the 28th international conference ofjms.akdeniz.edu.tr/_dinamik/306/136.pdf · · 2015-05-17the...

The 28th International Conference of

The Jangjeon Mathematical Society

15-19 May 2015

ANTALYA-TURKEY

Edited by

Yilmaz Simsek

Mustafa Alkan

Graphic Designer

Bihter Yigit

HONORARY PRESIDENT OF THE COMMITTEE

Prof. Dr. ISRAFIL KURTCEPHE

Rector of Akdeniz University, TURKEY

CHAIRMAN OF THE ORGANIZING COMMITTEE

Prof. Dr. YILMAZ SIMSEK,

Akdeniz University

CO-CHAIRMAN OF THE ORGANIZING COMMITTEE

Assoc. Prof. Dr. MUSTAFA ALKAN

Akdeniz University

Assoc. Prof. Dr. MELIH GUNAY

Akdeniz University

INTERNATIONAL ORGANIZING COMMITTEE

Prof. Dr. Chandrashekara Adiga, India

Assoc. Prof. Dr. Mustafa Alkan, Turkey

Prof. Dr. Abdelmejid Bayad, France

Prof. Dr. I. Naci Cangul, Turkey

Prof. Dr. A.Sinan Cevik, Turkey

Prof. Dr. Lee Chae Jang, S. Korea

Prof. Dr. Dae San Kim, S. Korea

Prof. Dr. Taekyun Kim, S. Korea

Prof. Dr. Veli Kurt, Turkey

Prof. Dr. Toufik Mansour, Israel

Assist. Prof .Dr. Hacer Ozden, Turkey

Prof. Dr. Seog Hoon Rim, S. Korea

Prof. Dr. Yilmaz Simsek, Turkey

LOCAL ORGANIZING COMMITTEE

Prof. Dr. Abdullah Aziz Ergin,

Prof. Dr. Huseyin Sumbul,

Prof. Dr. Veli Kurt,

Prof. Dr. Nuri Unal,

Prof. Dr. Ismail Boztosun,

Prof. Dr. Ugur Camci,

Prof. Dr. Gurhan Yalcin,

Assoc. Prof. Dr. Mustafa Ozdemir,

Assoc. Prof. Dr. Ahmet Yardimci,

Assoc. Prof. Dr. Timur Sahin,

Assist. Prof. Dr. Yusuf Sucu,

Assist. Prof. Dr. Fadi Al-Turjman,

Dr. Burak Kurt,

Dr. Ahmet Aykut Aygunes,

Dr. Secil Ceken,

Lecturer Fusun Yalcin,

Research Assistant Ayse Yilmaz Ceylan,

Research Assistant Rahime Dere,

Research Asistant Naci Er,

Irem Kucukoglu,

Gulsah Ozdemir,

Ortac Ones,

Mehmet Uc,

Dilek Soylemez Ozden.

SCIENTIFIC COMMITTEE

M. Acikgoz (Turkey) C. Adiga (India) M. Abdel-Aty (Egypt) M. Alkan (Turkey)

F. Al-Turjman (Turkey) K. Atanassov (Bulgaria) A. Bayad (France) M. Beck (USA)

I. Boztosun (Turkey) U. Camci (Turkey) I. N. Cangul (Turkey) A. S. Cevik (Turkey)

J. Choi (S. Korea) D. Cvijovi (Serbia) D. V. Dolgy (Russia) A. A. Ergin (Turkey) A.

Esi (Turkey) M. Gunay (Turkey) M.O. Hernane (Algerie) H. K. Hwang (S. Korea) S.

Iyengar (USA) T. Komatsu (Japan) T. Kim (S. Korea) D. S. Kim (S. Korea) V. Kurt

(Turkey) V. Lokesha (India) T. Mansour (Israel) G. V. Milovanovi (Serbia) E. Ozcag

(Turkey) H. K. Pak (Korea) . Pintr (Hungary) A. Raouj (Morocco) S. H. Rim (Korea)

C. S. Ryoo (Korea) M. Saraj (Iran) E. Savas (Turkey) A. I. Shtern (Russia) Y. Simsek

(Turkey) W. Sprig (Germany) H. M. Srivastava (Canada) N. Unal (Turkey)

About The Jangjeon Mathematical Society (JMS)

The Jangjeon Mathematical Society (JMS), born in historic Hapcheon, seeks to

carry on Hapcheon’s proud tradition of excellent scholarship coupled with unquestion-

able moral fidelity. Loyal to its Hapcheon heritage, JMS strives to maintain individual

excellence, faithfulness to responsibility, and development of talents and abilities while

adhering to core values of contributing to world peace and prosperity.

JMS was founded in 1996 by Doctor Taekyun Kim to fulfill the aforementioned val-

ues through free discussion and cooperation amongst voluntarily participating scholars

motivated by a common concern for the general welfare of mankind. This ideal of free

and open discussion is mirrored by societys name, Jangjeon, which rendered in pure

Korean, meaning Geul-Baat, the place of studies. With this significant symbolism in

mind, Dr. Kim selected his birthplace, Jangjeon, as the title of this society. Since

ancient times, Hapcheon has served as the training round of many scholars who carried

on the teachings of the great Korean scholars, Namyoung Jo Sik, and were renowned for

their utmost moral character and honor. The Hapcheon tradition of excellence may still

be seen in its profound influence on many modern scholars. The geographical attributes

of Hapcheon serve as fitting symbols of its metaphysical properties, The Hwang River,

flowing serenely past suggests a steadfastness of virtue, unshaken by secular concerns,

infusing energy into all living things. Nearby stands the towering Hwang-mae Mountain

whose sheer slopes represent the unwavering fidelity of Hapcheon’s scholars. There are

many great scholars who are the members of JMS such as Dr. Seog-Hoon Rim (Manag-

ing Editor, Kyungpook University), Dr. Hari M. Srivastava (Editor-in-Chief and Past

President of JMS; University of Victoria, Canada), Dr. Alexander Shtern (Assistant

Chief-in-Editors, Moscow State University), Dr. Krassimir Atanassov (Editor-in-Chief,

Bulgarian Academy), Dr. Lee Chae Jang (Assistant-Managing Editor, Kunkook Uni-

versity), Dr. Hongkyung Pak (Adjustor, Daegu Haany University), Dr. Taekyun Kim

(Founding Editor) etc. The 28th Congress of The Jangjeon Mathematical Society will

be held at Sherwood Club Kemer Hotel, Antalya -TURKEY. In conclusion, we are

really appreciative of participants in The 28th Congress of The Jangjeon Mathemati-

cal Society and do hope that all participants, understanding the meaning of Jangjeon,

enjoy this conference and work together for the development of world.

We hope that all participants have free and active Jangjeon meaning ”Geul-baat”

(place of studies) and meaningful discussions with other participants throughout the

conference. Organising Committees of the of the 28th International Conference of The

Jangjeon Mathematical Society (ICJMS2015).

FOREWORD

Dear distinguish participants of the 28th International Conference of The Jang-

jeon Mathematical Society (ICJMS2015). On behalf of the Scientific and Organising

Committees, I would like to welcome you all to Antalya, pretty city, for ICJMS2015

conference. It is my proud privilege to extend my deepest gratitude best wishes for

the 28th ICJMS2015 conference which is organized by Akdeniz University Mathemat-

ics Department at Sherwood Club Kemer Hotel, ANTALYA-TURKEY during 15-19

May 2015. Firstly I am going to give a few words about historic and pretty spectacu-

lar Antalya city, which was first settled about the 200 BC by the Attalid Dynasty of

Pergamon. After that, it was subdued by the Romans, which rule saw Antalya thrive,

including the construction of several new monuments. These are the Hadrian’s Gate

which is given in conference poster and also in the cover page of Abstract Book. The

city has changed hands several times, including to the Byzantine Empire in 1207 and an

expanding Ottoman Empire in 1391. Ottoman rule brought relative peace and stability

for the next five-hundred years (see for detail http://en.wikipedia.org/wiki/Antalya).

I hope you will spend nice time at not only touristic city, but also historical city.

I also give a few words about Akdeniz University and Mathematics Department.

Akdeniz University was founded in 1982, and incorporated the higher education insti-

tutions already established in Antalya, Burdur and Isparta. Akdeniz University is now

taking rapid and determined steps towards becoming a world class university which is

capable of making a significant contribution to the world of science with its current com-

plement of 17 Faculties, 7 Institutes, 5 Schools, 13 Vocational Schools, and 39 Research

and Application Centres (see for detail http://en.akdeniz.edu.tr/en/about-3/history).

Department of Mathematics was founded in 1990. Now there are 8 Professor, 4

Associated Professor, 7 Assistant Professor and 2 Lecturer, 4 Doctor, 6 assistant. Our

department has also PhD and Master program.

Mathematics, which is the oldest of Science, has contributed fundamentally to the

development of our world civilizations. Therefore, we can enter into the science and

technology center using the mathematics and its branches. So Mathematics and its

branches create the possibility of bridgework and communication between the Natural

Sciences and the Engineering Sciences as well as the Economic and also Social Science.

The aim of this conference is to bring to the fore the best of research and applications

that will help our world humanity and society. Due to the valuable idea of the Jangjeon

Mathematical Society, this conference welcomes speakers whose talk contents are mainly

related to the following two subjects:

Pure and Computational and Applied Mathematics Statistics

Mathematical Physics

(related to p-adic Analysis, Umbral Algebra and Their Applications)

Analysis

Algebra

Linear and Multilinear Algebra

Clifford Algebras and Applications

Real and Complex Functions

Orthogonal Polynomials

Special numbers and Functions

Fractional Calculus and q-theory

Number theory and Combinatorics

Approximation Theory and Optimization

Integral Transformations, Equations and Operational Calculus

Partial Differential Equations

Geometry and Its Applications

Numerical Methods and Algorithms

Probability and Statistics and Their Applications

Scientific Computation

Mathematical Methods in Physics and in Engineering

Mathematical Geosciences

I summarize my speech, this conference has provided a novel opportunity for our

distinguish participants to meet and share their scientific works and friendships in

the above areas. I am delighted to note that all participants have free and active

involvement and meaningful discussion with other participants during the conference.

It is my great pleasure to thank main members of Jangjeon Mathematical Society,

because they gave me this chance to organize this conference in Antalya again. It is

my great pleasure to thank local organizing committee especially, Assoc. Prof. Dr.

Mustafa ALKAN, Assoc. Prof. Dr. Melih GUNAY. It is my great pleasure to thank

Administrators of Akdeniz University. And also I send my thanks to Prof.Dr. Abdullah

Aziz ERGIN (Vice-Rector), Prof. Dr. Huseyin SUMBUL (Dean of faculty of Science),

Prof.Dr. Veli KURT and the other members. Finally, I also send my thanks to Omer

TURNA (Sales manager of Turkish Airlines), Muhittin BOCEK (Mayor of municipality

of Konyaaltı) and Ugur SERT (Manager of Karayol Muhendislik).

Consequently, I send my thanks to all distinguish invited speakers, and all partici-

pants. On behalf of the Scientific and Organising Committees

PROF. DR. YILMAZ SIMSEK

Akdeniz University, Faculty of Science, Department of Mathematics

ANTALYA TURKEY

Tel: +90 242 310 23 43, Fax:+90 242 227 89 11

e.mail: [email protected], [email protected],

[email protected], [email protected],

http://matematik.fen.akdeniz.edu.tr/akademik-personel.i85.prof-dr-yilmaz-simseki

http://jms.akdeniz.edu.tr/en

The abstract book of ICJMS 2015

Contents

1 INVITED SPEAKERS 9

Some Families of Double-Layer Potentials Associated with a Certain GeneralizedBi-Axially Symmetric Helmholtz Equation 11

H. M. Srivastava

Hypercomplex Analysis with Applications to fluid flow problems 12Wolfgang Sprossig

Generalized Gaussian quadratures for singular integrals and applications 13Gradimir V. Milovanovic

Lower tail independence of hitting times of two-dimension diffusions 14Satish Iyengar

Ramanujan’s Continued Fractions and their Generalizations and Evaluations 15Chandrashekar Adiga

Arithmetic of multiple Hurwitz-Lerch zetas functions 16Abdelmejid Bayad

Certain Generalized Hypergeometric and Other Classes of Generating Func-tions 17

Rekha Srivastava

Some properties of p-adic integral on the ring of p-adic integers associated withspecial polynomials 18

Taekyun Kim

2 CONTRIBUTED SPEAKERS 19

On Some New Circular Summation Formulas of Theta Functions 21S. N. Fathima, Yudhisthira Jamudulia

Asymptotic Formula For Vasyunin Cotangent Sum 22Mouloud Goubi

Hypergeometric type functions’ use in statistical moments derivation 23Tibor K. Pogany

About a new recurrence relation for the generalized Bernoulli polynomials 24Dmitry V. Kruchinin and Vladimir V. Kruchinin

Explicit formulas for Korobov polynomials 25Dmitry V. Kruchinin, Alexandr A. Shelupanov

Some identities of Barnes-type special polynomials 26Dongkyu Lim, Younghae Do

Current works on Daehee numbers and polynomials 27Seog-Hoon Rim

Two Generalizations of Power and Alternating Power Sum Identities 28Dae San Kim, Taekyun Kim

1 Antalya - TURKEY


A Modified Quadratic Lorenz Attractor in Geometric Multiplicative Calculus 29Mustafa Riza, Hatice Aktore, Bugce Eminaga

Approximation Properties of Jain-Stancu Operators 30Mehmet Ali Ozarslan

Stancu type q-Szasz-Schurer Operators 31Mehmet Ali Ozarslan and Tuba Vedi

On a class of q-Bernoulli, q-Euler and q-Genocchi polynomials 32N. I. Mahmudov, M. Momenzadeh

On existence results for nonlinear fractional differential equations with four-point boundary value problem 33

N. I. Mahmudov and H. Mahmoud

Existence of Solutions of Fractional Boundary Value Problem with IrregularConditions 34

Nazim I. Mahmudov and Sinem Unul

2-j variables Laguerre polynomials properties and applications 35Cemaliye Kurt, Mehmet Ali Ozarslan

On the q-analogue of Daehee numbers and polynomials 36Jin-Woo Park

Incomplete Bernoulli and Cauchy numbers associated with incomplete Stirlingnumbers 37

Takao Komatsu

Solvability of a linearized free surface flow problem under gravity-capillarity. 38Dahbia Hernane-Boukari, Nadjiba Foukroun, Rachida Ait-Yahia Djouadi.

Zeros of certain trinomials. 39Hernane Mohand Ouamar, Jean-Louis Nicolas.

On Generating Functions For Jacobsthal and Fibonacci Polynomials of HigherOrder 40

Gulsah Ozdemir, Yilmaz Simsek

Some Hermite Base Polynomials on q-Umbral Algebra 41Rahime Dere

Some identities of the higher order Barnes-type q-Bernoulli polynomials andthe higher order Barnes-type q-Euler polynomials 42

Lee-Chae Jang

A numerical verification on the structure of the zeros of Genocchi polynomials 43J. Y. Kang, C. S. Ryoo

A p-Adic Approach to Identities of Symmetry for Carlitzs q-Bernoulli Polyno-mials 44

Sang-Hun Lee

Unification of the B-Splines by using generating functions for the Bernstein typebasis functions 45

Irem Kucukoglu, Yilmaz Simsek

2 Antalya - TURKEY


Controllability problem for interval linear systems 46Dmitriy V. Dolgy

Bernstein basis functions related to combinatorial sums involving binomial co-efficients and special numbers 47

Yilmaz Simsek

Notes on Unified q-Apostol-Type Polynomials 48Burak KURT

Unified Apostol-Type Polynomials and Alternating Sums 49Veli KURT

Bilinear Multipliers of Function Spaces with Wavelet Transform 50Oznur Kulak

A Study About Approximation of Non-Convolution Type Double Singular In-tegral Operators 51

Mine Menekse Yilmaz, Gumrah Uysal

A symmetric identity on the q-Genocchi polynomials of higher order under thirddihedral group D3 52

Erkan Agyuz, Mehmet Acikgoz, Serkan Araci

Some new identities concerning some special polynomials under the theory ofmultiple q-calculus 53

Mehmet Acikgoz, Serkan Araci

On the von Staudt-Clausen theorem of q-Frobenius-Euler numbers 54Serkan Araci, Mehmet Acikgoz

Symmetric identities involving q-analog of Euler polynomials under S4 55Ugur Duran, Mehmet Acikgoz, Serkan Araci

Remarks on formulas related to modular forms 56Aykut Ahmet Aygunes

A Special Finite Sum Associated with the Dedekind and Hardy type Sums 57Elif Cetin

A general approach for enrichment of the nonconforming finite elements in anydimension 58

Yassine Zaim

High-order Schemes for the Klein-Gordon Equations 59Asuman Zeytinoglu, Murat Sari

Determinant line bundles over Teichmuller space 60David Radnell

A Matrix Approach to Solving Hyperbolic Partial Differential Equations UsingBernoulli Polynomials 61

Kubra Erdem Bicer, Salih Yalcinbas

On Periodic Solutions to Nonlinear Differential Equations In Banach Spaces 62Abdullah Cavus, Djavvat Khadjiev, Seda Ozturk

3 Antalya - TURKEY


On A Characterization of Compactness and the Abel-Poisson Summability OfFourier Coefficients In Banach Spaces 63

Seda Ozturk

Existence Results of Solutions for Nonlinear Fractional Differential Equations 64

Tugba Senlik Cerdik, Nuket Aykut Hamal, Fulya Yoruk Deren

A Sum Operator Method for the Existence and Uniqueness of Positive Solutionsto a Nonlinear Fractional Differential Equation 65

Fulya Yoruk Deren, Nuket Aykut Hamal, Tugba Senlik Cerdik

A Recurrence Relation for Orthogonal Polynomials on Triangular Domains 66

Abedallah Rababah

Legender operator matrix of differentiation for solving Chua’s System 67

A.K Alomari

New Results on Omega Paracompactness 68

Samer Al Ghour

Toeplitz operators in the analytic Bergman space 69

Mujo Mesanovic

Product of Toeplitz operators on the harmonic Bergman space 70

Issam Louhichi

A note on tribonacci numbers with particular matrices 71

Seyyed Hossein Jafari-Petroudi, Maryam Pirouz

Weighted composition operators on vector valued weighted Dirichlet typespaces 72

Hamid Vaezi, Sepideh Nasresfahani

Application of the Bernstein Polynomials for Solving Volterra Integral Equa-tions with Convolution Kernels 73

Ahmet Alturk

On some explicit and asymptotic formulas related to the m-arithmetic triangle 74

Armen Bagdasaryan

Inversion formula for analytic functions 75

Armen Bagdasaryan, Seifedine Kadry

Generalized Beltrami Systems with a Singular Point 76

Yesim Saglam Ozkan, Sezayi Hızlıyel

Some Sequence spaces of interval numbers defined by Orlicz Function 77

Ayten Esi

Generalized ideal convergence of double sequences in intuitionistic fuzzy 2-normed linear spaces 78

Ayhan Esi

A B-Spline Approach to q-Eulerian Polynomials 79

Cetin Disibuyuk, Sule Ulutas

4 Antalya - TURKEY


Asymptotic Behaviour of Resonance Eigenvalues of the Schrodinger Operatorwith a Matrix Potential 80

Sedef KARAKILIC,Setenay AKDUMAN,Didem COS. KAN

q-Peano Kernel and Its Applications 81Gulter Budakci, Halil Oruc

Solution for the Problem of the Best Uniform Approximation of the Grid Func-tion with Linear Splines and Applications for Making Decisions 82

B. Bayraktar, V. Kudaev

Vector-valued B-singular integral operators in Lebesgue spaces 83Seyda Keles, Vagif S. Guliyev

The Similarity Invariants of Non-lightlike Curves in the Minkowski 3-space 84Hakan Simsek, Mustafa Ozdemir

Matrices Over Hyperbolic Split Quaternions 85Melek Erdogdu, Mustafa Ozdemir

Mannheim Partner Curves in Cartan-Vranceanu 3-Space 86A. Yilmaz Ceylan, A. A. Ergin

On Rational Knots and Links in the Solid Torus 87Khaled Bataineh

On 2-dimensional Finsler manifold 88Morteza Faghfouri

A Note on Complex q−Baskakov-Stancu Operator with Divided Differences 89Dilek Soylemez Ozden, Didem Aydın Arı

A Characterization of Curvature Functions in R41 90

Esen Iyigun

A presentation and some finiteness conditions for a new version of the Schutzenbergerproduct of monoids 91

Firat Ates,I. Naci Cangul, A. Sinan Cevik, Eylem Guzel Karpuz

Effective results for diophantine equations over finitely generated domains 92Atilla Berczes

Semigroup algebra and nilpotent ideals 93Hasan Pourmahmood Aghababa, Mohammad Hossein Sattari

On weakly semiprime ideals of commutative rings 94Ayman Badawi

On Finiteness Conditions for Bruck-Reilly and Generalized Bruck-Reilly ∗-Extensions 95

Seda Oguz, Eylem Guzel Karpuz

Two-Sided Crossed Product of Groups 96Eylem Guzel Karpuz, Esra Kırmızı Cetinalp

On the residual algebraic free extension of a valuation on K to K(x) 97Figen Oke

5 Antalya - TURKEY


On Certain Extensions of Valuated Fields 98Burcu ozturk, Figen Oke

On Hadamard codes constructed over F2 + uF2 + ...+ umF2 99Mustafa Ozkan, Figen Oke

Minimal Polynomials Corresponding to Spectral Sets of some Graphs 100Togan, M., Yurttas, A., Cevik, A. S., Cangul, I. N.

Some Zagreb Indices of Subdivision and r-Subdivision of Doubles of SomeGraphs 101

Cangul, I. N., Yurttas, A., Togan, M., Cevik, A. S.

Quasigroup and its weak compatibility graph for the homogeneous space ofdegree 4 102

Bokhee Im, Ji-Young Ryu

Grobner-Shirshov Basis of an Exceptional Braid Group 103Eylem Guzel Karpuz, Nurten Urlu, A. Sinan Cevik

Eigenspaces of matrices associated with the Pascal matrix 104Ik-Pyo Kim

On the Weakly Second Spectrum of a Module 105Secil Ceken, Mustafa Alkan

On the radical of a submodule over a noncommutative ring 106Ortac Ones, Mustafa Alkan

On the Classical Zariski Topology Over Prime Spectrum of a Module 107Secil Ceken, Mustafa Alkan

Matrix and determinants division using Salihu’s method 108Armend Salihu, Fatlinda Musliu - Salihu

On Graded Semi-Prime Rings 109Rashid Abu-Dawwas

On Modules over A Group 110Mehmet Uc, Ortac Ones, Mustafa Alkan

On the Crossed Modules and 2-Crossed Modules 111Ozgun Gurmen Alansal

Multisimplicial Groups 112Ozgun Gurmen Alansal

Control of the chaotic dynamics of the Hindmarsh-Rose model 113Tounsia Benzekri

Multi Objective Geometric programming With Interval Coefficients: A para-metric Approach 114

M. Saraj, Z.Mousavi

Effects of Chosen Scalar Products on Gradient Descent Algorithms 115Evgin Goceri

6 Antalya - TURKEY


A Meta-Heuristic Approach for Course Scheduling in Akdeniz University 116Mehmet Karakoc, Melih Gunay, Guler Cigdem, Fadi Alturjman

Robust CT-Prediction Algorithm for RT-PCR 117Melih Gunay

A Novel Method to Characterize Data Requests in the Future Internet 118Melih Gunay, Irem Kucukoglu, Fadi Al-Turjman

On-line Heuristic Approach for Data-Collectors Assignment in ITS 120Mehmet Karakoc, Fadi Alturjman, Melih Gunay

Stay Connected in Vehicular Wireless Networks using Graph Theory and AI 121Recep Ozdemir, Fadi Al-Turjman,Melih Gunay

Combining Short Ultrasound Recordings for Long Duration Observation of FetalBreathing Movement 122

Umit Deniz ULUSAR

Statistical Assessment of Heavy Metals Distribution and Contamination of BeachSand Along the Manavgat Alanya Coastline of Antalya, Turkey 123

Fusun Yalcin, Daniel G. Nyamsari, Ebru Paksu, M. Gurhan Yalcin

Cluster analysis applied to alkaline geochemical data (Hamit, Turkey) 124Fusun Yalcin, Nurdane Ilbeyli

The Geothermal Model of Mersin (Turkey) Region 125Yusuf URAS, Alican Kop, Mahmut Dag

Automated Detection of Facial Disorders (ADFD): A Novel Approach Based-onDigital Photographs 126

Evgin Goceri, Melih Gunay, Fadi Al-Turjman

Associativity of Max-Min Compsition of Three Fuzzy Relations 127M. A. Shakhatreh, T. A. Qawasmeh

Fractional Order Logistic Equation Derived from Hanta Epidemics 128Zarife Gokcen Karadem, Mevlude Yakıt Ongun, Damla Arslan

An Algorithmic Finite Element Method for Noncoercive Variational Inequali-ties 129

Messaoud Boulbrachene

Determining Factors of FTA Negotiation Outcomes: An analysis using Instru-ment Variable Two Stage Least Squares 130

Jacob Wood, Jungsuk Kim

Revenue maximization policies for Queueing Networks with Flexible Servers 131Salih Tekin

Comparative Analysis of Simulation Tools in Biochemical Networks 132Gokce Tuncer, Vildan Purutcuoglu

Application of Impulsive Deterministic Simulations of Biochemical Networks via Sim-ulations Tools 133

Gokce Tuncer, Vildan Purutcuoglu

7 Antalya - TURKEY


Using Bezier Curves in Medical Applications 134Buket Simsek, Ahmet Yardimci

On the approximation of the Conway-Maxwell-Poisson normalizing constant 135Burcin Simsek, Satish Iyengar

A note on the analysis of Mathematical learning Conditions 136Jong Jin Seo, Taekyun Kim

Epidemic in Travnik 137Admir Hodzic, Adnan Behrem, Nina Bijedic PhD, Emir Slanjankic

Insensitive stochastic bounds for the stationary distribution of the embeddedMarkov chain 138

Mohamed Boualem

On interval-valued fuzzy lattices 139Jeong Gon Lee

A Soft Based Method to Solve the Analysis Problem of the Distance BetweenTwo Soft Points 140

Guzide Senel

Some inevitable remarks on the some recent trends in fixed point theory 141Erdal Karapinar

8 Antalya - TURKEY


1 INVITED SPEAKERS

9 Antalya - TURKEY


10 Antalya - TURKEY


Some Families of Double-Layer Potentials

Associated with a Certain Generalized

Bi-Axially Symmetric Helmholtz Equation

H. M. Srivastava

Abstract

Various classes of double-layer potentials are known to play an important role in solv-ing boundary value problems for elliptic equations. In our presentation here, we introduceand investigate some families of double-layer potentials which are associated with a cer-tain generalized bi-axially symmetric Helmholtz equation. By using several properties ofmultivariable hypergeometric functions (and, especially, of one of Appell’s hypergeomet-ric functions in two variables), we prove limiting theorems and derive integral equationsconcerning a denseness of double-layer potentials.

2010 Mathematics Subject Classifications : Primary 35J15, 35J70; Secondary 33C65,58J10, 58J20.

Keywords :Singular partial differential equations; Whittaker functions; Multivariable hy-pergeometric functions; Lauricella’s hypergeometric functions in n variables; Horn’s and Ap-pell’s hypergeometric functions in two variables; Generalized bi-axially symmetric Helmholtzequation; Degenerated elliptic equations; Generalized axially symmetric potentials; Double-layer potentials.

Department of Mathematics and Statistics University of VictoriaVictoria, British Columbia V8W 3R4, CanadaE-mail : [email protected]

11 Antalya - TURKEY


Hypercomplex Analysis with Applications to

fluid flow problems

Wolfgang Sprossig

Abstract

Hypercomplex analysis can be seen as some kind of ”‘complex function theory”’ forhigher dimensions, where complex numbers are replaced by quaternions, coquaternions,split quaternions, Clifford numbers, octonions, sedenions etc.. Hyperholomorphic functionsplay the role of holomophic functions of the complex function theory in the plane. They arezero solutions of higher-dimensional versions of Cauchy-Riemann equations (Riesz system,Fueter system, system of Moisil-Teodorescu, etc.).In this talk we reduce our considerationsto quaternion valued functions over 3D-domains. As in the classical function theory alsoin higher dimenional versions some operators are important: Dirac operator, Teodorescutransform, Cauchy-Fueter operator as well as the orthoprojections on the Bergman spaceof the Hilbert space (module) and on its complement. For boundary value problems wealso need so-called projections of Plemelj type which are connected with the Cauchy-Fueteroperator. We use and derive analoga of basic theorems of the plane function theory. For thetreatment of (initial) boundary value problems we still need a decomposition theorem ofBergman-Hodge type. We intent to show the advandages and benefits of the hypercomplexaccess for treatment of boundary value problems of several fluid flow problems.

Institute of Applied AnalysisTU FreibergPrferstrae 909695 FreibergGermanyE-mail : [email protected]

12 Antalya - TURKEY


Generalized Gaussian quadratures for singular

integrals and applicationsGradimir V. Milovanovic

AbstractIn this lecture we consider efficient methods for constructing weighted generalized

quadrature formulas of Gaussian type∫ b

a

f(x)w(x) dx =

n∑k=1

Akf(xk) +Rn(f)

for functions f having algebraic or/and logarithmic singularities. That kind of singularintegrals are appeared in several applications and are very common in the boundary elementmethod. We present several classes of quadratures, which are exact (1) on a space of Muntzpolynomials of dimension 2n; (2) on the so-called algebraic-logarithmic space M2n−2`,2` =P2n−2`−1 ⊕ L2`−1, with dimension

dimM2n−2`,2` = dimP2n−2`−1 + dimL2`−1 = (2n− 2`) + 2` = 2n,

where 1 ≤ ` ≤ n. The existence and uniqueness of such Gaussian quadrature rules fornonpolynomial systems are always guaranteed if the first 2n functions of such systemsconstitute Chebyshev systems on the interval of integration. In such a case, all the weightcoefficients in a generalized Gaussian quadrature formula are positive. In terms of momentspaces, the Gaussian rule corresponds to the unique lower principal representation of thegiven measure (see Karlin and Studden [3]). The metod for constructing genaralized Gaus-sian formulae is based on solving a system of nonlinear equations by Newton-Kantorovichmethod and method of continuation. Numerical examples and applications are included.

2010 Mathematics Subject Classification. 41A55, 65D30, 65D32, 33C45.

Keywords and phrases. Numerical integration; Singular integrals; Gaussian quadrature;Orthogonalization; Integral equations; Boundary element method.

References[1] A.S. Cvetkovic, G.V. Milovanovic, The Mathematica package “OrthogonalPolynomials”, Facta Univ. Ser.

Math. Inform. 19 (2004), 17–36.

[2] G. Golub, J. H. Welsch, Calculation of Gauss quadrature rules, Math. Comp. 23 (1969), 221–230.

[3] S. Karlin, W. J. Studden, Tchebycheff Systems: With Applications in Analysis and Statistics, Pure andAppl. Math. XV, Wiley Interscience, New York, 1966.

[4] P.K. Kythe, P. Puri, Computational Methods for Linear Integral Equations, Birkhauser, Boston – Basel –Berlin, 2002.

[5] J. Ma, V. Rokhlin, S. Wandzura, Generalized Gaussian quadrature rules for systems of arbitrary functions,SIAM J. Numer. Anal., 33 (1996), 971–996.

[6] G. Mastroianni, G.V. Milovanovic, Interpolation Processes – Basic Theory and Applications, Springer Mono-graphs in Mathematics, Springer – Verlag, Berlin – Heidelberg, 2008.

[7] G.V. Milovanovic, A.S. Cvetkovic, Gaussian type quadrature rules for Muntz systems, SIAM J. Sci. Comput.27 (2005), no. 3, 893–913.

[8] G.V. Milovanovic, A.S. Cvetkovic, Special classes of orthogonal polynomials and corresponding quadraturesof Gaussian type, Math. Balkanica 26 (2012), 169–184.

[9] G.V. Milovanovic, T.S. Igic, D. Turnic, Generalized quadrature rules of Gaussian type for numerical evalu-ation of singular integrals, J. Comput. Appl. Math. 278 (2015), 306–325.

Serbian Academy of Sciences and Arts, Belgrade, SERBIAE-mail : [email protected]

13 Antalya - TURKEY


Lower tail independence of hitting times of

two-dimension diffusions

Satish Iyengar

Abstract

The coefficient of tail dependence is a quantity that measures how extreme events in onecomponent of a bivariate distribution depend on extreme events in the other component.It is well-known that the Gaussian copula has zero tail dependence, a shortcoming forits application in credit risk modeling and quantitative risk management in general. Weshow that this property is shared by the joint distributions of hitting times of bivariate(uniformly elliptic) diffusion processes.

Statistics Department University of Pittsburgh Pittsburgh, PA 15260 USAE-mail : [email protected]

14 Antalya - TURKEY


Ramanujan’s Continued Fractions and their

Generalizations and Evaluations

Chandrashekar Adiga

Abstract

Srinivasa Ramanujan made some significant contributions to the theory of q-series andcontinued fractions. Most of his beautiful and useful continued fraction identities can befound in his notebooks and lost notebook. This part of Ramanujan’s work has been studiedand developed by various mathematicians including George E. Andrews, Bruce C. Berndt,R. Askey, S. Bhargava, C. Adiga, D. D. Somashekara, R. Y. Denis, K. R. Vasuki. In thistalk, we discuss some of Ramanujan’s continued fractions and its applications.

2010 Mathematics Subject Classifications : 11A55, 11J70

Keywords :q-series, q-continued fraction, Rogers-Ramanujan continued fraction

References

[1] C. Adiga, B. C. Berndt, S. Bhargava and G. N. Watson, Chapter 16 of Ramanujan’s secondnotebook; Theta-functions and q-series, Mem. Amer. Math. Soc., 315, 53 (1985), 1-91.

[2] C. Adiga and D. D. Somashekara, On some Rogers-Ramanujan type continued fractionidentities, Mathematica Balkanica, New Series 12, 1-2 (1998), 37-45.

[3] G. E. Andrews, B. C. Berndt, L. Jacobsen and R. L. Lamphere, The continued fractionsfound in the unorganized portions of Ramanujan’s notebooks, Mem. Amer. Math. Soc., 477,99 (1992), 1-71.

[4] S. Bhargava and C. Adiga, On some continued fraction identities of Srinivasa Ramanujan,Proc. Amer. Math. Soc., 92 (1984), 13-18.

Department of Studies in Mathematics, University of Mysore Manasagan-gotri, Mysore 570006; INDIAE-mail : [email protected]

15 Antalya - TURKEY


Arithmetic of multiple Hurwitz-Lerch zetas

functions

Abdelmejid Bayad

Abstract

We investigate the multiple Hurwitz-Lerch zeta ζN (s, x, λ), given by

ζN (s, x, λ) =∑

k1,...,kN≥0

λk1+···+kN

(x+ k1 + · · ·+ kN )s. (1)

We prove for ζN (s, x, λ) the following number-theoretic properties, which are well-knownonly for the Lerch transcendent function Φ(λ, s, x), like as:

1. The Lindelof-Wirtinger Fourier expansion [3, 7, 9],

2. Multiplication formula and its Inversion [2, 5, 8],

3. Erdelyi expansion [3],

4. Transcendental theorem [1, 5],

5. Relationships between the functions ζN (s, x, λ) and double gamma, Bose-Einsteinand Clausen integrals.

6. Reduction theorem for ζN (s, x, λ) in terms of Φ(λ, s, x) and Bernoulli polynomials oforder N ,

7. Dedekind sums.

Many others interesting applications and questions are stated.

2010 Mathematics Subject Classifications : 11B68, 11B73

Keywords :Multiple Hurwitz-Lerch zeta, Multiplication formula, Lindelof-Wirtinger ex-pansion, Reduction formula, transcendental numbers

References[1] A. Baker, Transcendental Number Theory. Cambridge Univ. Press, Cambridge (1975).

[2] C.H. Chang, C.-W. Ha, A multiplication theorem for the Lerch zeta function and explicit representations ofthe Bernoulli and Euler polynomials, J. Math. Anal. Appl. 315(2006), pp. 758–767.

[3] A. Erdelyi, Higher transcendental functions, Vol 1, McGraw-Hill, New York, 1953.

[4] Q-M. Luo, Fourier expansions and integral representations for the Apostol-Bernoulli and Apostol-Eulerpolynomials, Math. Comp., Volume 78 (2009), No. 268, pp. 2193-2208.

[5] T. Nakamura, Some formulas related to Hurwitz–Lerch zeta functions, Ramanujan Journal Vol. 21 (2010),No. 3, pp. 285–302.

[6] L.M. Navas, FJ. Ruiz, J L. Varona Some functional relations derived from the Lindlof-Wirtinger expansionof the Lerch transcendant function, to appear.

[7] L. M. Navas, F. J. Ruiz and J. L. Varona, Asymptotic behavior of the Lerch transcendent function, J.Approx. Theory textbf170 (2013), pp.21–31.

[8] H.M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments. Math.Proc.Camb. Philos. Soc. 129 (1) (2000), pp. 7784.

[9] W. Wirtinger,Uber eine besondere Dirichletsche Reihe, J. Reine Angew. Math. 129 (1905),pp. 214–219.

Abdelmejid BAYADDepartement de mathematiquesUniversite d’Evry Val d’Essonne, 23 Bd. De France91037 Evry Cedex, France

E-mail : [email protected]

16 Antalya - TURKEY


Certain Generalized Hypergeometric and Other

Classes of Generating Functions

Rekha Srivastava

Abstract

In the year 2012, H. M. Srivastava et al. introduced and initiated the study of manyinteresting fundamental properties and characteristics of a certain pair of potentially usefulfamilies of the so-called generalized incomplete hypergeometric functions. Ever since thenthere have appeared many closely-related works dealing substantially with notable devel-opments involving various classes of generalized hypergeometric functions and generalizedhypergeometric polynomials, which are defined by means of the corresponding incompleteand other novel extensions of the familiar Pochhammer symbol. Our aim in this lecture isto present a survey and investigation of some of these recent developments involving severalgeneral families of hypergeometric and other classes of generating functions by applying(for example) some such combinatorial identities as Gould’s identity, each of which stemsessentially from the Lagrange expansion theorem. Various (known or new) special casesand consequences of the results presented in this paper are also considered.

2010 Mathematics Subject Classifications : Primary 33B15, 33B20, 33C05, 33C15,33C20; Secondary 33B99, 33C99, 60B99.

Keywords :Gamma function; Incomplete Gamma functions; Pochhammer symbol; In-complete Pochhammer symbols; Incomplete hypergeometric functions; Incomplete hypergeo-metric polynomials; Binomial coefficients; Generating functions; Lagrange expansion theorem;Srivastava-Buschman generating function; Combinatorial identities; Gould’s identity; Reduc-tion formulas; Chu-Vandermonde summation formula.

Department of Mathematics and Statistics University of VictoriaVictoria, British Columbia V8W 3R4, CanadaE-mail : [email protected] Site: http://www.math.uvic.ca/other/rekhas/

17 Antalya - TURKEY


Some properties of p-adic integral on the ring of

p-adic integers associated with special

polynomials

Taekyun Kim

Abstract

Abstract. In this paper, we introduce some properties of p-adic integrals on the ringof p-adic integers and we apply these properties to derive some identities and formulae ofspecial polynomials.

Department of Mathematics, Kwangwoon University, Seoul 139-701, Republicof KoreaE-mail : [email protected]

18 Antalya - TURKEY


2 CONTRIBUTED SPEAKERS

19 Antalya - TURKEY


20 Antalya - TURKEY


On Some New Circular Summation Formulas of

Theta Functions

S. N. Fathima, Yudhisthira Jamudulia

Abstract

In this paper, we prove new circular summation formulas using the theory of ellipticfunctions. As a special case of identities we obtain interesting identities related to thetafunctions.

2010 Mathematics Subject Classifications : 11F27, 11F20, 33E05

Keywords : Circular summation, Elliptic functions, Theta functions, Ramanujan, Jacobi.

Department of MathematicsRamanujan School of Mathematical SciencesPondicherry UniversityPuducherry - 605 014INDIAE-mail : [email protected],[email protected].

21 Antalya - TURKEY


Asymptotic Formula For Vasyunin Cotangent

Sum

Mouloud Goubi

Abstract

In this work, we study the cotangent sum c(q/p) and formulate it’s asymptotic expres-sion. In order to found the expression of c(q/p) + c(p/q) which is related directly to theNyman-Beurling criterion for the Riemann hypothesis.

2010 Mathematics Subject Classifications :11T23, 20G40, 94B05.

Keywords :Vasyunin formula, zeta function, fractional part function, Nyman-Beurlingcriterion for (HR).

References

[1] L. Baez-Duarte, On Beurling Real Variable Re formulation of the Riemann Hypothesis,Advances in Mathemathematics 101 (1993), pp.10-30.

[2] L. Baez-Duarte, News versions of the Nyman Beurling criterion for the Riemann hypothesis,IJMMS (2002), pp.387-406.

[3] L. Baez-Duarte, A strengthening of the Nyman-Beurling criterion for the a Riemann hy-pothesis, Rend. Mat. Acc. Lincei (9), 14 (2003), pp. 511.

[4] L. Baez-Duarte, A general strong Nyman-Beurling criterion for the Riemann hypothesis,Publication del’Institut Mathematiques. Nouvelle serie, 78 (92) (2005), pp.117 125.

[5] L. Baez-Duarte, M. Balazard, B. Landreau, E. Saias, Etude de l’autocorrelation multiplica-tive de la fonction partie fractionnaire, Ramanujan Journal, 9 (2005), pp. 215-240.

[6] M. Balazard, Sur les Dilatees entires de la Fonction Partie Fractionnaire, Functionset Ap-proximatio. XXXV. (2006), pp.37-49.

[7] S. Bettin, B. Conrey Period functions and contangent sums, Algebra and Number Theory17(1)(2013), 215-242.

[8] L. Takas, On generalized Dedekind Sums, Journal of Number Theory, 11,(1979), pp.264-272

[9] V. I. Vasyunin, On a biorthogonal system associated with the Riemann hypothesis Algebrai Analiz 7(3)(1995), 118-135.

Mouloud Goubi, Department of Mathematics, University of UMMTO, P.O.Box17,RP 15000, Tizi-ouzou, Algeria, and Laboratoire d’Algebre et Theorie desNombres USTHB (Alger)E-mail : [email protected]

22 Antalya - TURKEY


Hypergeometric type functions’ use in

statistical moments derivation

Tibor K. Pogany

Abstract

The first main aim of this talk is to describe the general real order moments for therandom variable ξ having three parameter exponentiated exponential Poisson distribution.We show that the existing [1] series and integral form expressions for positive integer ordermoments Eξν , ν ∈ N are valid for all ν > 1 − α, α > 0. Next, the moments for the rvhaving four-parameter gamma–exponentiated exponential–Weibull distribution have beendetermined in terms of Fox–Wright 1Ψ∗0 and Meijer G3,1

1,3. Finally, we expose the seriesrepresentation of the moments for a novel four-parameter Marshall–Olkin exponential–Weibull distribution, discussing by the way the distribution’s modality. The moments andthe quantile function are now expressed via Goyal–Laddha generalized Hurwitz–Lerch ZetaΦ∗µ and Fox–Wright 1Ψ∗0.

2010 MSC : 33CXX, 33E20, 60E05, 60E10, 62E15, 62F10

Keywords : Exponentiated exponential (Poisson, Gamma-Weibull, Marshall-Olkin exponential-Weibull) distribution, moments, quantile function, Fox–Wright pΨq, Goyal–Laddha HLZeta Φ∗

µ,unimodality.

References[1] M. M. Ristic, S. A. Nadarajah, A new lifetime distribution. J Statist. Comput. Simul. 84 (2014), No. 1,

135–150.

[2] H. M. Srivastava, R. K. Saxena, T. K. Pogany, R. Saxena, Integral and computational representations ofthe extended Hurwitz-Lerch Zeta function, Integral Transforms Spec. Funct. 22 (2011), 487-506.

[3] T. K. Pogany, The exponentiated exponential Poisson distribution revisited, Statistics (2014), (to appear).

[4] T. K. Pogany, Abdus Saboor, The Gamma exponentiated exponential-Weibull distribution, Filomat (2014),(to appear).

[5] T. K. Pogany, A. Saboor, S. Provost, The Marshall-Olkin exponential Weibull distribution, Hacettepe Journalof Mathematics and Statistics (2015), (to appear).

Faculty of Maritime Studies, University of Rijeka, 51000 Rijeka, CroatiaE-mail : [email protected]

23 Antalya - TURKEY


About a new recurrence relation for the

generalized Bernoulli polynomials

Dmitry V. Kruchinin and Vladimir V. Kruchinin

Abstract

In this work, using a logarithmic derivative, we derive new recurrence relations for thegeneralized Bernoulli polynomials:

Bαn (x) = xBαn−1(x)− α

n

n−1∑i=0

(−1)n−i(n

i

)Bn−iB

αi (x),

where Bn−i are the Bernoulli numbers.According obtained result, we get several corollaries for Bernoulli polynomials, Norlund

polynomials, function log(1 + x), the Bernoulli numbers, and Cauchy numbers of secondtype (sequence A002657 in [1]).

2010 Mathematics Subject Classifications : 11B68, 05A15

Keywords : generating function, recurrence relation, Bernoulli polynomial, Bernoulli num-ber

References

[1] N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, Published electronicallyat http://oeis.org (2015).

[2] L. Carlitz, Note on Norlund’s polynomial B(n(z)), Proc. Amer. Math. Soc., 11: 452–455

(1960).

[3] H. M. Srivastava and P. G. Todorov, An explicit formula for the generalized Bernoullipolynomials, J. Math. Anal. Appl., 130: 509–513 (1988).

[4] D. V. Kruchinin and V. V. Kruchinin, Application of a composition of generating functionsfor obtaining explicit formulas of polynomials, J. Math. Anal. Appl. 404: 161–171 (2013).

Address: Tomsk State University of Control Systems and Radioelectronics,Tomsk, RussiaE-mail : [email protected] or [email protected]

24 Antalya - TURKEY


Explicit formulas for Korobov polynomials

Dmitry V. Kruchinin, Alexandr A. Shelupanov

Abstract

Korobov [1] introduced special numbers Pn and special polynomials Pn(x) for interpo-lation of several variables functions. The Korobov numbers and polynomials are discreteanalogues of the Bernoulli numbers and polynomials, respectively.

In this work, using notions of composita and composition of generating functions, weobtain explicit formulas for the Korobov numbers and polynomials of both first and secondkinds, respectively.

Also we get some interesting recurrence relations and new identities which involve theKorobov numbers of both first and second kinds.

This work was partially supported by the Ministry of education and science of Russia,government order No 3657 (TUSUR).

2010 Mathematics Subject Classifications : 33C47, 05A15

Keywords : composita, generating function, composition of generating function, Korobovpolynomial, Korobov number

References

[1] N. M. Korobov, Mathematical Notes, 2: 77–89 (1996).

[2] D. V. Kruchinin and V. V. Kruchinin, Application of a composition of generating functionsfor obtaining explicit formulas of polynomials, J. Math. Anal. Appl. 404: 161–171 (2013).

[3] D. V. Kruchinin and V. V. Kruchinin, Explicit formulas for some generalized polynomials,Applied Mathematics and Information Sciences 7: 2085–2090 (2013).

[4] D. V. Kruchinin, Explicit formula for the generalized Mott polynomials, Adv. Studies Con-temp. Math. 24(3): 327–332 (2014).

[5] D. V. Kruchinin and Y. V. Shablya, International Journal of Mathematics and MathematicalSciences in press.

Address: Tomsk State University of Control Systems and Radioelectronics,Tomsk, RussiaE-mail : [email protected]

25 Antalya - TURKEY


Some identities of Barnes-type special

polynomials

Dongkyu Lim, Younghae Do

Abstract

In this paper, we consider Barnes-type special polynomials and give some identitiesof their polynomials which are derived from the bosonic p-adic integral or the fermionicp-adic integral on Zp.

2010 Mathematics Subject Classifications : 11B68, 11S40

Keywords :Barnes-type Bernoulli polynomial, higher order Euler polynomial, multivariatep-adic fermionic integral, Barnes-type Euler polynomial

Department of Mathematics, Kyungpook National University, 702-701, Daegu,S. KoreaE-mail : [email protected]

Department of Mathematics, Kyungpook National University, 702-701, Daegu,S. KoreaE-mail : [email protected]

26 Antalya - TURKEY


Current works on Daehee numbers and

polynomials

Seog-Hoon Rim

Abstract

Daehee numbers and polynomials are investigated by many authors . In this talk werepresent recent works on Daehee numbers and polynomials related with other numbersand polynomials.

Kyungpook UniversityE-mail : [email protected]

27 Antalya - TURKEY


Two Generalizations of Power and Alternating

Power Sum IdentitiesDae San Kim, Taekyun Kim

Abstract

The classical power sum and alternating power sum identities can be stated as

m∑i=0

sn (i) =1

n+ 1(Bn+1 (m+ 1)−Bn+1) ,

m∑i=0

(−1)i sn (i) =1

2((−1)mEn (m+ 1) + En) ,

where sn (x) = xn ∼ (1, t) is the simplest possible Appell polynomial. As one generalizationof these, we obtain power and alternating power sum identities for any Appell polynomialsand illustrate our results by many examples. As another generalization of those, we willconsider one family of Sheffer sequences satisfying a generalization of the classical powersum identity and another one satisfying that of the classical alternating power sum identitiy.Here again we present many examples for our results.

2010 Mathematics Subject Classification. 05A40, 11B68, 11B75, 11B83.

Power sum identity, Alternating power sum identity, Appell polynomial, Shef-fer polynomial

References[1] S. Araci and M. Acikgoz, A note on the Frobenius-Euler numbers and polynomials associated with Bernstein

polynomials, Adv. Stud. Contemp. Math. (Kyungshang) 22 (2012), no. 3, 399–406.

[2] A. Bayad, Modular properties of elliptic Bernoulli and Euler functions, Adv. Stud. Contemp. Math. (Kyung-shang) 20 (2010), no. 3, 389–401.

[3] L. Carlitz, A degenerate Staudt-Clausen theorem, Arch. Math. (Basel) 7 (1956), 28–33.

[4] L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math. 15 (1979), 51–88.

[5] D. V. Dolgy, D. S. Kim, T. Kim, and T. Komatsu, Barnes’ multiple Bernoulli and poly-Bernoulli mixed-typepolynomials, J. Comput. Anal. Appl. 18 (2015), no. 5, 933–951.

[6] D. S. Kim and T. Kim, Higher-order Frobenius-Euler and poly-Bernoulli mixed-type polynomials, Adv.Difference Equ. (2013), 2013:251.

[7] D. S. Kim and T. Kim, Higher-order Bernoulli and poly-Bernoulli mixed-type polynomial, Georgian Math.J. (2015), to appear.

[8] D. S. Kim and T. Kim, Barnes-type degenerate Euler polynomials, (Communicated).

[9] D. S. Kim and T. Kim, Higher-order degenerate Bernoulli polynomials, (Communicated).

[10] D. S. Kim and T. Kim, Higher-order degenerate Euler polynomials, Appl. Math. Sci. (Ruse) 9 (2015), no. 2,57–73.

[11] D. S. Kim and T. Kim, A generalization of power and alternating power sums to any appell polynomials,(communicated).

[12] D. S. Kim and T. Kim, Families of Sheffer sequences satisfying generalizations of power and alternatingpower sum identities, Adv. Stud. Theor. Phys. 9 (2015), no. 4, 155–170.

Department of Mathematics, Sogang University, Seoul 121-742, KoreaE-mail : [email protected]

Department of Mathematics, Kwangwoon University, Seoul 139-701, KoreaE-mail : [email protected]

28 Antalya - TURKEY


A Modified Quadratic Lorenz Attractor in

Geometric Multiplicative Calculus

Mustafa Riza, Hatice Aktore, Bugce Eminaga

Abstract

A new three-dimensional multiplicative chaotic system, the modified quadratic geo-metric Lorenz attractor is analysed in the framework of geometric multiplicative calculus.The basic dynamical properties of this new chaotic system, as the equilibrium points, Lya-punov exponents, fractional dimension, Time-series analysis, bifurcation are worked out.The geometric multiplicative Runge-Kutta method is used to carry out the simulations.

2010 Mathematics Subject Classifications : 37N30, 65P20, 65L06

Keywords :Dynamic Systems, Lorenz Attractor,Numerical Solution, Geometric Multi-plicative Runge-Kutta Method, Multiplicative Calculus

References

[1] E. N Lorenz, Deterministic nonperiodic flow, Journal of the atmospheric sciences 20 (2)(1963) 130-141

[2] I. Pehlivan, Y. Uyaroglu, A new chaotic attractor from general Lorenz system family andits electronic experimental implementation, Turkish Journal of Electrical Engineering andComputer Science 18 (2010) 171184.

[3] M. Riza, H. Aktore, The Runge-Kutta Method in Geometric Multiplicative Calculus. arXivpreprint (2015), arXiv:1311.6108v2.

Department of Physics, Eastern Mediterranean University, Famagusta, NorthCyprus, via Mersin 10, TurkeyE-mail : [email protected]

Department of Mathematics, Eastern Mediterranean University, Famagusta,North Cyprus, via Mersin 10, TurkeyE-mail : [email protected]

Department of Computer Engineering, Girne American University, Kyrenia,North Cyprus, via Mersin 10, TurkeyE-mail : [email protected]

29 Antalya - TURKEY


Approximation Properties of Jain-Stancu

Operators

Mehmet Ali Ozarslan

Abstract

In the present paper, we introduce the Stancu type Jain operators, which general-ize the well-known Szazs operators via Lagrange expansion. We investigate the weightedapproximation properties of them and obtain the error of approximation by using the mod-ulus of continuity and certain Lipschitz class functions. Finally, we obtain an asymptoticexpansion of Voronovskaya type.

2010 Mathematics Subject Classifications :41A10,41A25

Keywords :Szsz.Mirakyan operators, Modulus of continuity, Jain operators, Voronovskaya-type theorem

References

[1] G.C. Jain, Approximation of functions by a new class of linear operators, J. Austral. Math.Soc. 13(3) (1972), 271-276.

[2] O. Duman and M.A. Ozarslan, Szasz-Mirakjan type operators providing a better errorestimation, Appl. Math. Lett. 20 (2007) 1184-1188.

Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, TurkeyE-mail : [email protected]

30 Antalya - TURKEY


Stancu type q-Szasz-Schurer Operators

Mehmet Ali Ozarslan and Tuba Vedi

Abstract

In this paper, the q-Szasz-Schurer-Stancu operators is introduced and Korovkin typetheorem is proved. Then, the error of the approximation is obtained by means of modulusof continuties. Furthermore, an estimate for the approximation of certain Lipschitz classfunction is given.

2010 Mathematics Subject Classifications : Primary 41A10, 41A25; Secondary41A36.

Keywords : q-Szasz-Schurer operators, weighted modulus of continuity.

References

[1] Aral, A.: A generalization of Szasz-Mirakyan operators based on q-integers, Math. Comput.Modelling, 47 (9-10), 1052-1062 (2008).

[2] Mahmudov, NI.: q-Szasz operators which preserve x2, Math. Slovaca, 63 (5), 1059-1072,(2013).

[3] Mahmudov, NI: q-Szasz Mirakyan operators which preserve x2, Journal of Computationaland Applied Mathematics, 236 (16), 4621-4628 (2011).

[4] Mahmudov, NI.: Approximation by q-Szasz operators, arXiv:1005.3934 [math.FA], (2010).

[5] Ozarslan, MA: q-Szasz Schurer operators, Miscolc Mathematical Notes, 12, 225-235 (2011).



31 Antalya - TURKEY


On a class of q-Bernoulli, q-Euler and

q-Genocchi polynomials

N. I. Mahmudov, M. Momenzadeh

Abstract

The main purpose of this paper is to introduce and investigate a class of q-Bernoulli,q-Euler and q-Genocchi polynomials. The q-analogues of well-known formulas are derived.The q-analogue of the Srivastava–Pinter addition theorem is obtained. Some new identitiesinvolving q-polynomials are proved.

References

[1] G. E. Andrews, R. Askey and R. Roy Special functions, volume 71 of Encyclopedia ofMathematics and its Applications, Cambridge University Press, Cambridge, 1999.

[2] L. Carlitz, q-Bernoulli numbers and polynomials, Duke Math. J. 15 (1948) 987–1000.

[3] Jan L. Cieslinski, Improved q-exponential and q-trigonometric functions, Applied Mathe-matics Letters, Volume 24, Issue 12, December 2011, Pages 2110–2114.

[4] M. Cenkci, V. Kurt, S. Rim. and Y. Simsek., On (i; q) Bernoulli and Euler numbers, Appl.Math. Letter, 21 (2008), 706-711.

[5] Cheon G. S., A note on the Bernoulli and Euler polynomials, Appl. Math. Letter, 16(2003), 365-368.

[6] Mahmudov N. I. and Keleshteri M. E., On a class of generalized q-Bernoulli and q-Eulerpolynomials, Adv. Difference Equ. 2013,2013:115.

[7] H. M. Srivastava and A. Pinter, Remarks on some relationships between the Bernoulli andEuler polynomials, Appl. Math. Lett. 17 (2004), no. 4, 375-380.

[8] T. Kim , On the q-extension of Euler and Genocchi numbers, J. Math. Anal. Appl. 326(2007), no. 2, 1458-1465.

[9] Daeyeoul Kim, Burak Kurt, and Veli Kurt, “Some Identities on the Generalized q-Bernoulli,q-Euler, and q−Genocchi Polynomials,” Abstract and Applied Analysis, vol. 2013, ArticleID 293532, 6 pages, 2013. doi:10.1155/2013/293532

[10] S. Nalci and O. K. Pashaev, q-Bernoulli Numbers and Zeros of q-Sine Function,http://arxiv.org/abs/1202.2265v1.

[11] Y. Simsek, I. N. Cangul, V. Kurt, and D. Kim, q-Genocchi numbers and polynomialsassociated with q-Genocchi-type l-functions, Adv. Difference Equ. 2008 (2008), Art. ID.

Eastern Mediterranean UniversityGazimagusa, TRNC, Mersiin 10, TurkeyE-mail : [email protected]@emu.edu.tr

32 Antalya - TURKEY


On existence results for nonlinear fractional

differential equations with four-point boundary

value problem

N. I. Mahmudov and H. Mahmoud

Abstract

We discuss the existence and uniqueness of solution for nonlinear fractional differentialequation with nonlocal four-point boundary condition for the following equation:

CDα0+x (t) = f (t, x (t)) , 0 ≤ t ≤ T, 1 < α < 2,

x (0) + µ0x (T ) = σ0x (η0) , 0 < η0 < η1 < T,CDα

0+x (0) + µC1 Dα0+x (T ) = σ1x (η1) ,

where CDα0+ is a Caputo derivative of order α. Our results are based on the Banach fixed

point theorem and Schauder’s fixed point theorems.

2010 Mathematics Subject Classifications : 34C10

References

[1] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of FractionalDifferential Equations.In:Norrh-Holland Mathematics studies, vol.204 (2006) Elsevier, Am-sterdam.

[2] B. Ahmad and J. J.Nieto, Riemann-Lioville fractional integro-differential equations withfractional non-local integral boundary conditions. Bound.Value Prob. 1.36 (2011) 1-9.

Eastern Mediterranean UniversityGazimagusa, TRNCMersin 10, TurkeyE-mail : [email protected]

Eastern Mediterranean UniversityGazimagusa, TRNCMersin 10, TurkeyE-mail : [email protected]

33 Antalya - TURKEY


Existence of Solutions of Fractional Boundary

Value Problem with Irregular Conditions

Nazim I. Mahmudov and Sinem Unul

Abstract

In this paper, we investigate the existence and uniqueness of solution for nonlinear frac-tional differential equation with integral and irregular boundary conditions. By the Greenfunction and the fixed point theorems, we state and prove the existence and uniquenessresults of the problem. An example is given to illustrate the result.

2010 Mathematics Subject Classifications : 34C10

Keywords : fractional, differential equations, irregular conditions, boundary value problem

References

[1] Ahmad, Bashir; ”Existence of solutions for irregular boundary value problems of nonlinearfractional differential equations”; Appl. Math. Lett. 23 (2010), no. 4, 390–394.

[2] Zhi-Wei, Lv; ”Existence results of fractional differential equations with irregular boundaryconditions and p-Laplacian operator”; J. Appl. Math. Comput. 46 (2014), no. 1-2, 33–49.

[3] Guotao,Wang; Bashir, Ahmad; Lihong, Zhang; ”On impulsive boundary value problemsof fractional differential equations with irregular boundary conditions”; Abstr. Appl. Anal.2012, Art. ID 356132, 18 pp.

[N.I. Mahmudov] Eastern Mediterranean University, Gazimagusa, TRNC, Mersin10, TurkeyE-mail : [email protected]

[S. Unul]Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10,TurkeyE-mail : [email protected]

34 Antalya - TURKEY


2-j variables Laguerre polynomials properties

and applications

Cemaliye Kurt, Mehmet Ali Ozarslan

Abstract

In this paper, we introduce the 2-j variables Laguerre polynomials as

Z(α)n1,...,nj

(x1, ..., xj ; y1, ..., yj ; p1, ..., pj)

= yn11 , ..., y

nj

j

n1,...,nj∑k1,...,kj=0

(−n1)k1 ...(−nj)kjΓ(p1k1 + ...+ pjkj + α+ 1)

(x1y1

)p1k1 ...(xjyj

)pjkj

k1!...kj !

We investigate fractional integrals and derivative properties of the abovementioned polyno-mials. We further obtain linear, multilinear and mixed multiliteral generating function forthe 2j- variables Laguerre polynomials in terms of the multivariate Mittag-Leffler function(see [1]). Finally, we calculate the Laplace transform of the above mentioned classes andthen we consider a general singular integral equation with the 2-j variables La-guerre poly-nomials in the kernel and obtain the solution by means of the multivariate Mittag-Leffler

function E(γ1,...,γj)

p1,...,pj ,λ

(x1y1, ...,

xjyj

).

2010 Mathematics Subject Classifications : 33E12, 33C45, 44A10.

Keywords : Laguerre polynomials, fractional integrals and derivatives, generating func-tion, Laplace transform, integral equation.

References

[1] R.K. Saxena, S.L. Kalla, R. Saxena, Multivariate analogue of generalized Mittag-Lefflerfunction, Int. Trans. Special Funct. 27 (7) (2011), 533–548.

C.Kurt) EASTERN MEDITERRANEAN UNIVERSITY, GAZIMAGUSA, T.R.N.C,MERSIN 10, TURKEYE-mail : [email protected]

M.A.Ozarslan) EASTERN MEDITERRANEAN UNIVERSITY, GAZIMAGUSA,T.R.N.C, MERSIN 10, TURKEYE-mail : [email protected]

35 Antalya - TURKEY


On the q-analogue of Daehee numbers and

polynomials

Jin-Woo Park

Abstract

In this paper, we introduce a new q-analogue of the Daehee numbers and polynomialsof the first kind and the second kind, and derive some new interesting identities.

Department of Mathematics Education, Daegu University, Gyeongsan-si, Gyeongsangbuk-do, 712-714, Republic of Korea.E-mail : [email protected]

36 Antalya - TURKEY


Incomplete Bernoulli and Cauchy numbers

associated with incomplete Stirling numbers

Takao Komatsu

Abstract

We introduce the associate Stirling numbers of the first kind and of the second kind, andthe restricted Stirling numbers of the first kind and of the second kind, as generalizationsof the classical Stirling numbers of the first kind and of the second kind. By using theirarithmetical and combinatorial properties, we define and study associated and restrictedBernoulli and Cauchy numbers.

2010 Mathematics Subject Classifications : 11B73, 11B75, 05A15, 05A19

Keywords :Stirling numbers, Bernoulli numbers, Cauchy numbers

References

[1] C. A. Charalambides, Enumerative Combinatorics (Discrete Mathematics and Its Applica-tions), Chapman and Hall/CRC, 2002.

[2] J. Y. Choi, Multi-restrained Stirling numbers, Ars Combin. (to appear).

[3] F. T. Howard, Associated Stirling numbers, Fibonacci Quart. 18 (1980), 303–315.

[4] I. Mezo, Periodicity of the last digits of some combinatorial sequences, J. Integer Seq. 17(2014), Article 14.1.1.

[5] F.-Z. Zhao, Some properties of associated Stirling numbers, J. Integer Seq. 11 (2008), Article08.1.7, 9 pages.

School of Mathematics and Statistics, Wuhan University, Wuhan 430072 ChinaE-mail : [email protected]

37 Antalya - TURKEY


Solvability of a linearized free surface flow

problem under gravity-capillarity.

Dahbia Hernane-Boukari, Nadjiba Foukroun, Rachida Ait-Yahia Djouadi.

Abstract

In this work, we consider a problem of a free surface flow over an obstacle lying on thebottom of a channel in 2D. The flow is irrotational, stationary and the fluid is ideal andincompressible. We take into account both of the gravity and the effects of the superficialtension. The problem is non linear, it is formulated by the Laplace operator on the fluiddomain, the dynamic condition defined on the free surface of the fluid domain (Bernoulliequation) and Dirichlet equation on the bottom of the channel, we give a priori propertiesof its solution, which allow us to construct a space where we can use the Lax-Milgram’stheorem to prove the existence and the uniqueness of the solution of this problem.


Keywords :Free surface problem, Capillarity, Gravity, Bernoulli’s equation, Froude num-ber, Linearized problem.

References

[1] D. Pierotti, The subcritical motion of surface-piercing cylinder: Existence and regularity ofwaveless solutions of the linearized problem, Advanced in differentiel Equations, Volume 7,Number 4, (2002), 385-418.

[2] D. Pierotti, Uniqueness and trapped modes in the linear problem of the steady flow over asubmerged hollow, Wave motion 43, (2006), 222-231.

[3] F. Abergel, J.L Bona, A mathematical theory for viscous free surface flows over a perturbedplane, Arch. Rational Mech. Anal, 118(1), Univ. Paris-Sud, lab. analyse numerique, 91404Orsay, France, (1992), 71-93.

University of Science and Technology Houari-Boumediene, Faculty of Math-ematics, BP. 32, El-Alia, Bab-Ezzouar, Algiers-Algeria.E-mail : [email protected], [email protected], [email protected]

38 Antalya - TURKEY


Zeros of certain trinomials.

Hernane Mohand Ouamar, Jean-Louis Nicolas.

Abstract

Let us define fn, a(z) = zn+1 − az + a − 1 where a is a real number, Gn(z) = (ϕ −1)zn+1−ϕzn + 1 and Hn(z) = ϕzn+1− (ϕ− 1)zn− 1 where ϕ = (1 +

√5)/2, is the golden

ratio. We have Gn(z) = zn+1fn, ϕ(1/z), and therefore Gn is the reciprocal polynomial offn, ϕ.In this talk, we give explicit estimations of some roots of these three families of trinomialsby three different methods.

2010 Mathematics Subject Classifications : 30C15, 26C10

Keywords :trinomials, zero, localization, estimation, reciprocal polynomial.

References

[1] J.-L. Nicolas et A. Schinzel, Localisation de zeros de polynomes intervenant en theorie dusignal, In Cinquante ans de polynomes,ed. M. Langevin et M. Waldschmidt, Lecture Notes in Math. 1415, Springer Verlag, (1990),167-179.

[2] K. Dilcher, J.D. Nulton and K.B. Stolarski, The zeros of a certain family of trinomials,Glasgow Math. J., 34, (1992), 55-74.

[3] K. Dilcher, Zeros of certain cyclotomy-generated polynomials, Fibonacci Quart. 29, (1991),150-156.

[4] A.F. Horadam and A.G. Shannon, Cyclotomy-generated Polynomials of Fibonacci Type,In Fibonacci Numbers and Their Applications, 81-97, edited by A.N. Philippou et al.,Dordrecht : D. Reidel, 1986.

University of Science and Technology Houari-Boumediene, Faculty of Math-ematics, BP. 32, El-Alia, Bab-Ezzouar, Algiers-Algeria.E-mail : [email protected] & [email protected]

Institut Camille Jordan Universit Claude Bernard Lyon 1, 43 boulevard du11 novembre 1918 69622 Villeurbanne cedex France.E-mail : [email protected]

39 Antalya - TURKEY


On Generating Functions For Jacobsthal and

Fibonacci Polynomials of Higher Order

Gulsah Ozdemir, Yilmaz Simsek

Abstract

The purpose of this paper is to construct generating functions for the Jacobsthal andthe Fibonacci polynomials of higher-order. Using these generating functions and theirfunctional equations, we investigate some properties of these polynomials. We also giverelationships between the Jacobsthal polynomials and the Fibonacci polynomials. Finally,we give some applications related to these polynomials and their generating functions.

2010 Mathematics Subject Classifications : 11B39, 11L10, 11B83.

Keywords :Fibonacci numbers, Lucas numbers, Pell numbers, Fibonacci polynomials, Ja-cobsthal polynomials, generating functions.

References

[1] C. K. Cook and M. R. Bacon, Some identities for Jacobsthal and Jacobsthal-Lucas num-bers satisfying higher order recurrence relations, Annales Mathematicae et Informaticae 41(2013), 27-39.

[2] V. E. Hoggatt, Jr. and M. Bicknell, Convolution triangles, The Fibonacci Quarterly 10(6)(1972), 599-608.

[3] V. E. Hoggatt, Jr. and G.E. Bergum, Generalized convolution arrays, The Fibonacci Quar-terly 13(3) (1975), 193-198.

[4] A. F. Horodam and B. J. M. Mahon, Convolution for pell polynomials, Fibonacci numbersand their app. (1986), 55-80.

[5] M. Z. Spivey, Combinatorial sums and finite differences, Discrete Mathematics 307 (24)(2007), 3130-3146.

Department of Mathematics, Faculty of Science, University of Akdeniz TR-07058 Antalya, TurkeyE-mail : [email protected] and [email protected]

40 Antalya - TURKEY


Some Hermite Base Polynomials on q-Umbral

Algebra

Rahime Dere

Abstract

The aim of this paper is to investigate q-Hermite polynomials by using umbral calculusmethods. Also, we derive new type polynomials which are related to the q-Bernoullipolynomials and the q-Hermite polynomials. Besides, we give some new identities of thosepolynomials which are derived from q-umbral calculus.

2010 Mathematics Subject Classifications : 05A40, 11B83, 11B68.

Keywords :Appell sequences, Bernoulli polynomials of higher order, Hermite polynomialsof higher order, Umbral algebra, Umbral calculus.

References

[1] R. Dere, Y. Simsek and H. M. Srivastava, A unified presentation of three families of gen-eralized Apostol type polynomials based upon the theory of the umbral calculus and theumbral algebra, Journal of Number Theory 133 (2013), 3245-3263.

[2] R. Dere and Y. Simsek, Hermite Base Bernoulli Type Polynomials on the Umbral Algebra,Russian Journal of Mathematical Physics 22(1) (2015), 1-5.

[3] D. S. Kim, T. Kim, D. V. Dolgy and S.-H. Rim, Some new identities of Bernoulli, Eulerand Hermite polynomials arising from umbral calculus, Advances in Difference Equations(2013), 2013:73.

[4] D.S. Kim and T. Kim, q-Bernoulli polynomials and q-umbral calculus, Science China Math-ematics 57(9) (2014), 1867-1874.

[5] L. M. Milne-Thomson, Two classes of generalized polynomials, Proc. London Math. Soc.s2-35(1) (1933), 514-522.

[6] S. Roman, The Umbral Calculus, Dover Publ. Inc. New York, 2005.

Department of Mathematics, Faculty of Science, University of Akdeniz TR-07058 Antalya, TurkeyE-mail : [email protected] and [email protected]

41 Antalya - TURKEY


Some identities of the higher order Barnes-type

q-Bernoulli polynomials and the higher order

Barnes-type q-Euler polynomials

Lee-Chae Jang

Abstract

Many researchers have studied the topics of the Bernoulli polynomials, the Euler polynomials, the higher order Bernoulli polynomials, the higher order Euler polynomials, thehigher order Barnes-type Bernoulli polynomials, and the higher order Barnes-type Eulerpolynomials including the identity properties of them and some applications of them. Inthis paper, we consider the higher order Barnes-type q-Bernoulli polynomials and numbersand investigate some identities of them. Furthermore, we discuss some identities of thehigher order Barnes-type q-Euler polynomials and numbers.

Graduate School of Education, Dept. of Mathematics Education, KonkukUniversity, Seoul 143-701, KoreaE-mail : [email protected]

42 Antalya - TURKEY


A numerical verification on the structure of the

zeros of Genocchi polynomials

J. Y. Kang, C. S. Ryoo

Abstract

We find the behavior of complex roots of the Genocchi polynomials by using numer-ical investigation. By means of numerical experiments, we exhibit a remarkably regularstructure of the complex roots of the Genocchi polynomials. We indicate the Julia set ofNewton iteration function ultimately.

2010 Mathematics Subject Classifications : 11B68, 11S40, 11S80

Keywords :Genocchi numbers and polynomials, Newton iteration, complex roots, Juliaset

Department of Mathematics, Hannam University, Daejeon 306-791, KoreaE-mail : [email protected]

43 Antalya - TURKEY


A p-Adic Approach to Identities of Symmetry

for Carlitzs q-Bernoulli Polynomials

Sang-Hun Lee

Abstract

Y. He derived several identities of symmetry for Carlitzs q-Bernoulli numbers andpolynomials by working over the complex field and using q-zeta functions and standardtechniques. In this paper, we work over the q-adic field and use the q-adic q-integrals onZZp in order to get the results obtained earlier by him.

Kwangwoon University, South KoreaE-mail : [email protected]

44 Antalya - TURKEY


Unification of the B-Splines by using generating

functions for the Bernstein type basis functions

Irem Kucukoglu, Yilmaz Simsek

Abstract

The aim of this paper is to construct a new family of B-Spline type basis functions.By using a knots sequence, we define a sequences of generating functions for the Bernsteinbasis functions. By multiplying the functions of this sequence of functions, we derivedecomposition of the generating functions for the B-Spline type basis functions. Finally, weinvestigate some properties of these sequences. We also give some graphs and applicationsrelated to these type functions.

2010 Mathematics Subject Classifications : 65D07, 11B83, 40A30, 65D17, 65D18,68U07, 11Y16, 14F10, 26C05

Keywords : Bernstein basis functions; Generating function; Bezier curves; Sequences offunctions; B-splines; Knot vector; Computer Aided Geometric Design(CAGD); Partial differ-ential equations

References

[1] Y. Simsek, Construction a new generating function of Bernstein type polynomials, AppliedMathematics and Computation, 218, (2011), 1072-1076

[2] R. Goldman, Generating Functions for Uniform B-splines, Mathematical Methods forCurves and Surfaces Lecture Notes in Computer Science Volume 8177, 2014, pp 172-188.

[3] Y. Simsek, On Generating functions for the Bernstein basis functions and their applications,Eighth International Conference on Mathematical Methods for Curves and Surfaces 28 June-03 July 2012, Oslo-Norway.

[4] Y. Simsek, Generating functions for the Bernstein type polynomials: A new approach toderiving identities and applications for these polynomials, Hacettepe Journal of Mathematicsand Statistics 43(1), 1-14, (2014)

[5] Y. Simsek and M. Acikgoz, A new generating function of (q-) Bernstein-type polynomialsand their interpolation function, Abstr. Appl. Anal. 2010, Art. ID 769095, 12 pp.

[6] M. Acikgoz and S. Araci, On generating function of the Bernstein polynomials, NumericalAnal. Appl. Math., Amer. Inst. Phys. Conf. Proc. CP1281, 11411143, 2010.

Department of Mathematics, Faculty of Science University of Akdeniz TR-07058 Antalya, TurkeyE-mail : [email protected], [email protected]

45 Antalya - TURKEY


Controllability problem for interval linear

systems

Dmitriy V. Dolgy

Abstract

The problem of controllability of linear system

·x = A(t)x+B(t)u, u ∈ U(t),

with interval coefficients

A(t) ≤ A(t) ≤ A(t), B(t) ≤ B(t) ≤ B(t)

is considered. The universal and sub-universal solutions are introduced. It is solved aparticular problem of controllability of linear interval system into origin. A sub-universalcontrol transferring a system from arbitrary state into a stability point x = 0 is obtained asa solution of a special linear problem. Some interesting properties of sub-universal controlare derived.

2010 Mathematics Subject Classifications : Primary 34K35, 47N70, 93-XX; Sec-ondary 91G80, 93Cxx.

Keywords :Controlled system, interval matrices, sub-universal solution, linear problem.

Institute of Natural Sciences, Far Eastern Federal University, Vladivos-tok,RussiaE-mail : d [email protected]

Hanrimwon, Kwangwoon University, Seoul 139-701, Republic of KoreaE-mail :

46 Antalya - TURKEY


Bernstein basis functions related to

combinatorial sums involving binomial

coefficients and special numbers

Yilmaz Simsek

Abstract

By using generating functions, which contained alternative forms, we derive identities,some new and old, for the Bernstein basis functions. Integrating these identities, we alsoderive combinatorial sums involving binomial coefficients. We give relations between thesecombinatorial sums and generating functions for special numbers, we investigate relationsrelated to finite sums of the powers of integers and alternating finite sums of the powersof integers associated with the special numbers. Finally, we give some comments, remarksand applications on our results.

2010 Mathematics Subject Classifications : 14F10, 12D10, 26C05, 26C10, 30B40.

Keywords :Bernstein polynomials; Generating function; Beta type polynomials; Gammafunction; Beta function; Combinatorial sums; Catalan numbers, Bernoulli numbers; Euler num-bers.

References[1] M. Acikgoz and S. Araci, On generating function of the Bernstein polynomials, AIP Conf. Proc. 1281 (2010),

1141-1143.

[2] J. Choi and H. M. Srivastava, Certain families of series associated with the Hurwitz-Lerch zeta function,Appl. Math. Comput. 170 (2005), 399-409.

[3] R. Goldman, P. Simeonovand Y. Simsek, Generating functions for the q-Bernstein bases, SIAM J. DiscreteMath. 28(3) (2014), 1009-1025.

[4] T. Mansour, Combinatoral identities and inverse binomial coefficients, Adv. in Appl. Math. 28 ( 2002),196-202.

[5] Y. Simsek, q-Beta polynomials and their applications, Appl. Math. Inf. Sci. 7(6) (2013), 2539-2547.

[6] Y. Simsek, Unification of the Bernstein-type polynomials and their applications, Boundary Value Problems2013, 2013:56 .

[7] Y. Simsek, Generating functions for the Bernstein type polynomials: A new approach to deriving identitiesand applications for these polynomials, Hacettepe J. Math. Stat. 43 (2014), 1-14.

[8] H. M. Srivastava, Some generalizations of a combinatorial identities of L. Vietories, Discrete Math. 65(1987), 99-102.

[9] H. M. Srivastava, J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Acedemic Pub-lishers, Dordrecht, Boston and London, (2001).

Department of Mathematics, Faculty of Sciences University of Akdeniz TR-07058 Antalya, Turkey


47 Antalya - TURKEY


Notes on Unified q-Apostol-Type Polynomials

Burak KURT

Abstract

Recently, many mathematicians (Karande and Thakare [4], Ozarslan [7], Ozden et.al. [8], El-Deouky et. al. [3]) have studied on the unification of Bernoulli, Euler andGenocchi polynomials. They gave some recurrence relations and proved the some theorems.Mahmudov [6] defined the new q-Apostol-Bernoulli and q-Apostol-Euler polynomials. Alsohe gave the analogous of the Srivastava-Pinter addition theorems. Kurt [5] gave the newidentities and some relations for these polynomials. In this work, we give some recurrencerelations for the unified q-Apostol-type polynomials related to multiple sums. By usinggenerating functions for the unification of the q-Apostol-type Bernoulli, Euler and Genocchipolynomials and numbers, we derive many new identities and recurrence relations for thesepolynomials. We obtain new identity related to the generalized Stirling type polynomialsof the second kind.

2010 Mathematics Subject Classifications : 05A10, 11B65,11B68, 28B99.

Keywords :Bernoulli polynomials and numbers, Euler polynomials and numbers, Apostol-Bernoulli polynomials and numbers, Apostol-Euler polynomials and numbers, Alternating sums.

References[1] J. Choi, P. J. Anderson and H. M. Srivastava, Some q-extensions of the Apostol-Bernoulli and Apostol-

Euler polynomials of order n and the multiple Hurwitz zeta functions, App. Math. and Comp. (2008), 199,723-737.

[2] R. Dere, Y. Simsek and H. M. Srivastava, A Unified presentation of three families of generalized Apostol-typepolynomials based upon the theory of the umbral calculus and the umbral algebra, J. of Number Theo. 133(2013), 3245-3263.

[3] B. S. El-Desouky and R. S. Gamma, A new unified family of generalized Apostol-Euler, Bernoulli andGenocchi polynomials, App. Math. and Computer 247 (2014), 695-702.

[4] B. K. Karande and N. K. Thakare, On the unification of the Bernoulli and Euler polynomials, Indian of J.Pure App. Math. 6(1) (1975), 98-107.

[5] V. Kurt, New identities and relations derived from the generalized Bernoulli polynomials, Euler polynomialsand Genocchi polynomials, Advances in Difference Equations, 2014:5, doi:10.1186/1687-1847-2014-5.

[6] N. I. Mahmudov, On a class of q-Bernoulli and q-Euler polynomials, Advances in Difference Equations,2013, doi: 10.1186/1687-1847-2013-103.

[7] M. A. Ozarslan, Unified Apostol-Bernoulli, Euler and Genocchi polynomials, Computer and Math. withApll. 62 (2011), 2452-2462.

[8] H. Ozden, Y. Simsek and H. M. Srivastava, A unified presentation of the generating functions of the gener-alized Bernoulli, Euler and Genocchi polynomials, Computers and Math. with App. 60 (2010), 2779-2789.

Department of Mathematics, Faculty of Sciences University of Akdeniz TR-07058 Antalya, Turkey


48 Antalya - TURKEY


Unified Apostol-Type Polynomials and

Alternating Sums

Veli KURT

Abstract

In last ten years, many mathematicians studied on the unification of the Bernoulliand Euler polynomials. Firstly Karande B. K. and Thakare N. K. [4] introduced andgeneralized the multiplication formula. Ozden et. al. [6] defined the unified Apostol-Bernoulli, Euler and Genocchi polynomials Yn,β(x; k; a, b) and proved some relations. M. A.Ozarslan [5] proved the explicit relations, symmetry identities and multiplication formula.El-Desouky et. al. in ([2], [3]) defined a new unified family of the generalized Apostol-Euler, Apostol-Bernoulli and Apostol-Genocchi polynomials and gave some relations forthe unification of multiparameter Apostol-type polynomials and numbers. In this work,we give some symmetry identities and recurrence relations for the unified Apostol-typepolynomials related to multiple alternating sums.

2010 Mathematics Subject Classifications : 05A10, 11B65,11B68, 28B99.

Keywords :Bernoulli polynomials and numbers, Euler polynomials and numbers, Apostol-Bernoulli polynomials and numbers, Apostol-Euler polynomials and numbers, Alternating sums.

References

[1] R. Dere, Y. Simsek and H. M. Srivastava, A Unified presentation of three families of gener-alized Apostol-type polynomials based upon the theory of the umbral calculus and the umbralalgebra, J. of Number Theo. 133 (2013), 3245-3263.

[2] B. S. El-Desouky and R. S. Gamma, A new unified family of generalized Apostol-Euler,Bernoulli and Genocchi polynomials, App. Math. and Computer 247 (2014), 695-702.

[3] B. S. El-Desouky and R. S. Gamma, New extension of unified family of Apostol-type ofpolynomials and numbers, arxiv:1412.8258 [Math.co], 2014.

[4] B. K. Karande and N. K. Thakare, On the unification of the Bernoulli and Euler polynomials,Indian of J. Pure App. Math. 6(1) (1975), 98-107.

[5] M. A. Ozarslan, Unified Apostol-Bernoulli, Euler and Genocchi polynomials, Computer andMath. with Apll. 62 (2011), 2452-2462.

[6] H. Ozden, Y. Simsek and H. M. Srivastava, A unified presentation of the generating functionsof the generalized Bernoulli, Euler and Genocchi polynomials, Computers and Math. withApp. 60 (2010), 2779-2789.

Department of Mathematics, Faculty of Sciences University of Akdeniz TR-07058 Antalya, TurkeyE-mail : [email protected]

49 Antalya - TURKEY


Bilinear Multipliers of Function Spaces with

Wavelet Transform

Oznur Kulak

Abstract

Let ω1, ω2, ϑ1, ϑ2 be slowly increasing weight functions and ω3, ϑ3be any weightfunctions on Rn. Assume that m (ξ, η) is a bounded function on Rn× Rn. Define that

Bm (f, g) (x) =

∫Rn

∫Rn

∧f (ξ)

∧g (η)m (ξ, η) e2πi〈ξ+η,x〉dξdη

for all f, g εC∞c (Rn). m (ξ, η) is said to be a bilinear multiplier on Rn of type(D (p1, q1, ω1, ϑ1; p2, q2, ω2, ϑ2; p3, q3, ω3, ϑ3)) if Bm is bounded operator from(Dp1,q1ω1,ϑ1

)s

(Rn)×(Dp2,q2ω2,ϑ2

)s

(Rn) to(Dp3,q3ω3,ϑ3

)s

(Rn) where 1 ≤ p1, q1, p2, q2, p3, q3 < ∞,

s ∈ R+ . Denote by BM (D (p1, q1, ω1, ϑ1; p2, q2, ω2, ϑ2; p3, q3, ω3, ϑ3)) the vector spaceof bilinear multipliers of type (D (p1, q1, ω1, ϑ1; p2, q2, ω2, ϑ2; p3, q3, ω3, ϑ3)). In this work,some properties of this space are investigated and some examples of these bilinear multi-pliers are given.

References

[1] Blasco, O: Notes on the spaces of bilinear multipliers. Rev. Un. Mat. Argentina. 50(2), 23-37(2009)

[2] Kulak, O., Gurkanlı AT: On Function Spaces with Wavelet Transform in Lpω(Rd × R+

),

Hacettepe Journal of Mathematics and Statistics, 40(2)(2011), 163-177

[3] Kulak, O., Gurkanlı AT: Bilinear multipliers of weighted Lebesgue spaces and variableexponent Lebesgue spaces, Journal of Inequalities and Applications, 2013:259, 1-21 (2013).

[4] Kulak, O., Gurkanlı AT: Bilinear multipliers of weighted Wiener amalgam spaces andvariable exponent Wiener amalgam spaces, Journal of Inequalities and Applications,2014/1/476.

Giresun UniversityE-mail : [email protected]

50 Antalya - TURKEY


A Study About Approximation of

Non-Convolution Type Double Singular Integral

Operators

Mine Menekse Yilmaz, Gumrah Uysal

Abstract

In this paper we study the pointwise convergence of functions by the non-convolutiontype singular integral operators to the functions that are in Lp−space at the Lebesguepoints and obtaining the rate of convergence at this points. Also these theoretical resultsare supported by example.

2010 Mathematics Subject Classifications : 41A35; 41A25

Keywords :pointwise convergence, Lebesgue points.

References

[1] L. Angeloni, G. Vinti, Approximation with Respect to Goffman-Serrin Variation by Meansof Non-Convolution Type Integral Operators. Numerical Functional Analysis and Optimiza-tion, Vol. 31,(2010), 519-548

[2] C. Bardaro, On approximation properties for some classes of linear operators of convolutiontype. Atti Sem. Mat. Fis. Univ. Modena 33, no. 2,(1984), 329–356

[3] C. Bardaro, G. Vinti, H. Karsli, Nonlinear integral operators with homogeneous kernels:pointwise approximation theorems. Appl. Anal. 90, no. 3-4, (2011), 463–474

[4] C. Bardaro, H. Karsli, G. Vinti, On pointwise convergence of Mellin type nonlinear m-singular integral operators. Comm. Appl. Nonlinear Anal. 20, no. 2, (2013), 25–39

[5] A.D. Gadjiev, The order of convergence of singular integrals which depend on two param-eters. Special Problems of Functional Analysis and their Appl. to the Theory of Diff. Eq.and the Theory of Func., Izdat. Akad. Nauk Azerbaıdazan. SSR., pp. 40–44 (1968)

[6] H. Karsli, Convergence and rate of convergence by nonlinear singular integral operatorsdepending on two parameters, Appl. Anal. 85, 6-7, (2006), 781-791

[7] H. Karsli, On the approximation properties of a class of convolution type nonlinear singularintegral operators. Georgian Math. J. 15, no. 1, (2008), 77–86

[8] H. Karsli, Fatou type convergence of nonlinear m-singular integral operators, Applied Math.and Comp. 246,(2014)

Gaziantep University, Faculty of Arts and Sciences, Department of Mathe-matics, Gaziantep-TurkeyE-mail : [email protected]

Karabuk University, Faculty of Science, Department of Mathematics, Karabuk,TurkeyE-mail : [email protected]

51 Antalya - TURKEY


A symmetric identity on the q-Genocchi

polynomials of higher order under third

dihedral group D3

Erkan Agyuz, Mehmet Acikgoz, Serkan Araci

Abstract

In the present paper, we perform a further investigation for the q-Genocchi numbersand polynomials of higher order under third Dihedral group D3 and establish some closedformulae of the symmetric identities. We also establish some known identities for theclassical Genocchi numbers and polynomials by using fermionic p-adic integral on ZZp.

2010 Mathematics Subject Classification. Primary 05A10, 11B65; Secondary 11B68,11B73.

Keywords and phrases. Genocchi polynomials and numbers, Higher order q-Genocchi poly-nomials and numbers, fermionic p-adic q-integral on ZZp, Dihedral group D3.

References

[1] S. Araci, Novel identities involving Genocchi numbers and polynomials arising from appli-cations of umbral calculus, Applied Mathematics and Computation 233 (2014) 599-607.

[2] I. N. Cangul, V. Kurt, H. Ozden, Y. Simsek, On the higher-order w-q-Genocchi numbers,Adv. Stud. Contemp. Math. 19 (1), 39-57 (2009)

[3] D. V. Dolgy, Y. S. Jang, T. Kim, H. I. Kwon, J.-J. Seo, Identities of Symmetry for q-EulerPolynomials Derived from Fermionic Integral on ZZp under Symmetry Group S3, AppliedMathematical Sciences, Vol. 8, 2014, no. 113, 5599-5607.

[4] T. Kim, Symmetry p-adic invariant integral on ZZp for Bernoulli and Euler polynomials, J.Difference Equations Appl. 14, 1267-1277 (2008).

[5] H. M. Srivastava, Some generalizations and basic (or q-) extensions of the Bernoulli, Eulerand Genocchi polynomials, Appl. Math. Inform. Sci. 5 (2011), 390–444.

Department of Mathematics, Faculty of Arts and Science, University ofGaziantep, TR-27310 Gaziantep, TurkeyE-mail : [email protected]


Department of Economics, Faculty of Economics, Administrative and SocialSciences, Hasan Kalyoncu University, TR-27410 Gaziantep, TurkeyE-mail : [email protected]

52 Antalya - TURKEY


Some new identities concerning some special

polynomials under the theory of multiple

q-calculus

Mehmet Acikgoz, Serkan Araci

Abstract

In this paper, we aim to construct some new relations and identities of some specialpolynomials under the theory of multiple quantum calculus.

2010 Mathematics Subject Classifications : 33E20, 81S25.

Keywords :q-calculus, multiple q-calculus, q-Bernstein polynomials, q-Euler polynomials,q-Bernoulli polynomials.

References[1] O. K. Pashaev and S. Nalci, q-analytic functions, fractals and generalized analytic functions, J. Phys. A:

Math. Theor. 47 (2014) 45204-45228.

[2] S. Nalci, Exactly solvable q-extended nonlinear classical and quantum models, Ph.D. Thesis (2011). IzmirInstitute of Technology: Turkey.

[3] T. Kim, L.-C. Jang and H. Yi, A note on the modified q-Bernstein polynomials, Discrete Dynamics inNature and Society Vol. 2010 (2010), Article ID 706483, 12 pages.

[4] T. Kim, q-Volkenborn integration, Russian Journal of Mathematical Physics Vol. 9, no.3, pp. 288-299,2002.

[5] V. Kac and P. Cheung, Quantum Calculus, New York: Springer, 2002.

[6] C. S. Ryoo, A note on q-Bernoulli numbers and polynomials, Appl. Math. Lett. 20 (2007) 524-531.

[7] M. Acikgoz and S. Araci, On the generating function of the Bernstein polynomials, AIP Conf. Proc. 1281(2010), 1141-1143.

[8] S. Araci, E. Agyuz and M. Acikgoz, On a q-analog of some numbers and polynomials, J. Ineq. Appl. (2015)2015:19.

[9] S. Araci, M. Acikgoz, A note on the values of weighted q-Bernstein polynomials and weighted q-Genocchinumbers, Adv. Diff. Equa. (2015) 2015: 30.

[10] G. M. Philips, Bernstein polynomials based on the q-integers, Annals of Numerical Mathematics, vol. 4,no. 1-4, pp. 511-518, 1997.

[11] G. M. Philips, A survey of results on the q-Bernstein polynomials, IMA J. Numer. Anal. (2010) 30 (1):277-288.

Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, TR-27310Gaziantep, TurkeyE-mail : [email protected]

Department of Economics, Faculty of Economics, Administrative and Social Sciences, HasanKalyoncu University, TR-27410 Gaziantep, TurkeyE-mail : [email protected]

53 Antalya - TURKEY


On the von Staudt-Clausen theorem of

q-Frobenius-Euler numbers

Serkan Araci, Mehmet Acikgoz

Abstract

In this talk, we will mention about a family of Frobenius-Euler numbers with a param-eter q and give some basic properties for them. From those properties, we shall introducethese numbers are p-adic integers and these numbers can be expressed by von Staudt-Clausen’s theorem. In the final part of this talk, we get a type of kummer congruences forthese numbers.

2010 Mathematics Subject Classifications : 11S80, 11B68.

Keywords :Frobenius-Euler numbers, von Staudt clausen’s theorem, kummer congruence,p-adic integer.

References

[1] T. Kim, On the von Staudt-Clausen theorem for q-Euler numbers, Russ. J. Math. Phys. 20(1), 33-38 (2013).

[2] S. Araci, M. Acikgoz, E. Sen, On the von Staudt-Clausen’s theorem associated with q-Genocchi numbers, Appl. Math.Comput. 247, 780-785 (2014).

[3] B. M. Kim, L.-C. Jang, A note on the Von Staudt-Clausen’s theorem for the weighted q-Genocchi numbers, Adv. Dif. Equa. (2015), 2015:4.

[4] C. S. Ryoo, A note on q-Bernoulli numbers and polynomials, Appl. Math. Lett. 20 (2007)524-531.

[5] D. S. Kim, T. Kim, S.-H. Lee and J.-J. Seo, A note on q-Frobenius-Euler numbers andpolynomials, Adv. Studies Theor. Phys., Vol. 7, 2013, No. 18, 881-889.

[6] Y. Simsek, Generating functions for q-Apostol type Frobenius–Euler numbers and polyno-mials, Axioms 2012, 1, 395-403; doi:10.3390/axioms1030395.

[7] H. M. Srivastava, Some generalizations and basic (or q-) extensions of the Bernoulli, Eulerand Genocchi polynomials, Appl. Math. Inform. Sci. 5, 390-444 (2011)

[8] Y. He and S. J. Wang, New formulae of products of the Frobenius-Euler polynomials, J.Ineq. Appl. (2014), 2014:261.



54 Antalya - TURKEY


Symmetric identities involving q-analog of Euler

polynomials under S4

Ugur Duran, Mehmet Acikgoz, Serkan Araci

Abstract

Motivated by the paper of Kim et al [6], we obtain some new symmetric identities ofq-Euler polynomials using the fermionic p-adic q-integral on ZZp.

2010 Mathematics Subject Classifications : 11S80, 11B68, 05A19, 05A30.

Keywords :Identities of symmetry, q-Euler polynomials, Fermionic p-adic q-integral, In-variant under S4

References

[1] S. Araci, M. Acikgoz, E. Sen, On the extended Kim’s p-adic q-deformed fermionic integralsin the p-adic integer ring, J. Number Theory 133 (2013) 3348-3361.

[2] D. V. Dolgy, Y. S. Jang, T. Kim, H. I. Kwon, J.-J. Seo, Identities of Symmetry for q-EulerPolynomials Derived from Fermionic Integral on ZZp under Symmetry Group S3, AppliedMathematical Sciences, Vol. 8, 2014, no. 113, 5599-5607.

[3] T. Kim, Some identities on the q-Euler polynomials of higher order and q-Stirling numbersby the fermionic p-adic integral on ZZp, Russian J. Math. Phys., 16, 484-491 (2009).

[4] D. V. Dolgy, T. Kim, S.-H. Rim, S.-H. Lee, Some Symmetric Identities for h-Extension of q-Euler Polynomials under Third Dihedral Group D3, International Journal of MathematicalAnalysis Vol. 8, 2014, no. 48, 2369-2374.

[5] L.-C. Jang, T. Kim, q-Genocchi numbers and polynomials associated with fermionic p-adicinvariant integrals on ZZp, Abstract and Applied Analysis Vol. 2008 (2008), Article ID232187, 8 pages

[6] D. S. Kim and T. Kim, Some identities of symmetry for Carlitz q-Bernoulli polynomialsinvariant under S4, preprint.

[7] H. Ozden, Y. Simsek and I. N. Cangul, Euler polynomials associated with p-adic q-Eulermeasure, General Mathematics Vol. 15, Nr. 2-3 (2007), 24-37.

[8] H. M. Srivastava, Some generalizations and basic (or q-) extensions of the Bernoulli, Eulerand Genocchi polynomials, Appl. Math. Inform. Sci. 5, 390-444 (2011)




55 Antalya - TURKEY


Remarks on formulas related to modular forms

Aykut Ahmet Aygunes

Abstract

In this talk, we study modular forms and their applications. We give some remarkson Eisenstein series, modular forms and Jacobi modular function. Finally we give someformulas and relations related to Eisenstein series and Jacobi modular functions. We alsogive differential equation and its application related to modular forms.

2010 Mathematics Subject Classifications : Primary 11F03, 11F30; Secondary42A16, 11M36.

Keywords :Eisenstein series; Modular forms; Cusp forms; Fourier series; Operators; Deriva-tive formula; Theta function, Jacobi theta function.

References[1] T. M. Apostol, Modular functions and Dirichlet series in Number Theory, (Berlin, Heidelberg and New

York) Springer-Verlag (1976).

[2] A. A. Aygunes, A new operator related to generating modular forms and their applications, preprint.

[3] A. A. Aygunes, Y. Simsek, Hecke Operators Related to the Generalized Dedekind Eta Functions andApplications, Numer. Anal. Appl. Math.Vol. I-III Book Series: AIP Conference Proceedings Volume: 1281(2010), 1098-1101.

[4] A. A. Aygunes, Y. Simsek, H. M. Srivastava, A sequence of modular forms associated with higher orderderivative Weierstrass-type functions, preprint.

[5] E. Hecke, Mathematische Werke, Vandenhoeck & Ruprecht in Gottingen, 1983.

[6] A. Hurwitz, Ueber die Differentialgleichungen dritter Ordnung, welchen die Formen mit linearen Transfor-mationen in sich genugen, Math. Ann. 33 (1889), 345-352.

[7] L. J. P. Kilford, Modular forms: a classical and computational introduction, Imperial College Press (2008).

[8] C. H. Kim, J. K. Koo, On the modular function j4 of level 4, J. Korean Math. Soc. 35 (1998), 903-931.

[9] C. H. Kim, J. K. Koo, Arithmetic of the modular function j4, J. Korean Math. Soc. 36 (1999), 707-723.

[10] F. Klein, Ueber Multiplicatorgleichungen, Math. Ann. 15 (1879), 86-88.

[11] N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer-Verlag, New York (1993).

[12] S. Ramanujan, On certain arithmetical functions, Trans. Cambridge Philos. Soc. 22 (1916), 159-184.

[13] A. Sebbar, A. Sebbar, Eisenstein Series and Modular Differential Equations, Canad. Math. Bull. 55 (2011),400-409.

[14] J. H. Silverman, Advanced topics in the arithmetic of elliptic curves, New York, Heidelberg and Berlin,Springer-Verlag (1994).

[15] Y. Simsek, On normalized Eisenstein series and new theta functions, Proc. Jangjeon Math. Soc. 8 (2005),25-34.

[16] Y. Simsek, Relations between theta-functions Hardy sums Eisenstein series and Lambert series in thetransformation formula of log ηg,h(z), J. Number Theory 99 (2003), 338-360.

[17] B. Van der Pol, On a non-linear partial differential equation satisfied by the logarithm of the Jacobiantheta-functions, with arithmetical applications. I, II, Nederl. Akad. Wetensch. Proc. Ser. A, Indag. Math.13 (1951), 261-271.

Akdeniz UniversityE-mail : [email protected]

56 Antalya - TURKEY


A Special Finite Sum Associated with the

Dedekind and Hardy type Sums

Elif Cetin

Abstract

In this paper, we study about a special finite sum which was defined by the authorsin [1] as C1(h, k) after they come up with this sum in several calculations with other well-known similar sums. We focus on this sum because of its advantage: when we calculateexplicit values of the sum C1(h, k), we saw that it depends on just one variable.The sumC1(h, k) has many stunning properties which are related to the Hardy sums, the Dedekindsums and the Simsek sums Y (h, k). By using the Fibonacci numbers, we also computeexplicit value of this sum.

2010 Mathematics Subject Classifications : Primary 11F20; Secondary 11C08

Keywords :Hardy Sums, Dedekind Sums, Y (h, k) Sums

References

[1] E. Cetin, Y. Simsek and I. N. Cangul, Some special finite sums related to the three-termpolynomial relations and their applications, Advances in Difference Equations, 283 (2014),1-18.

[2] G. H. Hardy, On certain series of discontinues functions connected with the modular func-tions, Quart. J. Math. 36 (1905), 93-123.

[3] M. R. Pettet and R. Sitaramachandraro, Three-Term relations for Hardy sums, J. NumberTheory 25 (1989), 328-339.

[4] Y. Simsek, On Analytic properties and character analogs of Hardy Sums, Taiwanese J.Math. 13 (2009), 253-268.

[5] Y. Simsek, Relations between theta-functions Hardy sums Eisenstein series and Lambertseries in the transformation formula of log ηg,h(z), J. Number Theory 99 (2003), 338-360.

Uludag University Faculty of Art and Science Bursa-TURKEYE-mail : [email protected]

57 Antalya - TURKEY


A general approach for enrichment of the

nonconforming finite elements in any dimension

Yassine Zaim

Abstract

In the first part of the presentation, we give a general approach for constructing anew class of enriched nonconforming finite elements on arbitrary convex polytope. Thismethod is based on the enrichment of the standard linear finite element. The enrichmentfunctions can be non-polynomial basis functions, which turns the method powerful to solveproblems, since they can provide better approximation than standard polynomial shapefunctions used in the classical conforming or nonconforming finite element methods. Thisenriched nonconformig finite element method was recently introduced in [1, 2]. We willgive an overview of this approach and also discuss how the above enrichment techniquecan be extended to any finite element approximation. It should be mentioned that thoughin this talk only the enrichment of the standard linear finite element case is discussed, thegeneral problem associated with any finite element approximation has been considered andsome extended results have also been proved there.In the second part of the presentation, we exploited this approach to develop a new classof enriched nonconforming Rannacher and Turek in any dimension. This class is based ona single univariate function e and some arbitrary number of free parameters. The shapefunction space and the degrees of freedom of the element used here are:

K = [−1, 1]d ,σK = 1

|Fi|

∫Fifdσ i = 1, . . . , 2d,here Fi, i = 1, . . . , 2d denote the 2d facets of K,

P (K) = {1, x1, . . . , xd}+ span {e1, . . . , ed−1} , with ei : x→∑d−1k=1 αike(xk).

Keywords and phrases. Convex polytopes; Crouzeix-Raviart finite element; Nonconformingfinite element; Rotated Q1 element.

References

[1] B. Achchab, A. Agouzal, K. Bouihat, A simple nonconforming quadrilateral finite element,C. R. Acad. Sci. Paris, Ser. I , 352 (2014) 529–533.

[2] B. Achchab, K. Bouihat, A. Guessab, G. Schmeisser, A general approach to the con-struction of nonconforming finite elements on convex polytope, submitted for publication,(2015).

Laboratory of Mathematics and Its Applications, UMR CNRS 5142, Pau Uni-versity, France AND Laboratory for the Analysis and Modeling of DecisionAid Systems,Hassan 1st University “EST Berrechid”, B.P. 218, MoroccoE-mail : [email protected]

58 Antalya - TURKEY


High-order Schemes for the Klein-Gordon

EquationsAsuman Zeytinoglu, Murat Sari

Abstract

This paper suggests numerical algorithms based on some high-order finite differenceschemes in treating the nonlinear Klein-Gordon equations. The corresponding algorithmsare implemented by taking into account the high-order spatial discretizations. Then theresulting system is integrated by considering the MacCormack approach. Various testproblems are solved using those schemes. The produced results revealed that the presentschemes are efficient and easily applicable. The considered schemes have been seen tobe more accurate comparison to their most rivals. The validity of the current numericalmodels has been verified through the obtained results and the literature.

2010 Mathematics Subject Classification. 33F05, 74H15, 35C08.

Keywords and phrases. Klein-Gordon equation, High-order finite difference scheme, predictor-corrector method, MacCormack method.

References

[1] H. Arodz, L. Hadasz, Lectures on classical and quantum theory of fields, Springer, London,351p., (2010).

[2] R.K. Dodd, I.C. Eilbeck, J.D. Gibbon, H.C. Morris, Solitons and nonlinear wave equations,Academic London, (1982).

[3] M. Dehghan, A. Shokri, Numerical solution of the nonlinear Klein-Gordon equation usingradial basis functions, J Comput Appl Math. 230 (2009), 400-410.

[4] S.A. Khuri, A. Sayfy, A spline collocation approach for the numerical solution of a general-ized nonlinear Klein-Gordon equation, Appl Math Comput. 216 (2010), 1047-1056.

[5] J. Rashidinia, R. Mohammadi, Tension spline approach for the numerical solution of non-linear Klein-Gordon equation, Comput Phys Commun. 181 (2010), 78-91.

[6] M. Sari, G. Gurarslan, A. Zeytinoglu, High-order finite difference schemes for solving theadvection diffusion equation, Math Comput Appl. 15 (2010), 449-460.

[7] R.H. Pletcher, J.C. Tannehill, D.A. Anderson, Computational fluid mechanics and heattransfer, Third Ed., Taylor&Francis, (2013).

Department of Mathematics, Faculty of Art and Science, Suleyman DemirelUniversity, Isparta, TurkeyE-mail : [email protected]

Department of Mathematics, Faculty of Art and Science, Yildiz TechnicalUniversity, Istanbul, TurkeyE-mail : [email protected]

59 Antalya - TURKEY


Determinant line bundles over Teichmuller space

David Radnell

Abstract

Determinant lines bundle over the moduli space of Riemann surfaces with parame-terized boundary components are an important ingredient in conformal field theory. Thismoduli space is closely connected to the infinite-dimensional Teichmuller space of borderedRiemann surfaces. Additional regularity of the boundary curves is needed for certain op-erators to exist, and so a refinement of the Teichmuller space must be used. A generaloverview of the subject will be given, followed by some recent results.

2010 Mathematics Subject Classifications : 30F60, 81T40

Keywords :Teichmuller space, conformal field theory.

Department of Mathematics and Statistics, American University of Sharjah,United Arab EmiratesE-mail : [email protected]

60 Antalya - TURKEY


A Matrix Approach to Solving Hyperbolic

Partial Differential Equations Using Bernoulli

Polynomials

Kubra Erdem Bicer, Salih Yalcinbas

Abstract

The present study considers the solutions of hyperbolic partial differential equations.For this, an approximate method based on Bernoulli polynomials is developed. Thismethod transforms the equation into the matrix equation and the unknown of this equa-tion is a Bernoulli coefficients matrix. To demostrate the validity and applicability ofthe method, an error analysis developed based on residual function. Also examples arepresented to illustrate the accuracy of the method.

2010 Mathematics Subject Classifications : 35L10, 58J45, 11B68, 40C05.

Keywords : Second-order hyperbolic equations, Bernoulli and Euler numbers and poly-nomials, Matrix methods.

References

[1] K. Erdem, S. Yalcinbas, Bernoulli Polynomial Approach to High-Order Linear Differential-Difference Equations, AIP Conf. Proc. 1479 (2012), 360-364.

[2] K. Erdem, S. Yalcinbas, Numerical approach of linear delay difference equations with vari-able coefficients in terms of Bernoulli polynomials, AIP Conf. Proc. 1493 (2012), 338-344.

[3] K. Erdem, S. Yalcinbas, M. Sezer, A Bernoulli Polynomial Approach with Residual Correc-tion for Solving Mixed Linear Fredholm Integro-Differential-Difference Equations, Journalof Difference Equations and Applications 19(10) (2013), 1619-1631.

[4] J. Rauch, Hyperbolic Partial Differential Equations And Geometric Optics, American Math-ematical Society, 2012.

Department of Mathematics, Faculty of Science and Art, Celal Bayar Uni-versity TR- 45140 Manisa, TurkeyE-mail : [email protected] and [email protected]

61 Antalya - TURKEY


On Periodic Solutions to Nonlinear Differential

Equations In Banach Spaces

Abdullah Cavus, Djavvat Khadjiev, Seda Ozturk

Abstract

Let A denote the generator of a strongly continuous periodic one-parameter group ofbounded linear operators in a complex Banach space H. In this work, an analog of theresolvent operator which is called quasi-resolvent operator and denoted by Rλ is defined forpoints of the spectrum and pertinent properties of the resolvent and quasi-resolvent oper-ators are included. Compactness conditions of the resolvent operator and quasi-resolventoperator are obtained. Using these and some results of the theory of Fourier series inBanach spaces, some theorems on existence of periodic solutions to the non-linear equa-tions Φ(A)x = f(x) are given for functions f satisfying some conditions, where Φ(A) is apolynomial of A with complex cofficients and f is a continuous mapping of H into itself.

2010 Mathematics Subject Classification. 34G, 47D, 42A.Keywords and phrases. Periodic solution, Duffing equation, Nonlinear differential equation.

References[1] Andres, J, Krajc, B: Periodic solutions in a given set of differential systems J. Math. Anal. Appl., 264,

495-509 (2001)

[2] Bart, H: Periodic strongly continuous semigroups, Ann. Mat. Pura. Appl. 115, 311-318 (1977)

[3] Bartha, M: Periodic solutions for differential equations with state-dependent delay and positive feedback,Nonlinear Analysis, 53, 839-857 (2003)

[4] Cavus¸ , A, Khadjiev, D, Kunt, M: On periodic one-parameter groups of linear operators in a Banach spaceand applications, Journal of Inequalities and Applications, 288, 1-20 (2013)

[5] Cid, J, A, Sanchez, L: Periodic solutions for second order differential equations with discontinuous restoringforces, J. Math. Anal. Appl.. 288, 349-364 (2003)

[6] Fuzhong, C: Periodic solutions for of 2kth-order ordinary differential equations with nonresonance, Nonlin-ear Anal. TMA 32 (6), 787-793 (1998)

[7] Engel, K, J, Nagel, R: One-Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, NewYork.

[8] Jiang, D, Nieto, J, J, Zuo, W: On monotone method for first and second order periodic boundary valueproblems and periodic solutions of functional differential equations, J. Math. Anal. Appl.. 289, 691-699(2004)

[9] Katznelson, Y: An Introduction to Harmonic Analysis, Dover Publications, INC., New York (1976)

Department of Mathematics, Karadeniz Technical University,Trabzon,TURKEYE-mail : [email protected]

Academy of Sciences of UzbekistanE-mail : [email protected]

Department of Mathematics, Karadeniz Technical University,Trabzon,TURKEYE-mail : [email protected]

62 Antalya - TURKEY


On A Characterization of Compactness and the

Abel-Poisson Summability Of Fourier

Coefficients In Banach Spaces

Seda Ozturk

Abstract

Let (C,+, .) denote the field of the complex numbers, T be the topological group of theunit circle with respect to the Euclidean topology, H be a complex Banach space, α be astrongly continuous isometric linear representation of T in H, x be an element of H and{Fαk (x)}k∈Z be the family of Fourier coefficients of x with respect to α. In this work, anintegral representation for Abel-Poisson mean operator is given and using this, it is provedthat the family {Fαk (x)}k∈Z is Abel-Poisson summable to x. Also a test for compactnessof a subset of the Banach space H is obtained in terms of the Abel-Poisson mean operatorwith respect to α.

2010 Mathematics Subject Classification. 42B05,42B08,46A35,46B15, 43A65e.

Keywords and phrases. Poisson Kernel,Dirichlet Problem,Abel-Poisson summability.

References

[1] Khadjiev, D., Cavus, A: Fourier series in Banach spaces, in: M.M. Lavrentyev (Ed.), Ill-posed and Non-classical Problems of Mathematical Physics and Analysis, Proc. of the Inter-nat. Conf., Samarkand, Uzbekistan, in: Inverse Ill-posed Probl. Ser., VSP, Utrehct/Boston,71-80 (2003)

[2] Katznelson, Y: An Introduction to Harmonic Analysis, Dover Publications, INC., New York(1976)

[3] Khadjiev, D., Aripov, R.G: Linear representations of the rotation group of the circle inlocally convex spaces, Doklady Acad. Nauk Resp, Uzbekistan 5,5-8 (1997)

[4] Lyubich, Y.I: Introduction to the Theory of Banach Representations of Groups, Birkhauser,Berlin (1988)

[5] Khadjiev, D: The widest continuous integral. J. Math. Anal. Appl. 326 , 1101-1115 (2007)

Karadeniz Technical University, Faculty of Science,Department of Mathe-matics, Trabzon, TurkeyE-mail : [email protected]

63 Antalya - TURKEY


Existence Results of Solutions for Nonlinear

Fractional Differential Equations

Tugba Senlik Cerdik, Nuket Aykut Hamal, Fulya Yoruk Deren

Abstract

In this talk, we study the existence of solutions for boundary value problems of nonlinearfractional differential equations. Here, we investigate the existence results by means of somefixed point theorems.


Keywords :Fractional differential equations, boundary value problems; fixed point theo-rems.

References

[1] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego (1999).

[2] K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985.

[3] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differ-ential Equations, in: North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V,Amsterdam, 2006.

[4] A. Guezane-Lakouda, R. Khaldi, Solvability of a Fractional Boundary Value Problem withFractional Integral Condition, Nonlinear Analysis, 75, 2692-2700, 2012.

[5] B. Ahmad, A. Alsaedi, A. Assolami, and R. P. Agarwal, a Study of Riemann-LiouvilleFractional Nonlocal Integral Boundary Value Problems, Boundary Value Problems 2013,2013:274.

Department of Mathematics, Ege University, Izmir, TurkeyE-mail : [email protected], [email protected], [email protected].

64 Antalya - TURKEY


A Sum Operator Method for the Existence and

Uniqueness of Positive Solutions to a Nonlinear

Fractional Differential Equation

Fulya Yoruk Deren, Nuket Aykut Hamal, Tugba Senlik Cerdik

Abstract

The aim of this paper is to investigate the existence and uniqueness of positive solutionsfor boundary value problems of fractional order. Our analysis is based on a fixed pointtheorem of a sum operator.


Keywords :Fractional differential equations, existence and uniqueness; fixed point theo-rems.

References

[1] C. Zhai, D. R. Anderson, A sum operator equation and applications to nonlinear elastic beamequations and Lane-Emden-Fowler equations, J. Math. Anal. Appl. 375 (2011) 388-400.

[2] C. Yang, C. Zhai, Uniqueness of positive solutions for a fractional differential equation viaa fixed point theorem of a sum operator, Electronic Journal of Differential Equations, Vol.2012 (2012), No. 70, pp. 1-8.

[3] C. Zhai, W. Yan, C. Yang, A sum operator method for the existence and uniqueness of posi-tive solutions to Riemann-Liouville fractional differential equation boundary value problems,Commun Nonlinear Sci Numer Simulat 18 (2013) 858-866.

[4] K. Deimling, Nonlinear Functional Analysis,, Springer, Berlin, 1985.

[5] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and applications of fractional differ-ential equations, in: North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V,Amsterdam, 2006.

Department of Mathematics, Ege University, Izmir, TurkeyE-mail : [email protected], [email protected], [email protected]

65 Antalya - TURKEY


A Recurrence Relation for Orthogonal

Polynomials on Triangular Domains

Abedallah Rababah

Abstract

Farouki, Goodman, and Sauer determined Legendre-weighted orthogonal polynomialsPn,r(u, v, w), r = 0, 1, . . . , n, n ≥ 0 on the triangular domain T = {(u, v, w) : u, v, w ≥0, u + v + w = 1}. Unfortunately, the method of construction is complicated, time con-suming, impractical, and needs a lot of computations. So, there is a need for a method offinding these orthogonal polynomials. The most convenient method is finding a recurrencerelation for these orthogonal polynomials. This is the aim of our consideration in this talkby determining a recurrence relation that enables us to find these polynomials easily; thisis done by considering the cases of r = n, r = n − 1, r ≤ n − 2 separately. We also showthat the recurrence relation for the case of univariate Legendre polynomials is retrievedfrom the general Legendre-weighted orthogonal polynomials Pn,r(u, v, w) on the triangulardomain T .

References

[1] Farouki, R.T., Goodman, T.N.T. and Sauer, T., Construction of orthogonal bases for poly-nomials in Bernstein form on triangular and simplex domains, Comput. Aided Geom. Design(2003),20(4), 209-230.

[2] Rababah, A., Distance for degree raising and reduction of triangular Bezier surfaces, J.Comput. Appl. Math. (2003),158, 233-241.

[3] Rababah, A. and M. Al-Qudah, Jacobi-weighted orthogonal polynomials on triangular do-mains, Journal of Applied Mathematics, (2005), Vol. 2005, Issue 3, 205-217.

[4] Rababah, A. Bivariate Orthogonal Polynomials on Triangular Domains, Mathematics andComputers in Simulation(2008), 78, 107-111.

Department of Mathematics, Jordan University of Science and TechnologyE-mail : [email protected]

66 Antalya - TURKEY


Legender operator matrix of differentiation for

solving Chua’s System

A.K Alomari

Abstract

This paper presents new method for solving chaotic system based on Legender polynomial.New modified is obtained to solve the system for globally time. Error analysis is given for thepresent solution. Comparing with Rang–kutta method and the present method yield that thepresent method is very effect for solving this kind of problems.

2010 Mathematics Subject Classification. 65P20, 26A33, 34A08.

Keywords and phrases. Legender polynomial, Chua’s system, Analytic Solution.

References

[1] Zhu H,Zhou S,He Z. Chaos synchronization of the fractional-order Chens system, Chaos,Solitons & Fractals 41:2733–2740 (2009)

[2] Li C, Peng G. Chaos in Chens system with a fractional order, Chaos, Solitons & Fractals22:443-450 (2004)

[3] Wanga J, Xionga X, Zhang Y. Extending synchronization scheme to chaotic fractional-orderChen systems, Physica A 370:279285 (2006)

Department of Mathematics, Faculty of Science, Yarmouk University, 211-63Irbid, JordanE-mail : [email protected]

67 Antalya - TURKEY


New Results on Omega ParacompactnessSamer Al Ghour

AbstractIn [7], Al Ghour dened ω-paracompactness as follows: A Hausdorspace X is called ω-

paracompact if each open covering of X admits an ω-locally nite open renement. In thispaper, we obtain several new results related to ω-paracompactness.

2010 Mathematics Subject Classifications : 54D20

Keywords :ω-open set, ω-paracompactness, sun theorem.

References

[1] Engelking R., General Topology, Hilderman, Berlin, (1989).

[2] Hdeib, H. Z. !-closed mappings. Rev. Colombiana Mat. 16 (1982), no. 1-2, 6578.

[3] Hdeib, H. !-continuous Functions, Dirasat Journal 16 (1989), 136-153.

[4] Al-Zoubi, K; Al-Nashef, B. The Topology of !-open subsets, Al-Manarah Journal 9 (2003),169-179.

[5] Sarsak, M. !-almost Lindelof Spaces, Questions Answers Gen. Topol- ogy 21 (2003), no. 1,2735.

[6] Al-Zoubi, K. On generalized !-closed sets. Int. J. Math. Math. Sci. 13 (2005), 20112021.

[7] Al Ghour, S. Some generalizations of paracompactness, Missouri J. Math. Sci. 18 (2006),no. 1, 64-77.

[8] Al-Omari, A.; Noorani, M. Regular generalized !-closed sets. Int. J. Math. Math. Sci. 2007,Art. ID 16292, 11 pp.

[9] Al-Omari, A.; Noorani, M. Contra-!-continuous and almost contra-!- continuous. Int. J.Math. Math. Sci. 2007, Art. ID 40469, 13 pp.1

[10] Zorlutuna, I. !-continuous multifunctions. Filomat 27 (2013), no. 1, 165172.

[11] Carpintero, C.; Rosas, E.; Salas, M.; Sanabria, J.; Vasquez, L. Gener- alization of !-closedsets via operators and ideals. Sarajevo J. Math. 9(22) (2013), no. 2, 293301.

[12] Carpintero, C.; Rajesh, N.; Rosas, E.; Saranyasri, S. On slightly !- continuous multifunc-tions. Punjab Univ. J. Math. (Lahore) 46 (2014), 5157.

[13] Banerjee, R. N. Closed maps and countably metacompact spaces. J. London Math. Soc.(2) 8 (1974), 4950.

[14] Hanai, Sitiro. On closed mappings. II. Proc. Japan Acad. 32 (1956), 388391.

[15] Arya, Shashi Prabha. Sum theorems for topological spaces. Math. Student 41 (1973),117135.

Department of Mathematics and Statistics, Jordan University of Sci- enceand Technology, Irbid 22110, JordanE-mail : [email protected]

68 Antalya - TURKEY


Toeplitz operators in the analytic Bergman

space

Mujo Mesanovic

Abstract

Describing the set (called the commutant) of all Toeplitz operators that commute (ina sense of composition) with a given one is a major question in the theory of Toeplitzoperators defined on the analytic Bergman space of the unit disk. The main aim of thistalk is to introduce some recent results related to this problem, with a particular attentionto a family of operators called quasihomogeneous Toeplitz operators.


Keywords :Holomorphic weighted shift, Quasihomogeneous Toeplitz operator, Mellin trans-form.

References

[1] P. Ahern and Z. Cuckovic, A Theorem of Brown-Halmos type for Bergman space Toeplitzoperators, J. Funct. Anal. 187 (2001), 200-210.

[2] S. Axler, Z. Cuckovic, Commuting Toeplitz operators with harmonic symbols, Integral equa-tion and Operator Theory 14 (1991), 1-12.

[3] S. Axler, Z. Cuckovic, N. V. Rao, Commutants of analytic Toeplitz operators on theBergman space, Proc. Amer. Math. Soc. 128 (2000), 1951-1953.

[4] Z. Cuckovic and N. V. Rao, Mellin transform, monomial Symbols, and commuting Toeplitzoperators, J. Funct. Anal. 154 (1998), 195-214.

[5] I. Louhichi, Powers and roots of Toeplitz operators, Proc. Amer. Math. Soc. 135, (2007),1465-1475.

[6] I. Louhichi and N. V. Rao, Bicommutants of Toeplitz operators, Arch. Math. 91 (2008),256-264.

[7] L. Carlitz, Gauss sums over finite fields of order 2n, Acta Arith. 15 (1969), 247-265.

American University of Sharjah, UAEE-mail : [email protected]

69 Antalya - TURKEY


Product of Toeplitz operators on the harmonic

Bergman space

Issam Louhichi

Abstract

We have recently witnessed a new trend in the theory of Toeplitz operators consisting ofstudying their products on the harmonic Bergman space of the unit disk D in the complexplane C. Those operators differ in many aspects from the classical ones defined on theunweighted analytic Bergman space. In this presentation I will survey recent developmentsin this area and point out the properties that are true for ones but not for others.

2010 Mathematics Subject Classifications : 47B35, 47B38.

Keywords :Quasihomogeneous Toeplitz operator, Mellin transform.

References

[1] X. T. Dong, C. Liu, and Z. H Zhou, Quasihomogeneous Toeplitz operators with integrablesymbols on the harmonic Bergman space, Bull. Aust. Math. Soc. 90 (2014), 494-503.

[2] X. T. Dong and Z. H Zhou, Products of Toeplitz operators on the harmonic Bergman space,Proc. Amer. Math. Soc. 138, (2010), 1765-1773.

[3] X. T. Dong and Z. H Zhou, Commuting quasihomogeneous Toeplitz operators on the har-monic Bergman space, Complex Anal. Oper. Theory 7 (2013), 1267-1285.

[4] X. T. Dong and Z. H Zhou, Products equivalence of quasihomogeneous Toeplitz operators onthe harmonic Bergman space, Studia Math. 219 (2013), 163-175.

[5] I. Louhichi and L. Zakariasy, Quasihomogeneous Toeplitz operators on the harmonicBergman space, Arch. Math. 98, Issue 1 (2012), 49-60.

[6] I. Louhichi, F. Randriamahaleo, and L. Zakariasy, On the commutativity of a certain classof Toeplitz operators, Concr. Oper. 2014; 2:17.

American University of Sharjah, UAEE-mail : [email protected]

70 Antalya - TURKEY


A note on tribonacci numbers with particular

matrices

Seyyed Hossein Jafari-Petroudi, Maryam Pirouz

Abstract

In this paper we study a particular n × n matrix F = [Fki,j ]ni,j=1 and its Hadamard

exponential matrix e◦F = [eFk ], where ki,j = min(i, j) + 1 and Fk is the kth tribonaccinumbers. We find some relations about determinants and inversion of these matrices. ThenSome spectral bounds of these matrices are represented. Finally some other properties ofthese matrices are shown.

2010 Mathematics Subject Classifications : Primary 15A36; Secondary 15A15,11B39

Keywords :tribonacci numbers, Spectral norm, Hadamard inverse, determinant

References

[1] D.Bozkurt, A note on the spectral norms of the matrices connected integer numbers se-quence, Math.GM,.1724v1 (2011), 171-190.

[2] E. Dupree, B.Mathes, Singular values of k-Fibonacci and k-Lucas Hankel matrix, Int. J.Contemp. Math. Science. Vol 7 (2012), no. 47, 2327–2339.

[3] L. Liu, Z. jiang, Explicit form of the inverse matrices of tribonacch circulant type matrices,Abstr. Appl. Anal., (2014), 1-11.

[4] S. Solak, M. Bahsi, On the spectral norms of Toeplitz matrices with Fibonacci and Lucasnumbers, Nonlinear Analysis, Hacettepe Journal of Mathematics and Statistics. Vol 42,(2013),no. 1, 15–19.

[5] F.Zhang, Matrix Theory, Basic results and techniques, Springer , 2011.

Department of Mathematics, Payame Noor University, P.O .Box, 1935 − 3697,Tehran, IranE-mail : hossein [email protected]

Department of computer sciences, Guilan university, Rasht, IranE-mail : [email protected]

71 Antalya - TURKEY


Weighted composition operators on vector

valued weighted Dirichlet type spaces

Hamid Vaezi, Sepideh Nasresfahani

Abstract

In this article we investigate the weighted composition operator on the vector valuedweighted Dirichlet type spaces Dpv(X) for complex Banach space X and 1 ≤ p ≤ 2. Weprove that this operator is bounded(compact) on these spaces if the related measure µp,v,ψis an (compact) Carleson.

2010 Mathematics Subject Classifications : 47B33, 31C25.

Keywords :Weighted composition operator, Weighted Dirichlet type spaces, Carleson mea-sure.

References

[1] JA. Cima, WR. Wogan, A Carleson measure theorem for the Bergman spaces on the ball,J. Operator Theory, 7 (1982), 157-165.

[2] C. Cowen, B. MacCluer, Composition operators on spaces of Analytic functions, Studies inAdvanced Mathematics, Boca Raton, CRC Pres, 1995.

[3] M. Wang, Weighted composition operators between Dirichlet spaces, Acta Math. Sci., 31B(2)(2011), 671-651.

[4] N. Zorboska, Composition operators on weighted Dirichlet spaces, Proc. Amer. Math. Soc.,126 (1998), 2013-2023.

Faculty of Mathematical Sciences, University of Tabriz, Tabriz, IranE-mail : [email protected]

Faculty of Mathematical Sciences, University of Tabriz, Tabriz, IranE-mail : s [email protected]

72 Antalya - TURKEY


Application of the Bernstein Polynomials for

Solving Volterra Integral Equations with

Convolution Kernels

Ahmet Alturk

Abstract

In this study, we consider the second-type linear Volterra integral equations whose ker-nels based upon the difference of the arguments. The aim is to convert the integral equationto an algebraic one. This is achieved by approximating functions appearing in the integralequation with Bernstein polynomials. Since the kernel is of convolution type, the integralis represented as a convolution product. Taylor expansion of kernel along with the proper-ties of convolution are used to represent the integral in terms of Bernstein polynomials sothat a set of algebraic equations is obtained. This set of algebraic equations is solved andapproximate solution is obtained. We also provide a simple algorithm which depends bothon the degree of the Bernstein polynomials and that of monomials. Illustrative examplesare provided to show the validity and applicability of the method.

2010 Mathematics Subject Classifications : 45A05, 45D05, 45E10.

Keywords :

References

[1] M. Alipour and Davood Rostamy Bernstein polynomials for solving Abel’s integral equation,The Journal of Mathematics and Computer Science, 3(4): (2011), 403-412.

[2] Subhra Bhattacharya and B. N. Mandal Use of bernstein polynomials in numerical solutionsof volterra integral equations, Applied Mathematical Sciences, 2(36): (2008), 1773-1787.

DEPARTMENT OF MATHEMATICS, AMASYA UNIVERSITY, AMASYA, TURKEY


73 Antalya - TURKEY


On some explicit and asymptotic formulas

related to the m-arithmetic triangle

Armen Bagdasaryan

Abstract

In this talk, we first introduce the m-arithmetic triangle which is a generalization ofPascal’s triangle. Then, we derive an explicit formula for the numbers of the m-arithmetictriangle, and we also discuss some asymptotic expansions for these numbers.

2010 Mathematics Subject Classifications : 11B65, 05A10, 11B37

Keywords : m-arithmetic triangle, Pascal’s triangle, explicit formula, asymptotic formula

References

[1] A.M. Moghaddamfar, et al., On the matrices related to the m-arithmetic triangle, LinearAlgebra Appl. 432 (2010), 53-69.

[2] B.A. Bondarenko, Generalized Pascal Triangles and Pyramids, their Fractals, Graphs andApplications, The Fibonacci Association, 1993.

[3] R. Graham, D. Knuth, O. Patashnik, Concrete Mathematics, Addison-Wesley, 2nd ed., 1994.

Department of Mathematics and Statistics, American University of the Mid-dle East, Kuwait and Institute for Control Sciences of Russian Academy ofSciences, Moscow, RussiaE-mail : [email protected]

74 Antalya - TURKEY


Inversion formula for analytic functions

Armen Bagdasaryan, Seifedine Kadry

Abstract

In this talk, we introduce a new formula for inversion of analytic functions. It is simpleto use and it is easier to apply than the Lagrange-Burmann inversion formula, since notaking limits is required. By applying this formula we get some inversion formulas for cer-tain functions. As a side result of this application, we also find new special numbers, whichcan also be defined using an analogue of Pascal’s triangle, and which have a simple relationwith Bernoulli numbers. Using the formula for these numbers, we derive a new explicitformula for Bernoulli numbers. In conclusion, we also present power series expansions forsome elementary functions as well as asymptotic expansions of certain special functionsthat involve these new numbers.

2010 Mathematics Subject Classifications : 11A25, 40E99, 32A05

Keywords : Lagrange-Burmann inversion formula, analytic functions, inversion of func-tions, reversion of series, Bernoulli numbers

References

[1] D. Merlini, D. Sprugnoli, M. Verri, Lagrange inversion: when and how, Acta Appl. Math.94 (2006), 233–249.

[2] I.P. Goulden, D.M. Jackson, Combinatorial Enumeration, Wiley, 1983.

[3] R. Graham, D. Knuth, O. Patashnik, Concrete Mathematics, 2nd ed., Addison-Wesley,Reading, 1994.

[4] R.P. Stanley, Enumerative Combinatorics, vol. 2, Cambridge University Press, New York,1999.

[5] N. de Bruijn, Asymptotic Methods in Analysis, 3rd ed., North-Holland, Amsterdam, 1970.

Department of Mathematics and Statistics, American University of the Mid-dle East, KuwaitE-mail : [email protected]; [email protected]

75 Antalya - TURKEY


Generalized Beltrami Systems with a Singular

Point

Yesim Saglam Ozkan, Sezayi Hızlıyel

Abstract

In this work, we consider the model equation

∂w(z)

∂φ(z)− 1

2B(z)[φ(z)]−1w(z) = f(z),

and construct the general solution of this equation. Where the unknown w(z) = (wij(z))is m × s matrix valued function f(z) is a given m × s matrix valued function, φ(z) isa generating solution for Q-holomorphic function and B(z) = bij is a complex matrixcommuting with Q.

2010 Mathematics Subject Classifications : 30G20, 30G35

Keywords :Generalized Beltrami Systems, Q-holomorphic functions

References

[1] G. N. Hile, Function Theory for Generalized Beltrami Systems, Comp. Math. 11 (1982),101-125.

[2] I. N. Vekua, Generalized Analytic Functions, Pergamon, Oxford, (1962).

[3] L. Bers, Theory of Pseudo-Analytic Functions, New York: Ins. Math. Mech., New YorkUniversity (Lecture Notes) (1953).

[4] S. Hızlıyel, M. Caglıyan, Generalized Q-Holomorphic Functions, Complex Var. Theory Appl.49 (2004), 427-447.

[5] S. Hızlıyel, M. Caglıyan, Pseudo Q-holomorphic functions, Complex Var. Theory Appl. 49(2004), 941-955.

[6] Z. D. Usmanov, Generalized Cauchy-Riemann systems with a singular point, Harlow: Long-man, (1997).

[7] Z. D. Usmanov, On the theory of the equation 2z∂zΦ−λΦ = 0.(Russian),Dokl. Akad. NaukTajik. SSR 15 (1972),no:5, 13-16.

Uludag University Faculty of Art and Science Department of MathematicsBursa-TURKEYE-mail : [email protected]

Uludag University Faculty of Art and Science Department of MathematicsBursa-TURKEYE-mail : [email protected]

76 Antalya - TURKEY


Some Sequence spaces of interval numbers

defined by Orlicz Function

Ayten Esi

Abstract

In this study, we introduce some new spaces of sequences of interval numbers usingby Orlicz function and examine some properties of resulting sequence classes of intervalnumbers.

References

[1] A. Esi, -Sequence spaces of interval numbers, Appl.Math.Inf.Sci.8(3)(2014), 1099-1102.

[2] A. Esi, A new class of interval numbers, Journal of Qafqaz University, Mathematics andComputer Science, pp.98-102,(2012).

[3] A. Esi, Lacunary sequence spaces of interval numbers, Thai Journal of Mathematics, 10(2),pp.445-451,(2012).

[4] A. Esi, Double lacunary sequence spaces of double sequence of interval numbers, Proyec-ciones Journal of Mathematics, 31(1)(2012), 297-306.

[5] A.Esi, Strongly almost -convergence and statistically almost -convergence of interval num-bers, Scientia Magna, 7(2)(2011), 117-122.

[6] A.Esi, Statistical and lacunary statistical convergence of interval numbers in topologicalgroups, Acta Scientarium Technology, 36(3)(2014), 491-495.

[7] A.Esi and N.Braha, On asymptotically -statistical equivalent sequences of interval numbers,Acta Scientarium Technology, 35(3)(2013), 515-520.

Adiyaman UniversityE-mail : [email protected]

77 Antalya - TURKEY


Generalized ideal convergence of double

sequences in intuitionistic fuzzy 2-normed linear

spaces

Ayhan Esi

Abstract

An ideal I is a family of subsets of positive integers N which is closed under takingfinite unions and subsets of its elements. In [?], Esi and Hazarika introduced the concept ofλ-ideal convergence in intuitionistic fuzzy 2-normed space. The aim of this paper is to intro-duce and study the notion of (λ; τ)-ideal convergence of double sequences in intuitionisticfuzzy 2-normed space as a variant of the notion of ideal convergence of double sequences.Also Iλ;τ–limit points and Iλ;τ–cluster points have been de. . . ned and the relation betweenthem are established. Furthermore, Cauchy and Iλ;τ–Cauchy of double sequences are in-troduced and studied, where λ = (λm) and τ = (τn) be two non-decreasing sequences ofpositive numbers tending to ∞ such that λm+1 ≤ λm + 1;λ1 = 1, τm+1 ≤ τm + 1; τ1 = 1.

2010 Mathematics Subject Classifications : Primary 40A99; Secondary 40A05

Keywords :Ideal-convergence; Intuitionistic fuzzy normed space; λ-convergence.

References

[1] Esi, A. and Hazarika, B. 2013. λ-ideal convergence in intuitionistic fuzzy 2-normed linearspaces. Journal of Intelligent and Fuzzy Systems, 24(4), 725-732, DOI: 10.3233/IFS-2012-0592

[2] Esi, A. and Hazarika, B. 2014. Lacunary summable sequence spaces of Fuzzy numbersdefined by ideal convergence and an Orlicz function. Afrika Matematika, 25(2), 331-343,DOI: 10.1007/s13370-012-0117-3

[3] Cakallı, H. and Hazarika, B. 2012. Ideal quasi-Cauchy sequences. Journal of Inequalitiesand Applications, 2012(234), 1-11, doi:10.1186/1029-242X-2012-234.

[4] Connor, J. and Swardson, M.A. 1993. Measures and ideals of C∗(X) . Ann. N.Y. Acad.Sci.,704, 80-91.

[5] Fast, H. 1951. Sur la convergence statistique. Colloq. Math., 2, 241-244.

[6] Fridy, J. A. 1985. On statistical convergence. Analysis, 5, 301-313.

[7] Gahler, S. 1965. Linear 2-normietre Raume. Math. Nachr., 28, 1-43.

[8] Hazarika, B. 2009. Lacunary I-convergent sequence of fuzzy real numbers. The PacificJour. Sci. Techno., 10(2), 203-206.

Adyaman University Science and Art Faculty, Department of Mathematics,02040, Adiyaman, TurkeyE-mail : [email protected]

78 Antalya - TURKEY


A B-Spline Approach to q-Eulerian Polynomials

Cetin Disibuyuk, Sule Ulutas

Abstract

We investigate the relations between q-Eulerian numbers, q-Eulerian polynomials, q-Eulerian Frobenius polynomials and B-splines with knots both at q-integers and in geomet-ric progression. We derive q-Euler-Frobenius polynomials using q-analogue of exponentialsplines. It is shown that B-splines with knots at q-integers and B-splines with knots in ge-ometric progression have same values on their knot points. We also construct q-analoguesof Worpitzky identity.

Keywords: q-Eulerian numbers, q-Eulerian polynomials, q-Euler Frobenius polynomials, Wor-pitzky identity, B-splines with knots at q-integers, B-splines with knots in geometric progressionMathematics Subject Classification (2000): 65D07, 65D17, 05A30

Department of Mathematics, Dokuz Eylul University, Fen Fakultesi, TınaztepeKampusu, 35160 Buca, Izmir.E-mail : [email protected]

Graduate School of Natural and Applied Sciences, Dokuz Eylul University,35390 Buca, IzmirE-mail : [email protected]

79 Antalya - TURKEY


Asymptotic Behaviour of Resonance

Eigenvalues of the Schrodinger Operator with a

Matrix Potential

Sedef KARAKILIC,Setenay AKDUMAN,Didem COS. KAN

Abstract

We will discuss the asymptotic behaviour of the eigenvalues of Schrodinger operatorwith a matrix potential defined by Neumann boundary condition in Lm2 (F ), where F isd-dimensional rectangle and the potential is a m ×m matrix with m ≥ 2, d ≥ 2 , whenthe eigenvalues belong to the resonance domain, roughly speaking they lie near planes ofdiffraction.

2010 Mathematics Subject Classifications : 47F05, 35P15

Keywords :Schrodinger operator, Neumann condition, Resonance eigenvalue, Perturbationtheory.

References

[1] Veliev, O. A. (2007). Perturbation Theory for the Periodic Multidimensional SchrodingerOperator and the Bethe-Sommerfeld Conjecture. International Journal of ContemporaryMathematical Sciences, 2 (2), 19-87.

[2] Cos.kan, D., Karakılıc, S. (2011). High energy asymptotics for eigenvalues of the Schrodingeroperator with a matrix potential, Mathematical Communications, 16(2).

[3] Karakılıc, S. & Akduman S. (2015). Eigenvalue Asymptotics for the Schrodinger Operatorwith a Matrix Potential in a Single Resonance Domain. Filomat, 29:1, 21-38.

Department of Mathematics, Faculty of Science, Dokuz Eylul University,Tınaztepe Camp., Buca, 35290, Izmir, TurkeyE-mail : [email protected]



80 Antalya - TURKEY


q-Peano Kernel and Its Applications

Gulter Budakci, Halil Oruc

Abstract

We introduce a q-analogue of Peano kernel theorem by replacing ordinary derivativesand integrals by quantum derivatives and quantum integrals respectively. In the limitq → 1, it reduces to the classical Peano kernel. We also give applications to polynomialinterpolation and q-B-splines.

2010 Mathematics Subject Classifications : 65D07, 65D17, 41A15

Keywords :Peano Kernel, q-Taylor formula, divided differences, quantum derivatives,quantumintegrals, q-B-splines

References

[1] Budakcı, G., Disibuyuk, C., Goldman, R., Oruc, H., Extending Fundamental Formulasfrom Classical B-Splines to Quantum B-Splines, Journal of Computational and AppliedMathematics, 282, 17-33 (2015)

[2] Gauchman H., Integral Inequalities in q-Calculus, Computers and Mathematics with Appli-cations, 47, 281-300 (2004)

[3] Hammerlin G.,Hoffmann, K., Ewing, J., Gehring, F., Halmos, P., Numerical Mathematics.Springer-Verlag, New York (1991)

[4] Powell, M.J.D., Approximation Theory and Methods. Cambridge University Press (1981)

[5] Rajkovic, P. M., Stankovic, M. S.,Marinkovic, S. D., Mean value theorems in q-calculus,Proceedings of the 5th International Symposium on Mathematical Analysis and its Appli-cations, Mat. Vesnik, 54, 3-4, 171–178 (2002)



81 Antalya - TURKEY


Solution for the Problem of the Best Uniform

Approximation of the Grid Function with Linear

Splines and Applications for Making Decisions

B. Bayraktar, V. Kudaev

Abstract

The problem of the best uniform approximation of the grid function linear splines withthe best choice of nodes spline is solved on the base of discrete dynamic programming.Initial solve is close to optimal one and is defined with the method of traveling wave. Italso allows decrease problem dimension. One can use developed method, algorithm andsoftware in information systems, computational mathematics systems optimal control andadjustment, regression analysis. The method is applied for optimal adjustment networksystems on the example of water supply. The software with modern visual tools is developed(Builder C++).

2010 Mathematics Subject Classifications : 68W25, 41A15, 49K35, 49K10

Keywords :algorithm approximation, a linear spline, grid function, optimal regulation, thenetwork system.

References[1] Karl de Boor, A Practical Guide to Splines. M., Radio and Communication, 1985, 303.

[2] A.A. Ligun., A.A.Shumeiko, Asymptotic methods of recovery curves, Monograph. - Kyiv: Institute of Math-ematics National Academy of Sciences of Ukraine, 1997. - 358.

[3] A. I. Grebennikov, The choice of nodes in the spline approximation of functions, Zhurnal vychislitel’noimatematiki i matematicheskoi fiziki , V.16, No:1. (1976), 219-223.

[4] H.J. Walters, A Newton-Type Method for Computing Best Segment Approximations, Communications onPure and Applied Analysis, v.3(1), (2004), 133-149.

[5] K. Thamaratnam, G. Claeskens, C. Croux, M. Salibian-Barrera, Journal of Computational and GraphicalStatistics, (2010), 19 (3), 609-625.

[6] A.A. Shumeiko, E.A. Shumeiko, On the construction of asymptotically optimal piecewise-linear regression.Informatics and mathematical methods in simulation, V. 1, No:2, (2011), 99-106.

[7] I.A. Pakhnoutov, Optimal choice of knots for smoothing by linear splines, Izvestia KaliningradskogoGosu-darstvennogo Tecnicheskogo Universiteta, No:2, (2011), 28-32.

[8] B. Bayraktar, Problem of constructing a step function fluctuating least around a given function. TWMS J.Pure Appl. Math., V.4, N.2, (2013), 131-145.

[9] I. A. Vatel, A. F. Kononenko, A certain numerical scheme for the solution of optimal control problems.Zhurnal vychislitel’noi matematiki i matematicheskoi fiziki , V.10, No:1, (1970), 67-73.

[10] N. N. Abramov, Theory and methods of calculating systems of water supply and distribution. M. Stroyizdat,1972.

Uludag University Faculty of Art and Science Department of Mathematics Bursa-TURKEYE-mail : [email protected]

INSTITUTE OF COMPUTER SCIENCE AND PROBLEMS OF REGIONAL MANAGEMENT, KABARDINO- BALKARIAN RESEARCH CENTER OF RUSSIAN ACADEMY OF SCIENCES, RUSSIAE-mail :

E-mail: [email protected]*Researched with the support by Russian Fond of Basic Researches grants 13-01-00929-a, 13-07-01002-a

82 Antalya - TURKEY


Vector-valued B-singular integral operators in

Lebesgue spaces

Seyda Keles, Vagif S. Guliyev

Abstract

We consider the generalized shift operator, associated with the Laplace-Bessel differ-ential operator

∆B =

n−1∑k=1

∂2

∂x2k+

(∂2

∂x2n+

2ν

xn

∂

∂xn

), ν > 0

and B-singular integral operators for vector-valued functions are investigated. For 1 < p <∞ and H1, H2 separable Hilbert space we obtain boundedness of vector-valued B-singularintegral operators from Lp,ν (Rn+, H1) to Lp,ν (Rn+, H2).

2010 Mathematics Subject Classifications : 42B20, 42B99, 47G10

Keywords :Singular integrals,Laplace-Bessel differential operator, generalized translationoperator, vector-valued B-singular integral operator.

References

[1] A. P. Calderon, A. Zygmund, On Singular Integrals, Amer. J. Math. 78 (1956), 289-309.

[2] A. Benedek, A. P. Calderon, R. Panzone, Convolution operators on Banach space valuedfunction, Proc. Nat. Acad. Sci. USA, 48 (1962), 356-365.

[3] V.S. Guliyev, A.K. Narimanov, On the Lp,ν boundedness of the anisotropic Fourier- Besselsingular integrals, Trans. Acad. Sci. Azerb. Ser. Phys. Tech. Math. Sci. 5 (1999), 32-41.

Department of Mathematics, Akdeniz University, Antalya,TurkeyE-mail : [email protected]

Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, De-partment of Mathematics, Ahi Evran University, Kirsehir, TurkeyE-mail : [email protected]

83 Antalya - TURKEY


The Similarity Invariants of Non-lightlike

Curves in the Minkowski 3-space

Hakan Simsek, Mustafa Ozdemir

Abstract

In this paper, we firstly introduce the group of similarity transformations in the Minkowski-3 space. We describe geometric invariants of a non-lightlike curve according to the groupof similarity transformations of the Minkowski 3-space. We show extension of fundamentaltheorem for non-lightlike curves under the group of similarity of the Minkowski 3-space.Besides, by using the similarity invariants, we construct the non-lightlike similar curves bymeans of the pseudo-spherical curves on S2

1 and H2(−1).

2010 Mathematics Subject Classifications : 53A35, 53A55, 53B30.

Keywords : Lorentzian Similarity Geometry, Similarity invariants, Similarity Transforma-tion, Non-lightlike Similar Curves.

References

[1] A. Brook, A. M. Bruckstein and Ron Kimmel, On Similarity-Invariant Fairness Measures,LNCS 3459, pp. 456–467, 2005.

[2] H. Sahbi, Kernel PCA for similarity invariant shape recognition, Neurocomputing, 70,3034–3045, 2007.

[3] J. E. Hutchinson, Fractals and Self-Similarity, Indiana University Mathematics Journal,Vol. 30, N:5, 1981.

[4] J. G. Alcazar, C. Hermosoa and G. Muntinghb, Detecting similarity of rational planecurves, Journal of Computational and Applied Mathematics, 269, 1–13, 2014.

[5] M. Ozdemir, A. A. Ergin, Rotations with unit timelike quaternions in Minkowski 3-space,Journal of Geometry and Physics 56, 322–336, 2006.

[6] M. Ozdemir, A. A. Ergin, Spacelike Darboux Curves in Minkowski 3-Space, Differ. Geom.Dyn. Syst. 9, 131-137, 2007.

[7] R. Encheva and G. Georgiev, Shapes of space curves., J. Geom. Graph., 145-155, 2003.

[8] S. Izumiya, D. He Pei, T. Sano and E. Torii, Evolutes of Hyperbolic Plane Curves, ActaMathematica Sinica, English Series, Vol.20, No.3, pp. 543–550, 2004.

[9] S. Izumiya and M. Takahashi, Spacelike parallels and evolutes in Minkowski pseudo-spheres,Journal of Geometry and Physics 57, 1569–1600, 2007.

[10] Y. Kamishima, Lorentzian similarity manifolds, Cent. Eur. J. Math., 10(5), 1771-1788,2012.

Department of Mathematics, Akdeniz University Antalya, TURKEYE-mail : [email protected], mozdemirakdeniz.edu.tr

84 Antalya - TURKEY


Matrices Over Hyperbolic Split Quaternions

Melek Erdogdu, Mustafa Ozdemir

Abstract

In this paper, we present some important properties of matrices over hyperbolic splitquaternions. We examine hyperbolic split quaternion matrices by their split quaternionmatrix representation.

2010 Mathematics Subject Classifications : 20G20, 11R52

Keywords :Split Quaternion, Hyperbolic Split Quaternion.

References

[1] Y. Alagoz, K. H. Oral, S. Yuce, Split Quaternion Matrices. Miskolc Mathematical Notes,13 (2012), 223-232.

[2] M. Erdogdu, M. Ozdemir, On Eigenvalues of Split Quaternion Matrices. Advances in Ap-plied Clifford Algebras, 23 (2013), 615-623.

[3] M. Erdogdu, M. Ozdemir, On Complex Split Quaternion Matrices. Advances in AppliedClifford Algebras, 23 (2013), 625-638.

[4] M. Ozdemir, A.A. Ergin, Rotations with unit timelike quaternions in Minkowski 3-space.Journal of Geometry and Physics, 56 (2006) 322-336.

[5] M. Ozdemir, M. Erdogdu, H. Simsek, On Eigenvalues and Eigenvectors of a LorentzianRotation Matrix by Using Split Quaternions. Advances in Applied Clifford Algebras, 24(2014), 179-192.

[6] F. Zhang, Quaternions and Matrices of Quaternions. Linear Algebra and its Applications,251 (1997), 21-57.

Necmettin Erbakan University, Department of Mathematics-Computer Sci-ences, Konya/ TURKEY.E-mail : [email protected]

Akdeniz University, Department of Mathematics, Antalya/ TURKEY.E-mail : [email protected]

85 Antalya - TURKEY


Mannheim Partner Curves in Cartan-Vranceanu

3-Space

A. Yilmaz Ceylan, A. A. Ergin

Abstract

In this paper, we characterize parametric equations of Mannheim mate of a biharmoniccurve in the Cartan-Vranceanu 3-space. We show that the distance between correspondingpoints of the Mannheim pair is constant in Cartan-Vranceanu 3-dimensional spaces.

2010 Mathematics Subject Classifications : 53A04, 53C30

Keywords :Cartan-Vranceanu Space, Biharmonic curves, Mannheim curve

References

[1] Liu H, Wang F.: Mannheim Partner Curve in 3-Space. J. Geom., 88: 120-126 (2008)

[2] Turhan, E., Korpınar, T. and Lopez-Bonilla, J.: Characterization Mannheim Curves in theHeisenberg group Heis3. Journal of Vectorial Relativity JVR 6(1), 29-36 (2011)

[3] Caddeo, R., Montaldo, S., Oniciuc, C., Piu, P.: The Classification of Biharmonic Curvesof Cartan-Vranceanu 3-Dimensional Spaces. Modern trends in geometry and topology, ClujUniv. Press, Cluj-Napoca, 121-131 (2006)

[4] Choi, J.H., Kang, T.H., Kim, Y.H.: Bertrand curves in 3− dimensional space forms. Appl.Math. Comput., 219, 1040-1046 (2012)

[5] Choi, J.H., Kang, T.H., Kim, Y.H.: Mannheim curves in 3− dimensional space forms. Bull.Korean Soc., 50, 1099-1108 (2013)

Department of Mathematics, Science Faculty, Akdeniz University, Antalya07058,TurkeyE-mail : [email protected]

Department of Mathematics, Science Faculty, Akdeniz University, Antalya07058,TurkeyE-mail : [email protected]

86 Antalya - TURKEY


On Rational Knots and Links in the Solid Torus

Khaled Bataineh

Abstract

Rational knots and links in the three-space form an important class of knots and links.The notion of a rational knot was introduced in 1967 by J. Conway in his work on classifyingknots and links. They have been studied by many researchers. We introduce the notionof a rational knot or link in the solid torus. We use continued fractions to classify thisimportant class of knots and links in this three-dimensional manifold.

Jordan University of Science and TechnologyE-mail : [email protected]

87 Antalya - TURKEY


On 2-dimensional Finsler manifold

Morteza Faghfouri

Abstract

We solve the following problem for n = 2 : Is any n-dimensional Finsler manifold

(M,F ) with a function f which is nonconstant and smooth on M satisfying ∂gij

∂yk∂f∂xi

= 0,a Riemannian manifold?

2010 Mathematics Subject Classifications : 53C60, 53C25.

Keywords :Berwaldian metric, Finsler manifold, partial differential equation,doubly warpedproduct metric.

References

[1] S.-S. Chern and Z. Shen, Riemann-Finsler geometry, vol. 6 of Nankai Tracts in Mathemat-ics, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005.

[2] L. Kozma, R. Peter, and C. Varga, Warped product of Finsler manifolds, Ann. Univ. Sci.Budapest. Eotvos Sect. Math., 2001, 44:157–170.

[3] E. Peyghan and A. Tayebi, On doubly warped product Finsler manifolds, Nonlinear Anal.Real World Appl., 2012, 13:1703–1720.

[4] E. Peyghan, A. Tayebi, and B. Najafi, Doubly warped product Finsler manifolds with somenon-Riemannian curvature properties, Ann. Polon. Math., 2012, 105:293–311.

[5] I. N. Sneddon, Elements of partial differential equations, Dover Publications, Inc., Mineola,NY, 2006. Unabridged republication of the 1957 original.

Faculty of Mathematics, University of Tabriz, Tabriz, Iran.E-mail : [email protected]

88 Antalya - TURKEY


A Note on Complex q−Baskakov-Stancu

Operator with Divided Differences

Dilek Soylemez Ozden, Didem Aydın Arı

Abstract

In this paper, we consider complex q-Baskakov-Stancu operator and study some ap-proximation properties. We give quantitative estimate of the convergence, Voronovskaja-type result and exact order of approximation in compact disks.

2010 Mathematics Subject Classifications : 30E10, 41A25, 41A28

Keywords : complex q-Baskakov-Stancu operator, divided differences, complex approxi-

mation

References

[1] T. Ernst, The history of q−calculus and a new method, U.U.U.D.M Report 2000, 16, ISSN1101-3591, Department of Mathematics, Upsala University (2000)

[2] S.G. Gal, Approximation by complex Bernstein and convolution type operators, Series onConcrete and Applicable Mathematics, 8. World Scientific Publishing Co. Pte. Ltd., Hack-ensack, NJ (2009)

[3] S.G. Gal,V.Gupta, D.K.Verma, P.N.Agrawal, Approximation by complex Baskakov-Stancuoperators in compact disks, Rend. Circ. Mat. Palermo 61, 153-165 (2012)

[4] A. Lupas, Some properties of the linear positive operators, II. Mathematica (Cluj) 9 32,295–298 (1967)

[5] G.M. Phillips, Interpolation and approximation by polynomials. CMS Books in Mathemat-ics/Ouvrages de Mathematiques de la SMC, 14. Springer-Verlag, New York (2003)

Ankara University Elmadag Meslek Yuksekokulu 06780 AnkaraE-mail : [email protected]

Kırıkkale University Deparment of Mathematics KırıkkaleE-mail : [email protected]

89 Antalya - TURKEY


A Characterization of Curvature Functions in R41

Esen Iyigun

Abstract

In this paper; we study on curvature functions and constant curvature ratios of curvesin R4

1. We obtain the characterization of a non-null curve with every constant curvaturesand give some special results. We handle the special results for a non-null curve in R4

1 onan example.

2010 Mathematics Subject Classifications : 53C40, 53C42.

Keywords :Lorentz Minkowski space, Frenet curvatures, constant curvature ratios, har-monic curvatures

References

[1] E. Iyigun and K. Arslan, On harmonic curvatures of curves in Lorentzian n-space, Commun.Fac. Sci.Univ. Ank. Series A1, 54(2005), No.1, 29-34.

[2] B. O’neill, Semi-Riemannian geometry with applications to relativity, Academic Pres. New-York, (1983).

[3] N. Ekmekci, H.H. Hacisalihoglu and K. Ilarslan, Harmonic curvatures in Lorentzian space,Bull. Malaysian Math. Sc. Soc. (Second Series), 23(2000), 173-179.

[4] G. Ozturk, K. Arslan and H. H. Hacısalihoglu, A characterization of ccr-curves in Rm,Proceedings of the Estonian Academy of Sciences, 57, 4 (2008), 217-224.

[5] S. Yılmaz, E. Ozyılmaz and M. Turgut, On The Differential Geometry Of The CurvesIn Minkowski Space-Time II, International Journal of Computational and MathematicalSciences, 3, 2(2009), 53-55.

[6] A.F. Yalınız and H.H. Hacisalihoglu Null generalized helices in L3 and L4,3 and 4-dimensional Lorentzian space, Mathematical and Computational Applications, 10: 1(2005),105-111.

Uludag University, Art and Science Faculty, Department of Mathematics,16059, Bursa-TURKEYE-mail : [email protected]

90 Antalya - TURKEY


A presentation and some finiteness conditions

for a new version of the Schutzenberger product

of monoids

Firat Ates,I. Naci Cangul, A. Sinan Cevik, Eylem Guzel Karpuz

Abstract

In this study we first define a new version of the Schutzenberger product for any twomonoids A and B, and then, by defining a generating and relator set, we present somefinite and infinite consequences of the main result. At the final part of this paper, we givenecessary and sufficent conditions of this new version to be periodic and locally finite.

2010 Mathematics Subject Classifications : 20E22, 20F05, 20L05, 20M05.

Keywords :Schutzenberger and wreath products, periodicity, local finiteness.

References

[1] F. Ates, A.S. Cevik, Minimal but inefficient presentations for semi-direct products of finitecyclic monoids, Groups St Andrews 2005 in St Andrews, L.M.S Lecture Note Series, CUP,Vol 1 (2006), 175-180.

[2] G. Baumslag, Wreath products and finitely presented groups, Math. Z. 75 (1961), 22-28.

[3] J.M. Howie, Fundamentals of Semigroup Theory, Oxford University Press, 1995.

[4] J.M. Howie, N. Ruskuc, Constructions and presentations for monoids, Comm. in Alg. 22(15)(1994), 6209-6224.

[5] J.D.P. Meldrum, Wreath products of Groups and Semigroups, Longman-Harlow, 1995.

Balikesir University, Faculty of Art and Science, Department of Mathemat-ics, Balikesir-TurkeyE-mail : [email protected]

Uludag University, Faculty of Art and Sciences, Department of Mathemat-ics, Bursa-TurkeyE-mail : [email protected]

Selcuk University, Faculty of Science, Department of Mathematics, Konya-TurkeyE-mail : [email protected]

Karamanoglu Mehmetbey University, Kamil Ozdag Science Faculty, Depart-ment of Mathematics, Karaman-TurkeyE-mail : [email protected]

91 Antalya - TURKEY


Effective results for diophantine equations over

finitely generated domains

Atilla Berczes

Abstract

Let A := ZZ[z1, . . . , zr] be a finitely generated domain over ZZ, and let K denote itsquotient field, and denote by K∗ the multiplicative group of non-zero elements of K. LetΓ be a finitely generated subgroup of K∗, and let Γ denote the division group of Γ. LetF (X,Y ) ∈ A[X,Y ] be a polynomial. In 1960 S. Lang proved that the equation

F (x, y) = 0 in x, y ∈ Γ (1)

has only finitely many solutions, provided F is not divisible by any polynomial of the form

XmY n − α or Xm − αY n (2)

for any non-negative integers m,n, not both zero, and any α ∈ K∗. The conditions

imposed in Lang’s theorem, i.e., that Γ be finitely generated and F not be divisible by anypolynomial of type (2), are essentially necessary. Lang’s proof of this result is ineffective.Lang also conjectured that the above equations has finitely many solutions in x, y ∈ Γunder the same condition (2). In 1974 Liardet proved this conjecture of Lang, however,the proof of Liardet is also ineffective.

An effective version of Liardet’s Theorem in the number filed case is due to Berczes,Evertse, Gyory and Pontreau (2009), however, in the general case no effective result hasbeen proved.

In the talk an effective version of the result of Liardet will be presented in the mostgeneral case. Our result is not only effective, but also quantitative in the sense that anupper bound for the size of the solutions x, y ∈ Γ is provided. This result implies that thesolutions of the equation under investigation can be determined in principle.

In the proofs we combine effective finiteness results for these types of equations overnumber fields and over function fields, along with a specialization method developed byGyory in the 1980’s and refined recently by Evertse and Gyory.

Debrecen University Department of Mathematics Debrecen HungaryE-mail : [email protected]

92 Antalya - TURKEY


Semigroup algebra and nilpotent ideals

Hasan Pourmahmood Aghababa, Mohammad Hossein Sattari

Abstract

In this paper we characterize approximate biprojectivity (in the sense of [10]) of Brandtinverse semigroup algebras and then we show that nilpotent ideals in certain Banach alge-bras cannot be boundedly approximately complemented.

] 2010 Mathematics Subject Classifications : 43A20, 20M18, 46H20

Keywords : Banach algebras, approximately complemented subspaces, nilpotent ideals,approximate and pseudo-amenability, biprojectivity, inverse semigroups.

References[1] O. Yu. Aristov, On approximation of at Banach modules by free modules, Sbornik,Mathematics (2005),

1553-1583.

[2] Y. Choi, Biatness of ‘1-semilattice algebras, Semigroup Forum 75, (2007) 253-271.

[3] P. C. Curtis, Jr. and R. J. Loy, The structure of amenable Banach algebras, J. London. Math. Soc. (2) 40(1989), 89-104.

[4] H. G. Dales, A. T. Lau, and D. Strauss, Banach algebras on semigroups and on their compacti cations,Mem. Amer. Math. Soc., 205 (2010), 1-165.

[5] H. G. Dales, R. J. Loy, and Y. Zhang, Approximate amenability for Banach sequence algebras, Studia Math.,177 (2006), 81-96.

[6] F. Ghahramani and R. J. Loy, Generalized notions of amenability, J. Funct. Anal. 208 (2004), 229-260.

[7] F. Ghahramani and Y. Zhang, Pseudo-amenable and pseudo-contractible Banach algebras, Math. Proc.Camb. Phil. Soc. 142 (2007), 111-123.

[8] R. J. Loy and G. A. Willis, The approximation property and nilpotent ideals in amenable Banach algebras,Bull. Austral. Math. Soc. 49 (1994), 341-346. MR 94m:46083

[9] A. R. Medghalchi and H. Pourmahmood-Aghababa, Fig a-Talamanca-Herz algebras for restricted inversesemigroups and Cli ord semigroups, J. Math. Anal. Appl. 395 (2012), 473-485.

[10] H. Pourmahmood-Aghababa, Approximately biprojective Banach algebras and nilpotent ideals, Bull. Aust.Math. Soc. 87 (2013) 158{173.[11] P. Ramsden, Biatness of semigroup algebras, Semigroup Forum, 79 (2009),515-530.

[11] V. Runde, Lectures on amenability, in: Lecture Notes in Mathematics, Vol. 1774, Springer, Berlin, 2002.

[12] Y. Zhang, Approximate complementation and its application in studying ideals of Banach algebras, Math.Scand. 92 (2003), 301-308.

[13] Y. Zhang, Nilpotent ideals in class of Banach algebras, Proc. Amer. Math. Soc. Vol.127 (1999), 3237-3242.

Department of Mathematics, Tabriz University, Tabriz, IranE-mail : [email protected]

Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranE-mail : [email protected]

93 Antalya - TURKEY


On weakly semiprime ideals of commutative

rings

Ayman Badawi

Abstract

Let R be a commutative ring with identity 1 6= 0 and let I be a proper ideal of R. D.D. Anderson and E. Smith called I weakly prime if a, b ∈ R and 0 6= ab ∈ I implies a ∈ Ior b ∈ I. In this paper, we define I to be weakly semiprime if a ∈ R and 0 6= a2 ∈ I impliesa ∈ I. For example, every proper ideal of a quasilocal ring (R,M) with M2 = 0 is weaklysemiprime. We give examples of weakly semiprime ideals that are neither semiprime norweakly prime. We show that a weakly semiprime ideal of R that is not semiprime is a nilideal of R. We show that if I is a weakly semiprime ideal of R that is not semiprime and 2is not a zero-divisor of of R, then I2 = {0}(and hence i2 = 0 for every i ∈ I). We give anexample of a ring R that admits a weakly semiprime ideal I that is not semiprime wherei2 6= 0 for some i ∈ I. If R = R1 × R2 for some rings R1, R2, then we characterize allweakly semiprime ideals of R that are not semiprime. We characterize all weakly semiprimeideals of of Zm that are not semiprime. We show that every proper ideal of R is weaklysemiprime if and only if either R is von Neumann regular or R is quasilocal with maximalideal Nil(R) such that w2 = 0 for every w ∈ Nil(R).

2010 Mathematics Subject Classifications : 13A15

Keywords :prime,weakly prime, radical ideal, semiprime

References

[1] D. D. Anderson and M. Bataineh, Generalizations of prime ideals, Comm. Algebra 36 (2008),686-696.

[2] D. D. Anderson and E. Smith,, Weakly prime ideals, Houston J. Math. 29 (4)(2003), 831—840.

[3] A. Badawi and A. Y. Darani, On weakly 2-absorbing ideals of commutative rings, HoustonJ. Math. 39 (2)(2013), 441-452.

Department of Mathematics, American University of Sharjah, P.O.Box 26666,Sharjah, UAEE-mail : [email protected]

94 Antalya - TURKEY


On Finiteness Conditions for Bruck-Reilly and

Generalized Bruck-Reilly ∗-Extensions

Seda Oguz, Eylem Guzel Karpuz

Abstract

The purpose of this work is to examine some finiteness conditions for Bruck-Reilly andgeneralized Bruck-Reilly ∗-extensions. We determine necessary and sufficient conditionsto be locally finite and periodic for these extensions. Moreover, finite presentability andfinitely generated conditions are investigated for generalized Bruck-Reilly *-extension of aClifford monoid and of direct product of groups, respectively.

References

[1] I.M. Araujo , N. Ruskuc, Finite presentability of Bruck-Reilly extensions of groups, Journalof Algebra. 242 (2001), 20-30.

[2] R.H. Bruck, A survey of binary systems, Berlin, Germany, Springer. (1958).

[3] C. Carvalho, On presentations of Bruck Reilly extensions, Communications in Algebra. 34(2009), 2871-2886.

[4] C. Carvalho, Bruck Reilly extensions of direct products of monoids and completely(0−)simple semigroups, Semigroup Forum. 79 (2009), 145-158.

[5] C. Kocapinar, E.G. Karpuz, F. Ates , A.S. Cevik, Grobner-Shirshov bases of the generalizedBruck-Reilly ∗-extension, Algebra Colloquium. 19 (2012), 813-820.

Cumhuriyet University, Education Faculty, Department of Secondary SchoolScience and Mathematics Education, 58140, Sivas-TurkeyE-mail : [email protected]

Karamanoglu Mehmetbey University, Kamil Ozdag Science Faculty, Depart-ment of Mathematics, Yunus Emre Campus, 70100, Karaman-TurkeyE-mail : [email protected]

95 Antalya - TURKEY


Two-Sided Crossed Product of Groups

Eylem Guzel Karpuz, Esra Kırmızı Cetinalp

Abstract

In this work, we first define a new group extension, two-sided crossed product, which can beconsidered a generalization of crossed product of groups. Then we give a presentation for two-sidedcrossed product of cyclic groups and obtain complete rewriting system for this new group.

This work is supported by the Scientific Research Fund of Karamanoglu Mehmet bey UniversityProject No: 08-YL-15.

2010 Mathematics Subject Classifications : 16S15, 20E22, 20M05

Keywords :Crossed product, rewriting system, word problem

References

[1] A. L. Agore, D. Fratila, Crossed product of cyclic groups, Czechoslovak Mathematical Jour-nal 60 (2010), 889-901.

[2] A. L. Agore, G. Militaru, Crossed product of groups applications, Arabian J. Sci. Eng. 33(2008), 1-17.

[3] F. Ates, A.S. Cevik, Knit products of some groups and their applications, Randiconti delSeminario Mathematics delta Universita di Padova 2 (2009), 1-12.



96 Antalya - TURKEY


On the residual algebraic free extension of a

valuation on K to K(x)

Figen Oke

Abstract

In this study the residual algebraic free extension of a valuation on a field K to K(x) isstudied. It is assumed that v is a valuation on K with rankv=2 and the residual algebraicfree extension w of v to K(x) with rankw=3 is defined for a special case.

2010 Mathematics Subject Classifications : 2J10, 12F210, 12J20

Keywords : extensions of valuations, residual algebraic free extensions, valued fields

References

[1] V. Alexandru - N. Popescu - A. Zaharescu, A theorem of characterization of residual tran-scendental extension of a valuation, J. Math. Kyoto Univ. 28 (1988), 579-592.

[2] V. Alexandru - N. Popescu - A. Zaharescu, Minimal pair of definition of a residual tran-scendental extension of a valuation, J. Math. Kyoto Univ. 30 (1990), 207-225.

[3] V. Alexandru - N. Popescu - A. Zaharescu, All valuations on K(X), J. Math. Kyoto Univ.30 (1990), 281-296.

[4] N. Bourbaki, Algebre Commutative, Ch. V: Entiers, Ch. VI: Valuations, Hermann, Paris(1964).

[5] 5. N. Popescu-Constantin Vraciu, On the extension of valuations on a field K to K(x).-I,Rendiconti del Seminario Matematico della Universita di Padova, 87(1992), 151-168.

[6] N. Popescu-Constantin Vraciu, On the extension of valuations on a field K to K(x).-II,Rendiconti del Seminario Matematico della Universita di Padova, 96(1996), 1-14.

Trakya Univ. Department of Mathematics Edirne/TURKEYE-mail : [email protected]

97 Antalya - TURKEY


On Certain Extensions of Valuated Fields

Burcu ozturk, Figen Oke

Abstract

Let v be a valuation of a field K. Some extensions of K are studied when rank of vis bigger than one. Also some properties of lifting polynomials that are used for definingresidual trancendental extensions of K are given.

2010 Mathematics Subject Classifications : 12F05, 12J10, 12J20.

Keywords :Valued Fields, Residual Transcendental Extensions, Lifting Polynomials.

References

[1] O. Endler., Valuation Theory, Springer-Verlag. (1972).

[2] O. Zariski, P. Samuel, Commutative Algebra Volume II, Von. Nostrand, Princeton, (1960).

[3] N. Popescu, C. Vraciu, On the Extension of a valuation on a field K to K(x) -II, Rend.Sem. Mat. Univ. Padova, 96, (1996),1-14.

[4] N. Popescu, A. Zaharescu, On the Structure of the Irreducible Polynomials over Local Fields,J. Number Theory, 52, No.1, (1995), 98-118.

[5] V. Alexandru, N. Popescu, A. Zaharescu, A Theorem of Characterization of Residual Tran-scendental Extensions of a Valuation, J. Math. Kyoto Univ., 28,4, (1988), 579-592.

Burcu OZTURKDepartment of Mathematics, Faculty of Science, Trakya University, 22030,

Edirne, TurkeyE-mail : [email protected],[email protected]

Figen OKEDepartment of Mathematics, Faculty of Science, Trakya University, 22030,


98 Antalya - TURKEY


On Hadamard codes constructed over

F2 + uF2 + ... + umF2

Mustafa Ozkan, Figen Oke

Abstract

In this paper; using the elements of the ring F2+uF2+...+umF2, the generator matricesGα,β are constructed. Here the colums of these matrices are lexicographically ordered.The codes Cα,β generated by the matrices Gα,β are described where α, β are non-negativeintegers. It is shown that the Gray images of these codes are (2m.n, 2m+1.n, 2m−1.n)Hadamard codes over F 2 . It is also shown that the Gray images of these codes arequasi-cyclic codes of index 2m in except the case β = 0.

2010 Mathematics Subject Classifications : 94B15, 94B60.

Keywords :Hadamard Codes, Quasi-Cyclic Codes, Codes Over Ring.

References

[1] Krotov, D. S., Z4-linear perfect codes, Diskretn. Anal. Issled. Oper. Ser.1.Vol. 7, 4. (2000),78-90.

[2] Krotov, D. S., Z4-linear Hadamard and extended perfect codes, Procs. of the InternationalWorkshop on Coding and Cryptography, (2001), 329-334.

[3] Al-Ashker M, Hamoudeh M., Cylic codes overZ2 + uZ2 + u2Z2 + ... + uk−1Z2, Turk J.Math,35, (2011), 737-749.

[4] Jian-Fa Qian, Li-Na Zhang and Shi-Xin Zhu, (1 + u)- cyclic and cyclic codes over the ringF2 + uF2, Applied Mathematics Letters,19, (2006), 820-823.

[5] Jian-Fa Qian, Li-Na Zhang and Shi-Xin Zhu,Constacyclic and cyclic codes overF2 + uF2 +u2F2, IEICE Trans. Fundamentals E89-A, 6, (2006), 1863-1865.

[6] Vermani, L. R., Elements of Algebraic Coding Theory, Chapman Hall, India, (1996).

[7] W. C. Huffman and Vera Pless, Fundamentals of Error Correcting Codes, Cambridge,(2003).

Mustafa OZKANDepartment of Mathematics, Faculty of Science, Trakya University, 22030,


Figen OKEDepartment of Mathematics, Faculty of Science, Trakya University, 22030,

Edirne, TurkeyE-mail : [email protected], [email protected]

99 Antalya - TURKEY


Minimal Polynomials Corresponding to Spectral

Sets of some Graphs

Togan, M., Yurttas, A., Cevik, A. S., Cangul, I. N.

Abstract

In this talk, we shall consider the spectral set of some graph types and obtain theminimal polynomials having the elemants of this set as roots. These polynomials are alsocalled characteristic polynomials.

Although there are many results on the spectral set of graphs, there is not much knownabout the characteristic polynomials. So we shall consider these polynomials and giverecurrence relations for path, cycle, star, complete, complete bipartite and tadpole graphsand also obtain exact formulae for path, star and complete bipartite graphs.

2010 Mathematics Subject Classifications : 05C10, 05C30, 05C31

Keywords :characteristic polynomial of a graph, spectral set, energy of a graph, minimalpolynomial

References

[1] K. Ch. Das, P. Kumar, Some new bounds on the spectral radius of graphs, Discrete Math-ematics, 281 (2004), 149-161.

[2] A. Yu, M. Lu, F. Tian, On the spectral radius of graphs, Linear Algebra and its Applications,387 (2004), 41-49.

[3] M. K. Kumar, Characteristic Polynomial & Domination Energy of some special class ofgraphs, International J. Math. Combin., 1 (2014), 37-48.

Ismail Naci CANGUL, Aysun YURTTAS, Muge TOGANDepartment of Mathematics, Uludag University, 16059 Bursa, TURKEYE-mail : [email protected], [email protected], [email protected]

Ahmet Sinan CEVIKDepartment of Mathematics, Selcuk University, Konya, TURKEYE-mail : [email protected]

100 Antalya - TURKEY


Some Zagreb Indices of Subdivision and

r-Subdivision of Doubles of Some Graphs

Cangul, I. N., Yurttas, A., Togan, M., Cevik, A. S.

Abstract

In this talk, we shall consider double graphs of some well-known graph types. Thereare many results on subdivision graphs, but there is none on their Zagreb indices. Herewe give formulae for the Zagreb indices of subdivision graphs of double graphs. Also wegeneralize these to r-subdivision graphs which were defined by the authors in [2].

2010 Mathematics Subject Classifications : 05C10, 05C30, 68R10

Keywords :Zagreb indices, Zagreb coindices, topological indices, double graphs, subdivi-sion graph, r-subdivision graph

References

[1] K. Ch. Das, A. Yurttas, M. Togan, I. N. Cangul, A. S. Cevik, The multiplicative Zagrebindices of graph operations, Journal of Inequalities and Applications, 90, (2013), 1-14.

[2] M. Togan, A. Yurttas, I. Naci Cangul, All versions of Zagreb indices and coindices of r-subdivision graphs of certain graph types (submitted).

[3] P. S. Ranjini, V. Lokesha, I. N. Cangul, On the Zagreb indices of the line graphs of thesubdivision graphs, Appl. Math. Comput., 218 (2011), 699-702.

[4] E. Munarini, C. P. Cippo, A. Scagliola, N. Z. Salvi, Double graphs, Discrete Math., 308(2008), 242-254.

Ismail Naci CANGUL, Aysun YURTTAS, Muge TOGANDepartment of Mathematics, Uludag University, 16059 Bursa, TURKEYE-mail : [email protected], [email protected], [email protected]

Ahmet Sinan CEVIKDepartment of Mathematics, Selcuk University, Konya, TURKEYE-mail : [email protected]



Quasigroup and its weak compatibility graph for

the homogeneous space of degree 4

Bokhee Im, Ji-Young Ryu

Abstract

For the graph-theoretical characterization of a quasigroup, one studies the compatibil-ity. If G is a group of permutations on a finite set S, two permutations g and h are saidto be compatible precisely when g(s) 6= h(s) for any s in S. In other words, the quotientg/h = gh−1 has no fixed points. One then defines the compatibility graph of G on S asthe undirected graph on the vertex set G, in which an edge joins two permutations if andonly if they are compatible.

Based on the weak compatibility defined for a quasigroup in the action on the ho-mogeneous space as in [1], we study the weak compatibility characterization of certainquasigroupss for the homogeneous space of degree 4 as explained in [2]. And we show theweak compatibility graph of such quasigroups.

2010 Mathematics Subject Classifications : 20N05, 05C25, 05E15

Keywords :quasigroup, quasigroup action, homogeneous space, weak compatibility, com-patibility graph

References

[1] B. Im, J.-Y. Ryu and J.D.H. Smith, Sharply transitive sets in quasigroup actions, J. Algebr.Comb. 33 (2011), 81–93.

[2] B. Im and J.-Y. Ryu, Compatibility in certain quasigroup homogeneous space, Bull. KoreanMath. Soc. 50 (2013), no. 2, 667-674.

[3] J.D.H. Smith, An Introduction to Quasigroups and Their Representations, Chapman andHall/CRC, Boca Raton, FL, 2007.

Department of Mathematics, Chonnam National University, Gwangju 500-757,Republic of KoreaE-mail : [email protected]




Grobner-Shirshov Basis of an Exceptional Braid

Group

Eylem Guzel Karpuz, Nurten Urlu, A. Sinan Cevik

Abstract

The Grobner-Shirshov basis theory was developed by A.I. Shirshov for Lie algebra [2]and B. Buchberger for commutative algebras [1]. It was also generalized by G. M. Bergmanand L. A. Bokut to the case of associative algebras. This theory is a powerful tool to solvemany problems; normal form, word problem, embedding theorems, ets. In this work, weobtain Grobner-Shirshov basis of a braid group associated with the complex reflectiongroup G24. It gives a new algorithm for getting normal form, and thus a new algorithmfor solving the word problem in that group.

This work is supported by Tubitak Project No 113F294.

2010 Mathematics Subject Classifications : 13P10, 20F10, 20F36

Keywords :Grobner-Shirshov basis, presentation, Braid group, word problem

References

[1] B. Buchberger, An Algorithm for Finding a Basis for the Residue Class Ring of a Zero-Dimensional Ideal, Ph.D. Thesis, University of Innsbruck. (1965).

[2] A.I. Shirshov, Some algorithmic problems for Lie algebras, Siberian Math. J. 3 (1962) 292-296.


Selcuk University, Faculty of Science, Department of Mathematics, AlaaddinKeykubat Campus, 42075, Konya-TurkeyE-mail : [email protected]

Selcuk University, Faculty of Science, Department of Mathematics, AlaaddinKeykubat Campus, 42075, Konya-TurkeyE-mail : [email protected]



Eigenspaces of matrices associated with the

Pascal matrix

Ik-Pyo Kim

Abstract

Let P = [ (ij) ] , (i, j = 0, 1, . . .) and D = diag((−1)0, (−1)1, . . .). Choi et al. [G.S. Choi,

S.G. Hwang, I.P. Kim, B.L. Shader, (±1)-Invariant sequences and truncated Fibonaccisequences, Linear Algebra Appl. 395 (2005) 303-312] has found some matrices associatedwith P whose columns form bases for the eigenspaces of PD. The eigenspaces of (PD)T ,which is similar to PTD, have not known yet and the relationships between the eigenspacesof PD and (PD)T have not presented also. This paper proves the existence of nonsingularmatrices N and G such that N(PTD)N−1 = (PT1 D1)

⊕(PT1 D1)

⊕· · · and G−1(PD)G =

(P1D1)⊕

(P1D1)⊕· · · , from which eigenspaces of PD and PTD are characterized at

the same time as some sets associated with the standard basis vectors by much simplermethods than them of Choi et al.

2010 Mathematics Subject Classifications : Primary 15A18; Secondary 11B39, 11B65

Keywords :Similarity transformation, Spectrum, Eigenvector, Eigenspace

References

[1] R.A. Brualdi, Introductory Combinatorics, fourth ed., Prentice-Hall, Upper Saddle River,2004, pp.276-303.

[2] G.S. Choi, S.G. Hwang, I.P. Kim, B.L. Shader, (±1)-Invariant sequences and truncatedFibonacci sequences, Linear Algebra Appl. 395 (2005) 303-312.

[3] L. Comtet, Advanced Combinatorics, Reidel, Dordrechet, 1974.

[4] R.A. Horn, C.R. Johnson, Matrix Analysis, Second ed., Cambridge University Press, NewYork, 2013.

[5] Z.H. Sun, Invariant sequences under binomial transformation, Fibonacci Quarterly 39 (2001)324-333.

[6] D.S. Watkins, Product Eigenvalue Problems, SIAM Review, 47 (2005) 3-40.

[7] D.S. Watkins, Fundamentals of Matrix Computations, Third ed., John Wiley & Sons, Inc.,New Jersey, 2010.

[8] J.H. Wilkinson, The Algebraic Eigenvalue Problem, The Oxford University Press, Inc., NewYork, 1965.

Department of Mathematics Education, Daegu University, Kyungbuk 712-714,Republic of KoreaE-mail : [email protected]



On the Weakly Second Spectrum of a Module

Secil Ceken, Mustafa Alkan

Abstract

Let R be an associative ring with identity and M be a right R-module. In this paper,we extend the definition of weakly second submodules of modules over commutative ringsto modules over arbitrary rings. We denote the set of all weakly second submodules of Mby Specws(M). First, we investigate some properties of weakly second submodules, andthen we introduce and study a topology on Specws(M) called the weakly second classicalZariski topology of M . We define the weakly second radical of a submodule N of Mto be the sum of all weakly second submodules of N . We determine the weakly secondradical of some modules. We define the notion of weak m∗-system and characterize theweakly second radical of a submodule in terms of weak m∗-systems. Then we study sometopological properties of the weakly second classical Zariski topology of M . We investigatethe irreducibility of subsets of Specws(M). We give an interrelation between irreduciblecomponents of Specws(M) and maximal weakly second submodules of M . Finally, weprove that if M satisfies descending chain condition on weakly second radical submodulesthen Specws(M) is a spectral space.

2010 Mathematics Subject Classifications : 16D10, 16D80

Keywords : Weakly second submodule, second submodule, weakly second radical, weaklysecond classical Zariski topology.

References

[1] H. Ansari-Toroghy and F. Farshadifar, The dual notions of some generalizations of primesubmodules, Comm. Algebra 39 (7), (2011), 2396-2416.

[2] M. Behboodi, H. Koohy, Weakly prime modules, Vietnam J. Math. 32 (2) (2004) 185–195.

[3] M. Behboodi, On weakly prime radical of modules and semi-compatible modules, ActaMath. Hungar., 113 (2006), 239-250.

[4] S. Ceken and M. Alkan, Dual of Zariski topology for modules, Book Series: AIP ConferenceProceedings, 1389 (1), (2011), 357-360.

[5] S. Ceken, M. Alkan and P. F. Smith, The dual notion of the prime radical of a module,Journal of Algebra, 392 (2013), 265–275.

[6] S. Ceken, M. Alkan, On the second spectrum and the second classical Zariskitopology of a module, Journal of Algebra And Its Applications (2015), DOI:10.1142/S0219498815501509.

Akdeniz University Department of Mathematics, Antalya, TurkeyE-mail : [email protected], [email protected]



On the radical of a submodule over a

noncommutative ring

Ortac Ones, Mustafa Alkan

Abstract

In this paper, we deal with the radical of a submodule N of a left module M over anoncommutative ring R. We investigate that the radical of some module class has certainforms; i)radM (N) = WM (N) = WR(0)M+N for a submodule N of a module M over a ringR such that R = R/radR(0) is semisimple ii) radM (0) = WM (0) = radR(0)M where Mis a projective R–module Moreover, we investigate that a finitely generated module overan HNP -ring can be decomposed into a direct sum of a torsion module and extendingmodule. Under a condition, using the prime submodule of RR, we also prove that the leftsocle of a left extending ring is in the Jacobson radical. (i.e. Soc(RR) ⊆ J(R)).

2010 Mathematics Subject Classifications : 16N40,16N80,16S90

Keywords :Strongly Nilpotent Elements; Radical Formula; Prime Submodule;Radical ofa Module.

References

[1] M. Alkan and Y. Tıras, On prime submodules, Rocky Mountain J. Math. 37 (3) (2007),709–722.

[2] M. Alkan and Y. Tıras, Projective modules and prime submodules, Czechoslovak Math. J.56 (131) no. 2 (2006), 601–611.

[3] A.Azizi, On prime radical of submodules, Publ. Math. Debrecen, 82-2 (2013), 309-324.

[4] W. Anderson and K.R. Fuller, Rings and Categories of Modules, Springer-Verlag, NewYork-Heidelberg-Berlin, 1992.

[5] M. Behboodi, On The Prime Radical And Baer’s Lower Nilradical of Modules, Acta Math.Hungar., 122 (3) (2009), 293-306.

[6] M. Behboodi, A Generalization of Baer’s Lower Nilradical for Modules, Journal of Algebraand Its Applications Vol. 6, No. 2 (2007) 1-17.

[7] S. Ceken, and M. Alkan, On τ–extending modules, Med.J.Math. 9, (2012), 129-142.

[8] D. S. Dummit, and R. M. Foote, Abstract Algebra, Prentice Hall, Upper Saddle River, N.J. 1999.

[9] T. Y. Lam, A First Course in Noncommutative Rings, Springer, 2001.

Akdeniz University Department of Mathematics Antalya-TurkeyE-mail : [email protected] [email protected]



On the Classical Zariski Topology Over Prime

Spectrum of a Module

Secil Ceken, Mustafa Alkan

Abstract

Let R be an associative ring with identity and Spec(M) denote the set of all primesubmodules of a right R-module M . In this talk, we deal with the classical Zariski topologyon Spec(M) which is denoted by τ c. We prove that if (Spec(M), τ c) is a Noetheriantopological space, then M has finitely many minimal prime submodules. We characterizeall the irreducible components of (Spec(M), τ c) and all the minimal prime submodulesof M for a non-zero flat module M over a commutative ring R. We obtain some resultsconcerning compactness and connectedness of (Spec(M), τ c) by using algebraic propertiesof the module M . We give some equivalent conditions for (Spec(M), τ c) to be a Hausdorffspace or T1-space when M is a right module over a left perfect ring R.

2010 Mathematics Subject Classifications : 16D10, 13C11, 54B99.

Keywords :Prime submodule, Prime spectrum, Classical Zariski topology.

References

[1] A. Abbasi and D. Hassanzadeh-Lelekaami, Modules and spectral spaces, Comm. Algebra40 (2012), no. 11, 4111–4129.

[2] Ansari-Toroghy, H., Ovlyaee-Sarmazdeh, R. (2010). On the prime spectrum of a moduleand zariski topologies. Comm. Algebra 38, 4461–4475.

[3] M. Behboodi and M. R. Haddadi, Classical Zariski Topology of Modules and SpectralSpaces I, Inter. Electronic J. Alg. 4 (2008), 104-130.

[4] M. Behboodi and M. R. Haddadi, Classical Zariski Topology of Modules and SpectralSpaces II, Inter. Electronic J. Alg. 4 (2008), 131-148.

[5] S. Ceken, M. Alkan and P. F. Smith, Second modules over noncommutative rings, Com-munications in Algebra, 41 (1), (2013), 83-98.

[6] T. Duraivel, (1994). Topology on spectrum of modules. J. Ramanujan Math. Soc. 9:25–34.

[7] C-P. Lu, Prime submodules of modules. Comm. Math. Univ. Sancti Pauli 33, (1984), 61–69.

[8] C.P. Lu, The Zariski topology on the prime spectrum of a module, Houston J. Math. 25(3) (1999) 417-432.

[9] R. L. McCasland, M. E. Moore and P. F. Smith, On the spectrum of a module over acommutative ring, Comm. Algebra 25 (1997), 79-103.

Akdeniz University Department of Mathematics, Antalya, TurkeyE-mail : [email protected], [email protected]



Matrix and determinants division using Salihu’s

method

Armend Salihu, Fatlinda Musliu - Salihu

Abstract

In this paper we will present division of matrices and determinants. The result of thedivision of determinants will again be determinant of the same order nxn, and the finalresult is the same if we calculate determinants. While the division of the matrix as a resultwe will have a matrix of the same order mxn with the first respectively second matrixdepending on whether it is right or left division. In order to apply this formula for divisionof matrices then the matrices must have the same number of columns, the divisor matrixshould be square matrix and its determinant should be different from zero.

2010 Mathematics Subject Classifications : 11C20, 65F40, 15A15, 11R52.

Keywords :Division of matrices, Division of determinants, Left division, Right Division.

References

[1] E. Hamiti, Matematika 1, Universiteti i Prishtines: Fakulteti Elektroteknik, Prishtine,(2000).

[2] H. Eves, An Introduction to the History of Mathematics, Saunders College Publishing, 1990.

[3] J. R. Bunch and J. E. Hopcroft, Triangular factorization and inversion by fast matrixmultiplication, Mathematics of Computation (1974).

[4] P. H. Hanus, An Elementary Treatise on the Theory of Determinants, A textbook forcolleges, Ithaca, New York: Cornell University Library, Boston, Ginn and Company (1886).

[5] Pierre-Simon (de) Laplace, Expansion of determinants in terms of minors, Researches surle calcul integral et sur le systeme du monde, Histoire de lAcademie Royale des Sciences(Paris), seconde partie (1772).

[6] R. F. Scott, The theory of determinants and their applications, Ithaca, New York: CornellUniversity Library, Cambridge: University Press, (1904).

[7] S. Barnard and J. M. Child, Higher Algebra, London Macmillan LTD New York, ST MartinsPress (1959).

[8] W. L. Ferrar, Algebra, A Text-Book of Determinants, Matrices, and Algebraic Forms, Sec-ond edition, Fellow and tutor of Hertford College Oxford, (1957).

University of Prishtina ”Hasan Prishtina”, Faculty of Electrical and Com-puter EngineeringE-mail : [email protected]

University of Prishtina ”Hasan Prishtina”, Faculty of Electrical and Com-puter EngineeringE-mail : linda [email protected]



On Graded Semi-Prime Rings

Rashid Abu-Dawwas

Abstract

Let G be a group with identity e and let R be a G-graded ring. In this article, weintroduce the concept of graded semi-prime rings and we give some results on this concept.For example, we prove that if R is graded semi-prime and I is a graded ideal of R, then theset of all left annihilators of I equals the set of all right annihilators of I. Also, we provethat certain subsets should lie in the center of the graded semi-prime ring R.

2010 Mathematics Subject Classifications : 13A02

Keywords :graded rings, graded prime rings.

References

[1] Dade, E. C. Group graded rings and modules, Math. Z.,174, (1980), 241-262.

[2] Nastasescu, C. and Van Oystaeyen, F. Graded ring theory, Mathematical Library 28, NorthHolland, Amesterdam (1982).

[3] Refai, M. and Al-Zoubi, K. On graded primary ideals, Turkish Journal of Mathematics, 28,(2004), 217-229.

Department of Mathematics, Yarmouk University, Irbid, JordanE-mail : [email protected]



On Modules over A Group

Mehmet Uc, Ortac Ones, Mustafa Alkan

Abstract

In this talking, for a group G, using of the endomorphism group of a module M over acommutative ring R, we define a structure for M to become RG–module and we study therelations between the properties of R–modules and the properties of RG–modules. Mainly,we prove that;

i) RadR(M) = RadRG(M) where RadA(M) is the intersection of the maximal A–submodule of module M over a ring A.

ii) M is injective R–module if and only if M is an injective RG–module.

2010 Mathematics Subject Classifications : 6D50, 16D60,16E50

Keywords :Group ring, Group module Maschkes Theorem Semisimple module Regularmodule Injective module FP-injective module

References

[1] G.Karpilovsky Induced Modules Over Group Algebras Noth-Holland Math. Studies (1990)

[2] G. James M. Liebeck Repesentations and Characters of Group Cambridge Press (2003)

[3] T.Y. Lam, A First Course in Noncommutative Rings, Springer,New York (2001)

[4] D.S. Passman, The Algebraic Structure of Group Rings. Pure and AppliedMathematics.Wiley- Interscience (1977).

Akdeniz University Department of Mathematics Antalya-TurkeyE-mail : [email protected]

Mehmet Akif Ersoy University Department of Mathematics Burdur-TurkeyE-mail : [email protected]

Akdeniz University Department of Mathematics Antalya-TurkeyE-mail : [email protected]



On the Crossed Modules and 2-Crossed Modules

Ozgun Gurmen Alansal

Abstract

In this work, we explain crossed modules and 2-crossed modules and give some of theircategorical features.

2010 Mathematics Subject Classifications : 18A40,18A30,13A99

Keywords :crossed module, cat1, 2-crossed module, crossed square

References

[1] Z. Arvasi, T. Porter, Simplicial and Crossed Resolutions of Commutative Algebras, Journalof Algebras, 181, (1996), 426-448.

[2] U.E. Arslan, G. Onarli, Categorical Results in the Theory of Two-Crossed Modules of Com-mutative Algebras, http://arxiv.org/PS cache/arxiv/pdf/1108.3209v2.pdf , (2012).

[3] R. Brown, P. J. Higgins, On the Connection between the Second Relative Homotopy Groupsof Some Related Spaces, Proc. London Math. Soc.,3, 36, (1978), 193-212.

[4] R. Brown, R. Sivera , Algebraic Colimit Calculations in Homotopy Theory using Fibred andCofibred Categories, Theory and Applications of Categories , Vol. 22, (2009), 221-251.

[5] S. Mac Lane, Extension and Obstructions for Rings, Illinois Journal of Mathematics, 121,(1958), 316-345.

[6] T. Porter, Some Categorical Results in the Category of Crossed Modules in CommutativeAlgebra, J. Algebra, 109, (1978), 415-429.

[7] N.M. Shammu, Algebraic and Categorical Structure of Categories of Crossed Modules ofAlgebras, Ph.D. Thesis,U.C.N.W, (1992).

[8] J. H. C. Whitehead, Combinatorial Homotopy I and II, Bull. Amer. Math. Soc.,55, (1949),231-245 and 453-496.

Dumlupınar UniversityE-mail : [email protected]



Multisimplicial Groups

Ozgun Gurmen Alansal

Abstract

In this work, n-simplicial groups and give their applications for crossed modules.

2010 Mathematics Subject Classifications : 13D25, 18G30, 18G55

Keywords :simplicial group, crossed module

References

[1] Z. Arvasi and T. Porter, Higher dimensional Peiffer elements in simplicial commutativealgebras. Theory and Applications of Categories Vol.3, No 1, (1997),1-23.

[2] Z. Arvasi and T. Porter, Freeness conditions for 2-crossed module of commutative algebras,Applied Categorical Structures, 6, (1998), 455-477.

[3] R. Brown and J.-L. Loday, van Kampen theorems for diagrams of spaces. Topology, 26,(1987), 311-335.

[4] P. Carrasco and A.M. Cegarra, Group-theoretic algebraic models for homotopy types. Jour-nal Pure Appl. Algebra, 75, (1991), 195-235.

[5] D. Conduche, Modules croises generalies de longueur 2, Journal Pure Appl. Algebra, 34,(1984), 155-178.

[6] D. Conduche, Simplicial crossed modules and mapping cones. Georgian Mathematical Jour-nal, Volume 10, Number 4, (2003), 623636.

[7] J. Duskin, Simplicial methods and the interpretation of triple cohomology. Memoirs A.M.S.vol.3, 163, (1975).

Dumlupınar UniversityE-mail : [email protected]



Control of the chaotic dynamics of the

Hindmarsh-Rose model

Tounsia Benzekri

Abstract

In this work, we use a method to control a nonlinear model: the Hindmarsh-Rosemodel which describes a neuronal activity. This model can exhibit regular dynamics, likespiking and bursting solutions, and chaotic dynamics. The aim of this method is to entraincomplex dynamics to arbitrary given goal dynamics, by adding a suitable control term tothe system. We use this method to suppress chaos by steering chaotic dynamics to aperiodic one for the Hindmarsh-Rose model.

2010 Mathematics Subject Classifications : 34H10, 34G20

Keywords :control, chaos,neuronal model

References

[1] S.Rajasekar, M.Lakshmanan, Bifurcation, chaos and suppression of chaos in FitzHughNagumo nerve conduction model equation, J Theor Biol. 166 (1994), 275-88.

[2] Yu-Chu. Tian, M.O. Tade, J.Y. Tang, Nonlinear open-plus-closed-loop (NOPCL) control ofdynamic systems, Chaos Solitons and Fractals. 11 (1993), 1029-1035.

University of Sciences and Technology Houari Boumedien, Faculty of math-ematics, BP 32, EL ALIA, Bab Ezzouar, Algiers, Algeria.E-mail : [email protected]



Multi Objective Geometric programming With

Interval Coefficients: A parametric Approach

M. Saraj, Z.Mousavi

Abstract

Geometric programming provides a powerful tool for solving nonlinear problems. Inthe real world, many applications of geometric programming are engineering design prob-lems. Generally, an engineering design problem has multi-objective functions. Some ofthese problems can be formulated as multi-objective geometric programming models. Thispaper develops a solution method when the cost, the constraint coefficients, and the right-hand sides in the multi-objective geometric programming problems are imprecise and rep-resented as interval values. This problem is then reduced with weighting method to asingle objective function and further by applying interval-valued function, we then solvethe problem by geometric programming technique. The ability of calculating the boundsof the objective value developed in this paper might help lead to more realistic modelingefforts in engineering optimization areas. Finally a numerical example is given to illustratethe methodology of solution.

Keywords :Multi-Objective Programming, Geometric Programming, Weighting method,Parametric Interval

Department of Mathematics, Faculty of Mathematical Sciences and Com-puter, Shahid Chamran University, Ahvaz- IRANE-mail : [email protected]



Effects of Chosen Scalar Products on Gradient

Descent Algorithms

Evgin Goceri

Abstract

Steepest gradient descent algorithm, which is a line search method for finding a relativeminimum or maximum of a function, is a simple and widely applied optimization technique.Steepest gradient descent is implemented without the need to solve or evaluate a Jacobianequation or associated linear system. The steepest descent algorithm can be improvedby considering different aspects of a problem with the conjugate gradient technique. Thechoice of the metric, which the gradient depends on, notably affects the results of a gradientdescent algorithm. In other words, the direction of the downhill depends on the chosenscalar product for the chosen function space. Careful design of the metric is crucial to reachbetter local minima of the function. Therefore, excellent convergence and smooth gradientscan be obtained using different inner products. Generally, Euclidean type gradient (L2)is used to find the minimum or maximum point of a function. However, there are manyundesired properties of the standard L2 type gradient. For instance, there is nothing inthe definition of the L2 type inner product to discourage gradient flows in the space ofcurves when the flows are not smooth. Smooth but infinite dimensional function spacesprovide several advantages. For instance, finding the minimum value of a function can bedirectly achieved without any restriction related to a finite dimensional space.

References[1] J. Nocedal, SJ. Wright. Numerical Optimization. Second Edition Springer New York: Springer. (2006),

497-528.

[2] G. Sundaramoorthi, A. Yezzi, A. Mennucci, G. Sapiro. New Possibilities with Sobolev Active Contour.International Journal of Computer Vision (2009);84(1):113-129.

[3] X. Duan, H. Sun, L. Peng, X. Zhao. A Natural Gradient Descent Algorithm for The Solution of DiscreteAlgebraic Lyapunov Equations Based on the Geodesic Distance. Applied Mathematics and Computation(2013);219(19):9899-9905.

[4] PA. Absil, R. Mahony, R. Sepulchrer. Optimization Algorithm on Matrix Manifolds. Princeton UniversityPress. (2008)

[5] H. Lee, L. Xing, R. Davidi, R. Li, J. Qian, R. Lee. Improved Compressed Sensing-based Cone-beam CTReconstruction Using Adaptive Prior Image Constraints. Physics in Medicine and Biology (2012); DOI:10.1088/0031-9155/57/8/2287.

[6] X. Zhang, J. Wang, L. Xing. Metal Artifact Reduction in X-ray Computed Tomography (CT) by ConstrainedOptimization. Medical Physics 2011;38(2):701-711.

[7] Z. Zhu. Using QIGSO with Steepest Gradient Descent Strategy to Direct Orbits of Chaotic Systems. Inter-national Journal of Computational Science and Engineering 2012;7(2):133-138.

Akdeniz UniversityFaculty of EngineeringDepartment of Computer EngineeringE-mail : [email protected]



A Meta-Heuristic Approach for Course

Scheduling in Akdeniz University

Mehmet Karakoc, Melih Gunay, Guler Cigdem, Fadi Alturjman

Abstract

The course scheduling involves assigning a number of courses to a number of classroomsat various time slots while satisfying a set of constraints. One of these constraints is thatany class cannot be overlapped with another class at the same time slot. In an idealassignment every course is assigned while all of the constraints are satisfied. However, thisis rarely achieved often due to conflicting constraints. The objective of this study is thusto minimize the overlapping/conflicts while assigning all of the courses to specific classes.Hence the assignment problem can be formulated as an optimization problem with the leastconflict and the most satisfaction. Since the problem is NP-hard, often using conventionalmethods and brute force searching, the optimum solution could not be computed withina reasonable time. Consequently, we develop a meta-heuristic approach that uses geneticalgorithms with local search heuristics that provides a set of alternative course schedules.Finally, we tested our approach using the real-world course scheduling situations at AkdenizUniversity; and computed the performance of the algorithms theoretically and verifiedthem practically in terms of time and space. Results show that the proposed approach ispractical and may be used to support decisions in course time assignment applications.

Keywords :Course Scheduling, Meta-Heuristic, Genetic Algorithms, Local Search

References[1] Abdullah Elen, Ibrahim Cayiroglu, Solving of Scheduling Problem with Heuristic Optimization Approach,

Technology, 13(3), (2010), 159-172.

[2] Yong-Ming Huang, Chao-Chun Chen, Ding-Chau Wang, Optimizing T-Learning Course Scheduling based onGenetic Algorithm in Benefit-Oriented Data Broadcast Environments, TOJET: The Turkish Online Journalof Educational Technology, volume 11 Issue 3, (July 2012).

[3] Danial Qaurooni, Mohammad-R, Akbarzadeh-T, Course timetabling using evolutionary operators, AppliedSoft Computing, Volume 13, Issue 5, (May 2013), 2504-2514.

[4] Rakesh P. Badoni, D.K. Gupta, Pallavi Mishra, A new hybrid algorithm for university course timetablingproblem using events based on groupings of students, Computers Industrial Engineering, Volume 78, (De-cember 2014), 12-25.

[5] E.K. Burke, A.J. Eckersley, B. McCollum, S. Petrovic, R. Qu, Hybrid variable neighbourhood approaches touniversity exam timetabling, European Journal of Operational Research, Volume 206, Issue 1, (1 October2010), 46-53.

Computer Sciences Research and Application Centre, University of Akdeniz TR-07058 Antalya,TurkeyE-mail : [email protected]

Department of Computer Engineering, Faculty of Engineering, University of Akdeniz TR-07058Antalya, TurkeyE-mail : [email protected]

Vice General Secretary, University of Akdeniz TR-07058 Antalya, TurkeyE-mail : [email protected]

Electrical Computer Engineering Dept., Queens University, Kingston, Ontario, Canada K7L3N6E-mail : [email protected]



Robust CT-Prediction Algorithm for RT-PCR

Melih Gunay

Abstract

RT-PCR is used to detect pathogens for multiple samples in relatively short time. Thecurve that is generated by RT-PCR could be modelled by a logistic function. This isbecause the generation of pathogens are limited by the number of available sites which isaboundant at the beginning of test and the rate of increase drops significantly by time.However, using the logistic function itself is not sufficient due to noise in signal in RT-PCRdata. Therefore, in this research we used 3 steps to obtain the data in the right format.The first step includes the curation of the signal, 2nd step includes the identification ofcritical points in the signal and the third step includes the fitting of the data in the regionof interest. Results show that the algorithm developed generates at least 99.9% correctresults.

2010 Mathematics Subject Classifications : 00A71, 65K05, 92B99, 93A30, 97N60

Keywords :Pathogens; RT-PCR; Logistic function; Mathematical modelling; Mathemati-cal algorithms

Department of Computer Engineering, Faculty of Engineering, University ofAkdeniz TR-07058 Antalya, TurkeyE-mail : [email protected]



A Novel Method to Characterize Data Requests

in the Future Internet

Melih Gunay, Irem Kucukoglu, Fadi Al-Turjman

Abstract

Recent interest in Information Centric Networks (ICNs) is gaining significant momen-tum as Internet evolved from a network with a few terminals to an intractable network ofmillions of nodes. In this study, we introduce a new framework to characterize the cyclicnetwork traffic by mapping the request timing and distribution to elliptical model. Usingthis model, network optimization could be achieved by focusing on efficient content accessand distribution as opposed to more communication between data clients and servers. Weemploy an approach where requests are characterized by arrival time and frequency. Casesstudies are used to demonstrate that critical properties of ellipses may be used characterizethe content requests irregularity in a cycle during peak and normal time. Depending on thedegree of anistoropy in network traffic, the curve we plot becomes elliptic with a positiveeccentricity less than one, oriented with an angle and bias around the origin. Extensivesimulation results are used to demonstrate how various data demand/request types changethe shape and orientation of ellipses.

2010 Mathematics Subject Classifications : 68M10, 65K05, 68M11, 90B18, 90B20,60K30, 65D10, 97R20, 94A99

Keywords :Information-Centric Networks (ICNs); Future Internet; Traffic Characteriza-tion; Elliptical model; Eccentricity, Orientation Angle, Curve Fitting

References

[1] L. Atzori, A. Iera, G. Morabito, The Internet of Things: A survey, Computer Networks,vol. 54, no. 15, pp. 2787-2805, October 2010.

[2] G. Singh, and F. Al-Turjman, A Data Delivery Framework for Cognitive Information-Centric Sensor Networks in Smart Outdoor Monitoring, Elsevier Computer Communica-tions Journal, 2015.

[3] F. Al-Turjman and H. Hassanein, Enhanced data delivery framework for dynamicInformation-Centric Networks (ICNs), In Proc. of the IEEE Local Computer Networks(LCN), Sydney, Australia, 2013, pp. 831-838.

[4] B. Ahlgren, et al., A survey of information-centric networking in IEEE CommunicationsMagazine , vol. 50, no. 7, pp. 26-36, July 2012.22

[5] F. Al-Turjman, W. Alsalih, and H. Hassanein, Towards augmented connectivity in feder-ated wireless sensor networks, In Proc. of the IEEE International Conference on WirelessCommunications and Networking (WCNC12), Paris, France, Sep. 2012, pp. 1882 -1886.

Department of Computer Engineering, Faculty of Engineering, University ofAkdeniz TR-07058 Antalya, TurkeyE-mail : [email protected]



Department of Mathematics, Faculty of Science, University of Akdeniz TR-07058 Antalya, TurkeyE-mail : [email protected]

Electrical & Computer Engineering, Queens University, Kingston, Ontario,Canada K7L 3N6E-mail : [email protected]



On-line Heuristic Approach for Data-Collectors

Assignment in ITS

Mehmet Karakoc, Fadi Alturjman, Melih Gunay

Abstract

In this paper, we target the data delivery problem in Intelligent Transportation Systems(ITS). It is assumed that each data collector, with a specific storage capacity, starts froma base station as a central location in an ITS, completes its route while visiting a set ofintermediate nodes in a wireless network with the shortest path and returns to the startinglocation (base station). The objective of this study is to optimize the data collectors countwhile maintaining their minimum travelling distance. Each intermediate node has a certainlevel of traffic demand to be delivered via these data collectors. As the total collected trafficon a route cannot be more than the data collectors capacity, it is important to decide onthe data-packets size and the order of the targeted intermediate nodes to be visited. Inthis regards, we propose a hybrid-genetic approach for optimized solutions. Extensivesimulation results are performed to confirm the effectiveness of the proposed approach.

Keywords :Data Delivery, Intelligent Transportation Systems, Genetic Algorithms, LocalSearch Heuristic

References[1] D. Turgut and L. Blni, Heuristic approaches for transmission scheduling in sensor networks with multiple

mobile sinks, The Computer Journal, 54(3):332344, Oxford University Press, March 2011.

[2] Al-Fagih, F. Al-Turjman, W. Alsalih and H. Hassanein, A priced public sensing framework for heterogeneousIoT architectures, IEEE Transactions on Emerging Topics in Computing, vol. 1, no. 1, pp. 135-147, Oct.2013.

[3] G. Singh, and F. Al-Turjman, A Data Delivery Framework for Cognitive Information-Centric Sensor Net-works in Smart Outdoor Monitoring, Elsevier Computer Communications Journal, 2015. (Accepted) DOI:10.1016/j.comcom.2015.01.002.

[4] D. Turgut and L. Blni, Three heuristics for transmission scheduling in sensor networks with multiple mobilesinks, In Proceedings of International Workshop on Agent Technology for Sensor Networks (ATSN-08), inconjunction with the Seventh Joint Conference on Autonomous and Multi-Agent Systems (AAMAS 2008),pp. 18, May 2008.

[5] F. Al-Turjman, H. Hassanein, W. Alsalih, and M. Ibnkahla, Optimized Relay Placement for Wireless SensorNetworks Federation in Environmental Applications, Wiley: Wireless Communication, Mobile ComputingJournal, vol. 11, no. 12, pp. 1677-1688, Dec. 2011.

Computer Sciences Research and Application Centre, University of Akdeniz TR-07058 Antalya,TurkeyE-mail : [email protected]

Electrical, Computer Engineering Dept., Queens University, Kingston, Ontario, Canada K7L3N6E-mail : [email protected]




Stay Connected in Vehicular Wireless Networks

using Graph Theory and AI

Recep Ozdemir, Fadi Al-Turjman,Melih Gunay

Abstract

Vehicular transportation is about to change with innovative applications using wirelesscommunications and smart phone technology. Recently, companies and government agen-cies began to invest in Intelligent Transportation Systems (ITS) for both economical andsafety reasons and new standards for vehicular wireless connectivity are coming soon [1].With these new standards automotive companies will be able to work on same architectureas mobile operators do with the GSM standards [2]. Implementation of ITS technologiesrelies heavily on robust and continuous connectivity of nowadays vehicles with the Inter-net. While it may be easy to establish robust and uninterrupted network connectivity ata fixed point, it is challenging to ensure stable and robust connection in a fast moving ve-hicle through obstacles. In this study we discuss graph theory approaches that maximizesconnectivity in these dynamic environments. In our study, vertices are cars and edges withweights represent the inverse of the wireless connection quality. Consequently, connectiv-ity problem is formulated as a Minimum Spanning Tree (MST). Unlike traditional graphtheory problems, in this model both the vertices and edges are constantly calculated. Inorder to compensate for week points in the formulated MST, artificial neural networks isused.

Keywords :Data Delivery, Intelligent Transportation Systems, Graph Theory, Neural Net-works

References[1] Global System for Mobile Communications (GSM), http://en.wikipedia.org/wiki/GSM

[2] A. Al-Fagih, F. Al-Turjman, W. Alsalih and H. Hassanein, A priced public sensing framework for heteroge-neous IoT architectures, IEEE Transactions on Emerging Topics in Computing, vol. 1, no. 1, pp. 135-147,Oct. 2013.

[3] G. Singh, and F. Al-Turjman, A Data Delivery Framework for Cognitive Information-Centric Sensor Net-works in Smart Outdoor Monitoring, Elsevier Computer Communications Journal, 2015. (Accepted) DOI:10.1016/j.comcom.2015.01.002.

[4] M.R. Brust, C. Ribeiro, D. Turgut, and S. Rothkugel, LSWTC: A Local Small-World Topology Control Al-gorithm for Backbone-Assisted Mobile Ad Hoc Networks, In Proceedings of IEEE Local Computer Networks(LCN’10), pp. 144-151, October 2010.

[5] A. Boukerche, M.Z. Ahmad, B. Turgut, and D. Turgut, A Taxonomy of Ad Hoc Routing Protocols, InAlgorithms and Protocols for Wireless, Mobile Ad hoc Networks, pp. 129-164, Wiley, 2008.

[6] D. Turgut, B. Turgut, R. Elmasri, and Than V. Le. Optimizing Clustering Algorithm in Mobile Ad hocNetworks Using Simulated Annealing, In Proceedings of WCNC’03, pp. 1492-1497, March 2003.



Electrical & Computer Engineering Dept., Queens University, Kingston, Ontario, Canada K7L3N6E-mail : [email protected]



Combining Short Ultrasound Recordings for

Long Duration Observation of Fetal Breathing

Movement

Umit Deniz ULUSAR

Long duration observation of the fetal breathing movement (FBM) with an ultrasound-basedvideo technique offers the opportunity to visualize the activity and extract activity relatedparameters. Long duration recording is challenging since keeping mother and fetus steadyis usually not possible. Due to this limitation, observation of fetal movements in utero arediscontinuous. This study proposes an image processing methodology to combine discontinuousobservations of subjects and extract FBM related parameters. The technique was applied to 5ultrasound recording obtained from mothers between 34-37 weeks of gestation and results arepresented.



Statistical Assessment of Heavy Metals

Distribution and Contamination of Beach Sand

Along the Manavgat Alanya Coastline of

Antalya, Turkey

Fusun Yalcin, Daniel G. Nyamsari, Ebru Paksu, M. Gurhan Yalcin

Abstract

The distribution of heavy metal concentrations in the beach sand samples collected from44 different locations along the Manavgat Alanya coastline of Antalya covering differentcoastal sandy beaches was studied. The average concentration level of these metals inthe beach sand was calculated and compared to those of the Earth Crust, Sandstone,Ultrabasic Rock and the acceptable limit for Turkey in order to determine their anomalies.Heavy metal (Cr, Zn, Ni, As, Cu, Pb, Co, Mo, Sb and Cd; along with Al, Fe, Mg,Mn, Na, K, Ba, Ca and W) were determined. The elements occurred in abundance asCa > Na > Mg > Fe > Al > K > Ti > Mn > Cr > Ba > V > Zn > Ni > As >Cu > Pb > Co > Mo > Sb > W > Cd. The sufficiency of the number of samples usedfrom the study area is revealed by the high explanatory power R2 = 96.9, of the Modelsummary ANOVA. Using the box plot, it was also noted that some heavy metals such asAs (in samples 1, 19, 25, 28 and 29); Mn (in Samples 23 and 39); Na (in samples 23, 24and 45); Cr (in Sample 33) and Ti (in Sample 15) had very high anomalies. Heavy metalcontents show high anomaly concentrations when compared to some background values(Earth Crust, Sandstone, Ultrabasic and Turkey acceptable limit).

Keywords :Heavy Metals, Beach sand sample, Anomaly.

AKDENIZ UNIVERSITY, FACULTY OF SCIENCE, DEPARTMENT OF MATH-EMATICS, ANTALYAE-mail : [email protected]

AKDENIZ UNVERSITY, FACULTY OF ENGINEERING, DEPARTMENT OFGEOLOGICAL ENGINEERING, ANTALYAE-mail : [email protected]





Cluster analysis applied to alkaline geochemical

data (Hamit, Turkey)

Fusun Yalcin, Nurdane Ilbeyli

Abstract

Cluster analysis can be benefited to group samples and also evolve ideas about themultivariate geochemistry of the dataset (Templ et al., 2008). Therefore, in this study,this analysis has been used to determine the statistical significance of geochemical char-acteristics of alkaline rocks from the Hamit pluton (Turkey). Cluster analysis has appliedto sixty-three major and trace elements belonging to the Hamid pluton rock samples andthere is no data loss in the application. All data entered into evaluation as 100 In clusteranalysis, firstly, we have looked at the relationships amongst locations. According to linenumbers of the dendrograms, two groups were formed between 1-23 and 24-63. There arethe closest relations between 17-20 and 43-51locations. Since these samples were takenfrom the same area. These groups are bonded to a high value. However, the locationnumber 12 is connected to the first group from outside and location number 16 is tied inwith the second group from outside. Similar groups describe samples from similar rocks.They are consistent with the geological map. Secondly, two groups were formed amongstthe elements. Sr and Ba were the first group. Rest of elements constitutes the secondgroup. While Zr is connected to the second group from the most outside, and Rb and Ceare connected to the second group from outside. Similar groups show that the elementshave similar properties. This study indicates that cluster analysis application to alkalinegeochemical data is efficient.

Keywords :Cluster analysis, multivariate statistics, geochemical data, alkaline rocks, Hamit.

Akdeniz University, Faculty of Science, Department of Mathemetics, 07058Antalya, Turkey ([email protected])E-mail : [email protected]

Akdeniz University, Faculty of Engineering, Department of Geological En-gineering, 07058 Antalya, TurkeyE-mail : [email protected]



The Geothermal Model of Mersin (Turkey)

Region

Yusuf URAS, Alican Kop, Mahmut Dag

Abstract

The purpose of the study is to present the geothermal model of Mersin (Camili) regiongeothermal area with its geology, hydrogeology, hydrogeochemistry and isotope hydrology.The 1/25000 scale geology map obtained from the literature research is revised. In order toobtain a geothermal model, geological cross-sections are extracted in certain points on therevised geology map. There are 3 hot water outlets. There are MC-1, C-1 and Uclu CesmedeepUclu Cesme well, but its average temperature is 37.5C and it has a very low flowrate. Isotope analyses of the water samples obtained from these three wells and the IcmeStream are carried out by using the IRMS method with 18O and 2H (Deuterium) andIAEA method with 3H (Tritium). Radioactive Alpha-Beta determination and Physico-chemical and Bacteriological analyses of MC-1 well are made by using EPA 900.00. In thelight of all this information, the revised 1/25000 scare geology map of Mersin Guneyyolu(Camili) geothermal area is obtained; it is found out that hot waters are of meteoric origin;and the isotope hydrology and hydro-chemical assessment of the area is conducted to shapethe geothermal model.

Keywords :Mersin, Guneyyolu, Geothermal, Hydrogeology, Isotope, Hydrogeochemistry

Kahramanmaras Sutcu Imam University, Geology Engineering Department,Kahramanmaras, TurkeyE-mail : [email protected]

Milcan Turizm Tarim Sanayi ve Ticaret A.S.Gaziantep Yolu Uzeri 3.km ArikanMensucat A.S. Binasi Kahramanmaras,E-mail :



Automated Detection of Facial Disorders

(ADFD): A Novel Approach Based-on Digital

Photographs

Evgin Goceri, Melih Gunay, Fadi Al-Turjman

Abstract

Abnormal regions on a face are often indicative of facial dermatological diseases suchas rosacea, eczema, allergy, burn injury, facial rash, fifth disease and acne. Identificationand quantitative evaluation of these facial disorders is often subjective and currently doneby expert dermatologists. However, with the advances in image processing techniques, it isnow possible to consistently identify, classify and objectively quantify facial skin disordersusing digital photographs. Furthermore, digital photographs have not only the ability todiagnose facial disorders, but also to assess progress in their treatment by applying time-series analysis on infected (abnormal) facial regions of the photograph. In this paper, wepropose a novel real-time approach for abnormal facial regions detection and segmentation.Extensive experiments have been applied on real cases in practice. Achieved results assureour approach superiority in identifying abnormal regions in comparison to existing classical(traditional) approaches. It outperforms traditional approaches in terms of accuracy andtime complexity, which makes it a potential candidate for online emergency/urgent cases,such as acute respiratory syndrome, rosacea, facial fever, etc.

References

[1] B., Que, S.K.T., D’Souza, L., Suchecki, J., Finch, J.J. Laser treatment of periocular skinconditions, Clinics in Dermatology, Volume 33, Issue 2, March–April 2015, Pages 197-206,ISSN 0738-081X, http://dx.doi.org/10.1016/j.clindermatol.2014.10.011

[2] Larson, S.K., Dawson, A.L., Dunnick, C.A., Dellavalle, R.P. Acne Vulgaris: Pathogenesis,Treatment, and Needs Assessment, Dermatologic Clinics, Volume 30, Issue 1, January2012, Pages 99-106, ISSN 0733-8635, http://dx.doi.org/10.1016/j.det.2011.09.001.

[3] M.W.S., Bashir, S.J. Fractional laser resurfacing for acne scars: a review. British Journalof Dermatology, vol. 166, No:6, pg. 1160-1169, 2012

[4] Tan, J., Berg, M. Rosacea: Current state of epidemiology, Journal of the AmericanAcademy of Dermatology, Volume 69, Issue 6, Supplement 1, December 2013, Pages S27-S35, ISSN 0190-9622, http://dx.doi.org/10.1016/j.jaad.2013.04.043.

DEPARTMENT OF COMPUTER ENGINEERING, FACULTY OF ENGINEER-ING, UNIVERSITY OF AKDENIZ TR-07058 ANTALYA, TURKEYE-mail : [email protected]

DEPARTMENT OF COMPUTER ENGINEERING, FACULTY OF ENGINEER-ING, UNIVERSITY OF AKDENIZ TR-07058 ANTALYA, TURKEYE-mail : [email protected]

ELECTRICAL COMPUTER ENGINEERING, QUEENS UNIVERSITY, KINGSTON,ONTARIO, CANADA K7L 3N6E-mail : [email protected]



Associativity of Max-Min Compsition of Three

Fuzzy Relations

M. A. Shakhatreh, T. A. Qawasmeh

Abstract

In this paper we are going to give some definitions related to Max-Min compostionof fuzzy relations,reaching to prove Associativity of Max-Min composition of three fuzzyrelations. Let R1 be a fuzzy relaton in X×Y ⊆ N ×N , R2 be a fuzzy relation in Y ×Z ⊆N×N , and R3be a fuzzy relation in Z×W ⊆ N×N . Then (R1 ◦R2)◦R3 = R1◦(R2 ◦R3).

2010 Mathematics Subject Classifications : 03E20,02E72,03F03

Keywords :Sets, Fuzzy Relations, Max-Min Composition of Fuzzy Relation

References

[1] H. J. Zimmerman, Fuzzy Sets Theory, Third Edition, Kluwer Academic Publisher, 1996.

[2] A. Kaufman, Theory of Fuzzy Subsets, Volume 1, Academic Press, 1975.

[3]

Yarmouk University Department of Mathematics, Irbid - JordanE-mail : [email protected] – [email protected]



Fractional Order Logistic Equation Derived

from Hanta Epidemics

Zarife Gokcen Karadem, Mevlude Yakıt Ongun, Damla Arslan

Abstract

Fractional calculus has been successfully exploited in a multitude of aplications inseverel areas. In this paper we introduce fractional order into the model of Hanta virusepidemics in (Abramson, 2002).This new system is given as the set of fractional differentialequation

cDα0,tX(t) = (b− c)X(t) + bY (t)− X2(t)

K− ( 1+aK

K)X(t)Y (t)

cDα0,tY (t) = −cY (t)− Y 2(t)

K− ( 1−aK

K)X(t)Y (t)

(1)

Here cDα0,t denotes the fractional derivative operator. To discretize the fractional-order

nonlinear system (1), we apply Nonstandart Finite Difference (NSFD) schemes with thetruncation of the Grunwald-Letnikov operator. We use the fractional NSFD scheme, weobtain fractional order logistic equation. Some numerical solutions are illustrated by meansof some graphs.

2010 Mathematics Subject Classifications : 34A08,34A34,47N70, 65L12,65L07

Keywords :Fractional differantial equation, Hanta virus epidemics,Logistic Equation

References

[1] G.Abramson, V.M.Kenkre, Spatio-temporal patterns in the Hantavirus infection, PysicalRewiev E, 66(2002)011912.

[2] R.E.Mickens, Calculation of denominator functions for nonstandart finite differenceschemes for differential equations satisfying a positivity contition,Numerical Methods forPartial Differential Equations,23(3)(2007) 672-691

[3] A.M.A. El-Sayeda, A.E.M.El-Mesiryb, H.A.A. El-Saka, On the fractional order logisticequation, Applied Mathematics Letters, 20 (2007) 817-823

[4] I.Pudlubny, Fractional differential equations,Academis Press Inc. 1999

Suleyman Demirel University, Graduate School of Natural and Applied Sci-ences, Isparta,TurkeyE-mail : [email protected]

Suleyman Demirel University, Department of Mathematics, Isparta,TurkeyE-mail : [email protected]

Suleyman Demirel University, Graduate School of Natural and Applied Sci-ences, Isparta,TurkeyE-mail : [email protected]



An Algorithmic Finite Element Method for

Noncoercive Variational Inequalities

Messaoud Boulbrachene

Abstract

In this paper, we introduce a new method to analyze the standard finite element ap-proximation in the maximum norm of variational inequalities with non coercive operators.Unlike in [1], the well-known Bensoussan-Lions algorithm [2] plays a crucial role in deriv-ing the optimal convergence order of the approximation. In fact, the proposed methodprovides a theoretical justification for the use of this algorithm in the computation of theappoximate solution.

2010 Mathematics Subject Classifications : 65N30, 65N15

Keywords : Variational inequalities, Bensoussan-Lions Algorithm, Finite element, Errorestimate

References

[1] P. Cortey-Dumont, Sur les inequations variationnelles a operateurs noncoercifs. RAIRO,V.2, (1985),195-212.

[2] Bensousan, A., Lions, J.L., Application of variational inequalities to stochastic control prob-lems. Gauthiers-Villars, Paris, 1982.

Department of Mathematics and Statistics, Sultan Qaboos University, P.O.Box 36, Muscat, OmanE-mail : [email protected]



Determining Factors of FTA Negotiation

Outcomes: An analysis using Instrument

Variable Two Stage Least Squares

Jacob Wood, Jungsuk Kim

Abstract

This study examines the impact that domestic non-economic and economic factors haveon the outcome of international FTA negotiations. The successful FTA negotiation willdecide the scope of economic gain from the free market that help drive the engine of acountrys economic growth platform. Our study demonstrates that the result of negoti-ations, as measured by the average applied tariff rate, is significantly affected by bothnon-economic and economic factors. By using IV 2SLS as the primary form of analysis,this study showed that seven of the ten variables tested were statistically significant, ofwhich three were noneconomic and four were economic in nature. Among the noneconomicvariables, union membership (UNON) and ruling party ideology (RULP) and the popu-lation aged between 15 and 64 (POP1564) were statistically significant and supportive ofour initial expectations. Of the five economic variables tested four (SIMP, MFN, UNERand INEXP) are statistically robust and significant.

Korea University of Technology and Education Cheonan City 330-708, KoreaE-mail : [email protected]

Researcher at the Institute of International and Area Studies, SogangUniversity, Seoul 121-742, KoreaE-mail : [email protected]



Revenue maximization policies for Queueing

Networks with Flexible Servers

Salih Tekin

Abstract

In this research, we consider dynamic assignment of servers to tasks in queueing net-works with an objective to maximize the total system revenue. In the multiclass queueingnetwork, each finished part generates a different revenue depending on its class or exitpoint from the network. We use fluid limit analysis to show that the maximum possiblerevenue, and the maximum revenue for a given arrival rate can be computed by solving lin-ear programming problems. We develop policies for assigning servers to classes for a givenarrival rate and desired revenue, and prove that our policies achieve the desired revenueas long as this revenue is feasible for the given arrival rate.

2010 Mathematics Subject Classifications : 60K25, 68M20, 90B15, 62M02

Keywords :Queueing Theory, Performance Evaluation, Stochastic Network Models, Statis-tics

References

[1] Andradottir, S. and Ayhan, H. and Down, D. G., Server Assignment Policies for Maximizingthe Steady-State Throughput of Finite Queueing Systems, Management Science 47(2001),1421-1439.

[2] Andradottir, S. and Ayhan, H., Throughput Maximization for Tandem Lines with TwoStations and Flexible Servers, Operations Research 53(2005), 516-531.

[3] Dai, J. G. and Dai, W., A heavy traffic limit theorem for a class of open queueing networkswith finite buffers, Queueing Systems 32(1999), 5-40.

TOBB University of Economics and Technology, Ankara, TurkeyE-mail : [email protected]



Comparative Analysis of Simulation Tools in

Biochemical Networks


Abstract

As more advanced methods are developed to analyze biochemical systems, we canunderstand and model the actual behavior of the complex systems better. One of thedevelopments in this field is seen under the simulation of the networks under different as-sumptions. There are mainly two branches to simulate the biochemical processes, namely,stochastic and deterministic approaches [1]. Under the stochastic approaches, we cangenerate the random nature of the biochemical processes by describing the changes inmolecular numbers based on the chemical master equations. On the other hand if we per-form deterministic approaches, the behaviour of the systems is simulated by representingthe changes in concentration of species via the methods based on the ordinary differentialequations such as the Runge-Kutta or Euler techniques.

Hereby in order to perform these analyses by researches in distinct fields, various sim-ulation tools are developed. Although these tools have similar functionalities, they maydiffer in their algorithms and capabilities. In this study, we choose the most common toolslike COPASI, E-Cell and GENESIS [2] among many alternatives and compare them withrespect to some attributes such as the capacity of the networks size in the calculations, thevarieties of simulation algorithms for both stochastic and deterministic approaches and thefacilities in the parameter estimation as well as the metabolites’s analyses [2, 3]. Finally weshow our comparative evaluation by applying them in systems under different dimensions.By this way we aim to propose a list of tools for the researchers that best performs underour comparison criteria.

2010 Mathematics Subject Classifications : 00A72, 65C20, 68U20.

Keywords : Simulation of biochemical networks, comparison of computational tools.

Acknowledgement. The authors would like to thank the AGEP grant (Project No:BAP-08-11-2014-007) for its financial support.

References

[1] D. Wilkinson, Stochastic modelling for systems biology, Chapman and Hall/CRC (2006).

[2] A. Pettinen, T. Aho, O.-P. Smolander, T. Manninen, A. Saarinen, K.-L. Taattola, O. Yli-Harja, M.-L. Linne, Simulation tools for biochemical networks: evaluation of performanceand usability, Bioinformatics. 21, 3 (2005), 357363.

[3] T. Manninen, E. Makiraatikka, A. Ylipaa, A. Pettinen, K. Leinonen, M.-L. Linne, Discretestochastic simulation of cell signaling: comparison of computational tools, Proceedings ofthe 28th IEEE EMBS Annual International Conference (2006), 2013-2016.

Department of Statistics, Middle East Technical UniversityE-mail : [email protected]

Department of Statistics, Middle East Technical UniversityE-mail : [email protected]



Application of Impulsive Deterministic Simulations of Biochemical Networks viaSimulations Tools


AbstractIn order to understand the possible behaviour of biochemical networks, deterministic

and stochastic simulation methods have been developed. These methods are based on dif-ferent mathematical backgrounds and take into accounts distinct dynamics. For instance,the deterministic approach considers the network as a set of ordinary differential equationsin which every equation accounts for the rate of changes in the concentrations of speciesin the system. On the other hand, the stochastic approach suggests a random error termcoming from the Brownian motion in the description of the system’s activity and it isbased on the chemical master equations dependent on the change in molecular numbers ofspecies of the network [1]. However in some cases these methods are needed to be broaden.For example, if the biochemical system is subjected into the unexpected effects causingabrupt changes in the network, the ordinary simulation algorithms cannot capture theseimpulsive expressions [2].

In this study, we select the simulations tools, specifically COPASI and Systems BiologyToolbox for Matlab among alternatives, that enable us to represent the impulsive changesin the system via impulsive or adaptive deterministic simulation algorithms [3, 4]. Ac-cordingly, we compare these tools by applying the two major impulsive scenarios, namelyimpulses for fixed times and fixed states, based on their accuracies and computationaldemands. We evaluate our results under different dimensional systems, listed as theLotka-Volterra model, the Protein Kinase C (PKC) signal transduction pathway and theMAPK/ERK signaling pathway for the representative of small, moderately large and largesystems, respectively.

Acknowledgement. The authors would like to thank the AGEP grant (Project No: BAP-08-11-2014-007) forits financial support and thank Assoc. Prof. Dr. Omur Ugur from Middle East Technical University for hishelpful discussion in the analyses of the systems.

2010 Mathematics Subject Classification. 00A72, 34A37, 37M05, 65C20.

Keywords and phrases. Impulsive deterministic simulations of biochemical systems, impulses scenarios forbiochemical systems, comparison of simulation tools for biochemical systems.

References[1] D. Wilkinson, Stochastic modelling for systems biology, Chapman and Hall/CRC, (2006).

[2] Altıntan, D., Purutcuoglu, V. and Ugur, O., Impulsive expression in chemical master equation and stochasticsimulation algorithms, Proceeding of the 26th European Confer- ence on Operational Research, Rome, Italy(2013), 294.

[3] Hoops, S. et al. COPASI-a complex pathway simulator, Bioinformatics. 22(24) (2006), 3067-3074.

[4] Schmidt, H., & Jirstrand, M. Systems Biology Toolbox for MATLAB: a computational platform for researchin systems biology, Bioinformatics. 22(4) (2006), 514-515.

[5] A. Pettinen, T. Aho, O.-P. Smolander, T. Manninen, A. Saarinen, K.-L. Taattola, O. Yli-Harja, M.-L. Linne,Simulation tools for biochemical networks: evaluation of performance and usability, Bioinformatics. 21, 3(2005), 357363.1Department of Statistics, Middle East Technical University

E-mail : [email protected] of Statistics, Middle East Technical University




Using Bezier Curves in Medical Applications

Buket Simsek, Ahmet Yardimci

Abstract

3D reconstruction of an object from its 2D cross-sections has many applications indifferent fields of sciences such as medical physics and biomedical applications. In orderto perform 3D reconstruction, at first, desired boundaries at each slice are detected andthen using a correspondence between points of successive slices surface of desired objectis reconstructed. In many applications of medical physics, biomedical engineering, andComputer Aided Design (CAD), an object is often known by a sequence of 2D cross-sections (slices) [1, 2, 3]. These slices can be obtained using several imaging techniquessuch as Computed Tomography (CT), Magnetic Resonance Imaging (MRI), Single PhotonEmission Tomography (SPECT), and Positron Emission Tomography (PET). In this paper3D motion of the knee prosthesis from its 2D perspective projections such as X-ray imageshave estimated by using Bezier curves. Tracing boundaries using GVF algorithm and itsapproximation obtained contours by cubic Bezier Spline curves yield to final smooth surfaceis reconstructed in relatively fast procedure. Previous studies have shown that there is agood trade-off between speed and accuracy in using GVF algorithm and cubic Bezier Splinecurves for approximating the rough obtained edges during a 3D reconstruction method.Using cubic Bezier Spline curves instead of other mathematical curves like cubic spline,and B-spline curves yields a decrease time reconstruction.

References

[1] Park H, Kim K. Smooth surface approximation to serial cross-sections. Computer-AidedDesign. 1996;28(12):995-1005.

[2] Li Z, Ma L, Tan W. Three-dimensional object reconstruction from contour lines. Pro-ceedings of the 2006 ACM international conference on Virtual reality continuum and itsapplications; Hong Kong, China. 1128977: ACM; 2006. p. 319-22.

[3] Hossain MA, Hirokawa S, Ariyoshi S, Proposal to Improve Kinematic Estimation Algorithmof Knee Prosthesis, IFMBE Proceedings Vol. 14/4

[4] Souag N. Three Dimensional Reconstruction of the Left Ventricle using Cubic UniformB-Spline Curves, 3rd International Conference: Sciences of Electronic Technologies of In-formation and Telecommunications, Tunisia, March 27-31,2005.

Department of Biostatistic and Medical Informatics, Faculty of Medicine,Akdeniz University Antalya TurkeyE-mail : [email protected], [email protected]



On the approximation of the

Conway-Maxwell-Poisson normalizing constant

Burcin Simsek, Satish Iyengar

Abstract

The Conway-Maxwell-Poisson is a two-parameter family of distributions on {0, 1, 2, . . .}.Its parameters λ and ν model the intensity and the dispersion, respectively. Its normalizingconstant is not easy to compute, so good approximations are needed. Shmueli et al. (2005)derived an approximation assuming that ν is an integer, and gave an estimate of therelative error. We write the normalizing constant as the expectation of a certain functionof a Poisson random variable with mean α = λ1/ν . We then use the normal approximationto the square root of the Poisson, and expansions for the functions that arise to derive anapproximation which is valid for all ν0. Our error term is of a different order than theirs.We investigate the error terms numerically to compare the two approximations.

References

[1] Abramowitz M and Stegun I. (1965) Handbook of Mathematical Functions. Dover, NewYork.

[2] Bleistein N and Handelsman R. (1986) Asymptotic Expansion of Integrals. Dover, New York.

[3] Conway RW and Maxwell WL. (1962) A queuing model with state dependent service rates.Journal of Industrial Engineering. 12, 132–136.

[4] Minka T, Shmueli G, Kadane JB, Borle S, Boadwright P. (2003) Computing with the COM-Poisson distribution. Carnegie Mellon Statistics Department Technical Report. 776.

[5] Shmueli G, Minka T, Kadane JB, Borle S, Boatwright P. (2005) A useful distribution forfitting discrete data: revival of the Conway-Maxwell-Poisson distribution. Journal of RoyalStatistical Society, C. 54, 127 – 142.

Department of Statistics, University of Pittsburgh, PA 15260 USAE-mail : [email protected], [email protected]



A note on the analysis of Mathematical learning

Conditions

Jong Jin Seo, Taekyun Kim

Abstract

The objective of this article is to study a new method of analyzing individual mathe-matical learning conditions. In order to efficiently use the results of each students problemsolving, we was introduced connection of mathematical concepts and convergence of math-ematical concepts. This method is able to identify the students learning condition of thepast and present. Also, It is the advantage of being able to identify the lacking mathemat-ical contents or concept by each individual student.

Keywords : connection, convergence, plane, sphere.

Department of Applied Mathematics, Pukyong National University, Busan608- 737, Republic of KoreaE-mail : [email protected]

Department of Mathematics, Kwangwoon National University, Seoul 139-701, Republic of KoreaE-mail : [email protected]



Epidemic in Travnik

Admir Hodzic, Adnan Behrem, Nina Bijedic PhD, Emir Slanjankic

Abstract

Simulation of infectious disease spreading in the city of Travnik, Bosnia and Herzegovinais presented. Simulation is based on agents, real-world data and estimates based on author’sexperience living in Travnik. A simulation results varies depending on initial parametersand agents behavior. It presents potentially useful research tool for municipal officials andmedical institutions.

Keywords :simulation by agents, epidemic simulation, agent-based simulation

References

[1] Lang Moore, David Smith. The SIR Model for Spread of Disease, 2000.

[2] J. Dale, E. Mamdani, Open Standards for Interoperating Agent - based Systems, Foundationfor Intelligen Physical Agents Organisation.

[3] M. A. K. Niazi, Towards a novel unified framework for developing formal, network andvalidated agent - based simulation models of complex adaptive systems. Stifling, 2011.

[4] C. R. Shalizi, Methods and techniques of complex systems science: An overview.

[5] O. Paunovski, G. Eleftherakis, and A. J. Cowling, Disciplined exploration of emergenceusing multi-agent simulation framework, J. Comp. Info., vol. 28, pp. 369 391, 2009.

[6] M. A. K. Niazi and A. Hussain, Sensing Emergence in Complex Systems, IEEE Sensors,vol. 11, pp. 2479 2480, 2011.

[7] Travnik Municipality, Development strategies of Travnik municipality 2011-2015,http://www.opcinatravnik.com.ba/ba/filedownload.php?did=568

[8] Pr, J. W., Schnaubelt, R., Zacher, R. Infektionen. In: Mathematische Modelle in der Bi-ologie. Mathematik Kompakt. Birkhuser. 21- 42., 2008

[9] Skvortsov, Epidemic Modelling: Validation of Agent-based Simulation by Using SimpleMathematical Models, Defence Science and Technology Organisation, PO Box 4331, Mel-bourne, VIC, 3001

Admir Hodzic, FIT MostarE-mail : [email protected]

Adnan Bhrem, FIT MostarE-mail : [email protected]



Insensitive stochastic bounds for the stationary

distribution of the embedded Markov chain

Mohamed Boualem

Abstract

Retrial queues have been widely used to model many practical problems. They havebeen successfully applied in telephone switching systems, telecommunication networks,Packet switching networks, shared bus local area networks operating under the carrier sensemultiple access protocol and collision avoidance star local area networks, wireless sensornetworks, e-mail systems, etc. An examination of the literature reveals the remarkable factthat the non-homogeneity caused by the flow of repeated attempts is the key to understandmost analytical difficulties arising in the study of retrial queues [1, 2, 4]. Stochastic ordersare useful in comparing random variables measuring certain characteristics in many areas.Such areas include insurance, operations research; queuing theory, survival analysis andreliability theory. The simplest comparison is through comparing the expected value ofthe two comparable random variables [2, 3]. In this work, we use the general theory ofstochastic ordering to study monotonicity properties for a single server retrial queue withbreakdowns (the service station can fail only during the service period) relative to thestrong stochastic ordering, convex ordering and Laplace ordering. Instead of studyinga performance measure in a quantitative fashion, this approach attempts to reveal therelationship between the performance measures and the parameters of the system. Theobtained results give insensitive bounds for the stationary distribution of the consideredembedded Markov chain.

References

[1] M. Boualem, N. Djellab and D. Assani, 2009. Stochastic inequalities for M/G/1 retrialqueues with vacations and constant retrial policy. Mathematical and Computer Modelling,50, 207 - 212.

[2] M. Boualem, N. Djellab and D. Assani, 2012. Stochastic approximations and monotonicityof a single server feedback retrial queue. Mathematical Problems in Engineering, Vol. 2012,Article ID 536982, 1-13.

[3] M. Boualem, N. Djellab and D. Assani, 2014. Stochastic bounds for a single server queuewith general retrial times. Bulletin of the Iranian Mathematical Society, 40 (1), 183 - 198.

[4] M. Boualem, 2014. Insensitive bounds for the stationary distribution of a single serverretrial queue with server subject to active breakdowns. Advances in Operations Research,Vol. 2014, Article ID 985453, 1-12.

Research Unit LaMOS (Modeling and Optimization of Systems), Universityof Bejaia, 06000 Bejaia, AlgeriaE-mail : [email protected]



On interval-valued fuzzy lattices

Jeong Gon Lee

Abstract

We discuss the relationship between interval-valued fuzzy ideals and interval-valuedfuzzy congruence on a distributive lattice L and show that for a generalized Booleanalgebra the lattice of interval-valued fuzzy ideals is isomorphic to the lattice of interval-valued fuzzy congruences. Finally we consider the products of interval-valued fuzzy idealsand obtain a necessary and sufficient condition for an interval-valued fuzzy ideal on thedirect sum of lattices to be representable as a direct sum of interval-valued fuzzy ideals oneach lattice.

2010 Mathematics Subject Classifications : 03F55, 20N25

Keywords :interval-valued fuzzy sublattice, interval-valued fuzzy ideal, interval-valuedfuzzy filter, interval-valued fuzzy congruence.

References

[1] N. Ajmal and K. V. Thomas, Fuzzy lattices, Inform. Sci.79(1994), 271-291.

[2] M. B. Gorzalczany, A method of inference in approximate reasoning based on interval-valuesfuzzy sets, Fuzzy sets and Systems 21(1987), 1-17.

[3] K. Hur, J. G. Lee and J. Y. Choi, Interval-valued fuzzy relations, J. Korean Institute ofIntelligent systems 19(3)(2009), 425-432.

[4] B. Yuan and W. Wu, Fuzzy ideals on a distributive lattice, Fuzzy Sets and Systems(1990)

[5] K. Hur, H. W. Kang and H. K. Song, The concept of a linguistic variable and its applicationto approximate reasoning I, Inform. Sci. 8(1975), 199-249.

Division of Mathematics and Informational Statistics, and Nanoscale Scienceand Technology Institute, Wonkwang University, Iksancity Jeonbuk 570-749,Korea.E-mail : [email protected]



A Soft Based Method to Solve the Analysis

Problem of the Distance Between Two Soft

Points

Guzide Senel

Abstract

In this work, we briefly outline the ideas of modeling methods and analysis the distancebetween two soft points by generating the soft metric spaces whose structure is representedby soft distance function shown by d . In particular, we present a useful algorithm forfinding distance between two soft points. The presented conceptual algorithm is appliedto several types of soft metric spaces. The scope of this approach is exhibited by solvingspecial classes of soft metric spaces in a systematic way. Some examples which show howeasily our existence theorems can be applied in practice are also illustrated. Moreover, itis shown that the method of solving distance problem is provide in the form of improvablepropositions which call for stronger theorical and practical relationships to be developedbetween researchers in the different fields of mathematics.

Keywords : Soft set, soft point, soft function, soft topology, soft open set, soft metric.

References

[1] H. Aktas. And N. Caman, Soft sets and soft groups, Inform. Sci. 177 (2007), 2726- 2735.

[2] A. Aygnolu, H. Aygn, Some notes on soft topological spaces, Neural Comp. Appl. (2011),521-011-0722-3.

[3] N. Caman and S. Enginolu, Soft set theory and uni-int decision making, Eur. J. Oper. Res.207 (2010), 848-855.

[4] N.Caman, S. Karatas. and S. Enginolu, Soft Topology, Computers and Mathematics withApplications, 62 (2011), 351-358.

[5] D. N. Georgiou and A. C. Megaritis, Soft Set Theory and Topology, Applied GeneralTopology, 14, (2013). S. Hussain and B. Ahmad, Some properties of soft topological spaces,Comput. Math. Appl., 62, 40584067 (2011).

Amasya UniversityE-mail : [email protected]



Some inevitable remarks on the some recent

trends in fixed point theory

Erdal Karapinar

Abstract

In this talk, we discuss on the advances on metric fixed point theory and some otherabstract spaces via the recent publications on the topics. In particular, we point out theextension and improvement in various abstract spaces, such as generalized metric space.

ATILIM University, Department of Mathematics Ankara / TURKEYE-mail : http://www.atilim.edu.tr/ ekarapinar/


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