each ,n s , it

is well-known that the general Gauss-Turán quadrature formula

( )2

( )

, ,2

0 1

( ) ( ) ( )s n

v

i k v n s

v k

f t d t A f R f = =

= +

is exact for all polynomials of degree not exceeding 2( 1) 1s n+ − , i.e., ,2 ( ) 0n sR f = for all

2( 1) 1s nf P + − , where mP is the set of all algebraic polynomials of degree at most 𝑚. The nodes

, 1, 2,...,v v n = , are the zeros of the monic polynomial , ( )n s t , which minimizes the integral

2 2

0 1 1 ,( , ,..., ) ( ) ( )s

n n sF a a a t d t +

− = where

1

, 1 1 0( ) ... .n n

n s nt t a t a t a −

−= + + + +

This minimization gives the conditions

2 1

,

1( ) ( ) 0, 0,1,..., 1,

2 2

sk

n s

k

Ft t d t k n

s a

+ = = = − +

and such polynomials , ( )n s t are known as 𝑠-orthogonal polynomials on with respect to the

measure ( )d t . For 𝑠 = 0 they reduce to the standard orthogonal polynomials. The first attempt

in the numerical construction of s-orthogonal polynomials with respect to an even weight

function on a symmetric interval (−𝑐, 𝑐) was given in 1986 by Vincenti [6], who constructed an

iterative process for computing their coefficients. He applied it to Legendre s-orthogonal

polynomials, but the corresponding numerical results for coefficients were obtained only for low

degrees of polynomials n and relatively small values of s, because the process becomes

numerically unstable when n and s increase.

In 1987 we presented a stable method for numerically constructing s-orthogonal polynomials

and their zeros, which opened the door to the numerical construction of not only s-orthogonal

polynomials, but also to the quadrature rules of Gauss-Turán type and other generalized

quadratures of Gauss-Stancu type (cf. [1]–[5]).





www.icrapam.org

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6

Using ideas on reninterpretation the orthogonalitiy conditions for s-orthogonal polynomials in

terms of the ordinary orthogonality, in this lecture we present a method of continuation for a

stable constructinion of s-orthogonal polynomials. In addition, the construction of parameters

in the generalized Gauss-Turán quadrature formulas is also given. Examples for different

classical measures are presented.

Keywords: Positive measure, Moments, Gauss-Turán quadrature formula, Orthogonal and

s- orthogonal polynomials, Numerical construction, Method of continuation.

References:

[1] W. Gautschi, G.V. Milovanović, “S-orthogonality and construction of Gauss-Turán-type

quadrature formulae”, J. Comput. Appl. Math. 86 (1997), 205–218.

[2] G.V. Milovanović, “Construction of s-orthogonal polynomials and Turán quadrature

formulae”, in: G.V. Milovanović (Ed.), Numerical Methods and Approximation Theory III,

Niš, 1987, Univ. Niš, Niš, 1988, pp. 311–328.

[3] G.V. Milovanović, “Quadratures with multiple nodes, power orthogonality, and moment-

preserving spline approximation”, J. Comput. Appl. Math. 127 (2001), 267–286.

[4] G.V. Milovanović, M.M. Spalević, A.S. Cvetković, “Calculation of Gaussian type

quadratures with multiple nodes. Math. Comput. Modelling. 39 (2004), 325–347.

[5] G.V. Milovanović, M.S. Pranić, M.M. Spalević, “Quadratures with multiple nodes, power

orthogonality, and moment-preserving spline approximation, Part II”, Appl. Anal. Discrete

Math. 13 (2019), 1–27.

[6] G. Vincenti, “On the computation of the coefficients of s-orthogonal polynomials”, SIAM

J. Numer. Anal. 23 (1986), 129–1294.




www.icrapam.org

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7

Solvability of Infinite System of a Class of Boundary Value Problems

M. Mursaleen Department of Mathematics, Aligarh Muslim University,

Aligarh 202 002, India

[email protected]

Abstract: In this talk, we present a brief survey of theory and applications of measures of

noncompactness. The classical measures of noncompactness are discussed and their properties

are compared. The approaches for constructing measure of noncompactness in a general metric

or linear space are described, along with the classical results for existence of fixed point for

condensing operators. Also several generalization of classical results are mentioned and their

applications in various problems of analysis such as linear equation, di¤erential equations,

integral equations and common solutions of equations are discussed. Recently the measures of

noncompactness are applied in solving infinite system of diferential equations and integral

equations in sequence spaces [1, 2]. We considerhere the solvability of an infinite system of

second order diferential equations [3].

References: 1] J. Banas and M. Mursaleen, Sequence Spaces and Measures of Noncompactness with

Applications to Diferential and Integral Equations, Springer, 2014. [2] A. Das, B. Hazarika, R. Arab and M. Mursaleen, Solvability of the infinite system of integral

equations in two variables in the sequence spaces c0 and `1, Jour. Comput. Appl. Math., 326

(2017) 183-192. [3] M. Mursaleen and S.M.H. Rizvi, Solvability of infinite system of second order diferential

equations in c0 and `1 by Meir-Keeler condensing operator, Proc. Amer. Math. Soc., 144(10)

(2016) 4279-4289.





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8

Two parametric kinds of Apostol type numbers and polynomials related to

Eisenstein series and Dedekind sums

Yilmaz Simsek

Department of Mathematics, Faculty of Science University of Akdeniz TR-07058

Antalya, Turkey

[email protected]

Abstract: In this paper, we give a brief survey and history of generating functions for Apostol

type numbers and polynomials, the Eisenstein series and the Dedekind sums. The aim of this

paper is to give some relations and formulas about the special numbers and polynomials which

related to trigonometric function. By using generating functions and their functional equations,

we obtain various identities formulas and identities including two variables of Apostol-Bernoulli

and two variables of Apostol-Genocchi polynomials. Moreover, we give further remarks and

observations on relations between Apostol type numbers and polynomials, the Eisenstein series,

the Dedekind sums and cotangent functions.

Keywords: Generating function, Functional equation, Trigonometric function, Two variables of

Apostol-Bernoulli, Two variables of Apostol-Genocchi polynomials, Eisenstein series,

Dedekind sums and cotangent functions.

References:

[1] H. Rademacher and E. Grosswald, “Dedekind Sums”, Carus Mathematical Monographs,

Math. Asso. Amer. (1972).

[2] H. M. Srivastava, “Some generalizations and basic (or q-) extensions of the Bernoulli, Euler

and Genocchi polynomials”, Appl. Math. Inf. Sci. 5.3(2011), 390–444.

[3] H. M. Srivastava, and J. Choi, “Zeta and q- zeta functions and associated series and

integrals”, Elsevier, Amsterdam, (2012).

[4] H. M. Srivastava, M. Masjed-Jamei and M. R. Beyki, “A parametric type of the Apostol-

Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials”, Appl. Math. Inf. Sci.

12.5(2018), 907–916.

[5] J. Lewittes, “Analytic continuation of the series $\sum \left( m+nz\right) ^{-s}$”,

Transactions American Math. Soc. 159 (1971), 505-509.

[6] N. Kilar and Y. Simsek, “Relations on Bernoulli and Euler polynomials related to

trigonometric functions”, to appear in Adv. Stud. Contemp. Math. (2019).

[7] T. M. Apostol, “On the lerch zeta function”, Pac. J. Math. 1.2(1951), 161–167.

[8] T. Kim and C. S. Ryoo, “Some identities for Euler and Bernoulli polynomials and their

zeros”, Axioms, 7:3 56, (2018), 001–019.

[9] Y. Simsek, “Special numbers and polynomials including their generating functions in umbral

analysis methods, Axioms, 7.2:22 (2018).

[10] Y. Simsek, “Construction of some new families of Apostol-type numbers and polynomials

via Dirichlet character and p-adic q–integrals”, Turk. J. Math. 42(2018), 557 –577.





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9

E-duality results for E-differentiable E-convex vector

optimization problems

Najeeb Abdulaleem

Department of Mathematics, Hadhramout University,

Al-Mahrah, Yemen [email protected]

Abstract: In this paper, a class of E-differentiable E-convex multiobjective programming

problems with both inequality and equality constraints is considered. The so-called vector Mond-

Weir E-dual problem and vector mixed E-duality problem are defined for the considered E-

differentiable E-convex multiobjective programming problem with both inequality and

equality constraints and several Mond-Weir and mixed E-duality theorems are established under

(generalized) E-convexity hypotheses.





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10

E-duality results for E-differentiable vector

optimization problems under (generalized) E-convexity

Najeeb Abdulaleem

Department of Mathematics, Hadhramout University,

Al-Mahrah, Yemen

[email protected]

Abstract: In this paper, a class of E-differentiable multiobjective programming problems with

both inequality and equality constraints is considered. The so-called vector mixed E-dual

problem are defined for the considered E-differentiable multiobjective programming problem

with both inequality and equality constraints. Then, several mixed E-duality theorems are

established under (generalized) E-convexity hypotheses. Further, so-called vector Mond-Weir

E-dual and vector Wolfe E-dual problems are also defined for the considered E-differentiable

multiobjective programming problem as special cases of its vector mixed E-dual problem.





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11

Mathematical analysis of cochlear pressure in micromechanical model

Fatima-Ezzahra Aboulkhouatem(1), Fatiha Kouilily (1), Naceur Achtaich (1), Noura Yousfi (1) and

Mohammed El Khasmi (2)

(1) Laboratory Analysis Modeling and Simulation, Faculty of Sciences Ben M'sik, Hassan II University, Casablanca, Morroco

(2) Laboratory of Physiopathology and Genetic Molecular, Faculty of Sciences Ben M'sik,

Hassan II University, Casablanca, Morroco

[email protected]

Abstract: Hearing loss can be caused by an increase of pressure in the structure of cochlea. In

reality, the structure of the cochlea is very complicated, for that, many mathematical models are

proposed in order to understinding the cochlear function. In the latest searches, numerical

simulations remain a very important tool in the study of the mathematical problems of the

cochlea. In this present paper, we developped a mathematical model in order to establish the

relationship between the fluid pressure and the amplitude of displacement of the Basilar

Membrane in micromecanical model, including the feed-forward/feed-backward mechanisms of

the outer hair cell force amplification. The results of this study can be useful for understanding

cochlear dysfunction of the ear in active model.

Keywords: active model, mathematical analysis, hearing loss, numerical simulations, pressure

References:

[1] F.E. Aboulkhouetm, F. Kouilily, M. EL Khasmi, N. Achtaich and N.

Yousfi, The Active Model: The Effect of Stiffness on the Maximum Amplitude Displacement

of the Basilar Membrane, British J. Math. and Computer Sci. , 20(6)(2017), 1-11.

[2] F. Kouilily, F. E. Aboulkhouatem, M. EL Khasmi, N. Yousfi and N.

Achtaich, Predicting the Effect of Physical Parameters on the Amplitude of the Passive Cochlear

Model, Mex. J. BioMedical. Eng., 39(1)(2018), 105-112.

[3] G. Ni , S. J. Elliott, M. Ayat and P. D. Teal, Modelling cochlear mechanics, BioMed Res.

Int., 2014(2014), 1-42.

[4] J. B. Allen, Two dimensional cochlear fluid model: New results, J. Acoust. Soc. Am.,

61(1)(1977), 110-119.





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12

Mathematical study of the wind speed influence of on the annual profit of

purse seiners

I. Agmour(1), M. Bentounsi(1), N. Baba(1), N. Achtaich(1), Y. El Foutayeni(1,2)

(1) Analysis, Modeling and Simulation Laboratory, Hassan II University, Morocco (2)Unit for Mathematical and Computer Modeling of Complex Systems, IRD,

[email protected]

Abstract: Wind direction and wind speed are the most important parameters involved in the

seiners’ fishing activity. The wind creates conditions that are favorable to fishing. In this work,

we search to show the influence of the wind speed on the annual profit of purse seiners. We

consider a bioeconomic model of the marine populations: sardine, mackerel and horse mackerel

exploited by purse seiners in the southern athletic zone of Morocco. This zone is characterized

by major wind speed changes. We calculate the fishing effort and the amount of catch that allows

the seiners to have a maximum annual profit taking into account changes in wind speed in the

reporting year and the sustainability of the marine populations stocks. We compare our results

with those obtained by the National Institute of Fisheries Research of Morocco). One of the key

results of this study is the great difference seen between the fishing effort, the catches and the

profit calculated under the two constraints : wind speed changes and biodiversity conservation,

and those calculated under the only constraint of the biodiversity.

Keywords: Bio-economic model ; Fish populations ; Annual profit ; Fishing effort ; Wind

speed ; Nash equilibrium.

References:

[1] Bellon Humbert C., 1973 - Mollusques marins testacés du Maroc. Premier supplément. Trav.

Ins. Sc. Chérif, (zool.) 37 : 144 p.

[2] Clark, C.W., 1990. Mathematical Bioeconomics : The Optimal Management of Renewable

Resources, Second ed.. A Wiley-Interscience.

[3] I. Agmour, M. Bentounsi, N. Achtaich, and Y. EL Foutayeni, Optimization of the Two

Fishermen’s Profits

Exploiting Three Competing Species Where Prices Depend on Harvest, International Journal of

Differential Equations, Vol. 2017, Article ID 3157294.





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13

Approximation Properties of Multivariate Szasz-Gamma Type Operators

Based on Dunkl Analogue

Behar Baxhaku1, P. N. Agrawal 2, Ramadan Zejnullahu1 and Ruchi2

1 Department of Mathematics

University of Prishtina

Mother Teresa, 10000 Prishtina, Kosova

2 Department of Mathematics

Indian Institute of Technology Roorkee

Roorkee-247667, India

[email protected], 2 [email protected], 1 [email protected] and

2 [email protected]

Abstract: Sucu [1] defined a Dunkl analogue of the Szasz operators and studied the convergence

of these operators with the aid of the Korovkin type theorem. The rate of convergence was also

obtained by means of the Peetre’s K-functional and the weighted modulus of continuity. Wa and

Rao [2] presented Szasz Gamma operators based on Dunkl analogue and discussed pointwise

approximation, weighted approximation and the rate of approximation for functions with a

derivative of bounded variation. In the present paper we construct a bivariate generalization of

these operators and study a weighted Korovkin-type theorem. The rate of approximation is

examined by means of the complete and partial modululi of continuity. Using Steklov means,

the order of approximation is studied with the aid of the mixed modulus of smoothness and the

modulus of smoothness of first and second order. The rate of convergence for bivariate Lipschitz

class functions is also studied. Some direct results in weighted approximation are also obtained.

Lastly, we introduce a generalization of these operators for bounded and uniformly continuous

functions in Rm+ and study the degree of approximation by means of modulus of continuity.

References:

1. S. Sucu: Dunkl analogue of Szasz operator. Appl. Math. Comput. 244 (2014), 42-48.

2. A. Wa ; N. Rao: Szasz-Gamma operators based on Dunkl analogue. Iran. J. Sci. Technol. Sci.

43 (2019), 213-223.




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14

On (P,Q)-Lucas Polynomial coefficients for a New Class of Bi-Univalent

Functions Given by Subordination

Arzu Akgül

Department of Mathematics, KocaeliUniversity,

Kocaeli,Turkey

[email protected]

Abstract: Recently, Lucas polynomials, Fibonacci polynomials, Chebyshev polynomials, Pell

polynomials and other special polynomials became importance in the field of Geometric

Function Theory. In this study, by using this polynomials, subordination , we investigate a new

class of bi-univalent functions and obtained coefficient estimates for this new class.

Keywords:

(P,Q)-Lucas polynomials, Coefficient bounds, Bi-univalent functions,

Subordination.

References:

[1] A. Akgul, Identification of initial Taylor-Maclaurin coefficients for generalized subclasses

of bi-univalent functions, Sahand Communications in Mathematical Analysis (SCMA),

University of Maragheh, 11(1), (2018), 133-143.

[2] A. Akgul, The Fekete-Szegö coefficient inequality for a new class of m-fold symmetrıc bı-

unıvalent functıons satisfying subordınatıon condition, Honam Mathematical Journal, Korea

Science, 70(4) , (2018), 733-748.

[3] A. Akgul, Coefficient estimates for certain subclass of bi-univalent functions obtained with

polylogarithms, Mathematıcal Scıences and Applıcatıons E-Notes, An ınternational Electronic

Journal , 6 (1) (2018), 70-76.

[4] A. Akgul, Certain inequalities for a general class of analytic and bi-univalent functions,

Sahand Communications in Mathematical Analysis (SCMA) Vol. 14 No. 1 (2019), 1-13.

[5] A. Akgul, Second-order differential subordinations on a class of analytic functions defined

by the Rafid-Operator, Ukrainian Mathematical Journal, (70)(5), October, 2018 (Ukrainian

Original Vol. 70, No. 5, May, 2018),673-686.

[6] A. Özkoç, A. Porsuk, A note for the (p, q)-Fibonacci and Lucas quarternion polynomials.

Konuralp J. Math. 5, (2017), 36-46 .

[7] Ş. Altınkaya, S. Yalçın, On the (p, q)-Lucas polynomial coefficient bounds of the bi-

univalent function class, Boletín de la Sociedad Matemática Mexicana, (2018), pp.1-9.

[8] D. A. Brannan, T. S. Taha, On some classes of bi-univalent functions, Studia Univ. Babes¸-

Bolyai Math., 31 (1986), 70-77.

[9] H. Aldweby, M. Darus, Some Subordination Results on q-Analogue of Ruscheweyh

Differential Operator, Abstr. Appl. Anal., 2014 (2014), 6 pages. 1

[10] P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften,

Springer, New York, USA 259 (1983).

[11] P. Filipponi, A.F Horadam, Derivative sequences of Fibonacci and Lucas polynomials. In:

Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds.) Applications of Fibonacci Numbers, vol.

4, pp. 99-108. Kluwer Academic Publishers, Dordrecht (1991)




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15

The Arithmetic–Geometric Mean Inequalities

Hawari -Mohammad Al

Irbid National University, Jordan, Irbid

[email protected]: -E

Abstract: In this article, we will present some inequalities of the arithmetic–geometric mean

inequality with a different method based on some other inequalities .

Keywords: Heron mean; Young’s inequality; the geometric mean, the arithmetic mean.

References:

[1] Choi D.I. Inequalities related to Heron means for positive operators. J. Math.

Inequal.2017;11(1):217–223. doi: 10.7153/jmi-11-21. [CrossRef]

[2] Hirzallah O., Kittaneh F. Matrix Young inequalities for the Hilbert–Schmidt norm. Linear

Algebra Appl. 2000;308(1):77–84. doi: 10.1016/S0024-3795(99)00270-0. [CrossRef]

[3] Kittaneh F., Manasrah Y. Reverse Young and Heinz inequalities for matrices. J. Math. Anal.

Appl. 2010;361(1):262–269. doi: 10.1016/j.jmaa.2009.08.059. [CrossRef]

[4] Kittaneh F., Manasrah Y, Reverse Young and Heinz inequalities for matrices, Linear

Multilinear Algebra., 59, (2011), 1031–1037.

[5] Zhao J., Wu J. Operator inequalities involving improved Young and its reverse inequalities.J.

Math. Anal. Appl. 2015; 421(2): 1779–1789. doi:10.1016/j.jmaa. 2014.08.032. [CrossRef]


https://dx.doi.org/10.7153%2Fjmi-11-21

https://dx.doi.org/10.1016%2FS0024-3795(99)00270-0

https://dx.doi.org/10.1016%2Fj.jmaa.2009.08.059

https://dx.doi.org/10.1016%2Fj.jmaa.2014.08.032




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16

Characterization of rough weighted Norlund-Euler statistical limit set

Ekrem Aljimi (Alimi)

University of ”Kadri Zeka”, Faculty of Computer Science, St.”Zija Shemsiu” pn. 60000 Gjilan, Republic

of Kosova

[email protected]

Valdete Loku

University of Applied Sciences Ferizaj, St. Universiteti, p.n. 70000 Ferizaj, Republic of Kosova

Abstract: Our focus is to generalize the definition of the weighted Norlund-Euler statistical

convergence in a wider range of the weighted Norlund-Euler sequence {𝑝𝑛}𝑛∈𝛮 𝑎𝑛𝑑 {𝑞𝑛}𝑛∈𝛮 .

We extend the concept of weighted Norlund-Euler statistical convergence and rough statistical

convergence to renovate a new concept namely, rough weighted Norlund-Euler statistical

convergence. On a continuation we also define rough weighted Norlund-Euler statistical limit

set. We investigate whether the above mentioned three results are satisfied for rough weighted

statistical limit set or not? Answer is no.

So our main objective is to interpret above mentioned different behaviors of the new

convergence and characterize the rough weighted Norlund-Euler statistical limit set. Also we

show that this set satisfies some topological properties like boundedness, compactness, path

connectedness etc.

Keywords: Rough statistical convergence, Weighted Norlund-Euler statistical convergence,

Rough weighted Norlund-Euler statistical convergence, Rough weighted Norlund-Euler

statistical limit set.

References:

[1] Aytar, S.: The rough limit set and the core of a real sequence, Numer. Funct. Anal. Optim.

29(3-4) (2008), 283-290.

[2] Aytar, S.: Rough statistical convergence, Numer. Funct. Anal. Optim. 29(3-4) (2008), 291-

303.

[3] Gecit Akcay, F.Aytar, S.: Rough convergence of a sequence of fuzzy numbers, Bull. Math.

Anal. Appl. 7(4) (2015), 17-23.

[4] Connor, S. J.: The statistical and strong p-Cesaro convergence of sequences, Analysis 8(1-

2) (1988), 47-63.

[5] Pratulananda Das, Sanjoi Ghosal, Avishek Ghosh, Sumit Som. Characterization of rough

weighted statistical limit set , Math. Slovaca 68 (2018), No. 4,881-896.





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17

Generalized Monotone Iterative Techniques for Dynamic Equations with

the Initial Value Problem on Time Scales

Nour Alsharif and Coşkun Yakar

Department of Mathematics, Gebze Technical University,

Kocaeli, Turkey


Abstract: In this article, we develop a generalized monotone iterative technique by using

coupled lower and upper solutions for dynamic initial value problem (IVP) on time scale (T).

We construct monotone iterates which are solutions of dynamic initial value problems(IVP) on

time scale (T). We prove that these sequences converge uniformly and monotonically to extremal

solutions of the problem considered on time scale (T).

Keywords: Time scale(T), Monotone iterative technique, Comparison results, Upper and Lower

solutions, coupled upper and lower solutions, Coupled minimal and maximal solutions.

References:

[1] T. G. Bhaskar and F. A. McRae, “Monotone iterative techniques for nonlinear problems

involving the difference of two monotne functions”, Appl. Math. Comput. 133(2002), 187-192.

[2] Z.Denton and A.S.Vatsala, “Monotone iterative technique for finite systems of nonlinear

Riemann-Liouville fractional differential equations”,Opuscula Mathematica,31(2011),327–339.

[3] B. Kaymakcalan, “Existence and Comparison Results for Dynamic Systems on Time Scale”,

JMMA 172 (1993), 243-255.

[4] B. Kaymakcalan, “Monotone Iterative Method for Dynamic System on Time scales”, Dys.

Sys. and Appl. 1993, 213-220.

[5] G. S. Ladde, V. Lakshmikantham and A. S. Vatsala, “Monotone Iterative Technique for

Nonlinear Differential Equations”, Pitman Publishing Inc. Boston, 1985.

[6] V. Lakshmikantham and A.S. Vatsala, “Generalized Quasilinearization and Nonlinear

Problems”, 440(1998).

[7] M. Bohner and A. Peterson, “Advances in dynamic equations on time scales”, Birkh¨auser

Boston. Boston. MA. 2003.

[8] F.A. McRae, “Monotone iterative technique and existence results for fractional differential

Equations”, Nonlinear Analysis: Theory, Methods and Applications. 71(2009), 6093-6096.

[9] J. D. Ram´ırez and A. S. Vatsala, “Generalized monotone method for Caputo fractional

differential equation with periodic boundary condition”, In Proceedings of Neural, Parallel and

Scientific Computations, Dynamic. Atlanta. Ga. USA. 4(2010), 332–337.

[10] I. H. West and A. S. Vatsala, “Generalized monotone iterative method for integro-

differential equations with periodic boundary conditions”, Mathematical Inequalities

Applications, 10(2007), 151–163.

[11] I. H. West and A. S. Vatsala, “Generalized Monotone Iterative Method for Initial Value

Problem”, Appl. Math. Lett. 17(2004), 1231-1237.

[12] C. Yakar and A. Yakar, “Monotone Iterative Techniques for Fractional order Differential

Equations with Initial Time Difference”, Hacettepe Journal of Mathematics and Statistics, 2011,

331-340.





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18

Chain level proof for the isomorphism between

Lie and Hochschild homologies

Zuhier Altawallbeh

Department of Mathematics, Tafila Technical University,

Tafila, Jordan

[email protected]

Abstract: In this paper, we prove the commutativity of the square in the chain level of both

complexes Chevally Elinberge complexe of Lie homology and Hochschild complex and the

antisymmetrization map in between depending fully in the chain level. Originally, Loday [ 1]

proved this isomorphisim by constructing a certain map satisfying relations of a presimplicial

homotopy to prove the commutativity of the square that mentioned above. Here, we present a

difference approach for the proof of the commutativity without constructing that certain map

satisfying the relations of the presemlicial homotopy. Different authors used the induced

isomorphism between the Lie homology and Hochschild homology as result as Lodder [ 2] and

Altawallbeh in [3] and [4].

Keywords: Chain level complex, Hochschild homology, Lie homology.

References:

[1] J. L. Loday, “Cyclic Homology”, 2nd edition Grundlehlren. Math. Woss. 301 Springer-

Verlag. Berlin, (1998).

[2] J. Lodder, “A structure theorem for Liebniz homology”, Journal of algebra, 355(2012), 93-

110.

[3] Z. Altawallbeh, “Liebniz and Hochschild homology”, Communications in algebra,

46.1(2018), 62-68.

[4] Z. Altawallbeh, “Calculations on Lie Algebra of the group of Affine symplectomorphisms”,

Advances in mathematical physics, (2017).





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19

Approximate Solutions for Nonlinear Second order Differential Equation

by using Reprodusing Kernel Hilbert Space Method

Ali Ateiwi

Department of Mathematics, AL-Hussein Bin Talal University,

Ma'an, Jordan

[email protected]

Abstract: Second-order boundary value problems (BVPs) for ordinary differential equations are

encountered very often in applied mathematics, physics and engineering such as atomic

calculations, gas dynamics, and so on [1,2]. Recently, nonlinear second-order periodic BVPs,

which consist of second-order ordinary differential equations combined with periodic boundary

conditions, have been vastly studied due to their broad range of application. [3,4] But those BVPs

do not always have solutions which can be obtained using analytical methods, and must be

approached with various approximate and numerical methods.The reproducing kernel has been

effectively used as a base for constructing numerical solutions to applied sciences and various

other important applications.

Keywords:Reproducing Kernel Hilbert Space,Sobolev Space,Analytic Approximate Solutions.

References:

[1] F.M Atici. and G.S Guseinov. On the existence of positive solutions for nonlinear differential

equations with periodic boundary conditions, Journal of Computational and Applied

Mathematics, 132(2001),341-356.

[2] F. Li. and Z . Liang Existence of positive periodic solutions to nonlinear second-order

differential equations, Applied Mathematics Letters ,18(2005), 1256-1264.

[3] I . Komashynska. and M . Al-Smadi. Iterative Reproducing Kernel Method for Solving

Second-Order Integrodifferential Equations of Fredholm Type. Journal of Applied Mathematics,

Article ID 459509, (2014). 11 pages.

[4] A. Al e'damat, M. Al-Smadi, I. Komashynska, A. M. Ateiwi and A . Alrawajfi, "Analytical-

Numerical Solutions for First Order Periodic Boundary Value Problems Using the Reproducing

Kernel Algorithm".Differential and Difference Equations with Applications Springer

Proceedings in Mathematics & Statistics 164(2016), DOI 10.1007/978-3- 319-32857-7_2, pp. 9

– 23.





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20

Notes on nullnorms on an arbitrary bounded lattice Emel Aşıcı

Faculty of Technology, Department of Software Engineering,

Karadeniz Technical University, Trabzon, Turkey

[email protected]

Abstract: Triangular norms (t-norms) and triangular conorms (t-conorms) were introduced by

Schweizer and Sklar [1]. Later, t-operators were defined by Mas et al. in [5], and nullnorms by

Calvo et al. in [2]. Nullnorms generalize both t-norms and t-conorms, and they can be seen as a

particular ordinal sum of a t-conorm and a t-norm. Being characterized by an annihilator (zero

element) 𝑎 from [0,1], t-norms are related to 𝑎 = 0, while t-conorms are characterized by 𝑎 =

1. Nullnorms have numerous applications in different field, such as fuzzy logics, expert systems,

decision making, image processing, etc. One of the earliest applications of idempotent

nullnorms, known also as 𝑎-medians, appeared in the framework of decision making in a fuzzy

environment, see [4] see also [3]. The order comprising the 𝐹-partial order obtained from the

nullnorm were defined by [1]. In this paper, we investigate a partial order induced by a nullnorm

𝐹 on a bounded lattice 𝐿 introduced by [1]. Thus, the 𝑇-partial order obtained from the t-norm

and the 𝑆-partial order obtained from the t-conorm are extended to a more general form.

Keywords: Nullnorm, bounded lattice, partial order

References:

[1] E. Aşıcı, “An order induced by nullnorms and its properties”, Fuzzy Sets Syst. 325 (2017),

35-46.

[2] 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.

[3] J. Fodor, An extension of Fung-Fu theorem, “Internat. J. Uncertain. Fuzziness Knowledge-

Based Systems”, 4 (1996), 235-243.

[4] L. Fung and K. Fu, “An axiomatic approach to rational decision-making in a fuzzy

environment, K. Tanaka et al. eds., Fuzzy Sets and their Applications to Cognitive and Decision

Processes, Academic Press, New York, 1975, pp. 227-256.

[5] M. Mas, G. Mayor and J. Torrens, “t-operators”, Int. J. Uncertain. Fuzz. Knowl.-Based Syst.

7 (1999), 31-50.

[6] B. Schweizer and A. Sklar, “Statistical metric spaces”, Pacific J. Math. 10 (1960), 313-334.





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21

Predation of aristeus antennatus in protected and unprotected

fishing area

Nossaiba Baba, Imane Agmour, Youssef EL Foutayeni and Naceur Achtaich

Analysis, Modeling and Simulation Laboratory, Hassan II University,

Casablanca, Morocco

[email protected]

Abstract: This paper describes a prey-predator type fishery model with prey dispersal in a two-

patch environment, one of which is a free fishing zone and other is protected zone. The objective

of the paper is studying the existence and the stability of the equilibrium points by using

eigenvalues analysis. The importance of marine reserve is analyzed through the obtained results

of the numerical simulations of proposed model system. The results depict that reserves will be

most effective when coupled with harvesting controls in adjacent fisheries.

Keywords:

Mathematical model; Prey-predator model; Sustainable management of the resources; Marine

protected areas; Fish populations.

References:

[1] K. S. Chaudhuri, A bioeconomic model of harvesting a multispecies fishery, Ecol. Model,

32 (1986) 267-279

[2] K. S. Chaudhuri, Dynamic optimization of combined harvesting of a two species fishery,

Ecol. Model., 41 (1987) 17-25.

[3] P.D.N. Srinivasu, I.L. Gayatri, Influence of prey reserve capacity on predator prey

dynamics, Ecological Modelling 181 (2005) 191-202.

[4] Y. ELFoutayeni, M. Khaladi, A. ZEGZOUTI, Profit maximization of fishermen exploiting

two fish species in competition, Amer. J. Comput. Appl. Math. to appear.

[5] Y. ELFoutayeni, M. Khaladi, A. ZEGZOUTI, A generalized Nash equilibrium for a

bioeconomic porblem of fishing,Studia Informatica Universalis-Hermann, 10 (2012) 186-204.

[6] T.K. Kar, K. Chakraborty, Marine reserves and its consequences as a fisheries management

tool, World Journal of Modelling and Simulation 5 (2) (2009) 83-95.

[7] D. Ami, P. Cartigny, A. Rapaport, Can marine protected areas enhance both economic and

biological situations, C R. Biologies 328 (2005) 357-366.





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22

Parametric generalization of α-Bernstein Operators

Behar Baxhaku

Department of Mathematics, University of Pristina,

Kosova

[email protected]

Abstract: In the present paper we construct a sequence of generalized Bernstein operators based

on an infinitely differentiable function τ(x) satisfying the conditions τ(0) = 0, τ’(x) > 0, for all x

∈ [0,1]. The rate of convergence of new operators via a Peetre 𝒦-functional and corresponding

modulus of smoothness, quantitative Voronovskaya type theorem and Grüss–Voronovskaya type

theorem in quantitative mean are discussed. . Further, we also investigate the approximation of

functions with derivatives of bounded variation. Finally, the graphic for new operators with

special cases and for some values of n is also presented.

Keywords: Bernstein operators, modulus of smootness., bounded variation.

References:

[1] T. Acar, Asymptotic formulas for generalized SzszMirakyan operators. Appl. Math. Comput., 263

(2015), 233-239.

[2] S. Bernstein, Demo istration du theoreme de Weierstrass fondee sur le calcul des probabilites.Comm.

Soc. Math. Charkow S´er, 13(1)(1912), 1-2.

[3] X. Chen, J. Tan, Z. Liu and J. Xie, Approximation of functions by a new family of generalized Bernstein

operators, J. Math. Anal. Appll. 450(2017) 244-261.

[4] H. H. Gonska and R. K. Kovacheva, The second order modulus revisited: remarks, applications,

problems. Universit di Bari. (1994).

[5] H. Gonska, On the degree of approximation in Voronovskajas theorem, Studia Univ. Babe¸s-Bolyai,

Mathematica 52, 3 (2007), 103116.

[6] J. King, Positive linear operators which preserve x 2, Acta Math. Hungar. 99(3) (2003), 203-208.

[7] D. C´ardenas-Morales, P. Garrancho, and F. J. Munoz-Delgado, Shape preserving approximation by

Bernstein-type operators which fix polynomials, Appl. Math. Comput. 182(2)(2006), 1615-1622.





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23

Approximation of functions by Generalized Lototsky-Bernstein type

Operators Erdem Baytunç

Eastern Mediterrenian University,

Faculty of Arts and sciences, Department of Mathematics

Gazimağusa, North Cyprus.

[email protected]

Mehmet Salih Atamert




[email protected]

Halil Gezer

Department of Basic Science and Humanities, Cyprus International University,

Haspolat, Cyprus.

[email protected]

Hüseyin Aktuğlu




[email protected]

Abstract: Recently, α-Bernstein Polynomials are introduced and discuss in [1]. In this paper we

introduced a generalization of Lototsky matrices and the corresponding generalized Lototsky –

Bernstein type positive linear operators. The operators introduced here is a non-trivial

generalization of both Bernstein polynomials and α-Bernstein Polynomials. We also studied

some approximation properties of these operators.

Keywords: Lototsky Matrices, Jayasri Matrices, Bernstein Polinomials.

References:

[1]

X. Chen, J. Tan, Z. Liu and J. Xie, Approximation of functions by a new family of

generalized Bernstein Polynomials. J. Math. Anal. Appl., 450 (2017) 244-261.




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24

Behavior of new models of hybrid conjugate gradient algorithm Mohammed Belloufi 1, Badreddine Sellami 1, Yacine Chaib 1

1 Laboratory Informatics and Mathematics (LiM)

Mohamed Cherif Messaadia University

Souk Ahras, 41000, Algeria.

[email protected]

Abstract: In this paper, another hybrid conjugate gradient algorithm is subject to analysis. Under

suitable conditions, we prove that the proposed methods converge globally for general

nonconvex functions. Numerical comparisons with some conjugate gradient algorithms using a

set of 750 unconstrained optimization problems, some of them from the CUTE library, show that

the present hybrid conjugate gradient algorithm of ten behaves better than some known

algorithms.

Keywords: Unconstrained optimization, Conjugate gradient method, Numerical comparisons;

Sufficient descent condition.

References:

[1] A. Y. Al-Bayati, M. S. Al-Salih and M. M. M. Ali, A Modified Family of CG-Algorithm

with a New Closed-Form Line-Search Procedure, Australian Journal of Basic & Applied

Sciences, 7 (2013), 214-220.

[2] N. Andrei, An unconstrained optimization test functions collection, Advanced Modeling and

Optimization, 10 (2008), 147-161.

[3] N. Andrei, Another hybrid conjugate gradient algorithm for unconstrained optimization,

Numer. Algorithms 47 (2008) 143–156.

[4] E. D. Dolan and J. J. Mor, Benchmarking optimization software with performance profiles,

Mathematical Programming, 91 (2002), 201-213.

[5] D. Touati-Ahmed, C. Storey, Efficient hybrid conjugate gradient techniques, J. Optim.

Theory Appl. 64 (1990) 379–397.





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25

Extremal Graphs for a Bound on the Roman Domination Number

Ahmed Bouchou¹, Mostafa Blidia² and Mustapha Chellali²

¹University of Médéa, Algeria.

[email protected]

2University of Blida, Algeria

[email protected];[email protected]

Abstract: A Roman dominating function on a graph G = (V,E) is a function f :V→{0,1,2} such

that every vertex u for which f(u) = 0 is adjacent to at least one vertex v with f(v) = 2. The weight

of a Roman dominating function is the value w(f) = ∑u∈Vf(u). The minimum weight of a Roman

dominating function on a graph G is called the Roman domination number of G, denoted by

R(G). In 2009, Chambers, Kinnersley, Prince and West [2], proved that for any graph G with n

vertices and maximum degree , R(G) ≤ n+1-. In this paper, we give a characterization of

graphs attaining the previous bound including trees, regular and semiregular graphs. Moreover,

we prove that the problem of deciding whether R(G) = n + 1 - is co-NP-complete. Finally, we

provide a characterization of extremal graphs of a Nordhaus-Gaddum bound for R(G) + R(�̅�),

where �̅� is the complement graph of G.

Keywords: Roman domination, Roman domination number, Nordhaus-Gaddum inequalities.

References:

[1] E. W. Chambers, B. Kinnersley, N. Prince and D. B. West, Extremal problems for Roman

domination. SIAM J. Discreter. Math. 23 (2009) 1575-1586.

[2] E. J. Cockayne, P. A. Dreyer Jr., S. M. Hedetniemi and S. T. Hedetniemi, Roman domination

in graphs. Discrete Math. 278 (2004) 11-22.

[3] B.P. Mobaraky and S.M. Sheikholeslami, Bounds on Roman domination numbers of graphs.

Matematiqki Vesnik 60 (2008) 247-253.

[4] I. Stewart, Defend the Roman Empire!. Sci. Amer. 281 (6) (1999) 136-139.





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26

Some properties of Baskakov-Schurer-Szasz operators via power

summability methods

Naim Braha

Department of Mathematics and Computer Sciences, University of Prishtina

Avenue Mother Teresa, No-5, Prishtine, 10000,Kosova

[email protected]

Abstract: In this presentation we will give the Korovkin type theorem for Baskakov-Schurer-

Sz\'asz operators via the $A-$statistical convergence and the power summability method. Also

we give the rate of the convergence related to the above summability method and in the last

section we give a kind of Voronovskaya type theorem for the $A-$ statistical convergence and

Gr\"uss-Voronovskaya type theorem.

Keywords: $A-$ statistical convergence, Baskakov-Schurer-Sz\'asz operators, power

summability method, Korovkin type theorem, Voronovskaya type theorem, rate of convergence,

Gr\"uss-Voronovskaya

References:

T. Acar, (p,q)-Generalization of Szasz-Mirakyan operators, Math. Methods in the Appl.

Sciences, 39 (10), 2016, 2685-2695.

T. Acar, S.A. Mohiuddine, M. Mursaleen, Approximation by (p,q)-Baskakov-Durrmeyer-

Stancu operators, Comp. Anal. Op. Theo, 12(6), 2018, 1453-1468.

T. Acar, A. Aral, M. Mursaleen, Approximation by Baskakov-Durrmeyer operators based on

(p,q)-integers, Math. Slovaca, 68 (4), 2018, 897-906.

O.G. Atlihan, M. Unver, O. Duman, Korovkin theorems on weighted spaces: revisited. Period.

Math. Hungar. 75 (2017), no. 2, 201-209.

F. Basar, Summability theory and its applications, B\"{u}y\"{u}k\c{c}ekmece, Istanbul, 2011.

J. Boos, Classical and Modern Methods in Summability. Oxford University Press, Oxford

(2000).

N.L. Braha, Some weighted Equi-Statistical convergence and Korovkin type-theorem, Results

Math. 70 (2016), no. 3-4, 433-446.

N.L. Braha, Valdete Loku, H.M. Srivastava, $\Lambda^2-$Weighted statistical convergence

and Korovkin and Voronovskaya type theorems, Appl. Math. Comput. 266 (2015), 675-686.

N.L. Braha, H. M. Srivastava and S. A. Mohiuddine, A Korovkin Type Approximation

Theorem for Periodic Functions via the Summability of the Modified de la Vallee Poussin

Mean, Appl. Math. Comput. 228 (2014), 162-169.

N.L. Braha, Some properties of New Modified Sz\'asz-Mirakyan operators in polynomial

weight spaces via power summability method, Bull. Math. Anal. Appl. 10 (2018), no. 3, 53-65.

M. Bodur, O. G. Yilmaz, and A. Aral, Approximation by Baskakov-Szász-Stancu Operators

Preserving Exponential Functions, Constructive Mathematical Analysis, 1 (1), 2018, 1-8.

O. Duman, M.K. Khan, C. Orhan, A-Statistical convergence of approximating operators. Math.

Inequal. Appl. 6, 689-699 (2003)





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27

Complex and Real Optical soliton Solution of the Time Fractional

Resonant Davey-Stewartson Equations

Hasan Bulut1 and Hajar F. Ismael*,1

1Department of Mathematics, Firat University, Elazig, Turkey

[email protected] *Department of Mathematics, University of Zakho, Zakho, Iraq

[email protected]

Abstract: In this study, via the Bernoulli sub-equation [1], the analytical traveling wave

solution of the (2+1)-dimensional resonant Davey-Stewartson system is investigated. At the

begining, based on the Riemann-Liouville fractional derivative [2], the time-fractionalthe

imaginary (2+1)-dimensional resonant Davey-Stewatson equation [3] by using travelling wave

is changed into a nonlinear differential system. The homogeneous balance method between the

highest power terms and the highest derivative of the ordinary differential equation is authorized

on resultant outcome equation, and finally the ordinary differential equations are solved in order

to obtain some new exact solutions. Different cases as well as different values of physical

constants are used to investigate the optical soliton solutions of the resulting system. The

outcomes result of this study are shown in 3D dimensions and contour solution via Wolfram

Mathematica Package.

Keywords: Bernoulli sub-equation, Riemann-Liouville fractional, resonant Davey-Stewatson

equation.

References:

[1] H. M. Baskonus and H. Bulut, “On the complex structures of Kundu-Eckhaus equation

via improved Bernoulli sub-equation function method,” Waves in Random and

Complex Media, 2015.

[2] S. Koonprasert, S. Sirisubtawee, and S. Ampun, “More Explicit Solitary Solutions of

the Space-Time Fractional Fifth Order Nonlinear Sawada-Kotera Equation via the

Improved Generalized Riccati Equation Mapping Method,” 2017.

[3] M. F. Aghdaei and J. Manafian, “Optical soliton wave solutions to the resonant davey-

stewartson system,” Opt. Quantum Electron., 2016.




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28

Some Fixed Point and Best Proximity Point Results on −Admissible

Mappings via Simulation Functions

Abdurrahman Büyükkaya1, Mahpeyker Öztürk2

1. Department of Mathematics, Sakarya University, Sakarya, Turkey

[email protected]

2. Department of Mathematics,Karadeniz Technical University, Trabzon, Turkey

[email protected]

Abstract: In this article, we defined -contraction mappings involving -admissible

mappings of type 𝐹 via simulation functions and we establish common fixed point and best

proximity point theorems in the stting of metric spaces.

Keywords: Fixed Point, Simulation Function, -contraction, Type 𝐹, 𝛼-admissible mappings

References:

[1] S. Banach, Sur les operations dans les emsembles abstraits et leurs applications aux equation

sintegrales, Fund. Math., 1 (2012), 133-181.

[2] F. Khojasteh, S. Shukla, S. Radenovic, A new approach to the study of fixed point theorems

for simulation functions. Filomat, 29(2015), 1189-1194.

[3] A. Fulga, E. Karapınar, Some results on S-contractions of Type E, Mathematics, 195(6)

(2018), 1-9.

[4] E. Karapınar, Fixed Points Results via Simulation Functions, Filomat, 30(8) (2016), 2343-

2350.

[5] E. Karapınar, F. Khojasteh, An approach to best proximity points results via simulation

functions, J. Fixed Point Theory Appl. 19 (2017) 1983-1995.

[6] S. Sadiq Basha, N. Shahzad, Best proximity point theorems for generalized proximal

contractions, Fixed Point Theory and Applications, 42 (2012), 1-9.





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29

Comparison for Covariance Matrices of Predictors in General Linear

Mixed Model Melek Eriş Büyükkaya

Department of Statistics and Computer Sciences, Karadeniz Technical University, Trabzon, Turkey

[email protected]

Nesrin Güler

Department of Statistics, Sakarya University, Sakarya, Turkey

[email protected]

Abstract: General linear mixed models that include both fixed and random effects are used in

many statistical applications in a variety of fields. One of the main topics in linear models is to

predict or/and estimate all unknown parameters in the model. Best Linear Unbiased Predictors

(BLUPs) of unknown parameters are commonly used for statistical inferences from the model.

BLUPs of unknown parameters are based on minimum covariance matrices structure according

to Löwner partial ordering among all linear unbiased predictors. Matrix algebra is commonly

used for the characterization of predictors and comparison of their properties under linear mixed

models. Especially, some rank and inertia formulas of matrices are simplified some complicated

matrix expressions for the characterizations and they also provide building some inequalities and

equalities occurred in the comparison of the covariance matrices of predictors.

In this study, a general linear mixed model is considered with assuming correlated random

effects. Our main purpose is to establish some comparisons for covariance matrices of the BLUPs

of mixed effects which are combination of fixed and random effects. Some equalities and

inequalities based on ranks and inertias of matrices for the BLUPs of predictable mixed effects

under the model are given to compare them with the other types of predictor. There is an

extensive literature on linear mixed models which include the BLUPs of predictable mixed

effects and their properties, see, e.g., [1,2,5], inertias and ranks of symmetric matrices and

relations between inertias and Löwner partial ordering of symmetric matrices, see, e.g., [2-4,9],

rank and inertia formulas for covariance matrices of predictors/estimator see, e.g., [6-8].

Keywords: Best linear unbiased predictor (BLUP), General linear mixed model, Inertia, Rank.

References:

[1] Q. W. Wang and X. Liu, The equalities of BLUPs for linear combinations under two general

linear mixed models, Communications in Statistics – Theory and Methods, (2013), vol. 42(19),

pp. 3528-3543.

[2] S. J. Haslett and S. Puntanen, On the equality of the BLUPs under two linear mixed models,

Metrika, (2011), vol. 74(3), pp. 381–395.

[3] Y. Tian, Equalities and inequalities for inertias of hermitian matrices with applications,

Linear Algebra Appl., (2010), vol. 433(1), pp. 263-296.

[4] Y. Tian, Solving optimization problems on ranks and inertias of some constrained nonlinear

matrix functions via an algebraic linearization method. Nonlinear Analysis,(2012),75, 717-734.

[5] Y. Tian, A new derivation of BLUPs under random-effects model, Metrika, (2015), vol. 78

(8), pp. 905-918.





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30

Approximation of Nuclear Reaction Cross Section Data

Using Machine Learning Algorithm Veli Capali

Department of Material Science and Nanotechnology, Usak University,

Usak, Turkey

[email protected]

Abstract: The In this study; discusses the using machine learning algorithm for approximation

of data such as the nuclear reaction cross sections data. The rate of approximation of the fitting

criteria is determined by using the experimental and evaluated data. The some reactions cross-

section are calculated from data obtained using machine learning algorithm. The results show

the effectiveness and applicability of this new technique in the calculation of the some nuclear

reactions.

Keywords: Nuclear reaction cross section, Machine learning algorithm





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31

A Study on Utilization of 2 Analysis in Text Analytics Studies

Muhammed Işık

Applied Mathematics and Computational Sciences, Istanbul Medeniyet University,

Istanbul, Turkey

Elif Cesur

Industrial Engineering Department, Istanbul Medeniyet University,

Istanbul, Turkey

[email protected]

Abstract:

Text analytics method has been becoming very populer in various field such as emotion analysis

and removing subject from texts. It could be possible both to know customer approaches, prefers

and needs with this method and to rearrange particular strategies based on acquired results.

Analysis studies such as the 2 test are known as feature extraction studies and these studies

are used in various fields such as classification and clustering. Specially, 2 test is a method

utilized to determine the relationship between two variables statistically. Within the scope of this

study, 2 test is used in text analytics to find out whether there is a relationship between the

words that make up the text and the notes assigned to these texts. Customer comments will be

broken down into the words that form them. After the decomposition process, the existence of

the relationship between the words and the labels of the comments will be tested.

Keywords: 2 Test, Text Analytic, Customer Comments, Feature Extraction




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32

Fixed Point Results For f -Contraction Mappings Satisfying B -

Contractions in Modular Spaces

Şeyda Çakar, Mahpeyker Öztürk

Department of Mathematics, Sakarya University,

Sakarya, Turkey


Abstract: By using the concepts in fixed point theory of Beiranvand et al. [5], Berinde [2]- Rus

[3] and Van An et al. [4], we introduce the notion of fB -contractions in modular spaces. In this

framework, we establish the existence theorems of common fixed points for such mappings.

Also, we obtain some fixed point theorems for mappings satisfying integral type contractive

conditions.

Keyword: Fixed Point, Modular Space; B -Contraction; f -Contraction; Integral Type

Contraction.

References:

[1] J. Chen, Z. Li, Common fixed-points for Banach operator pairs in best approximation, J.

Math. Anal. Appl., 336 (2007), 1466-1475.

[2] V. Berinde, Contractii generalizate si aplicatii, Vol 2 , Editura Cub Press, Baia Mare,

Romania, (1997).

[3] I.A. Rus, Generalized contractions and applications, Cluj University Press, Cluj-Napoca,

Romania, (2001).

[4] T. Van An, N. Van Dung, V. Le Hang, General fixed point theorems on metric spaces and

2-metric spaces. Filomat, 28(10) (2014), 2037-2045.

[5] A. Beiranvand, S. Moradi, M. Omid, H. Pazandeh, Two fixed-point theorems for special

mappings, arXiv:0903.1504v1.





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33

Developing a route choice model based on fuzzy logic

in public transport system

Buket Çapalı

Department of Civil Engineering, Suleyman Demirel University, Isparta, Turkey

[email protected]

Abstract: Passengers want to have short travel time and waiting time when traveling by public

transport. The short waiting time depends on the frequency of the bus line. Depending on the

duration and frequency of travel, a utility is needed to improve a route choice model. These

utilities can be explained by appropriate fuzzy sets. The route choice model could be based on

the assumption that the perceived frequency values of the bus lines and travel times are "fuzzy".

This study aims to improve route choice model with fuzzy logic in public transport.





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34

Second Order Optimality Conditions for a Semilinear Elliptic Control

Problem of Infinite Order with Pointwise Control Constraints

S. A. El-Zahaby and Samira El-Tamimy

Department of Mathematics, Faculty of Science, Al-Azhar University [For Girls],Nasr City, Cairo, Egypt.

E-mail: [email protected], [email protected]

Abstract: An optimal control problem for semiliner elliptic equation with infinite order is

investigated, where pointwise constaints are given on the control.First order necessary optimality

conditions are derived, second order sufficient optimality condition is established that consider

strongly active constraints.

Keywords: Distributed control, semilinear elliptic equation, infinite order operator, pointwise

control constraint, necessary optimality conditions, second order sufficient optimality conditions

References:

[1] J.F. Bonnans., Second-order analysis for control constrained optimal control problems of

semilinear elliptic systems., Appl. Math. Optim., 38(3 ) (1998), 303–325.

[2] E. Casas, Pontyagins principle for optimal control problems governed by semilinear elliptic

equations, SIAM J.International series of numerical mathematics 118 (1994), 97–114.

[3] E. Casas and M. Mateos, second order optimality conditions for semilinear elliptic control

problems with finitely many state constraints, SIAMJ. Control. Optim. 40 (2002), 1431–1454.

[4] E. Casas, J. C. D. L. Reyes, and F. Tr¨oltzsch, Sufficient second-order optimality conditions

for semilinear control problems with pointwise state constraints, SIAMJ. Optim. 19 (2008), 616–

643.

[5] E. Casas and F. Tr¨oltzsch, Second order necessary and sufficient optimality conditions for

optimization problems and applications to control theory, SIAMJ. Control. Optim. 13 (202),

406–431.

[6] E. Casas, F. Troltzsch, and A. Unger, Second order sufficient optimality conditions for some

stateconstrained control problems of semilinear equations, SIAM J. Control and Optimization

38 (2000), no. 5, 1369–1391.





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35

On the location 𝑏𝑙-domatic number

Noureddine Ikhlef-Eschouf

Department of Mathematics and Computer Sciences, Médéa University,

Médéa, Algeria

[email protected]

Abstract: A location domatic partition P of a graph 𝐺 = (𝑉, 𝐸) is partition of V into classes that

are pairwise disjoint locating dominating sets. Such a partition P is called 𝑏𝑙-maximal if no larger

location domatic partition P′ can be obtained by gathering subsets of some classes of P to form

a new class. The location 𝑏𝑙-domatic number 𝑏𝑑𝑙(G) is the minimum cardinality of a 𝑏𝑙-maximal

location domatic partition of 𝐺. In this paper, we explain some properties of 𝑏𝑙-maximal location

domatic partition, and we provide a characterization of the graphs 𝐺 of order 𝑛 with 𝑏𝑑𝑙(G) +

𝑏𝑑𝑙(Gc) ∈ {n + 1, n, n − 1} as well as those graphs for which 𝑏𝑑𝑙(G)=𝑛

2, where Gc is the

complement graph of 𝐺.

Keywords: b-domatic number, location domatic number, location b-domatic number.

References:

[1] G. J. Chang, The domatic number problem. Discrete Math. 125 (1994), 115-122.

[2] O. Favaron, The b-domatic number of a graph. Discu. Math. Graph Theory 33 (2013), 747-

757.

[3] M. Benatallah, N. Ikhlef Eschouf and M. Mihoubi, On the b-domatic number of graphs.

Discu. Math. Graph Theory. 39 (2019), 313-324.

[4] J. E. Dunbar, T. W. Haynes and M. A. Henning, Nordhaus-Gaddum type results for the

domatic number of a graph. In Combinatorics, Graph Theory, and Algorithms, vols. I, II, New

Issues Press, Kalamazoo (1999), 303-312.

[5] Zelinka : B. Zelinka, Location-domatic number of a graph. Mathematica Bohemica. No. 1,

123 (1998), 67-71.





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36

Oscillation of Fourth-order Differential Equations with Noncanonical

Operators Nagehan Kılınç Geçer1, Pakize Temtek2

1Department of Mathematics, Kırşehir Ahi Evran University,

Kırşehir ,Turkey

[email protected] 2Department of Mathematics, Erciyes University,

Kayseri ,Turkey

[email protected]

Abstract: The oscillation theory was introduced by Sturm in 1836. A lot of works have been

made in this area since this date. For example these references [1-8] are the main books and

papers for the oscillation theory. In this paper, we shall study oscillatory behavior of solutions to

a linear fourth-order delay differential equation. New oscillation criteria for fourth-order delay

differential equations with noncanonical operators will be presented.

Acknowledgments: This work was supported by Kırşehir Ahi Evran University Scientific

Research Projects Coordination Unit. Project Number: FEF.A4.18.028.

Keywords: Oscillation, Nonoscillation, Delay, Fourth-order, Differential equation.

References:

[1] Swanson, C. A., “Comparison and Oscillation Theory of Linear Differential Equations”,

Academic Press, New York and London, (1968), 229pp.

[2] Ladde G. S., Lakshmikantham V., Zhang B. G., “Oscillation theory of differential equations

with deviating arguments”, Monographs and Textbooks in Pure and Applied Mathematics,

Marcel Dekker, Inc., New York, 110(1987).

[3] Gyori I., Ladas G., “Oscillation Theory of Delay Differential Equation with Application”,

Clarendon Press., Oxford, 1991.

[4] Li W. T., Quan H. S., “Oscillation of higher order neutral differential equations with positive

and negative coefficients”, Ann. Different. Equat., 2 (1995), 70-76.

[5] Chuanxi Q., Ladas G., Oscillation in differential equations with positive and negative

coefficients. Can. Math. Bull. 33 (1990), 442-450.

[6] Parhi N., Tripathy A. K., “On oscillatory fourth-order nonlinear neutral differential equations

I”, Math. Slovaca, 54 (2004), 389-410.

[7] Tripathy A. K., Panigrahi S., Basu R., “Oscillation results for fourth-order nonlinear neutral

differential equations with positive and negative coefficients”, Journal of Mathematical

Sciences, 194 (2013), no. 4, 453-471.

[8] Temtek P., Kılınç Geçer N., “Oscillation results for a class of fourth-order nonlinear

differential equations with positive and negative coefficients”, Mathematical Sciences and

Applications E-Notes, 5(1)(2017), 99-107.





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37

Generalized Lototsky and Jayasri matrices with Generelazied Bernstein

Operators Halil Gezer

Department of Basic Science and Humanities, Cyprus International University,

Haspolat, Cyprus.

[email protected]

Hüseyin Aktuğlu

Department of Mathematics, Eastern Mediterrenian University,

Mağusa, Cyprus.

[email protected]

Erdem Baytunҫ

Department of Mathematics, Eastern Mediterrenian University,

Mağusa, Cyprus

[email protected]

Abstract: Jayasri in [1], introduced a generalization of Lototsky matrices and studied some

summability properties of these matrices. In [2], King extended these matrices to construct a

sequence of positive linear operators that contains Bernstein operators as a special case. In this

work we introduce a generalization of Jayasri matrices which includes some well known matrix

methods such as Jayasri, Lototsky, Euler, etc. We use this matrices to define a generalized

Bernstein -Lototsky type operators which includes ordinary Bernstein operators and Bernstein –

Lototsky operators defined in [2] as a special case. We also studied some approximation

properties of this new operators.

Keywords: Lototsky Matrices, Jayasri Matrices, Bernstein Polinomials.

References:

[1]

C. Jayasri, On Generalized Lototsky Summability, Indian J. Pure App. Math., 13(7): 797-

806, 1982.

[2] J. P. King, Jayasri Summability, Indian J. Pure App. Math., 33(6) : 797-806, (2002).

[3] A. V. Lototsky, On a linear transformation of sequences and series,

Ivanov. Gos. Ped. Inst. Uc. Zap. Fiz.-Mat. Nauki 4, 61-91, 1953 (In Russian).





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38

Some fixed point results in non-Archimedean quasi modular metric spaces Ekber Girgin, Mahpeyker Öztürk

Department of Mathematics, Sakarya University,

Sakarya, Turkey


Abstract: In this paper we establish new contractive condition and prove the existence and

uniqueness of fixed point theorems on non-Archimedean quasi modular metric spaces. Our

results generalize and extend various comparable results in the existing literature.

Keywords: non-Archimedean quasi modular metric, Banach contraction principle, Simulation

Function, R-contraction.

References:

[1] E.Girgin, M.Öztürk “(alpha,beta)-psi type contraction in non-Archimedean quasi modular

metric”, Journal of Mathematical Analysis. Math. 10:1, (2019), 19-30.

[2] Antonio Francisco Roldan Lopez de Hiero, N. Shazad ‘’ New fixed point theorem under R-contractions’’, Fixed Point Theory Appl., 2015:98, (2015).

[3] M. Abbas, A. Latif, Y. Suleiman ‘’ Fixed points for cyclic R-contractions and solution of

nonlinear Volterra integro-differantial equations’’, Fixed Point Theory Appl., 2016:61, (2016).

[4] F. Khojasteh, S. Shukla, S. Radenovic ‘’A new approach to the study of fixed point theorems

via simulation functions’’, Filomat, 29:6, (2015), 1189-1194.




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39

Stability of Reduced Functional Differential Inclusions

Nurgül Gökgöz

Department of Mathematics, Çankaya University,

Ankara, Turkey

[email protected]

Abstract: In this work, the results in [1,2] are extended to Functional Differential Inclusions

(FDIs). Firstly, the reduction procedure for the case of FDIs is revised. Then, some stability

theorems related to the reduced FDIs are given.

Keywords: switched systems, functional differential inclusions, nonlinear systems

References:

[1] R. Kamalapurkar, W. Dixon, A. R. Teel. “On Reduction of differential inclusions and

Lyapunov Satbility”, arxiv.

[2] R. Kamalapurkar, J. A. Rosenfeld, A. Parikh, A.R. Teel, W.E. Dixon. “Invariance-Like

resultsfor Nonautonomous Switched Systems” IEEE Transactions on Automatic Control, vol.64,

614-627, 2019.





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40

𝐋∞ as a Dual Space

Banu Güntürk

Faculty of Engineering, Baskent University,

Ankara, Turkey

[email protected]

Bahaettin Cengiz

Faculty of Engineering, Baskent University,

Ankara, Turkey

[email protected]

Abstract: Let (𝑋, 𝒜, 𝜇) be an arbitraray positive measure space, 1 ≤ 𝑝 < ∞ and 𝑞 be such

that 1/𝑝 + 1/𝑞 = 1. For 𝑔 ∈ 𝐿𝑞(𝜇) define 𝜙𝑔(𝑓) = ∫𝑋𝑓𝑔𝑑𝜇, 𝑓 ∈ 𝐿𝑝(𝜇). The mapping 𝑔 → 𝜙𝑔

is a linear isometry of 𝐿𝑞(𝜇) into the dual of 𝐿𝑝(𝜇). It is always surjective if 1 < 𝑝 < ∞, and for

𝑝 = 1 it is also surjective if the measure space is decomposable ([7] or [8]); but in general, it

needn't be so ([11, p.249], [8, p. 349]). If 𝐿∞(𝜇) is a dual space, that is, the dual of some Banach space 𝐸, then 𝐸 must be isometric

to 𝐿¹(𝜇) ([6], [9], [1]). We should also point out that the dual of 𝐿¹(𝜇) is always an 𝐿∞ space of

some measure which may be different from 𝜇 ([3]). In this article we search for some reasonable necessary and sufficient conditions so that 𝐿∞(𝜇)

becomes the dual of 𝐿¹(𝜇). To be more precise, we shall prove the following theorem.

Theorem. Given an arbitrary positive measure space (𝑋, 𝒜, 𝜇). The following conditions are

equivalent:

(i) 𝐿∞(𝜇, ℝ) is the dual of 𝐿¹(𝜇); (ii) 𝐿∞(𝜇, ℝ) is order complete;

(iii) Its maksimal ideal space 𝛺 is extremally disconnected;

(iv) The Boolean algebra 𝒜╱𝜇 (modulo locally null sets) is complete;

(v) The Boolean algebra 𝒦(𝛺) of clopen subsets of 𝛺 is complete;

(vi) 𝐶(𝛺, ℝ) is order complete;

(vii) 𝛺 is hyperstonean.

Keywords: Dual space, measure space, hyperstonean space.

References:

[1] Behrends, E., et al, 1977. 𝐿𝑝-structure in real Banach spaces, Lecture Notes in

Mathematics, 613, Springer-Verlag, Berlin, New-York.

[2] Cambern, M. and Greim, P., 1982. The dual of a space of vector measures, Math. Z. 180,

373-378.

[3] Cengiz, B., 1992. On the duals of Lebesgue-Bochner 𝐿𝑝spaces, Proc. Amer. Soc., 114, 923-

926.

[4] Diestel, J. and Uhl, J. Jr., 1977. Vector Measures, Mathematical Surveys no.15, American

Mathematical Society, Providence, Rhode Island.

[5] Dinculeanu, 1967. Vector Measures, Pergamon Press, New York.





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41

On Numerical Analysis of General Coupled Systems of Time-Space

Fractional Schrödinger Equations

Betul Hicdurmaz

Department of Mathematics, Istanbul Medeniyet University,

Istanbul, Turkey

[email protected]

Abstract: In the present work, some new results on numerical analysis of general coupled

systems of time-space fractional Schrödinger equations are studied with a numerical approach.

One-dimensional and multi-dimensional cases are considered. General coupled systems of

fractional Schrödinger equations is rarely studied ([]-[]). Here, general coupled systems of time-

space fractional Schrödinger equations will be treated by a numerical approach.

Keywords: Numerical analysis, General Coupled system, Time-space fractional Schrödinger

equations.

References:

[1] X. Lü, and M. Peng, Painlév-integrability and explicit solutions of the general two-coupled

nonlinear Schrödinger system in the optical fiber communications, in Nonlinear Dyn, (2013),

Vol. 73, pp. 405-410.

[2] D, S. Wang, D. J. Zhang, and J. Yang, Integrable properties of the general coupled nonlinear

Schrödinger equations, in Journal of Mathematical Physics, (2010), 51, 023510.

[3] Y. Q. Yuan, B. Tian, L. Liu, and Y. Sun, Bright-dark solitons for a set of the general coupled

nonlinear Schrödinger equations in a birefringent fiber, in EPL, (2017), 120, 30001.





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42

On (n,k)-quasi class Q* Operators

Ilmi Hoxha1 and Naim L. Braha2

1Faculty of Education, University of Gjakova "Fehmi Agani", st. "Ismail Qemali" nn Gjakovë, 50000,

Kosovo 2Department of Mathematics and Computer Sciences, University of Prishtinë, st. "George Bush" nn

Prishtinë, 10000, Kosovo

[email protected]

Abstract: Let T be a bounded linear operator on a complex Hilbert space H . In this paper we

introduce a new class of operators: ( ),n k - quasi class *Q operators, superclass of ( ),n k -

quasi paranormal-*- operators. An operator T is said to be ( ),n k - quasi class *Q if it satisfies

( ) ( )2 2 2

* 11

1

k n k kT T x T T x n T xn

+ + +

for all x H and for some nonnegative integers n and k . We will prove the structural and

spectral properties of this class of operators, as well as the spectrum continuity. By means of an

example, we show that if T is an ( ),n k - quasi class *Q then their tensorial product is not

( ),n k - quasi class *Q .

Keywords: ( ),n k - quasi class *Q operators, ( ),n k - quasi paranormal-*- operators, spectrum

continuity.

References:

[1] S. C. Arora and J. K. Thukral, On a class of operators, Glasnik Math. 21 (1986), 381-386.

[2] S. K. Berberian, Approximate proper vectors, Proc. Amer. Math. Soc. 10(1959), 175-182.

[3] T. Furuta, On the Class of Paranormal Operators, Proc. Jap. Acad. (1967), 594-598.

[4] J. K. Han, H. Y. Lee, and W. Y. Lee, Invertible completions of 2x2 upper triangular operator

matrices, Proceedings of the American Mathematical Society, 128 (2000), 119-123.

[5] P. R. Halmos, A Hilbert Space Problem Book, Springer-Verlag, New York, 1982

[6] I. Hoxha and N. L. Braha, A note on k-quasi-*-paranormal operators, Journal of Inequalities

and Applications 2013, 2013:350

[7] I. Hoxha and N. L. Braha, On k-Quasi Class*

nA Operators, Bulletin of Mathematical Analysis

and Applications, Volume 6 Issue1 (2014), Pages 23-33

[8] J. D. Newburgh, The variation of Spectra, Duke Math. J.18 (1951), 165-176.

[9] S. Sanchez-Perales and V. A. Cruz-Barriguete, Continuity of approximate point spectrum on

the algebra B(X), Commun. Korean Math. Soc. 28(2013), No.3, pp. 487-500





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43

On the Fractional Resolvent Families and Fractional

Integro-differential Equations

Mamadsho Ilolov

Center of Innovative Development of Science and New Technologies, Academy of Sciences of the

Republic Tajikistan

Dushanbe, Tajikistan

[email protected]

Abstract: A theory for the abstract fractional Volterra integro-differential equations has been

developed due to its many applications to problems in physics, chemistry, engeneering, and

biology (see, for example [1,2]). In this presentation, we will be conserned with investigation of

existence, uniqueness and some qualitative properties of solutions for the fractional integro-

differential equations by means of an extended notion of fractional resolvent families. The

framework presented in this presentation seems to be very usefull to extend and improve most

of those known results for integrated fractional semigroups, and inteagrated fractional cosine

functions.

Keywords: Fractional resolvent families, Fractional Volterra integro-differential equation,

Existence, Uniqueness

References:

[1] M. Ilolov at. all. Equations of anomalous diffusion of cosmic ray, Volume 236 - The 34th

International Cosmic Ray Conference (ICRC2015) -Cosmic Ray Physics: Theory, Models and

Simulations, (2015), 1-7.

[2] Kh. M. Ahmedov, M. Ilolov, A.M. Ilolov On nonlocal problems of diffusion kinetics of

electrodes. News of the Academy of Sciences of the Republic of Tajikistan. Department of

physical, mathematical, chemical, geological and technical sciences. 1.169 (2017), 35-43.


https://pos.sissa.it/236/

https://pos.sissa.it/236/




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44

Orthogonal Lie Groups and Their Lie Algebras Mehmet Sezgin and Yasemin Işık

Department of Mathematics, Trakya University,

Edirne, Turkey


Abstract: Orthogonal Lie groups and their Lie algebras are expressed. Some of the basic ones,

such as 𝑂(2), 𝑂(3) groups and their Lie algbras are considered. Using representation theory,

the generators of the considering groups and then Casimir operators are given. The solutions to

the eigenvalue equations that are obtained by Casimir operators are obtained.

Keywords: Lie groups, Lie algebras, Casimir operator

References:

[1] N. Ja. Vilenkin and A. U. Klimyk, “Repsresentaiton of Lie Groups and Special Functions”,

Kluwer Academic Publishers, The Netherlands (1991).

[2] A. O. Barut and R. Raczka, “Theory of Group Representations and Applications”, Polish

Scientific Publishers, Warszawa (1980).

[3] E. G. Kalnins and W. Miller, Jr, “Lie Theory and the Wave Equation in the Space Time. I.

The Lorentz Groups”, Journal of Mathematical Physics, 18.1(1977).

[4] M. K. F. Wong, “Representations of Orthogonal Group. I-II. Lowering and Rasing Operators

the Orthogonal Group and Matrix Elements of Generators”, American Institute of Physics,

8(1967).

[5] J. Patera and P. Winternitz, “A New Basis for the Representations of the Rotation Group.

Lame and Heun Polynomials”, J. Math. Phys, 14.8(1973).





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45

Fixed Point Theorem For Generalized Hybird Mapping in Hyperbolic

Metric Spaces Amna Kalsoom

Department of Mathematics & Statistics, International Islamic University,

Islamabad, Pakistan

[email protected]

Abstract: Fixed point theorems for several types of mappings have already been introduced and

developed in different spaces by mathematicians. For instance W. Takahashi have contributed a

lot in the study of nonexpensive mapping [1], nonspreading mapping [2] and hybrid mappings

[3], Takahashi et al. then introduced a broader class of mapping which contains the class of

nonexpensive mapping, nonspreading mapping and hybrid mappings, known as generalized

hybrid mapping [4] and studied fixed point results for the related mapping. Lin et al.[5] extended

the idea of generalized hybrid mapping for CAT(0) spaces and studied fixed point results using

some iteration processes.

In the present article we have extended the idea of generalized hybrid mapping for 2-uniformly

convex hyperbolic metric space and have shown the existence of fixed point using Mann iteration

process.

Keywords:

Uniformly convex metric space, Generalized hybrid mapping, Mann iterative process.

References:

[1]Takahashi, W. (2009). Introduction to nonlinear and convex analysis (pp. iv+-234).

Yokohama: Yokohama Publishers.

[2] Kohsaka, F., & Takahashi, W. (2008). Fixed point theorems for a class of nonlinear

mappings related to maximal monotone operators in Banach spaces. Archiv der Mathematik,

91(2), 166-177.

[3]Takahashi, W. (2010). Fixed point theorems for new nonlinear mappings in a Hilbert space.

J. Nonlinear Convex Anal, 11(1), 79-88.

[4] Kocourek, P., Takahashi, W., & Yao, J. C. (2010). Fixed point theorems and weak

convergence theorems for generalized hybrid mappings in Hilbert spaces. Taiwanese Journal of

Mathematics, 2497-2511.

[5] Lin, L. J., Chuang, C. S., & Yu, Z. T. (2011). Fixed point theorems and del-convergence

theorems for generalized hybrid mappings on CAT (0) spaces. Fixed point theory and

applications, 2011(1), 49.




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46

Permanent Displacements in the Vicinity of a Cylindrical Canyon Covered

with an Anisotropic Layer

Hasan Faik Kara

Department of Civil Engineering, Trakya University,

Edirne, Turkey

[email protected]

Abstract: Permanent surface displacements in the vicinity of a cylindrical canyon due to a strike-

slip fault is studied. Cylindrical coordinates are used in the two-dimensional mathematical

model. The canyon is covered with a cylindrical linear elastic anisotropic layer such that the

shear modulus functionally changes with the radial coordinate. This anisotropic layer is

surrounded by a linear elastic homogeneous half-space. The strike-slip fault is at the interface

between the layer and the half-space. Between each side of the fault, a unit displacement

difference is defined. Governing equations for the half-space domain and the layer domain are

solved analytically by using Finite Fourier Transform. Closed-form solutions are obtained in

terms of infinite series with unknown coefficients. These unknown coefficients are determined

from the boundary conditions. Ultimately, displacement functions are presented in terms of the

problem parameters.

Keywords: Cylindrical Canyon, Anisotropic Layer, Strike-slip Fault, Static Surface

Displacements.

References:

[1] M. D. Trifunac, "Surface motion of a semi-cylindrical alluvial valley for incident plane SH

waves", Bulletin of the Seismological Society of America. 61.6(1971), 1755-1770.

[2] M. D. Trifunac, "Scattering of plane SH waves by a semi‐cylindrical canyon", Earthquake

Engineering & Structural Dynamics. 1.3(1972), 267-281.

[3] H. L. Wong and M. D. Trifunac, "Surface motion of a semi-elliptical alluvial valley for

incident plane SH waves", Bulletin of the Seismological Society of America. 64.5(1974), 1389-

1408.

[4] M. I. Todorovska and V. W. Lee, "Surface motion of shallow circular alluvial valleys for

incident plane SH waves-analytical solution", Soil Dynamics and Earthquake Engineering.

10.4(1991), 192-200.

[5] X. Yuan and Z. P. Liao, "Scattering of plane SH waves by a cylindrical alluvial valley of

circular‐arc cross‐section", Earthquake engineering & structural dynamics. 24.10(1995), 1303-

1313.

[6] T. Le, V. W. Lee VW and M. D. Trifunac, "SH waves in a moon-shaped valley", Soil

Dynamics and Earthquake Engineering. 101(2017), 162-75.

[7] H. F. Kara and M. D. Trifunac, "A note on plane-wave approximation", Soil Dynamics and

Earthquake Engineering. 51(2013), 9-13.




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47

𝑩𝒏-Maximal Operator and High Order Riesz-Bessel Transforms

on variable exponent Lebesgue spaces

Ismail Ekincioglu

Department of Mathematics, Kutahya Dumlupinar University,

Kutahya, Turkey

[email protected]

Esra Kaya

Department of Mathematics, Kutahya Dumlupinar University,

Kutahya, Turkey

[email protected]

Abstract: In this study, we prove the boundedness of the 𝐵𝑛-maximal operator and high order

Riesz-Bessel transforms associated with the Laplace-Bessel differential operator on variable

exponent Lebesgue spaces.

Keywords: Laplace-Bessel differential operator, maximal operator, Riesz-Bessel transform,

Variable exponent Lebesgue spaces,

References:

[1] D. Cruz-Uribe, A. Fiorenza, “Variable Lebesgue spaces”, Foundations and Harmonic

Analysis. Birkhauser (2003).

[2] I. Ekincioglu, “The boundedness of high order Riesz-Bessel transformations generated by

the generalized shift operator in weighted Lebesgue spaces with general weights”, Acta Appl.

Math. 109(2010), 591-598.

[3] V.S. Guliyev, “On maximal function and fractional integral, associated with the Bessel

differential operator”, Math Inequal. Appl. 6(2) (2003), 317-330.

[4] E. Kaya, “Maximal operators related to Laplace-Bessel operators on variable exponent

Lebesgue spaces”, PhD Thesis, Kutahya Dumlupinar University Institute of Science Studies,

(2018).





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48

A Note on Two Parametric Apostol Type Polynomials

Neslihan Kilar and Yilmaz Simsek

Department of Mathematics, Faculty of Science University of Akdeniz TR-07058

Antalya, Turkey

[email protected] and [email protected]

Abstract: The aim of this presentation is to study and survey some properties of some special

numbers and polynomials with their generating functions which have been many applications in

almost all branches of mathematics and other sciences. By using generating functions and

functional equation method, we derive some identities and relations including the Apostol-

Bernoulli polynomials and two parametric kinds of Apostol-Bernoulli polynomials, two

parametric kinds of Apostol-Genocchi polynomials and trigonometric functions. Finally, we give

some remarks and observation on these polynomials and their generating functions.

Keywords: Apostol-Bernoulli polynomials, two parametric Apostol-Bernoulli polynomials, two

parametric Apostol-Genocchi polynomials, Generating function, Functional equation,

Trigonometric function.

References:

[1] H. M. Srivastava, “Some generalizations and basic (or q-) extensions of the Bernoulli, Euler

and Genocchi polynomials”, Appl. Math. Inf. Sci. 5.3(2011), 390–444.

[2] H. M. Srivastava, and J. Choi, “Zeta and q- zeta functions and associated series and

integrals”, Elsevier, Amsterdam, (2012).

[3] H. M. Srivastava, M. Masjed-Jamei and M. R. Beyki, “A parametric type of the Apostol-

Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials”, Appl. Math. Inf. Sci.

12.5(2018), 907–916.

[4] N. Kilar and Y. Simsek, “Relations on Bernoulli and Euler polynomials related to

trigonometric functions”, to appear in Adv. Stud. Contemp. Math. (2019).

[5] T. M. Apostol, “On the lerch zeta function”, Pac. J. Math. 1.2(1951), 161–167.

[6] T. Kim and C. S. Ryoo, “Some identities for Euler and Bernoulli polynomials and their

zeros”, Axioms, 7:3 56, (2018), 001–019.

[7] Y. Simsek, “Special numbers and polynomials including their generating functions in

umbral analysis methods, Axioms, 7.2:22 (2018).

[8] Y. Simsek, “Construction of some new families of Apostol-type numbers and polynomials

via Dirichlet character and p-adic q–integrals”, Turk. J. Math. 42(2018), 557 –577.

[9] Q-M Luo and H. M. Srivastava, “Some generalizations of the Apostol–Bernoulli and

Apostol–Euler polynomials”, J. Math. Anal. Appl. 308(2005), 290–302.




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49

Set-Star Menger and Related Spaces

Sukran Konca1

, Ljubisa D.R. Kocinac2

1

Bitlis Eren University, Department of Mathematics,

13000, Bitlis, Turkey 2

University of Nis, Faculty of Sciences and Mathematics,

18000, Nis, Serbia


Abstract: In this paper, we introduce some new types of star covering properties such as set-star

Menger, set-star Rothberger and set-star Hurewicz properties. We investigate the relationships

between set-star Mengerness and some other Menger-type covering properties, and study

topological properties of set-star-Menger and related spaces.

Keywords: Selection principles, star selection principles, set-Menger, set-star Menger, quasi-

star Menger

References:

[1] E.K. van Douwen, G.M. Reed, A.W. Roscoe, I.J. Tree, “Star covering properties”, Topology

Appl. 39 (1991), 71--103.

[2] Lj.D.R. Kocinac, “Star selection principles: A survey”, Khayyam J. Math. 1 (2015),

82--106.

[3] Lj.D.R. Kocinac, “Variations of classical selection principles: An overview”, Quaest.

Math., in press.

[4] Lj.D.R. Kocinac, S. Konca, “Set-Menger and related properties”, Topology Appl., accepted.

[5] M.V. Matveev, “A survey on star covering properties”, Topology Atlas, Preprint No. 330,

1998.





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50

Numerical Solution of Two Dimensional Brusselator Model by Time

Splitting Method Sıla Övgü Korkut and Yeşim Çiçek

Department of Engineering Sciences, Izmir Kâtip Çelebi University,

İzmir, Turkey

[email protected]

Abstract: One of the significant model in chemical reactions with oscillations is the Brusselator

model. This model essentially describes a nonlinear reaction-diffusion equation. In this study,

two dimensional (2D) Brusselator model is solved numerically by the help of time splitting

method. After convergence issue has been proved, the accuracy of the method is also showed on

numerical examples. In addition, the obtained results are compared by the studies in literature.

Keywords: Local convergence, Brusselator model, Splitting method, Non-linear partial

differential equation, Reaction-Diffusion equation.

References:

[1] W.T. Ang, “The two-dimensional reaction–diffusion Brusselator system: a dual-reciprocity

boundary element solution”, Engineering Analysis with Boundary Elements, 27(2003), 897–

903.

[2] A. Shirzadi, V. Sladek, J. Sladek, “A Meshless Simulations for 2D Nonlinear Reaction-

diffusion Brusselator System”, Computer Modeling in Engineering and Sciences, 95.4(2013),

259-282.

[3] E.H. Twizell, A.B. Gumel, Q. Cao, “A second-order scheme for the ‘Brusselator’ reaction–

diffusion system”, J Math Chem, 26(1999), 297–316.

[4] A.M. Wazwaz, “The decomposition method applied to systems of partial differential

equations and to the reaction–diffusion Brusselator model.”, Applied Mathematics and

Computation, 110.2–3(2000), 251-264. [5] G. Adomian, “The diffusion-Brusselator equation”, Comput Math Appl, 29.1-3(1995), 1731-

1737.

[6] S. Islam, A. Ali, S. Haq, “A computational modeling of the behavior of the two-dimensional

reaction–diffusion Brusselator system”, Applied Mathematical Modelling, 34(2010), 3896–

3909.





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51

The effect of basilar membrane stiffness on the displacement of cochlear

partition

Fatiha Kouilily1, Fatima-Ezzahra Aboulkhouatem1, Noura Yousfi1,

Naceur Achtaich1, Mohammed El Khasmi2 1LAMS, Hassan II University of Casablanca, Casablanca, Morocco 2LPGM, Hassan II University of Casablanca, Casablanca, Morocco

[email protected]

Abstract: In this study, we analysis the active micromechanics model of the cochlea in order to

describe mathematically the displacement of cochlear partition by using finite difference method

and Cramer’s rule, then we study the effect of Basilar membrane stiffness on the response of

cochlear partition. As a result, the decrease of the maximum displacement of the basilar and

tectorial membranes was observed and presented numerically, these observations contribute to

understand that the mechanism of hearing loss may be the result of altered cochlear

micromechanics.

Keywords: Cochlea, Active michromehanics model, Basilar membrane, Tecoriel membrane,

Stifness.

References:

[1] F.Kouilily, FE. Aboulkhouatem, N Yousfi, M.El Khasmi and N. Achtaich, ‘Predicting the

Effect of Physical Parameters on the Amplitude of the Passive Cochlear Model’, revista

mexicana de ingeniería biomédica, 39 (1) 105-112, 2018.

[2] FZ. Aboulkhouatem, F. Kouilily, M. EL Khasmi, N. Achtaich , N. Yousfi, ‘The Effect of

Stiffness on the Maximum Amplitude Displacement of the Basilar Membrane’, British Journal

of British Journal of Mathematics Computer Science, (BJMCS.30856) 1-11, 2017.

[3] Stephen J. Elliott, Emery M. Ku, and Ben Lineton, ‘A state space model for cochlear

mechanics’, J. Acoust. Soc. Am, 43.64.Kc, 43.64.Jb, 43.40.Vn, 43.64.Bt [BLM] 2759-2771,

2007.





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52

L1-convergence of the sine series whose coefficients belong to some

generalized classes of sequences

Xhevat Krasniqi

Faculty of Education, University of Prishtina “Hasan Prishtina”

10000 Prishtina, Republic of Kosovo

[email protected]

Abstract: In this paper, we have introduced three generalized classes of sequences. In addition,

we have studied the L1 convergence of sine series whose coefficients belong to them. Finally,

we show that our results cover some results proved previously by others.

Keywords: Generalized modified sine sums; Generalized classes of sequences; Sine series; L1-

convergence; Dirichlet kernel.

References:

[1] N. L. Braha; Xh. Z. Krasniqi, On L1-convergence of certain cosine sums. Bull. Math. Anal.

Appl. (2009), 1, 55--61.

[2] S. K. Chouhan, J. Kaur, S. S. Bhatia, Extensions of M\'oricz classes and convergence of

trigonometric sine series in L1-norm. Mathematics, 2018, (12), 292.

[3] S. K. Chouhan, J. Kaur, S. S. Bhatia, Convergence and Summability of Fourier sine and

cosine series with its applications. Proc. Natl. Acad. Sci. India Sect. A. Phys. Sci. 2, 2018, 1–8.

[4] W.J. Garrett, C.V. Stanojevic,On L1-convergence of certain cosine sums. Proc. Amer. Math.

Soc. 1976,54,101-105. [5] N. Hooda, B. Ram, S. S. Bhatia, On L1-convergence of a modified cosine sum. Soochow J.

Math. 28 (2002), no. 3, 305--310.

[6] K. Kaur, S. S. Bhatia, B. Ram, Integrability and L1-convergence of modified sine sums.

Georgian Math. J. 11 (2004), no. 1, 99--104.

[7] J. Kaur, S. S. Bhatia, Convergence of new modified trigonometric sums in the metric space

L. J. Nonlinear Sci. Appl. 1 (2008), no. 3, 179--188.

[8] Xh. Z. Krasniqi, A note on L1-convergence of the sine and cosine trigonometric series with

semi-convex coefficients. Int. J. Open Probl. Comput. Sci. Math 2 (2009), no. 2, 231--239.

[9] Xh. Z. Krasniqi, Some new modified cosine sums and L1-convergence of cosine

trigonometric series. Arch. Math.} (Brno) 49 (2013), no. 1, 43--50.

[10] F. Móricz, On the integrability and L1-convergence of sine series. Studia Math. 1989, 335,

187--200.

[11] B. Ram, S. Kumari, On L1-convergence of certain trigonometric sums. Indian J. Pure Appl.

Math. 20 (1989), No. 9, 908--914.

[12] Shu Yun. Sheng, The extension of the theorems of C. V. Stanojevic and V. B. Stanojevic.

Proc. Amer. Math. Soc., 110 (1990), no. 4, 895--904.





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53

Lebesgue constants on the real projective spaces

Alexander Kushpel

Department of Mathematics, Çankaya University,

Ankara, Turkey

[email protected]

Abstract: Lebesgue constants is a classical topic of Approximation Theory and Functional

Analysis. On the circle Lebesgue constants were found by Fejer [1] in 1911. Then in 1914

Gronwall considered the case of two dimensional sphere [2]. The Lebesgue constants on d-

dimensional spheres, complex and quaternionic projective spaces and Kelly elliptic plane were

established by Kushpel [3]. Here we present Lebesgue constants on the real projective spaces.

References:

[1] L. Fejer, Lebesguesche Konstanten und divergente Fourierreihen, J. für reine und angew.

Math. 138(1910) 22-53.

[2] T. H. Gronwall, On the degree of convergence of Laplace series, Trans. Math. Soc. 15

(1914)(1) 1-30.

[3] A. Kushpel, On the Lebesgue constants, Ukrainian Math. Journ. (to appear).





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54

Packing chromatic number in some graphs Rachid Lemdani

Department of Mathematics and Computer science, Faculty of sciences, Medea University,

Algeria

[email protected]

Moncef Abbas

USTHB,Algiers, Algeria

[email protected]

Abstract: For a simple graph 𝐺 = (𝑉, 𝐸) with no isolated vertices, a packing coloring of order

𝑘 in 𝐺 is a function 𝜋: 𝑉 → {1, … , 𝑘} that is if 𝜋(𝑢) = 𝜋(𝑣) implies that 𝑑(𝑢, 𝑣) ≻ 𝜋(𝑢). The

minimum order of a packing coloring is called the packing chromatic number of 𝐺 and is denoted

by 𝜒𝑝(𝐺). It was introduced by Goddard et al. in [2] under the name Broadcast chromatic number

of graphs and study its properties. They showed that it is NP-hard to determine if 𝜒𝑝(𝐺) ≤ 4 and

they also determined the packing chromatic number of paths, cycles, trees of diameter at most 4.

The corona of two graphs 𝐺1 and 𝐺2 of order 𝑛1 and 𝑛2 respectively, 𝐺1⨀𝐺2 is the graph obtained

by taking 𝑛1 copies of 𝐺2 such that the 𝑖-th vertex in 𝐺1is adjacent to every vertex in the 𝑖-th

copy of 𝐺2. A finite super subdivision graph of 𝐺 denoted by 𝐹𝑆𝑆𝐷𝑚(𝐺) [4], is the graph

obtained from 𝐺 by replacing every edge in 𝐺 by a complete bipartite graph 𝐾2,𝑚 (𝑚 is finite).

In this paper we determine the packing chromatic number of graphs: Corona of 𝐾𝑛 with 𝑃𝑛and

the finite super subdivision of the corona of cycle with path.

Keywords: Packing chromatic number, Corona of graphs, Finite super subdivision graphs.

References:

[1] B. Brešar, S. Klavžar and D. F. Rall, On the packing chromatic number of Cartesian

products, Hexagonal lattice and trees, Discrete Appl. Math., 155 (2007), 2303-2311.

[2] W. Goddard, S.M. Hedetniemi, J. M. Harris, D.F. Rall, Broadcast chromatic numbers of

graphs, Ars Combin., 86:33-49, 2008.

[3] S. Kuntari and T. A. Kusmayadi. The eccentric digraph of the corona of Cn with Km, Cm or

Pm. J. Indones. Math. Soc., 18(2)(2012), 113-118.

[4] A. William and S. Roy. Packing chromatic number of certain graphs. Inter. J. Pure. App.

Math., 87(06)(2013), 731-739.




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55

θ-type contraction mappings in complete b-metric spaces and applications

to polynomial approximations

Nora Mahloul1, Hichem Ramoul2, Abdalah Rababah3

1USTHB, Faculty of Mathematics

Algebra and Number Theory Department

[email protected]

2ICOSI laboratory, Abbes Laghrour University-Khenchela,

Khenchela, Algeria

[email protected]

3Department of Mathematics and Statistics, University of Science and

Technology Irbid, Jordan

[email protected]

Abstract: In this paper some generalizations of fixed point results for θ-type contraction

mappings in complete b-metric spaces are given. Existence and uniqueness theorems of this type

of contraction are proved. At the end, an application concerning some polynomial operators is

given to illustrate the usability of our result.

Keywords: Fixed points, contraction-type mappings, polynomial approximation.

References:

[1] M. Jleli, B. Samet, A new generalization of the Banach contraction principle, Jourrnal of

Inequalities and Applications 2014:38 (2014).

[2] S. Ostrovska, q-Bernstein polynomials and their iterates, Journal of Approximation Theory,

123 (2003) 232-255.

[3] I. Altun, N. AL Arifi, M. Jleli, A. Lashin, B. Samet, A fixed point theorem for JS-contraction

type with applications to polynomial approximations. Filomat 31:15 (2017), 4969-4978




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56

Unsupervised classification of superficial waters quality of l’Oued

Moulouya (North East Morocco). Application of Self Organizing Maps

Abdelghani Talhaoui

Laboratory of Geo-Engineering and Environment, Team of Water Sciences and Environmental

Engineering, Department of Geology, Faculty of Sciences, University Moulay Ismail, B.P. 11201,

Zitoune, Meknes, Morocco

[email protected]

Imad Manssouri

Laboratory of Mechanics, Mechatronics and Control, Team of Electrical Energy, Maintenance and

Innovation, ENSAM-Meknes, University Moulay Ismail, B.P. 4042, 50000, Meknes, Morocco

[email protected]

Abdellah El Hmaidi

Laboratory of Geo-Engineering and Environment, Team of Water Sciences and Environmental

Engineering, Department of Geology, Faculty of Sciences, University Moulay Ismail, B.P. 11201,

Zitoune, Meknes, Morocco


Mohamed Berrada

Laboratory of Mathematical and computer modeling. (LM2I), ENSAM- Meknes, University Moulay

Ismail, B.P. 4042, 50000, Meknes, Morocco

[email protected]

Abstract: The quality of the superficial waters of Oued Moulouya shows considerable

variability in space and time under the influence of natural or anthropogenic phenomena.

This work is based on clustering methods using self-organizing maps of Kohonen (SOM) to predict the different classes of superficial waters quality of 22 stations on the Moulouya for three

prospecting campaigns spread over six months, from March to August 2014.

The database that will serve, on the one hand, as a learning base and on the other hand as a basis

for testing and validation of the Artificial Neural Networks-Self Organization Maps (ANN-

SOM) model, consists of nine physicochemical variables of the superficial waters of Moulouya

namely : the hydrogen potential (pH), water temperature in Celsius (°C), electrical conductivity

CE (μs.cm-1), dissolved oxygen in water OD (mg.l-1), ammonium NH+4 (mg.l-1), nitrates NO-

3

(mg.l-1), sulphates SO42- (mg.l-1), orthophosphates PO4

3- (mg.l-1) and the biological oxygen

demand during 5 days DBO5 (mg.l-1).

The choice of the size of the SOM card was made according to the following two criteria: the

quantization error (QE) and the topological error (TE). The performances relating to this model

(ANN-SOM) were evaluated by the calculation of determination coefficient R2.

The results obtained from the unsupervised classification of the superficial waters quality of

Moulouya have made it possible to highlight a dominant spatial typology marked by a reduced

seasonal influence and an important spatial influence.

Keywords: Oued Moulouya, Classification, Self-Organizing Maps, Quality, Physicochemical

parameters, Superficial Waters.





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57

Direct Torque Control using Neural Networks and Fuzzy Logic

Zineb Mekrini, Seddik Bri

Department of Electrical Engineering, University of Abdelmalek Essaadi

Faculty of Sciences and techniques of Tangier

[email protected]

Abstract: This communication investigates solution for the biggest problem of the Direct

Torque Control on the asynchronous machine to have the high dynamic performance with very

simple hysteresis control scheme. The Conventional Direct Torque Control (CDTC) suffers

from some drawbacks such as high current, flux and torque ripple, as well as flux control at

very low speed. In this paper, we propose an intelligent approach to improve the direct torque

control of induction machine which is an artificial neural networks control. The principle, the

numerical procedure and the performances of this method are presented. Simulations results

show that the proposed ANN-DTC strategy effectively reduces the torque and flux ripples at

low switching frequency, compared with Fuzzy Logic DTC and The Conventional DTC.

Keywords: Asynchronous Machine, Artificial neural networks,Torque ripple, Flux ripple,

Fuzzy logic.

References:

[1] Abbou A, Mahmoudi H,” Performance of a sensorless speed control for induction motor

using DTFC strategy and intelligent techniques”,Journal of Electrical Systems, Vol 5; N°3;

pp.64-81, 2009.

[2] Xuezhi Wu; Lipei Huang,” Direct torque control of three-level inverter using neural networks

as switching vector selector”, Industry Applications Conference. 2001,pp.939 – 944.

[3] Cirrincione, G, Cirrincione, M,Chuan Lu, Pucci,”M. Direct Torque Control of Induction

Motors by Use of The GMR Neural Network”, Neural Networks, Proceedings of the

International Joint Conference,pp. 20-24.

[4] Z.Mekrini, and S.Bri, “Fuzzy Logic Application for Intelligent Control of An Asynchronous

Machine”, Indonesian Journal of Electrical Engineering and Computer Science (IJEECS),Vol

7, N°1 , pp.61-70, July 2017.





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58

New Approach to q-Fractional Derivative M. Momenzadeh, S. Norozpour

Department of Mathematics, Near East University,

Nicosia, TRNC

[email protected]

[email protected]

Abstract: There are several approaches to fractional differential operators. A new class of q-

fractional integral operator is defined in [1] that is using iterated Cauchy q-integral method, with

an extra parameter. This is the first approach to q-analouge of Hadamard operator. Recently,

Hadamard operator and its properties are considered as a hot topic among researches, [2] but

there was no q-analouge of this operator. In [1], q-fractional integral operator and its peroperties

are investigated.

In the following paper, Caputo type q-derivative corresponding to the integral operator defined

in [1], is introduced with some classical properties of fractional derivative and integral.

Additionally, the general presentation of all q-absolutely continuous functions (𝐴𝐶𝑞[𝑎, 𝑏]) [3],

is characterized.

Keywords: q-Fractional Operators, Caputo Derivative, Hadamard integral operator.

References:

[1] M.Momenzadeh, N.Mahmudov. “Study of new class of q-fractional integral operator” ,

arXiv:1904.11724.

[2] Ahmad, B., Alsaedi, A., Ntouyas, S.K. and Tariboon, J., 2017. Hadamard-type fractional

differential equations, inclusions and inequalities. Springer International Publishing. [3] Annaby, M.H. and Mansour, Z.S., 2012. Q-fractional Calculus and Equations (Vol. 2056).

Springer.


https://arxiv.org/abs/1904.11724




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59

Full cycle extendability of triangulary connected partly claw-free graphs

Abdelkader Sahraoui

Department of Mathematics, Medea University,

Medea, Algeria

[email protected]

Abstract: The concept of full cycle extendable was introduced by Hendry [1]. A graph G is said

full cycle extendable if each vertex of G belongs to triagle et for any cycle C with |C|<|G|, there

exists a cycle C’ in G such that V(C) V(C’) and |C’|=|C|+1. In [5] Benmeziane and Abbas

introduced the concept of partly claw-free graphs. A graph G is said partly claw-free graph for

every vertex v A, the set of claws of G, there exist two vertices x, y V-A such that NG(v)

N[x] N[y]. A graph G is triangularly connected if for each pair of edges e1 et e2, G has a

sequence of 3-cycles C1, C2, ..., Ck such that , e1C1 , e2 Ck , and E(Ci) E(Ci+1) for 1

i k. In this paper, we will show that every triangularly connected K1,4-free, K4-free, and partly

claw-free graph on at least three vertices is fully cycle extendable if the set A of centers of claw

of G is a perfect matching in A. This paper generalizes the concept full cycle extendable of

Hendry in [1] to the biggest superclass of partly claw-free graphs of Benmeziane in [2].

Keywords: Partly claw-free graphs, triangularly connected graphs, fully extendablity, K1,4-free

graphs, K4-free graphs.

References:

[1] G.R.T. Hendry, “Extending cycles in graphs”, Descrete Math. 85 (1990), 59-72.

[2] Z. Benmeziane and M. Abbas, “Hamiltonicity in partly claw-free graphs”, RAIRO Oper.

Res., 43 1(2009), 103-113.

[3] M. Zhan,, “Full cycle extendability of triangulary connected almost claw-free graphs”, ABS

Combinatoria, vol. 96 (2010).





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60

A new sequence space and invariant mean

Ekrem Savaş

Department of Mathematics, Uşak University, Uşak, Turkey

[email protected] Abstract: The goal of this paper is to present some properties of the new sequence space defined

by using invariant mean, φ- function and de la Valee-Poussin mean. Further, some inclusion

theorems are studied.

Keywords: Modulus function, invariant mean, matrix transformations, new sequence spaces.

References:

1- J. Connor, On strong matrix summability with respect to a modulus and statistical convergent,

Canad. Math. Bull. 32(2),(1989), 194-198.

2- E. Malkowsksy and E. Savaş, Some - sequence spaces defined by a modulus, Archivum

Math. 36, (2000), 219-228.

3- F. Nuray and E. Savas, Some new sequence spaces defined by a modulus funcion, Indian J.

Pure. Appl. Math. 24(11), (1993), 657-663.

4- E. Savaş and R. Savaş Some -sequence spaces defined by Orlicz functions, Indian J. Pure.

Appl. Math. 34(12), (2003), 1673-1680.

5- E. Savaş, On some generalized sequence spaces defined by a modulus, Indian J. Pure. Appl.

Math. 30(5), (1999), 459-464.

6- S. K. Saraswat and S. K. Gupta, Spaces of strongly -summable sequences, Bull. Cal.

Math. Soc. 75, (1983), 179-184,

7- E. Savas On lacunary strong -convergence, Indian J. Pure Appl. Math., 21(4), (1990),

359-365.

8- E.Savas,On Strongly -regular summability method, Bull. Call. Math. Soc.,83,(1990),1-4.

9- P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc. 36, (1972), 104--

110.





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61

- mean and uniform (A, φ)- statistically convergent sequences

Rahmet Savaş

Department of Mathematics, Istanbul Medeniyet University, Istanbul, Turkey

[email protected]

Abstract: In this paper, we present uniform (A, φ)- invariant statistically convergent sequences,

defined by using - mean, φ- function and -convergence and also we study some inclusion

theorems.

Keywords: Modulus function, invariant mean, matrix transformations, new sequence spaces.

References:

1- H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.

2- J. A. Fridy, On statistical convergence, Analysis, 5 (1985), 301-313.

3- E. Malkowsksy and E. Savaş, Some - sequence spaces defined by a modulus, Archivum

Math. 36, (2000), 219-228.

4- E. Savaş and R. Savaş, Some -sequence spaces defined by Orlicz functions, Indian J. Pure.

Appl. Math. 34(12), (2003), 1673-1680.

5- E. Savaş, On some generalized sequence spaces defined by a modulus, Indian J. Pure. Appl.

Math. 30(5), (1999), 459-464.

6- E. Savas On lacunary strong -convergence, Indian J. Pure Appl. Math., 21(4), (1990),

359-365.

7- P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc. 36, (1972), 104--

110.

8- I. J. Schoenberg, The integrability of certain functions and related summability methods,

Amer. Math. Monthly, 66 (1959) 361-375.

9- A. Waszak, On the strong convergence in sequence spaces, Fasciculi Math. 33, (2002), 125-

137.





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62

Biharmonic Hypersurfaces in a Pseudo-Euclidean Space Rüya Yeğin Şen

Department of Mathematics, İstanbul Medeniyet University,

İstanbul, Turkey

[email protected]

Abstract: After Bang-Yen Chen conjectured that every biharmonic submanifold of a Euclidean

space is minimal, biharmonic and biconservative submanifolds in pseudo-Euclidean spaces have

been studied by many geometers, [1,2,3,4]. In this paper, we study biharmonic hypersurfaces of

index 2 in 5

2E . Firstly, all possible canonical forms of the shape operator of such a hypersurface

are obtained. Then, for each of these cases, some of geometrical properties of hypersurfaces is

investigated

Keywords: Biharmonic hypersurface, Biconservative hypersurface, shape operator, pseudo-

Euclidean Space.

References:

[1] B.-Y. Chen, “Some open problems and conjectures on submanifolds of finite type”, Soochow

J. Math. 17 (2) (1991), 169-188.

[2] B. -Y. Chen and M. I. Munteanu, “Biharmonic ideal hypersurfaces in Euclidean spaces”,

Differential Geom. Appl., 31 (2013), 1-16.

[3] N. C. Turgay, “Some classifications of biharmonic Lorentzian hypersurfaces in Minkowski

5-space”, Mediterr. J. Math., 13 (1) (2016), 401-412.

[4] N. C. Turgay, “A classification of biharmonic hypersurfacesin Minkowski space of arbitrary

dimension”, Hacet. J. Math. Stat. 45 (2016), 1125-1134.

[5] A., Upadhyay, “On the shape operator of biconservative hypersurfaces in5

2E ”, Proceedings

Book of International Workshop on Theory of Submanifolds 1 (2016), 166-186.





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63

Bade-property, Extremally rich JB*-triples and λ-property

Haifa M. Tahlawi

Department of Mathematics, College of Science, King Saud University

Riyadh, Kingdom of Saudi Arabia

[email protected]

Abstract: The notion of Bade-property which is a geometric property was originally introduced

by Bade [2]. Later, Aron and Lohman [1] introduced a stronger version of this property, called

the λ-property which was extensively studied in the algebraic structure of C*-algebras by Brown

and Pedersen [3] whose also defined an extremally rich C*-algebra. In [4] and [5], Jamjoom,

Peralta, Siddiqui and present author studied the generalization of λ-property and extremally

richness in the general setting of JB*-triples. In this note, we studied the relations between these

properties and the Bade-property in JB*-triples and we concluded the equivalence between these

properties with the help of the celebrated Russo-Dye Theorem.

Keywords: JB*-triples, Bade-property, λ-property, Extremally richness, Russo-Dye Theoerem.

References:

[1] Aron, R. M. and Lohman, R. H., A geometric function determined by extreme points of the

unit ball of a normed space, Pac. J. Math., vol. 127, (1987), 209-231.

[2] Bade, W. G., The Banach Space C(S). Lecture Note Series, vol. 26, Matematisk Institut,

Aarhus University, Aarhus, 1971.

[3] Brown, L. G. and Pedersen, G. K., On the geometry of the unit ball of a C∗-algebra, J.

Reine Angew. Math., vol. 469, (1995), 113 - 147.

[4] Jamjoom, F., Siddiqui, A. A., Tahlawi, H. M., On the geometry of the unit ball of a JB∗-

triple, Abstract and Applied Analysis, (2013), 8 pages.

[5] Jamjoom, F., Peralta, A. M., Siddiqui, A. A., Tahlawi, H. M., Extremally rich JB∗-Triples,

Ann. Funct. Anal. 7 (2016), no. 4, 578-592.




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64

Fixed point on modified semi-linear uniform spaces

Alhihi S.A.

Department of Mathematics, Al- Balqa` Applied University, Alsalt,

Jordan [email protected], suadalhihi@yahoo.

A.Tallafha

Department of Mathematics, The University of Jordan, Amman – Jordan


Abstract: In 2009 Tallafha, A. and Khalil, R. defined a new type of uniform space namely,

semi-linear uniform space [8]. Later Tallafha, A. in [9], [10] and [11], Alhihi, S. in [1] and

Tallafha, A. and Alhihi, S. in [12], gave more properties of semi-linear uniform spaces. Also

Lipschitz condition and contraction mapping on semi-linear uniform spaces are defined, which

enables one to study fixed point for such functions.

In this article we shall define a modified semi-linear uniform space and a new types of

contractions on semi-linear uniform spaces, finally we ask the following natural question. If f

is a contraction from a complete modified semi-linear uniform space (X,Γ) to it self, is f has a

unique fixed point.

Keywords: Uniform spaces, Semi-linear spaces, Contraction, Fixed Point, Best approximation

References:

[1]Alhihi, S. A., More properties of semi linear uniform spaces. Journal of applied

mathematics, Vol. 6, online, 2015.

[2]Alhihi, S. A., and Al-Fayyad M. Topological properties of semi linear uniform spaces.

Global journal of pure and applied mathematics. ISSN 0973-1768, 12.6(2016).5329- 5341.

[3]Bourbaki; Topologie Générale (General Topology); Paris 1940. ISBN 0-387-19374-X.

[4]Cohen, L. W. Uniformity properties in a topological space satisfying the first

denumerability postulate, Duke Math. J. 3(1937), 610-615.

[5]Cohen, L.W.;On imbedding a space in a complete space,Duke Math. J. 5(1939),174- 183.

[6]Engelking, R. Outline of General Topology, North-Holand, Amsterdam, 1968.

[7]Graves, L. M. : On the completing of a Housdroff space, Ann. Math. 38(1937,61-64.

[8]James, I.M. Topological and Uniform Spaces. Undergraduate Texts in Mathematics.

Springer-Verlag 1987.

[9]Rawashdeh, A. and Tallafha, A. Fixed Point in Semi-linear Uniform Spaces and Convex

Metric Spaces, submitted.

[10]Tallafha, A. and Khalil, R., Best Approximation in Uniformity type spaces. European

Journal of Pure and Applied Mathematics, Vol. 2, No. 2, 2009,(231-238).

[11]Tallafha, A. Some properties of semi-linear uniform spaces. Boletin da sociedade

paranaense dematematica, Vol. 29, No. 2 (2011). 9-14.

[12]Tallafha, A. Open Problems in Semi-Linear Uniform Spaces. J. Applied Functional

Analysis,Vol.8.No.2,223-228.







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65

Fuzzy Relational Graphs

Huda Mutab Al Mutab and Fairouz Tchier

Computer Science Department,

College of Science and Human studies in Durma,

Shaqra University, Saudi Arabia

Mathematics department,

King Saud University, Riyadh 11495

[email protected],

[email protected]

Abstract: The calculus of relations has been an important component of the development of

logic and discrete mathematics since the middle of the nineteenth century. In this paper,

neighbourly irregular fuzzy graphs, neighbourly total irregular fuzzy graphs, highly irregular

fuzzy graphs and highly total irregular fuzzy graphs are introduced. A necessary and sufficient

condition under which neighbourly irregular and highly irregular fuzzy graphs are equivalent is

provided. We define d2 degree of a vertex in fuzzy graphs and total d2 -degree of a vertex in

fuzzy graphs and (2,k)-regular fuzzy graphs, totally (2,k)- regular fuzzy graphs are introduced.

(2,k)- regular fuzzy graphs and totally (2,k)-regular fuzzy graphs are compared through various

examples.





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66

On Some Properties of a Normed Intersection Space Ismail Aydın, Cihan Unal

Department of Mathematics, Sinop University,

Sinop, Turkey

[email protected]

[email protected]

Abstract: Let G be a locally compact Abelian group. The main purpose of this study is to show

that 𝐴𝑝1,𝑝2

𝑞1,𝑞2 (𝐺) ∩ 𝐿1(𝐺) is an abstract Segal algebra by using amalgam spaces. Furthermore, we

investigate ideals, embeddings and multipliers of this space.

Keywords: Abstract Segal algebra, Convolution, Multipliers.

References:

[1] I. Aydın, “On vector-valued classical and variable exponent amalgam spaces”, Commun.

Fac. Sci. Univ. Ank. Series A1 2.2 (2017), 100-114.

[2] H. G. Feichtinger, “A characterization of Wiener's algebra on locally compact groups”, Arch.

Math. 66 (1977), 136-140.

[3] A. T. Gurkanli, “Multipliers of some Banach ideals and Wiener-Ditkin sets”, Math. Slovaca,

55.2(2005), 237-248.

[4] E. Hewitt, K. A. Ross, “Abstract Harmonic Analysis V. I, II”, Berlin-Heidelberg-New York,

Springer-Verlag (1979.

[5] J. Stewart, “Fourier transforms of unbounded measures”, Canad. J. Math. 31 (1979), 1281-

1292.





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67

Some Conditions over a Strongly Regular Graph in The Environement of

Euclidean Jordan algebras

Luís Vieira

Department of Cívil Engineering , University of Porto,

Porto, Portugal,

[email protected].

Abstract: Let G be a primive strongly regular graph of order n with three distinct eigenvalues

and is matrix of adjacency. In this paper we associate to the real Euclidean Jordan algebra

spanned by and the natural powers of and next, by the spectral analysis of some elements

of we establish some admissibility conditions recurring, in the environment of Euclidean Jordan

algebras, to the Generalized Krein parameters of a strongly regular graph as defined in [1]and

[2] .

Keywords: Algebraic theory, Euclidean Jordan algebras, Matrix theory, graph theory, spectra

of graphs.

References:

[1] L.A.Vieira&V.M. Mano, “Generalized Krein parameters of a strongly regular graph”,

Applied Mathematics, 6(2015),37-45.

[2] L.A. Vieira, V.M. Mano & E.M. Cascais, “Inequalities on the parameters of a strongly

regular graph”, Modeling, Dynamics, Optimization and Bioeconomics 1, (2014),1-14.




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68

Spectral Theory and Stability of Index for Multivalued Linear Operators Gerald Wanjala

Department of Mathematics, Sultan Qaboos University,

Muscat, Oman


Abstract: Let A:X→Y be a linear operator between two Banach spaces X and Y and let N(A)

and R(A) denote the null space and the range of A respectively. It is well known that the

quantities α(A) := dim N(A), β(A) := dim Y/R(A), and the index γ(A) := α(A) ̶ β(A) have some

kind of stability when subjected to a small perturbation under certain conditions (see[1]). In this

talk, we discuss the eigenvalue problem T(x) ⸦ S(x) where T and S are multivalued linear

operators on a Hilbert space H and its relationship to the stability of index and related quantities

for multivalued linear operators.

Keywords: Perturbation, stability of index.

References:

[1] T. Kato, “Perturbation theory for nullity, deficiency and other quantities of linear operators”,

J. d’Analyse Math., 6(1958), 273-322.






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69

Mixture of two Methods for Solving Some Differential Equations

Ervenila Xhaferraj

Department of Mathematics, Polytechnic University,

Tirana ,Albania

[email protected]

Abstract: In this paper, we present a new method, a mixture of spectral approximation method

and a new integral transform to solve some differential equations. Spectral methods for solving

differential/integral equations are characterized by the representation of the solution by a

truncated series of smooth functions . The method is applied to generalized ordinary diferential

equation , and finally, applications of these results in solving differential and integral equations

with varying polynomial coefficients .

Keywords: Spectral Method , New Integral Transform, Linear Differential Equation ,Integral

Equation.

References:

[1] A. Elsaid, Adomian polynomials: A powerful tool for iterative methods of series solution of

nonlinear equations, Journal of Applied Analysis and Computation, 2(4)(2012), 381–394.

[2] Tarig M. Elzaki, The New Integral Transform ”Elzaki” Transform, Global Journal of Pure

and Applied Mathematics, ISSN 0973-1768,1(2011), 57–64.

[3] Tarig M. Elzaki and Salih M. Elzaki, Application of New Transform ”Elzaki Transform” to

Partial Differential Equations, Global Journal of Pure and Applied Mathematics, ISSN 0973-

1768, 1(2011), 65–70.

[4] Doha, E.H.: On the coefficients of integrated expansions and integrals of ultraspherical

polynomials and their applications for solving differential equations. J. Comput. Appl. Math.

139, 275–298 (2002)

[5]. Esmaili, S., Eslahchi, M.R.: A modified spectral method for solving operator equations. J.

Comput. Appl. Math. 292, 105–135 (2016).





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70

Inverse Berezin number inequality and related problems

Ulas Yamanci1 and Mehmet Gurdal2 1Department of Statistics, Süleyman Demirel University, Isparta, Turkey

2Department of Mathematics, Süleyman Demirel University, Isparta, Turkey

[email protected]; [email protected]

Abstract: The notion of Berezin number was introduced by Karaev [3]. Recently, many results

about this concept have been obtained. By using Hilbert-type inequality, we give some inverse

Berezin number inequalities and obtain interesting results.

Keywords: Berezin number, positive operator, Hilbert type inequality.

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. Karaev, “Berezin symbol and invertibility of operators on the functional Hilbert spaces”,

J. Funct. Anal., 238(2006), 181-192.

[4] M. Kian, “Hardy-Hilbert type inequalities for Hilbert space operators”, Ann. Funct. Anal.,

3(2)(2012), 128-134.

[5] 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.

[6] M.T. Garayev, S. Saltan, M., D. Gundogdu, “On the inverse power inequality for the Berezin

number of operators”, J. Math. Inequal., 12(4)(2018), 997-1003.

[7] U. Yamanci, M.T. Garayev, C. Celik, “Hardy-Hilbert type in reproducing kernel Hilbert

space: its applications and related results”, Linear Multilinear Algebra, 67(4)(2019), 830-842.




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71

I -statistical convergence in n -normed spaces

Mehmet Gürdal and Ulaş Yamancı

Süleyman demirel University, Isparta, Turkey

[email protected]; [email protected]

Abstract: The concept of statistical convergence play a vital role not only in pure mathematics

but also in other branches of science involving mathematics. The notion of statistical

convergence was introduced by Fast [2]. In [6], Kostyrko et al. introduced the concept of I -

convergence of sequences in a metric space and studied some properties of such convergence.

Note that I -convergence is an interesting generalization of statistical convergence. The theory

of 2 -normed spaces was first developed by Gähler [4] in the mid of 1960's, while that of n -

normed spaces can be found in [7]. The notion of I -statistical convergence has not been studied

previously in the setting of I -normed spaces. Motivated by this fact, in this paper, as a variant

of statistical convergence, the notions of I -statistical convergence are introduced in a n -

normed space and some important results are established.

Keywords: Density, Statistical Convergence, ideal convergence, n-normed space.

References:

[1] P. Das., E. Savaş, S. Ghosal, On generalized of certain summability methods using ideals,

appl. Math. Lett., 26(2011), 1509-1514.

[2] H . Fast, “Sur la convergence statistique”, Colloq. Math. 2(1951), 241-244.

[3] S. Gahler, 2-metrische Raume und ihree topologische struktur, Math. Nachr., 26(1963), 115-

148.

[5] H. Gunawan, Mashadi, On n-normed spaces, Int. J. Math. Sci, 27(10)(2001), 631-639.

[6] P. Kostyrko, M. Macaj, T. Salat., I-convergence, Real Analysis Exchange, 26(2)(2000), 669-

686.

[7] A. Misiak, Orthogonality and orthogonormality in n-inner product spaces, Math.

Nach.,43(1989), 249-261.

[8] A. Nabiev, S. Pehlivan, M. Gürdal, On I-Cauchy sequence, Taiwanese J. Math., 11(2)(2007),

569-576.





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72

Degenerate maximal hyponormal differential operators for the first order

Meltem Sertbaş, Fatih Yılmaz

Department of Mathematics, Karadeniz Technical University,

Trabzon, Turkey

[email protected] [email protected]

Abstract: In this study, all maximal hyponormal extensions are given for the degenerate first

order in the Hilbert space of vector-functions on a finite interval. The extensions are defined in

terms of the boundary values. The structure of the spectrum of the maximal hyponormal

extensions is also investigated.

Keywords: Degenerate Differential Operator, Formally Hyponormal and Hyponormal Operator,

Minimal and Maximal Operators. Extension, Spectrum of an Operator

References:

[1] A. Favini, A. Yagi, ''Degenerate differential equations in Banach spaces'', Marcel Dekker Inc.

(1999).

[2] J. Janas, ''On unbounded hyponormal operators'', Ark. Mat. 27(1989), 273-281.

[3] V. Barbu, A. Favini, ''Periodic problems for degenerate differential equations'', Rend. Istit.

Mat. Univ. Trieste Supply, 28(1997), 29-57.

[4] Z. Ismailov, E. Unluyol, ''Hyponormal differential operators with discrete spectrum'',

Opuscula Math. 30(2010), 79-94.

[5] Z. Ismailov, M. Erol, ''Normal differential operators of first-order with smooth

coefficients'',Rocky Mt. J. Math. 42(2012), 1100-1110.




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73

IFRS 17: Impact to the life insurance companies in Albania

Oriana Zacaj1, Agron Tato 2, Edvin Hoxhaj 3

1 Department of Mathematics, Polytechnic University, Faculty of Mathematics and Physics Engineering 2 Department of Mathematics, Polytechnic University, Faculty of Mathematics and Physics Engineering

3 SIGAL LIFE UNIQA GROUP AUSTRIA

E-mail: 1 [email protected], 2 [email protected], 3 [email protected]

Abstract: IFRS 17 which is an amendment to IFRS 4 is going to enter in force in the year 2021.

Due to its complexity, the insurers are investing in professional resources in order to understand

and to implement it on time. The most involved and responsible professional resources for this

implementation are actuaries, IT, and the financial team.

Especially life actuaries are facing a big challenge as the main actor in the life insurance business

which due to its long term liabilities becomes even more difficult to manage compared to non –

life business.

In this presentation we’ll try to bring into attention the main issues and challenges that an

Albanian life insurance actuary will face in order to implement and set the impact coming from

the changes of IFRS 4 to IFRS 17 to any Albanian Life insurance Company.

Key words: IFRS 17 IFRS 4, life insurers, actuary.





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74

Characterizations of extremal graphs for some bounds on k-domination

number

Mohamed Zemir¹, Mostafa Blidia²and Ahmed Bouchou1

¹University of Médéa, Algeria, ²University of Blida, Algeria.

[email protected], [email protected],

[email protected].

Abstract: For an integer k≥1 and a graph G=(V,E), a subset S of V is said to be a k-dominating

set if every vertex in V-S has at least k neighbors in S. The k-domination number of G denoted

by γk(G) is the size of the largest dominating set of G. It is clear that k ≤ γk(G) ≤ n. Different

bounds on γk(G) are known in terms of the order n, the seize m, the maximum degree Δ and the

minimum degree δ of G. In this work, we give a characterization of extremal graphs for some

known bounds on γk(G). Also , we characterize graphs G with γk(G) =k, k+1, n-1, n-2,

respectively.

Keywords: k-domination number.

References:

[1] E. J. Cockayne, B. Gamble and B. Shepherd. An upper bound for the -domination number

of a graph. J . Graph Theory 9 (1985) 533-534.

[2] O. Favaron, A. Hansberg and L. Volkmann, On -dominationt and minimum degree in

graphs, J. Graph Theory 57 (2008) 33-40.

[3] J. F. Fink and M. S. Jacobson, -domination in graphs, in : Graph Theory with Applications

to Algorithms and Computer. John Wiley and Sons, New York (1985) 283-300..

[4] A. Hansberg and A. Pepper, On -domination and -dependence in graphs, Discrete Applied

Mathematics 161(10-11) (2013) 1472-1480.

[5 V. K. Wei, A lower bound on the stability number of a simple graph,Bell Laboratories

Technical, Memorandum, 81-11217-9, Murray Hill, NJ (1981).




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75

Common Fixed Points of Semigroup Actions Yong Zhang

Department of Mathematics, University of Manitoba,

Winnipeg, Canada

[email protected]

Abstract: We consider a semigroup acting on a subset of a Banach space as self mappings. The

existence of a common fixed point for the mappings is intrinsically determined by the

amenability property of the semigroup. We investigate this connection through the study of

common attractive points for the action. If E is a strictly convex and reflexive Banach space and

S is a semigroup acting on a closed convex subset C of E, we show that the existence of a common

attractive point implies the existence of a common fixed point for the action. For a nonexpansive

semigroup action on a subset of a Hilbert space, we show that the existence of a common

attractive point is ensured by the amenability property of the semigroup.

Keywords: Fixed point, semigroup, attractive point, nonexpansive mapping.

References:

[1] S. Atsushiba and W. Takahashi, Nonlinear ergodic theorems without convexity for

nonexpansive semigroups in Hilbert spaces, J. Nonlinear Convex Analysis, 14 (2013), 209-219.

[2] A. T.-M. Lau and Y. Zhang, Fixed point properties for semigroups of nonlinear mappings on

unbounded sets, J. Math. Anal. Appl. 433 (2016), 1206-1219.

[3] A. T.-M. Lau and Y. Zhang, Fixed point properties of nonexpansive on weakly compact

convex sets, J. Funct. Anal. 254 (2008), 2534-2554.

[4] T. Mitchell, Topological semigroups and fixed points, Illinois J. Math. 14 (1970), 630-641.





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76

On the Analytical and Numerical Solutions of Chemotaxis Model Kholiknazar Kuchakshoev

SAS, University of Central Asia,

Khorog, Tajikistan

[email protected]

Abstract: We consider analytical solutions for the simple chemotaxis model known as the

Keller-Segel model [1]. For the 1-dimensional case we obtained a bounded travelling wave-type

solution. For the N-dimensional case (N>1) we found two automodelling solutions: blow-up in-

time and global in-time [2]. We have also obtained a one-dimensional numerical solution for the

Keller-Segel model and are currently working on a two-dimensional solution that makes use of

finite element methods.

Keywords: Chemotaxis models, automodelling solutions, finite elements.

References:

[1] J. Dolbeault, Perthame B. “Optimal critical mass in two-dimensional Keller Segel model in

R2”, C.R. Math.Acad. Sci.Paris 339(2004), 611-616.

[2] A.A. Samarskii, V.A. Galaktionov, S.P. Kurdyumov. “Blow-up in problems for quasilinear

parabolic equations”, M. Nauka (1987), 470.




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77

Intelligent Control Using Fuzzy Logic

Saih Mohammed

Laboratory of Automatic, Energy Conversion and Microelectronics, Electrical Engineering Department,

University of Sultan Moulay Slimane, Faculty of Sciences and Technology of Béni Mellal

[email protected]

Mekrini Zineb

Department of Electrical Engineering,Universityof AbdelmalekEssaadi

Faculty of Sciences and techniques of Tangier

[email protected]

Rouijaa Hicham

Laboratory for Systems Analysis and Information Processing, Department of Applied

Physics, Hassan I university, Faculty of Sciences and Technology of Settat

[email protected]

Abstract:The aim of this communication is propose a method to improve the control which can

take necessary control action to provide the desired torque and flux of an induction machine. It’s

widely used in the industrial application areas due to several features such as fast torque response

and less dependence on the rotor parameters. The major problem that is usually associated with

Direct Torque Control 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. In this proposed technique, the two hysteresis controllers are replaced by fuzzy logic controllers and a

methodology for implementation of a rule based fuzzy logic controller are presented . The

simulation by Matlab/Simulink was built which includes induction motor d-q model, inverter

model, fuzzy logic switching table and the stator flux and torque estimator. The validity of the

proposed method is confirmed by the simulative results of the whole drive system and results

are compared with conventional DTC method.

Keywords:Asynchronous Machine ,Direct Torque Control,Fuzzy Logic, Electromagnetic

Torque.

References:

[1] Ronald R, Yager. Fuzzy Logics and Artificial Intelligence.Journal of the Fuzzy Sets and

Systems. 1997; 90(2):193–198.




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78

[2] F Zidani. R nait said. Direct Torque Control Of Induction Motor With Fuzzy

Minimization Torque Ripple. Journal of Electrical Engineering. 2005; 56(7): 183–188.

[3] S Allirani, V Jagannathan. Torque Ripples Minimization in DTC based Induction Motor

Drive using Fuzzy Logic Technique. International Journal of Computer

Applications.2012 ;40(1): 25–31.

[4] Alnasir Z, AAlmarhoon. Design of Direct Torque Controller of Induction Motor (DTC).

International Journal of Engineering and Technology (IJET). 2012; 4 (2): 54-70.

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