1st international eurasian conference on mathematical...

I

1st INTERNATIONAL EURASIAN CONFERENCE ON

MATHEMATICAL SCIENCES AND APPLICATIONS

PROCEEDING BOOK

SEPTEMBER 03-07, 2012

PRISHTINE KOSOVO

II

FOREWORD

The 1st International Eurasian Conference on Mathematical Sciences and

Applications (IECMSA) jointly organized by Bilecik University, Kocaeli University,

Sakarya University and Prishtine University will be hold on 03-07 September 2012 in

Prishtine, KOSOVO.

The aim of this conference is to bring the math society all over the Europa and Asia working

in the new trends of applications and progresses in mathematical science in Prishtine,

KOSOVO, the country in which the cemetery of the Soltan Murad Hudavendigar of Ottoman

Empire, the symbol of justice. With this conference we also aimed to promote the publicity of

Republic of Kosovo.

The organization scheme of this conference was formed by Organizing, Scientific and

Honorary committees. The Scientific committee is formed from different University

worldwide. Seven worldwide distinguished speakers are invited to the conference.

Although we have announced the conference within the limited time span we have taken a lot

of applications all over the world. These big numbers of applications have given us

opportunity to choose the best ones to reach the higher scientific level.

The first three days are organized for the scientific discussions and talks and the remaining

two days for the social program. In the social program, there will be trips to historical and

touristic place of Kosovo.

Within the social program there will be a Albanian and Turkish cultural program. We do

believe that with these cultural programs we will give the opportunity to the participants to

appreciate the Albanian and Turkish Culture to a certain extent.

The talks that are going to be delivered cover a wide range of mathematics which is one of the

goals of this organization. Among the topics that are going to be presented are mostly on pure

IECMSA-2012 1st International Eurasian Conference on Mathematical Sciences and Applications

III

and applied mathematics, engineering applications, statistics, algebra, computer mathematics,

geometry, etc. We aimed to promote the interdisciplinary collaborations.

We would like to thank to Bilecik University, Kocaeli University, Sakarya University and

Prishtine University for their invaluable supports. We would also like to thank to TKA for

their support.

We also thank to the invited speaker, who share their scientific knowledge with us, to the

Organizing and Scientific committee. Last but not least we thank to all presenters and

participants. We do believe and hope that each of them will get the maximum benefit from the

conference.

We hope to see you in the second, third,... International Eurasian Conference on

Mathematical Sciences and Applications in different countries and cities of Europe and Asia.

Sincerely yours,

Prof. Dr. Murat TOSUN, Chair

On behalf of the Organizing Committee


IV

HONORARY COMMITTEE

Professor Misir MARDANOV (Azerbaijan Minister of Education, TWMS President)

Professor Baktyzhan ZHUMAGULAV (Kazakhstan Minister of Education, TWMS Honorary

President)

Professor Sezer Sener KOMSUOGLU (Kocaeli University Rectorate)

Professor Muzaffer ELMAS (Sakarya University Rectorate)

Professor Rugova MUJE (Prishtine University Rectorate)

Professor Azmi OZCAN (Bilecik Seyh EdebaliUniversity Rectorate)

Professor H. Hilmi HACISALIHOGLU (TWMS Honorary President)

Professor Ilyas OZTURK (Sakarya University Faculty of Arts and Sciences Dean)

Professor Fikret ALIYEV (TWMS Vice President)

Professor Amanbek JAINAKOV (TWMS Vice President)

Professor Nargozy DANAEV (TWMS Vice President)

Professor Etibar PANAHOV (TWMS Vice President)

Professor Mahmut ERGUT (TWMS Member of Steering Board)

Professor Murat TOSUN (TWMS Member of Steering Board)


V

SCIENTIFIC COMMITTEE

Professor H.Hilmi HACISALIHOGLU (Bilecik Seyh Edebali University)

Professor Fikret ALIYEV (Baku State University)

Professor Eberhard MALKOWSKY (Giessen University)

Professor Ravi P. AGARWAL (Texas University)

Professor Mohammad MURSALEEN (Aligarh Muslim University)

Professor Ekrem SAVAS (Istanbul Commerce University)

Professor Amanbek JAINAKOV (National Academy of Sciences of Kyrgyz Republic)

Professor Kazim ILARSLAN (Kirikkale University)

Professor Selim JUSUFI (Prishtine University)

Professor Sergio AMAT (Polytecnic University of Cartagena)

Professor Cihan OZGUR (Balikesir University)

Professor Sui Sun CHENG (Tsing Hua University)

Professor Levent KULA (Ahi Evran University)

Professor Ibrahim OKUR (Sakarya University)

Professor Rexhep GJERGJI (Prishtine University)

Professor Arif SALIMOV (Atatrk University)

Professor Florim ISUFI (Prishtine University)


VI

Professor Etibar PANAHOV (Firat University)

Professor Danaev NARGOZY (El-Farabi National Kazakh University)

Professor Varga KALANTAROV (Koc University)

Professor Anatolij DVURECENSKIJ (Slovak Academy of Sciences)

Professor Yusif GASMOV (Baku State University)

Professor Irfan SIAP (Yildiz Tecnical University)

Professor Qendrim GASHI (Prishtine University)

Professor Nuri KURUOGLU (Bahcesehir University)

Professor Halis AYGUN (Kocaeli University)

Professor Muhib LOHAJ (Prishtine University)

Professor Mahmut ERGUT (Firat Universtiy)

Prof. Dr. Arjun K. GUPTA (Bowling Green State University)

Professor Fevzi BERISHA (Prishtine University)

Professor Nihal YILMAZ OZGUR (Balikesir University)

Professor Ali AKHMADOV (Baku State University)

Professor Ramadan ZEJNULLAHU (Prishtine University)

Professor Sadik KELES (Inonu University)

Professor Yusuf YAYLI (Ankara University)

Professor Faton BERISHA (Prishtine University)

Professor Kadri ARSLAN (Uludag University)


VII

Professor Qamil HAXHIBEQIRI (Prishtine University)

Professor Bayram SAHIN (Inonu University)

Professor Harry MILLER (International University of Sarajevo)

Professor Cengizhan MURATHAN (Uludag University)

Professor Soltan ALIYEV (National Academy of Sciences of Azarbaijan Republic)

Professor Fahir Talay AKYILDIZ (Gaziantep University)

Professor Omer AKIN (University of Economics and Technology)

Professor Naim BRAHA (Prishtine University)


VIII

ORGANIZING COMMITTEE

Professor H.Hilmi HACISALIHOGLU (Bilecik Seyh Edebali University)

Professor Murat TOSUN (Sakarya University)

Professor Munir EFENDIJA (Pristhine University)

Professor Kazim ILARSLAN (Kirikkale University)

Professor Cihan OZGUR (Balkesir University)

Professor Levent KULA (Ahi Evran University)

Professor Halis AYGUN (Kocaeli University)

Professor Avdulla ALIJA (Prishtine University)

Professor Gamar MAMMADOVA (Baku State University)

Professor Nargiz SAFAROVA (Baku State University)

Professor Agim GASHI (Prishtine University)

Professor Latifa AGAMALIEVA (Baku State University)

Professor Naser TRONI (Prishtine University)

Professor Musaj PACARIZI (Prishtine University)

Professor Mimoza DUSHI (Prishtine University)

Professor Naim SYLA (Prishtine University)

Associate Professor Mehmet Ali GUNGOR (Sakarya University)


IX

Associate Professor Hatice Gl INCE ILARSLAN (Gazi University)

Associate Professor Kamile SANLI KULA (Ahi Evran University)

Associate Professor Soley ERSOY (Sakarya University)

Assistant Professor Emrah Evren KARA (Bilecik Seyh Edebali University)

Assistant Professor Mahmut AKYIGIT (Sakarya University)

Assistant Professor Ergin JABLE (Prishtine University)

Assistant Professor Ercan MASAL (Sakarya University)

Assistant Professor Ayse Zeynep AZAK (Sakarya University)

Assistant Professor Murat SARDUVAN (Sakarya University)

Assistant Professor Mehmet GUNER (Sakarya University)

Assistant Professor Melek MASAL (Sakarya University)

Doctor Bujar FEJZULLAHU (Prishtine University)


X

SECRETARIAT

Professor Murat TOSUN (Sakarya University)

Lecturer Muhsin CELIK (Sakarya University)

Lecturer Dogan UNAL (Sakarya University)

Research Assistant Hidayet Huda KOSAL (Sakarya University)

Research Assistant Hatice PARLATICI (Sakarya University)

Research Assistant Tulay SOYFIDAN (Erzincan University)

Research Assistant Valbon BYTYQI (Prishtine University)

Research Assistant Fisnik ALIAJ (Prishtine University)


XI

CHAPTERS INVITED TALKS 1-8

ALGEBRA 9-38

ANALYSIS 39-76

APPLIED MATHEMATICS 77-146

DISCRETE MATHEMATICS 147-162

GEOMETRY 163-218

TOPOLOGY 219-246

STATISTICS 247-260

MATHEMATICS EDUCATION 261-280

THE OTHER AREAS 281-328

POSTER 329-372

PARTICIPIANTS 373-379


XII

CONTENTS

INVITED TALKS

Variable-range Approximate Systems: a unified approach to categories of fuzzy topology and theories of fuzzy rough sets Alexander Sostak

1

Minimax Solution of the Problem of The Choice of Optimum Modes for Gas-Lift Process F. A. Aliev, N. Ismayilov

2

Dimension of Fractals H. H. Hacsaliholu

3

The Borwein-Ditor Theorem and My Oxford Moment H. I. Miller

4

Bijective S-boxes and Self Dual Codes P. Sole

5

Index of a Subfactor in a Real Factor Sh. A. Ayupov, A. A. Rakhimov

6

ALGEBRA

Transfer of Orbital Integrals and Division Algebras A. Aydodu, R. ztrk, E. zkan, Y. Z. Flicker

9

A Combinatorial Discussion on Finite Dimensional Leavitt Path Algebras A. Ko, S. Esin, . Glolu, M. Kanuni

10

Inequalities Involving ( !)pv n A. Sh. Shabani, V. Krasniqi

11

Zbrthimi n vlera singular I nj matrice dhe zbatime A. Vrapi, F. Hoxha

12

Structure of Intuitionistic Fuzzy Sets in Semihyperrings B. A. Ersoy, B. Davvaz

13

-Vague Module D. Bayrak, S. Yamak

14

-Primitive Elements of Free Metabelian Lie Algebras D. Ersalan, Z. G. Esmerligil

15


XIII

A Note on Direct Product of Fuzzy Modules over Fuzzy Rings E. Yetkin

17

On Almost Prime Elements in Lattice Modules E. Yetkin, Z. Kl, . Tekir

18

On Multiplication Lattice Modules F. allalp, . Tekir

19

Comultiplication Lattice Modules F. allalp, . Tekir

20

On Closed Submodules of a Finite Rank Free Module over a Complete DVR H. Garminia, G. Rahmaputri, P. Astuti

21

Commutative and Normal Groups on Soft Sets . imek, N. aman, K. Kaygsz, . Deli

22

On topological Structure on Ternary Semihyperrings K. Hila, A. Sh. Shabani

23

N-dimensional (, )-fuzzy ideals of hemirings M. Aslam, S. Abdullah

24

Test Rank of The Lie Algebra [ ]/ ,F R F N. . l, N. Ekici

25

Pullback for Simplicial Lie Algebras . G. Alansal

27

Induced Inner Product on a Quotient Tensor Product Space P. Astuti

28

Normality and Quadraticity for Special Ample Line Bundles on Toric Varieties Arising from Root Systems Q. R. Gashi, T. Schedler

29

The Square Terms in Generalized Fibonacci Sequence R. Keskin, Z. iar

30

Generalized Fuzzy Bi-hyperideals in Semihypergroups S. Abdullah, K. Hila

31

Some Relations on Extending Modules S. Doruz

32

Generalized ( , )f g Derivations on Lattices . Ceran, M. Ac

33

Algebraic Hyperstructures of Soft Sets Associated to n-ary Polygroups . Ylmaz, O. Kazanc

34


XIV

Irreducible, Prime and Maximal Idealistics Soft WS-Algebra U. Acar, A. Harmanc

35

Some Regular Elements, Idempotents and Right Units of Complete Semigroups of Binary Relations Defined by Semilattices of the Class Lower Incomplete Nets Y. Diasamidze, A. Erdoan, N. Aydn

36

Parafree Lie Algebras with Certain Properties Z. Veliolu, N. Ekici

38

ANALYSIS

On Some New Paranormed Sequence Spaces of Non-Absolute Type A. A. Karaaslan, V. Karakaya

39

On saturation Order of Functions in the Space )1(),(

XV

Shpejtsia e Tentimit N Zero e Koeficientve Furie T Funksioneve Me Derivat T wely-it F. Berisha

52

Approximating Classes of Functions Defined by a Generalised Modulus of Smoothness F. M. Berisha, N. S. Berisha

54

Starlikeness and Convexity of Generalized Struve Functions H. Orhan, N. Yamur

55

An Extremum Problem in the Metric Space H.S. Akhundov, M.A. Sadygov

57

On the Boundedness of Riesz-Bessel Transforms associated with the B-GSO I. Ekincioglu, C. Keskin

58

On Privalov Type Estimates of High order Riesz-Bessel Transformations Generated by a Bessel Generalized Shift Operator I. Ekincioglu, C. Keskin

60

Some Structural Properties of Vector Valued Orlicz Sequence Space Generilazed by an Infinite Matrix M. Candan

62

Almost Convergence and Generalized Double Sequential Band Matrix M. Candan

63

On Pointwise and Uniform -Statistical Convergence of Order of Sequences of Functions M. Et, M. nar, M. Karaka

64

Some Results on dist -formulas, Toeplitz Operators and Berezin Symbols M. Grdal, M.T. Karaev, S. Saltan, U. Yamanc

65

Quasi-Diagonal Operators M. Lohaj, S. Lohaj

67

Radon-Nikodym Property for Vector Valued Measures M. ztrk, C. evik

68

On mt-Convexity M. Tun, H. Yldrm

69

On New Inequalities for h-Convex Functions via Riemann-Liouville Fractional Integration M. Tun

70

Two New Definitions on Convexity and Related Inequalities M. Tun

72

On One Class of Sequences and a Convolution Operator in This Class N. Ibadov

73


XVI

Mbius Transformations and Circles on the Complex Plane N. Y. zgr

75

APPLIED MATHEMATICS

Some Properties of a Family of Analytic Functions A. Altn

77

Numerical Approximation for Boundary Value Problem by a New Collocation Approach A. B. Ko, A. Kurnaz

78

Statistical Integral on Banach Space A. Caushi, A. Tato

79

Dynamical Problem for the Pre-Stressed Bi-Layered Plate-Strip with Finite Length under the Action of Arbitrary Time-Harmonic Forces Resting on a Rigid Foundation A. Dademir, M. Erz

81

On the Solution of Vibration (Eigenvalue) Problem of Ceramic Cylindrical Shells with FG Coatings A. Deniz, A. H. Sofiyev

82

Finite Difference/Spectral Approximations for the Time Fractional Higher Order Partial Differential Equations A. Kablan, F. T. Akyldz

84

Anew Metaheuristic Algorithm Based Chemical Process: Atom Algorithm A. Karc

85

The Measurement of the Effect of the Pre Crisis and Post Crisis Economic Dynamics (Parameters) over the Stock Index with the 2-factor Cross Classification Model of Variance Analysis Models and Turkey Example A. Mazmanolu

87

Exact Solutions of the Zakharov Equations by Using the First Integral Method A. n nal

89

About Existence of the Local and Global on Time Solutions of the Initial and Initial-Boundary Value Problems for One-Dimensional Nonlinear Boltzmanns Moment System Equations A. Sakabekov, Y. Auzhani

90

Cubic B-Spline Finite Element Method for the Numerical Solution of Fishers Equation A. ahin, H. Bilgil

91

The Problem of Constructing a Step Function, the Least Fluctuating around a Given Function B. Bayraktar

93

Matrix Analogues of Some Properties for Bessel Functions B. ekim, A. Altn

95


XVII

A General Solution Procedure for Fractionally Damped Beams D. Dnmez Demir, N. Bildik

96

Generalizations of Hlders Inequalities on Time Scales D. Uar, A. Deniz

97

Some Specials Results and Applications of Pseudo Measure Theory D. Valera

98

Numerical Solution for Two-Point Fuzzy Boundary Value Problem E. Can, C. Krolu, A. Golayolu Fatullayev

100

Modal Characteristics of Optical Waveguides with Cardioid-Shaped Cross Sections E. Erolu, H. Altural

101

Approximate Solution of a Model Describing Biological Species Living Together by Taylor Collocation Method E. Gkmen, M. Sezer

102

Laguerre-Krall Orthogonal Polynomials: Outer Relative Asymptotics and an Electrostatic Model for Their Zeros. E. J. Huertas, F. Marcelln, H. Pijeira

103

On the Inverse Problems for Singular Differential Operators E. S. Panakhov, M. Sat

104

A Problem with Mixed Boundary Conditions for an Elastic Strip When There Are Friction Forces in the Contact Area E. Yusufolu , H. Ouz

105

Numerical Solution of a Crack Problem with the Help of Gauss Quadrature Formulas E. Yusufolu, . Turhan

106

Method for the Solution of the Optimal Control Problem for the Linear Descriptor Systems F.A. Aliev, N.I. Velieva , Y.S. Gasimov, L.F. Agamalieva

107

Iterative Algorithms for the Solution of the Discrete Optimal Regulator Problem in Stationary and Periodic Cases F.A. Aliev, N.A. Safarova, N. I. Velieva

108

Polynomial Presentation of the Binary Multidimensional Nonlinear Modular Dynamic Systems F.G Feyziev, G.H Mammadova, Sh.T. Mammadov

109

A Kantorovich Type of Szasz Operators Including Brenke Type Polynomials F. Tadelen, R. Akta , A. Altn

110

The Energy Levels, Binding Energies, and Dipole Moment in a Gaas/Alas Spherical Quantum Dot as Function of the Donor Position H. Akbas, P. Bulut, C. Dane

111

Steady Stokes Flow in a Sectorial Cavity: Lids Moving in the Same Direction H. Bilgil, A. ahin

112


XVIII

A Crack Identification Method for Bridge Type Structures under Vehicular Load Using Wavelet Transform and Particle Swarm Optimization H. Gkda

114

Greens Functions for Elasto-hydrodynamic Model of 1D Quasicrystals H. K. Akmaz

115

An Efficient Scheme for Designing Substitution-boxes Based on TD-ERCS Chaotic Sequence I. Hussain, M. A. Gondal

116

Image Analysis with Differential Geometry Applications K. Hanbay, M. F. Talu

118

Transferring of Energy via Special Functions; A Special Case: Airy Function K. Kkl, E. Erolu, N. Eren

120

To properties of solutions of one nonlinear problem of heat onductivity in a heterogenic media M. Aripov, M. Khodjimurodova

121

About Extremum Problems with Constraints M. A. Sadygov

122

Koaks Acceleration Method Smoothly Gears Up Iterative Solvers M. . Koak

123

The Stress Field Problem for a Pre-Stressed Plate-Strip with Finite Length under the Action of Arbitrary Time-Harmonic Forces M. Erz

124

The Influence of Initial Stresses on a Pre-stressed Orthotropic Plate-strip with Finite Length Resting on a Rigid Foundation M. Erz

125

On Solving a Type of Fractional Volterra-Integro Differential Equations Using Homotopy Analysis Method M. F. Karaaslan, M. Kurulay

126

About one Problem of Solution Stabilization of the Loaded Heat Equation M.M.Amangaliyeva, M.T.Jenaliyev, K.B.Imanberdiyev and M.I.Ramazanov

127

On the Best Approximate (P,Q)-Orthogonal Symmetric and Skew-Symmetric Solution of the Matrix Equation AXB C= M. Sarduvan, S. imek, H. zdemir

128

A Fractional Order Nonlinear Dynamical Model N. zalp, . Koca

129

Some Approximation Results for Lupa Operators O. Doru, K. Kanat

130

Asymptotic of Solution Functions of a Sturm-Liouville-Type Problem and the Green Function O. Kuzu, M. Kadakal

131


XIX

Some Possible Fuzzy Solutions for Second Order Fuzzy Initial Value Problems Involving Forcing Terms . Akn, T. Khaniyev, . Oru, I. B. Trken

133

Travelling Wave Solutions to the Benney-Luke and the Higher-Order Improved Boussinesq Equations of Sobolev Type . F. Gzkzl, . Akal

135

Explicit Solutions for Fractional Schrdinger Equation R. Ylmazer, E. Bas

136

Sharp Weighted Rellich Type Inequalities for Generalized Greiner Vector Fields S. Ahmetolan, . Kombe

137

Review of special relativity mathematics S. Klinaku

138

Numerical Simulations of Coupled Sine-Gordon Equations by Reduced Differential Transform Method S. Servi, A. B. Ko, Y. Keskin

139

On Removable Sets of Solutions for Degenerate Linear Parabolic Equations T.S. Gadjiev, S.A. Aliev, O.S. Aliyev

141

Calculation of Shear Stresses Occurred on Elastic Soils under Rectangular Foundation with Analytical and Numerical Methods U. Dadeviren, Z. Gndz

142

On a Shape Design Problem for the Eigenfrequency of the Membrane with Fixed Boundary Lenth Y. S. Gasimov, L. I. Amirova

144

Reduced Differential Transform Method for Solving High-Dimensional PDEs Y. Keskin, A. Betl Ko, S. Servi

145

DISCRETE MATHEMATICS

Connected Dominating Sets in Unit Disk Graphs D. A. Mojdeh, S. Kordi

147

Perfect Codes in the Euclidean Metric F. Temiz, V. iap

149

On One Dimensional 2r+1-Cyclic Rule Cellular Automata . iap, H. Akn, M. E. Krolu

150

Image Representation as Skip Graph M. Aksu, M. Canayaz, A. Karc

152

On Generalized Gaussian Fibonacci Numbers and Matrix Methods M. Ac

154


XX

Content Based Image Retrieval via Graph Similarity M. Canayaz, M. Baykara, M. Aksu, T. zseven, A. Karc

155

Perfect Mannheim, Lipschitz and Hurwitz Weight Codes M. Gzeltepe

157

Codes over Hurwitz Integers M. Gzeltepe

158

A Study on Minimal Codewords of the Codes Associated with the Symmetric ,(v ,k ) Designs

S. alkavur, E. Balkanay

160

On MacWilliams Identity for M-spotty Weight Enumerators of Linear Codes over Frobenius Rings V. iap, M. zen

162

GEOMETRY

On Hypercomplex Structures A. A. Salimov

163

On the Energy and the Angle of a Frenet Vector Fields A. Altn

164

The Gauss Equations of Timelike Surface Invaryant under One Parameter Group of Lorentzian Isometry A. nalck, S. Ersoy

165

On Inclined Curves in Eucldean n -Space A. enol, E. Zplar, Y. Yayl, H. H. Hacsaliholu

166

On Three-Dimensional Normal Almost Contact Metric Manifolds Admitting Quarter Symmetric Non-Metric Connection A. Yldz, A. etinkaya

167

Weingarten and Linear Weingarten Type Tubes with Darboux Frame in 3E A. Z. Azak, M. Tosun

168

On Semiparallelity of Wintgen Ideal Surfaces B. Bulca, K. Arslan

169

Umbrella Motion in R3 B. Karaka, . Bayda

170

Umbrella Surfaces in R3 as an Orbit Surfaces B. Karaka, . Bayda

171


XXI

Anti-Invariant Riemannian Submersions from Almost Hermitian Manifolds:Curvatures B. ahin

172

B.-Y. Chen Inequalities for Submanifolds of a Conformally Flat Manifold C. zgr

174

On the Two Parameter Homothetic Motions in the Complex Plane D. nal, M. elik, M. A. Gngr

175

e-Curvature Functions in 4-Dimensional Lorentzian Space E. yign

176

f -Eikonal Helix Submanifolds and f -Eikonal Helix Curves E. Zplar, A. enol, Y. Yayl

177

Fractals of Finite Area F. ilingir

179

Half-Lightlike Hypersurfaces with Planar Normal Sections in F. E. Erdoan, R. Gne, B. ahin

180

On Weyl Manifolds with Semi-Symmetric Reccurent Metric Connection F. zdemir

181

Eulers Formula and De-Moivres Formula for Dual Hyperbolic Quaternions H. H. Ksal, M. Akyiit, M. Tosun

182

On the Geometry of the Sasaki semi-Riemann Manifold on the Tangent Sphere Bundle of the de-Sitter Space . Ayhan

183

Notes on Curves in Sasakian 3-manifolds . Gk, Y. Yayl

184

On Null Rectifying Curves in K. larslan

185

On Special Curves in Sol Space L. Sizer, H. Baemez, M. Altnok, L. Kula

186

Fibonacci Split Quaternions M. Akyiit, H. H. Ksal, M. Tosun

187

A Note on Fibonacci Generalized Quaternions M. Akyiit, H. H. Ksal, M. Tosun

188

Slant Helices Generated by Plane Curves and Applications M. Altnok, L. Kula

189

On the Two Parameter Lorentzian Homothetic Motions M. elik, D. nal, M. A. Gngr

190


XXII

On -Conformally and -Projecitvely Flat Lorentzian Sasakian Manifolds with Tanaka-Webster Connection M. Erdoan, J. Alo, G. Yilmaz

191

Special Curves in Three Dimensional Finsler Manifold F3 M. Ergt, M. Klahc

193

Some Characterizations on Biharmonic General Helices in Finsler Manifold F3 M. Ergt, M. Y. Ylmaz

194

Inextensible Flows of Curves in Three Dimensional Finsler Manifold F3 M. Ergt, A. O. renmi

195

Inverse Surfaces of Tangent, Principal Normal and Bi-normal Surfaces of a Space Curve in Euclidean 3-Space M. Ergt, M. E. Aydn

196

On the First Fundamental Theorem for Dual Orthogonal Group O(2, D) M. ncesu, O. Grsoy, D. Khadjev

197

On the B-Manifold Defined by Algebra of Plural Numbers M. can, A. Maden

198

CMC-Surfaces in Hyperbolic Space nH M. Mak, B. Karla

200

Torsion Tensors of Pure Connections N. Cengiz

202

Screen Semi-Invariant Half-Lightlike Submanifolds O. Bahadr

203

A Note on Inextensible Flows of Curves in nE . G. Yldz, M. Tosun, S. . Karaku

204

A Generalization of Some Well-Known Distances and Related Isometries R. Kaya

205

Bobillier Formula for One Parameter Motions in the Complex Plane S. Ersoy, N. Bayrak

206

Arc-Lenghts, Curvature and Natural Lifts of Spherical Indicatrix of Timelike Mannheim Curve with Spacelike Binormal Spacelike Curve Partner S. enyurt, S. Demet

208

Arc-Lenghts, Curvature and Natural Lifts of Spherical Indicatrix of Timelike Bertrand Curve Partner S. enyurt, . F. alkan

209

Lightlike Hypersurfaces of an ()-Para Sasakian Manifold S. Y. Perkta, E. Kl, M. M. Tripathi

210


XXIII

On the Ruled Surfaces Whose Frames are the Bishop Frame in the Euclidean 3-Space . Klolu, H. H. Hacsaliholu

211

Constant Angles Surfaces in Hyperbolic Space T. Mert, B. Karla

212

On the Quaternionic Curves According to Parallel Transport Frame T. Soyfidan, H. Parlatc, M. A. Gngr

214

On the Quaternionic Rectifying Curves in Semi-Euclidean Space 42 T. Soyfidan, M. A. Gngr

215

Conformal Triangles in Hyperbolic and Spherical Space . Tokeer, B. Karla

216

Framed-complex Submersions Y. Gndzalp

217

Affine Differential Invariants of a Pair of Curves Y. Sarolu

218

TOPOLOGY

On Multimetric Spaces A.A. Borubaev

219

On sequential Spaces A. A. Borubaev, B. A. Boljiev

220

On metric Spaces A.A. Borubaev, K. Ishmakhametov

222

On Some Types of Strongly Continuous Multifunctions A. Akgz, S. Gktepe

223

Simplicial Weak (4,2)-chain Complexes of Simplicial Complexes A. Ahmeti

224

Actions and Coverings of Topological Groupoids A. F. zcan

226

On ultracompact and bounded Spaces. B. A. Boljiev

227

Separation Axioms on Soft Topological Spaces B. P. Varol, H. Aygn

228


XXIV

Completeness Properties of Di-Uniform Texture Spaces F. Yldz

229

Topological Internal Groupoids and Their Coverings H. F. Akz, N. Alemdar, T. ahan, O. Mucuk

230

Some Properties of Polynomials G and N, and Tables of Knots and Links . Altnta

232

On Uniformly Paracompact Mappings K. B. Emenovich

234

Proper C Tameness and Proper Deformation Dimension M. Efendija

236

The Product of Shape Fibrations Q. Haxhibeqiri

237

Rough Topology on Covering-Based Rough Sets S. Akduman, E. Z.Yldz, A. Z. zcelik, S. Narl

239

Simplicial Homotopy in Digital Images S. ztun, N. Bildik, A. Mutlu

240

Semi-Compactness in Ditopological Texture Spaces . Dost

241

Some Generalized Closed Sets and Continuous Functions in Ideal Topological Spaces . Karabyk

242

Extension of Shis Quasi-Uniformity to the Fuzzy Soft Sets V. etkin, H. Aygn

245

STATISTICS

Weight Function Efficiency Against Outliers in Nonlinear Regression A. Pekgr, A. Gen

247

Transmuted Exponentiated Exponential Distribution F. Merovci

248

Comparisons of Imputation Methods for Missing Data in Mixture Discriminant Analysis M. Eriolu, . K. Sar

250

Determining Number of Clusters with Analytic Hierarchy Process M. Eriolu

251


XXV

Analysis of Divorces Using Survival Models N. Ata, T. P. Tacolu

252

A Study on an Additive Decomposition of the Blues in a Partitioned Linear Model and Its Two Small Models N. Gler

254

Properties of Systems with Nonidentical Components N. Torrado

256

Bayesian Approach of Structural Equation Models with Conjugate Priors for Discrete Distributions S. ehribanoglu, H. Okut

257

L-Moments Estimations for Mixture of Two Weibull Distributions . Eriolu, M. Eriolu

259

MATHEMATICS EDUCATION

Analysis of the Effect of Using Interactive Learning Objects on Critical Thinking Skills of Math Teacher Candidates A. . zdemir, A. B. Yaprakdal

261

The Relationship between 7th Grade Students Visual Literacy Competencies and Their Academic Achievement A. . zdemir, S. Gktepe

263

The Effects of History of Mathematics on Mathematics Education D. Demirolu, E. Aydn, A. Delice

264

The Correlation Between Achievement Test Scores and Creative Thinking Skills of Non-gifted Students E. Altnta, A. . zdemir, A. Kerpi

266

The Changes in the Cognitive and Affective Properties of the Pre-Service Elementary Mathematics Teachers from the Beginning of the Teacher Training Program to Graduation E. Masal, M. Masal, E. Akgn, M. Takunyac

267

Open Source Softwares in Mathematics Education E. zsalam, G. Bier, A. Atalay, P. Popo

269

Sequences and Series: What are These Concepts Through the Eyes of Pre Service Secondary Mathematics Teachers? G. Yazgan-Sa, Z. Argn

270

The Concept of Proof is Examined the Size of Teachers . Yavuz, M. Tatepe

272

Analysis of the Elementary 8th Grade Students Mathematical Ability Levels from the Perspective of PISA M. Altun, N. Aydn, R. Akkaya, D. Uzel

273


http://www.cgpublisher.com/works/38080/manage_workspacehttp://www.cgpublisher.com/works/38080/manage_workspace

XXVI

Proof Schemes Used by Mathematics Teacher Candidates S. engl, P. Gner

274

Preservice Elementary Mathematics Teachers Proving Skills Y. Kymaz, B. K. Doruk, T. Horzum

275

The Conceptual Methodical Approach in Training as a Mean of Increase of Degree of Social Protection of Disabled Children Z. K. Yuldashev, M. A. Yuldasheva

277

THE OTHER AREAS

Quartic B-Spline Collocation Method for Numerical Solutions of the Klein-Gordon Equation A. Boz, . Da

281

Vehicle Crashworthiness Optimization Using Differential Evolution Approach A. R. Yldz

282

Optimization of Vehicle Components Using Artificial Bee Colony Algorithm A.R. Yldz

285

Modeling of Flux Decline at Nanofiltration Membrane by Artificial Neural Networks B. Eren

287

Reduction of Dimensionality in the Problem of Diffraction From a Half-Plane B. Kamishi, R. Bejtullahu

288

Estimation of Lake Sapanca Daily Water Level Using Artificial Intelligent Techniques E. Doan, S. Demir

289

Seismic Q Estimation Using Artifical Neural Network E. Yldrm, R. Saatlar, G. Horasan, S. Ergintav 290

A Real-Time Virtual Sculpting Application with a Haptic Device G. Cit, K. Ayar, S. Sertta, C. z

291

Pre-Service Student Teachers Point, Line and Plane Concept Knowledges in Geometry and Used Multiply Representation G. Tuluk

293

Self-Dual Codes from Self-Dual Codes of Smaller Lengths and Recursive Algorithm H. Topcu, H.Aktas

295

Theoretical Calculation of the Ground-State Magnetic Moments in the Odd-Mass Nuclei H. Yakut, E. Tabar, E. Guliyev, O. rnek

297

Performans Ranking of Turkish Insurance Companies : the Anp Application . Akhisar

298

Relations on FP-Soft Sets Applied to Decision Making Problems . Deli, N. aman, . imek

299


XXVII

Assessing the Relationship Between Educational Performance and Attitudes of Turkish Students . Demir, S. Kl

300

Comparing Turkeys Domestic Debt Stock Increment with Linear Regression, Ridge Regression and Principle Component Regression . Demir, G. Altunel, E. Cene

301

The Adomian Decomposition Method for Solving Nonlocal Boundary Value Problems for First-Order Linear Hyperbolic Equation L. Bougoffa

303

Genetic Algorithm and Financial Optimisation M. A. nal

304

Uniform Time Controllability of Affine Control Systems on Semisimple Lie Groups M. Kule

305

The Effect of Instruction States Designed According to Van Hiele Geometrical Thinking Levels on the Geometrical Success M. Terzi, . Mirasyediolu

306

On a Problem of Thermal Convection with Unset Flow Rate N.T. Danaev, B.S. Darybaev, B.A. Urmashev

309

Solution of Spherical Triangles in Geodesy with the Equations Used in Spherical Trigonometry N. Ersoy, E. Yavuz, R. G. Hoba 310

Application of Incomplete Cylindrical Functions in the Diffraction of Gaussian Beam from a Half-Plane R. Bejtullahu, B. Kamishi, Z. Tolaj, F. Aliaj

311

Asynchronous Motor with Finite Element Method Nonlinear Analysis S. A. Korkmaz, H. Krm

312

Relationship Between Classical and Quantum Physic S. Ahmetaj, S. Kabashi, S. Bekteshi

314

Modeling of gas flow through a rectangular channel (variable leak valve) S. Avdiaj, N. Syla and F. Aliaj

314

Modelling Kosovos Power System and Scenarios for Sustainable Development S. Bekteshi, S. Kabashi, S. Ahmetaj

315

The Specific Exponential Stability of Solutions of Linear Homogeneous Volterra Integro-differential Equation of Sixth Order S. Iskandarov

317

Rendering Virtual Welding Seam Form S. Sertta, K. Ayar, C. z, G. Cit

318

The Relationships Among Interest Rate, Exchange Rate and Stock Price: A BEKK MGARCH Approach S. Trkylmaz, B. Yldz

321


XXVIII

The Causality Relationship Among Inflation, Output Growth and Their Uncertainties: Evidence For Turkey S. Trkylmaz, M. Balbey

323

Bounds on the Largest Eigenvalue of the Distance Signless Laplacian of Connected Graphs . B. Bozkurt, D. Bozkurt

325

An Historical Overview of Visual Mathematical Arts Z. Tez

326

Processing of Non-determined Results of Observations with Interval Interpolation Polynoms Z. Yuldashev, A. Ibragimov, S. Tadjibaev

328

POSTER

The Generalized Incomplete Pochhammer Symbols and Their Applications to Exponential Functions A. etinkaya, O. Kymaz

329

A Solution of the Radial Schrdinger Equation for the Potential Family

( ) 22A B

V r Cr Drrr

= + +

A. Glerolu , C. Dane, H. Akba

331

Modeling of Concentrators Influence on Stress Condition of Elastic-plastic Structures A.M. Polatov

332

The Special Solution of Schrdinger Equation with by Symmetries C. Dane, K. Kasapolu, H. Akba

333

An Analysis of Blood flow in the Human Descending Aorta with Different Reynolds Number D. Pandr, Y. Pandr

334

Ideals and Their Characterizatios in Factor - Near Rings E. Domi, I. Braja

335

Numerical Solution of Some Dynamic Problems in Nanomechanics E. Hazar, M.K. Cerraholu

336

Inclined Curves in the Lightlike Cone E. S. Yakc, . Gk, F. N. Ekmekci, Y. Yayl

337

A Study on The Spherical Null Curves and Bertrand Curves in Minkowski 4 Spacetime G. Gner, N. Ekmekci, Y. Sarolu

338

Reconstruction in Education H. Bozyoku

339


XXIX

State Estimation in Induction Motors via Block-Pulse Functions H. Kzmaz, S. Aksoy

340

Geodesics on the Tangent Sphere Bundle of the 3-sphere . Ayhan

342

One-Sided Similar Ideals in -Semigroups and Some Properties of the Principal Quasi-Ideals I. Braja, E. Domi

343

A Different Characterization of U1(ZC8) K. Ar , M. Grgl

344

The Dependence Described by Copulas in the Reinsurance Treaties K. Haxhi, O. Zacaj

345

Algebraic Hyperstructure of Soft Sets Associated to Ternary Semihypergroups K. Hila, S. Sadiku, K. Naka

346

Solution of Time-Independent One Dimensional Schrdinger Equation Using Symmetries K. Kasapolu, C. Dane, H. Akba

347

Parameter Estimation Based on Type-II Fuzzy Logic K. . Kula, T. E. Dalkl

348

Intrinsic Geometry of the NLS Equation According to Bishop Frame in Euclidean 3-Space M. Ergt, H. ztekin, S. Aykurt

349

On the Mcshane Integral on the Riesz space M. Shkmbi, I. Temaj

350

Developing Attitude Scale toward the Geometric Objects for the Preservice Teachers N. Grefe, A. Kan

352

Modeling the RC Electric Circuit with Finite Element Method N. Syla, F. Aliaj, S. Avdiaj

353

Extended Caputo Fractional Derivative and Its Applications O. Kymaz, A. etinkaya, Y. Skmen

354

Non-Symmetric Divisor Problem over the Ring of Gaussian Integers O. Savastru

356

Harmonic Curvature Function of Special Curves in Lie Groups O. Z. Okuyucu, . Gk, Y. Yayl, F. N. Ekmekci

357

Applications to Markov Chains: Introducing a BONUS-MALUS Model for the MTPL Portfolio in Albania O. Zacaj, K. Haxhi

358

Fractional Calculus Operator for a Singular Sturm-Liouville Equation R. Ylmazer, . ztrk

360


XXX

State Variables Computation Technique for Linear Systems by Using Block-Pulse Functions S. Aksoy, H. Kzmaz

361

On Fuzzy Soft -ring S. Onar, B. A. Ersoy

363

Some Examples of Crossed Modules T. S. Kuzpnar

364

Oscillation Criteria for Second Order Nonlinear Differential Equations X. Beqiri, E. Koci

365

Solutions of the Nonlinear Differential Equations by Use of Symmetric Fibonacci Functions Y. A. Tandoan, Y. Pandr

367

A New Approach to the Trial Equation Method Y. Grefe, Y. Pandr, E. Msrl

368

Elliptic Function Solutions of a Nonlinear Partial Differential Equation Y. Pandr, Y. Grefe, E. Msrl

369

On Parallel Surfaces in Minkowski 3-Space Y. nltrk, E. zsalam

370

Computation of Energies of Atoms Over Integer and Non Integer Quantum Numbers Y. Yakar, B. akr, A. zmen

371

Participiants 373


INVITED TALKS



Variable-range approximate systems: a unified approach to categories of fuzzy topology and theories of fuzzy rough sets

Alexander Sostak University of Latvia, Riga,Latvia, [email protected]

Abstract. In our paper A. Sostak, Towards the theory of -approximate systems: Fundamentals and examples, Fuzzy Sets and Syst. 161 (2010), 2440-2461. the concept of an -approximate system where is a fixed complete lattice was introduced and basic properties of the category of M-approximate systems were studied. We regard the concept of an approximate system and the corresponding category as the framework for a unified approach to various categories related to (fuzzy) (bi)toplogical spaces and to (fuzzy) rough sets. Although the attempts to study the relations between fuzzy topological space and fuzzy rough sets and to introduce a context allowing to give a unified view on these notions were undertaken also by other authors, the approach presented in our paper is essentially different. In this work we continue the research of -approximate systems. However, as different from our previous work here we consider the case of a variable range , that is allow to change lattice M. In particular this allows to include also the category of -topological spaces with varied lattices and in the scope of our research. The author gratefully acknowledge a partial financial support by the ESF research project 2009/0223/1DP/1.1.1.2.0/09/APIA/VIAA/008. 1

1


Minimax Solution of The Problem of The Choice of Optimum Modes for Gas-Lift Process

Aliev F. A. (1) and Ismayilov N. (2) (1) Baku State University, Baku, Azerbaijan, [email protected]

Abstract. As it is known [1], gas-lift method for oil production plays an important role after fountain process. In spite of this way is used for a long time, till now there are no exact mathematical models of the corresponding control problem [2]. Really, in [2] mathematical model of operation of the gas-lift where the initial motion of fluids is described by the system of ordinary differential equations is suggested. However, in [3] it is demonstrated that the motion of fluids is described by the partial differential equation of hyperbolic type. Here we try to solve the general problem (optimal modes and their stabilization), reducing it to the linear quadratic problem of optimization by means of the method of straight lines [5]. Introducing the small parameter an asymptotical method is proposed to the solution of the choice of program trajectory and control. Basically, it is supposed that the bulk of debit should be fixed. However, in practice the problem consists in a finding of minimal bulk of gas to provide maximal production of oil [1]. This is a mathematical statement of minimax problem [6]. By the aggregating of the positive weighting matrix coefficients in control and of the negative weighting coefficients, in debit it is possible to construct the quality criterion and to formulate the minimax problem. The purpose of the present work is study of this problem.

Keywords. minimax problem, Euler-Lagrange equation AMS 2010. 15A24

References

[1] Mirzadzhanzade A.H., Ahmetov I.M., Khasaev A.M., etc. Oil Production Technology and Equipment. Under the editorship of A.H.Mirzadzhanzade, Moscow, Nedra, 382p., 1986.

[2] Eikrem G.O., Aamo O.M. and Foss B.A. Stabilization of Gas-Distribution Instability in Single-Point Dual Gas Lift Wells, SPE Production & Operations, vol. 21, N2, pp.1-20, 2006.

[3] Aliev F.A., Ilyasov M. Kh, Dzhamalbekov M. A. Modeling the operation of a gas-lift well, Reports NAS Azerbaijan, N.4, pp.30-41, 2008.

[5] Aliev F.A., Ilyasov M. H, Nuriev N.B. Problem of mathematical modeling, optimization and gas-lift controls, Reports NAS Azerbaijan, 2, pp.43-57, 2009.

[6] Demyanov V.F, Malozemov V.N. The introducing to the minimax. M.:Nauka, 368p., 1972.

[7] Baar T., Bernhard P. I. H - optimal control and related minimax design problems. A dynamic game approach. Birkhauser, Boston, Basel, Berlin. 1995.

2


mailto:[email protected]

Dimension of Fractals

H. Hilmi Hacsaliholu

Bilecik Seyh Edebali University, Bilecik, Turkey, [email protected]

Abstract. MANDELBROT has been generalized the concept of fractal dimension

which was given by F.HAUSDOFF in 1919. This concept essentially was given by

KOLMOGOROV in 1958, as the capacity of a geometric figure. The concept of dimensional

has so much different mathematical meanings. The most common one of these is well known

as the topologic dimension. In regular geometry the dimension is an entire number. But for

the fractals, dimension is a rational number or a negative number also. For example L. E.

BROWER (1882-1926), F. HAUSDORFF (1886-1942), A. S. BERICOWICH (1891-1970)

and A. N. KOLMOGOROV (1903-1987) used the second kind numbers for the fractals. This

means that these dimensions were not the entire numbers.

A definition for fractal dimension was given by B. MANDELROT as

0

loglim1log

a

nd

a

=

where d denotes the dimension and a denotes the criterion for distance and n denotes the numbers a which gives the length af the fractal curve.

This definition gives us that

1 dna

=

and 11.

d

n aa

=

.

We calculated some fractal dimensions as examples.

Ex1. The dimension of Waclaw Siepinsky triangle as

log3 1,5850.log 2

d = =

Ex2. The dimension of the curve of KOCH as

log 4 1,26.log3

d = =

3


The Borwein-Ditor Theorem and My Oxford Moment

Harry I. Miller

International University of Sarajeevo, Bosnia and Herzegovina, [email protected]

Abstract. In 1978 Borwein and Ditor published a paper answering a real

analysis question of Erdos. Since then a series of authors have made contributions to this area.

I will review the work of these authors and in particular present the results from my joint

paper (with A.J. Ostaszewski) that just appeared in the JMA.

4


http://www.mail.sakarya.edu.tr/index.php?page=yeni&[email protected]

Bijective S-boxes and Self Dual Codes

Patrick Sole

University of Nice Sophia Antipolis, Nice, France, [email protected]

Abstract. We introduce a new class of rate one half binary codes: complementary

information set codes. A binary linear code of length 2n and dimension n is called

complementary information set code (CIS code for short) if it has two disjoint information

sets. This class of codes contains self-dual codes as a subclass. It is connected to graph

correlation immune Boolean functions of use in the security of hardware implementations of

cryptographic primitives. Such codes permit to improve the cost of masking cryptographic

algorithms against side channel attacks. In this work we investigate this new class of codes:

we give optimal or best known CIS codes of length < 132. We derive general constructions

based on cyclic codes and on double circulant codes. We derive a Varshamov-Gilbert bound

for long CIS codes, and show that they can all be classified in small lengths 12 by the

building up construction. Some nonlinear S-boxes are constructed by using Z4-codes, based

on the notion of dual distance of an unrestricted code. (joint work with Carlet, Gaborit, Kim).

5


Index of a Subfactor in a Real Factor

Sh.A.Ayupov (1) and A.A.Rakhimov (2)

(1) National University of Uzbekistan, Tashkent, Uzbekistan, [email protected]

(2) Tashkent Institute of Automobile and Road Construction, Tashkent, Uzbekistan,

[email protected]

Abstract. Let B(H) be the algebra of all bounded linear operators on a complex

Hilbert space H. A weakly closed *-subalgebra M containing the identity operator 1 in B(H)

is called a W*- algebra. A real *-subalgebra R of B(H) is called a real W*-algebra if it is

closed in the weak operator topology and R iR={0}. A real W*-algebra R is called a real

factor if its center consists of the elements { 1, R}. Let R be a real W*-algebra, and let

Q be a real W*-subalgebra of R. The set of normal faithful semi-finite operator-valued

weights from R to Q is denoted by P(R,Q). We have the following results.

Theorem 1. P(R,Q) P(R+iR,Q+iQ)

Theorem 2. If R' and Q' are the commutants of R and Q, respectively, then

P(R,Q) P(R',Q') ,

and there exists the canonical order-reversing bijection (denoted by : EE 1 ) between

P(R,Q) and P(Q',R').

Let now R be a -finite real factor and let Q be a real subfactor of R. We recall that a linear

positive mapping E:RQ is called a conditional expectation if it satisfies the following

conditions: E(1)=1, E(E(x)y)=E(x)E(y)=E(xE(y)) and E(x)*E(x)E(x*x), for all x,yR. We

fix a normal conditional expectation E from R onto Q. Since E is an operator-valued weight

we get E 1 P(Q', R'). For any unitary uR', we have u E 1 (1)u*= E 1 (u1u*)= E 1 (1). It is

obvious that E(1)=1, but in general we have E 1 (1) 1. Since R is a real factor the element

E 1 (1) is a scalar (possibly + ).

6


mailto:[email protected]

Definition. The number E 1 (1) is called the index of the subfactor Q in the real factor R, and

denoted by [R:Q].

By this definition it is clear that [R:Q]=[R+iR:Q+iQ].

Thus, we obtain the following real version of the index theorem.

Theorem 3. Let R be a -finite real factor and let Q be a real subfactor of R. Then one has

either [R:Q]=4cos 2 /q, for some integer q3 or [R:Q] 4.

7


8


ALGEBRA



Transfer of Orbital Integrals and Division Algebras

Ali Aydodu (1), Rukiye ztrk (1), Engin zkan (2) and Yuval Z.Flicker (3)

(1) Ataturk University, Turkey, [email protected]; [email protected]

(2) Erzincan University, Erzincan, Turkey, [email protected]

(3) The Ohio State University, Columbus, USA, [email protected]

Abstract Let uF be a local non-archimedean field, uG the multiplicative group of a

division algebra uD central of rank n over uF , and ( , )u uG GL n F = There is an embedding of

the set of conjugacy classes in uG as the set of elliptic conjugacy classes in uG defined

by p p = here p is the characteristic polynomial of and p is that of . In a

fundamental but unpublished work [2] ( see also [1] ) of the late 1970's, Deligne and Kazhdan proved: Theorem 1. There is a bijection from the set of equivalence classes of irreducible uG modules

u to the set of equivalence classes of irreducible square-integrable uG -modules u defined

by the character relation ( ) ( ) ( )11u u

n

= for every regular in in uG with image

in uG . Here u denotes the character of u and u that of u We shall briefly discuss the history of this important theorem, give a simple, global proof of it, which does not use matching of orbital integrals, and rather deduce this matching from the correspondence. Theorem 2. For every function uf in the Hecke algebra ( )c uC G there is a function uf in the Hecke algebra ( )c uC G and for every uf in ( )c uC G

there is uf in ( )c uC G whose orbital integrals match ( ) ( ), ,u uf f = for all regular in uG and in uG with p p =

Keywords. division algebra, automorphic representations, trace formula, L-functions AMS 2010. 11R52, 11F70, 11F72,11S40

References

[1] J. Bernstein, P. Deligne, D. Kazhdan, M.- F. Vigneras, Representations des groupes

reductifs sur un corps local, Hermann, Paris 1984.

[2] P. Deligne, D. Kazhdan, On representations of local division algebras, unpublished

manuscript.

9


A Combinatorial Discussion on Finite Dimensional Leavitt Path Algebras

A. Ko (1), S. Esin (2), . Glolu (2) and M. Kanuni (3)

(1) Istanbul Kultur University, Istanbul, Turkey, [email protected]

(2) Dogus University, Istanbul, Turkey, [email protected], [email protected]

(3) Bogazici University, Istanbul, Turkey, [email protected]

Abstract. Any finite dimensional semisimple algebra A over a field K is isomorphic

to a direct sum of finite dimensional full matrix rings over suitable division rings. In this

paper we will consider the special case where all division rings are exactly the field K. All

such finite dimensional semisimple algebras arise as a finite dimensional Leavitt path algebra.

For this specific finite dimensional semisimple algebra A over a field K, we define a uniquely

detemined specific graph - which we name as a truncated tree associated with A - whose

Leavitt path algebra is isomorphic to A. We define an algebraic invariant (A) for A and

count the number of isomorphism classes of Leavitt path algebras with (A)=n.

Moreover, we find the maximum and the minimum K-dimensions of the Leavitt path algebras

of possible trees with a given number of vertices and determine the number of distinct Leavitt

path algebras of a line graph with a given number of vertices.

Keywords. Finite dimensional semisimple algebra, Leavitt path algebra, Truncated

trees, Line graphs.

AMS 2010. 16D70, 05C60.

References

[1] Abrams, G., Pino, A., Molina, M.S., Finite-dimensional Leavitt path algebras, Journal of

Pure Appl. Algebra 209, 753 762, 2007.

[2] Lam, T.Y., A First Course In Noncommutative Rings, Springer-Verlag 2001.

[3] Abrams, G., Pino, A., The Leavitt path algebra of a graph, Journal of Algebra 293, 2, 319-

334, 2005.

10


mailto:[email protected]:[email protected]:[email protected]:[email protected]

Inequalities Involving ( !)pv n Armend Sh. Shabani (1) and Valmir Krasniqi (2)

(1) University of Prishtina, Prishtina, Kosovo, [email protected]


Abstract. We establish some inequalities involving ( !)pv n , the greatest power of

prime p in factorization of n!. Also, we give some partial solutions and comments to the

problems appeared in [2].

Keywords. Factorial function, Prime number, Inequality

AMS 2010. 05A10, 11A41, 26D15, 26D20.

References

[1] M.B. Nathanson, Elementary Methods in Number Theory, Springer 2000.

[2] M. Hassani, Equations and Inequalities involving ( !)pv n , J. Ineq. Pure Appl. Math., 6(2)

(2005), Article 29.

[3] A.M. Robert, A Course in p-adic Analysis, Springer, 2000.

11


mailto:[email protected]:[email protected]

Zbrthimi n vlera singular I nj matrice dhe zbatime

Alba Vrapi and Fatmir Hoxha

Abstract. The singular value decomposition of matrices stands as one of the most important

concepts in mathematics, because of its variety of applications in mathematics , statistics,

biology and many other areas of science. In this thesis , we present the singular value

decomposition and its relation to the spectral decomposition . We also investigate the singular

value decomposition of a matrix together with some of its applications.

Key words. Vector space,vector subspace,rank,base,matrix,eigen values, eigen vectors,

singular value, matrix rates.

12


Structure of Intuitionistic Fuzzy Sets in Semihyperrings

Bayram Ali Ersoy (1) and Bijan Davvaz (2)

(1) Yildiz Technical University, Istanbul, Turkey [email protected]

(2) Yazd University, Yazd, Iran, [email protected], [email protected]

Abstract. As we know, intuitionistic fuzzy sets are extensions of the

standard fuzzy sets. Now, in this paper, the basic definitions and properties of

intuitionistic fuzzy hyperideals of a semihyperring are introduced. A few

examples are presented. In particular, some characterizations of Artinian and

Noetherian semihyperring are given.

13


-Vague Module

Dilek Bayrak (1) and Sultan Yamak (2)

(1) Karadeniz Technical University, Trabzon, Turkey, [email protected]

(2) Karadeniz Technical University, Trabzon, Turkey, [email protected]

Abstract. Although the general theory of vague groups and vague rings has been

investigated, the concept of TL-vague module has not been examined yet. In this study, the

concept of TL-vague module is defined and some related basic properties are obtained.

Keywords. -vague group, -vague ring, -vague module.

AMS 2010. 03B52, 20N25.

References

[1] Demirci, M. ve Recasens, J., Fuzzy groups, fuzzy functions and fuzzy equivalence

relations, Fuzzy Sets Syst., 144, 441-458, 2004.

[2] Demirci, M., Vague groups, J. Math. Anal. Appl., 230, 142156, 1999.

[3] Sezer, S., Vague groups and generalized vague subgroups on the basis of ([0,1], , ),

Information Sciences, 174, 123-142, 2005.

[4] Mordeson, J. N. ve Bhutani, K. R., Vague groups and Vague Field, J. Fuzzy Math. 15,

No. 4, 927-944, 2007.

14


-Primitive Elements of Free Metabelian Lie Algebras

Dilek Ersalan (1) and Zerrin Gl Esmerligil (2)

(1) Cukurova University, Adana, Turkey, [email protected]


Abstract. Let L2 be a free metabelian Lie algebra of rank two. We obtain a

characterization of -primitive elements of L2. In particular, we prove that every

edomorphism of L2 is an automorphism if and only if takes a -primitive element of L2 to another -primitive element. Also we show that in a free metabelian Lie algebra of odd

rank there are no -primitive elements.

Keywords. Primitive element, Free Metabelian Lie algebra

AMS 2010. 17B01, 17B40.

References

[1] Drensky, V.; Automorphisms of relatively free algebras, Commun. In Algebra 18 No.12,

4323-4351, 1990.

[2] Fox, R.H.; Free differential calculus I.Derivation in free group ring, Ann.of Math.2,

No.57, 547-560, 1953.

[3] Mikhalev, A.A., Zolotykh, A.A.; The rank of element of a free Lie (p)superalgebra,

Doklady Akad. Nauk 334(1994), No.6, 690-693; Translation in Russian Acad. Sci. Dokl.

Math. 49 no.1,189-193, 1994.

[4] Mikhalev, A.A., Zolotykh, A.A.; Rank and primitivity of elements of free color Lie

(p)superalgebras, Int.J. of Algebra and Comp., 4,No.4, 617-655, 1994.

[5] Mikhalev, A.A., Yu, J.T.; Primitive, almost primitive, test and -primitive elements of free

algebras with the Nielsen-Schreier Property, J. of Algebra, 228,603-623, 2000.

[6] Shmelkin, A.L., Wreath products of Lie algebras and their application in the theory of

groups(Russian), Trudy Moskov. Math. Obshch., 29(1973) 247-260.Tanslation:Trans.

Moscow Math. Soc. 29,239-252, 1973.

15



[7] Shpilrain, V., On generators of L/R Lie algebras, Proc. Amer. Math. Soc. 119, No.4,

1039-1043,1993.

[8] Shpilrain, V., Yu, J.T.; On generators of polynomial algebras in two commuting or non-

commuting variables, J. Pure Appl. Algebra 132, 309-315, 1998.

[9] Shpilrain, V.; Generalized primitive elements of a free group, Arch. Math. 71, 270-278,

1998.

16


A Note on Direct Product of Fuzzy Modules over Fuzzy Rings

Ece Yetkin

Marmara University, Istanbul, Turkey, [email protected]

Abstract. In this study, a new kind of fuzzy module over a fuzzy ring is defined and

then direct product of fuzzy modules over fuzzy rings is introduced. Some of their basic

properties are presented analogous to ordinary module theory.

Keywords. Fuzzy ring, fuzzy module

AMS 2010. 08A72, 03E72, 20K25.

References

[1] Rosenfeld, A., Fuzzy groups, J. Math. Anal. Appl., 35, 512-517, 1971.

[2] Ersoy, B.A., A generalization of cartesian product of fuzzy subgroups and ideals, Pakistan

Journal of Applied Sciences, 3, 100-102, 2003.

[3] Malik, D.S., Mordeson, J.N., Fuzzy Commutative Algebra, World Scientific Publishing,

1998.

[4] Malik, D.S., Mordeson, J.N, Fuzzy relations on rings and groups, Fuzzy Sets and

Systems, 43, 117-123, 1991.

[5] Akta, H., aman, N., A type of fuzzy ring, Arch. Math. Logic, 46, 165-177, 2007.

[7] Yuan, X., Lee, E.S., Fuzzy group based on fuzzy binary operation, Comput. Math. App.,

47, 631-641, 2004.

[8] Liu, W.J., Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8, 133-

139, 1982.

17


On Almost Prime Elements in Lattice Modules

Ece Yetkin (1), Zeliha Kl (2) and nsal Tekir (3)

(1) Marmara University, Istanbul, Turkey, [email protected]



Abstract. In this study, we introduce the concept of almost prime elements in lattice

modules over a multiplicative lattice as a new generalization of prime and weakly primary

elements. Some characterizations of this type of elements are given in lattice modules.

Keywords. Almost prime element, lattice module, multiplicative lattice.

AMS 2010. 03G10, 06B99.

References

[1] Atani, S. E., Ferzalipour, F., On weakly primary ideals, Georgian Mathematical Journal,

12, 423-429, 2005.

[2] Bataineh, M., Kuhail, S., Generalizations of primary ideals and submodules, Int. J.

Contemp. Math. Sciences, 6, 811-824, 2011.

[3] Callialp, F., Jayaram, C., Tekir, U., Weakly prime elements in multiplicative lattices,

Communications in Algebra, 40, 1-16, 2012.

[4] Callialp, F., Tekir, U., Multiplication lattice modules, Iranian Journal of Science and

Technology, A4, 309-313, 2011.

[5] Jabbar, A. K., Ahmed, C. A., On almost primary ideals, International Journal of Algebra,

5, 627-636, 2011.

[6] Jayaram, C., Johnson, E.W., s-prime elements in multiplicative lattices, Periodica

Mathematica Hungarica, 31, 201-208, 1995.

[7] Jayaram, C., Johnson, E.W., Strong compact elements in multiplicative lattices,

Czechoslovak Mathematical Journal, 47, 105-112, 1997.

[8] Jayaram, C., Laskerian lattices, Czechoslovak Mathematical Journal, 53, 351-363, 2003.

18


On Multiplication Lattice Modules

Fethi allalp (1) and nsal Tekir (2)

(1) Dogus University, Istanbul,Turkey, [email protected]

(2) Marmara University, Istanbul,Turkey,[email protected]

Abstract. This study concerns with the further investigation of multiplicaiton lattice

modules especially faithful and principally generated multiplication lattice modules over a

multiplicaitive lattice Multiplication lattice modules have been studied in [5]. In this work we

continue to the characterization of multiplication lattice modules, in particular, the proofs of

Cohen theorem and Nakayama lemma are given in multiplication lattice modules.

Afterwards, a small element is defined in a lattice module and a new type of lattice module is

characterized called hollow lattice module by means of small elements. Several results

concerning with these elements and hollow lattice modules are considered.

Keywords. Multiplicative lattices, Lattices modules, prime elements.

AMS 2000. Primary 16F10; Secondary 16F05.

References

[1] C.Jayaram and E.W.Johnson. (1995) : Some results on almost principal element lattices,

Period.Math.Hungar, 31; 33 - 42:

[2] C.Jayaram and E.W.Johnson.(1997): Dedekind lattices, Acta. Sci. Math.(Szeged); 63;

367-378:

[3] C.Jayaram and E.W.Johnson, Strong compact elements in multiplicative lattices. (1997) :

Czechoslovak Math. J, 47 (122) ; 105 112:

[4] D. Scott Culhan. (2005) : Associated Primes and Primal Decomposition in modules and

Lattice modules, and their duals, Thesis, University of California Riverside.

[5] Fethi allalp and nsal Tekir. (2011):Multiplication lattice modules, Iranian Journal of

Science & Technology,no.4, 309 - 313:

[6] Z.A.El-Bast and P.F.Smith. (1985) : Multiplication modules, Comm. Algebra 16; 755 -

799:

19


Comultiplication Lattice Modules

Fethi allalp (1) and nsal Tekir (2)

(1) Dogus University, Istanbul,Turkey, [email protected]

(2) Marmara University, Istanbul,Turkey,[email protected]

Abstract. Let L be a multiplicative lattice and M be a lattice L-module. M is said to be

a comultiplication L-module if for every element N of M there exists an element such

that = (0: ). This study is devoted to investigate some properties of comultiplicaiton

lattice modules. In this work, K-lattice is defined and a sufficient condition is given to say that

every element of a comultiplication K-lattice module has a primary decomposition.

Furthermore, we introduce the definition of a second element in comultiplication lattice

module and the relation between prime element and second element is given. Afterwards,

coprime element is defined and some related results are proved. Additionally, large and small

elements are defined and various properties concerning the relation between small elements

and large elements are obtained.

AMS 2000. Primary 16F10; Secondary 16F05.

Keywords . Multiplicative lattices, Lattices modules, comultiplication lattice

modules, coprime elements.

References.

[1] C.Jayaram. (2003) : Laskerian lattices, CzechoslovakMath. J, 53 (128) ; 351- 363:

[2] D. Scott Culhan. (2005) : Associated Primes and Primal Decomposition in modules and

Lattice modules,and their duals, Thesis, University of California Riverside.

[3] Eaman A.Al-Khouja. (2003) : Maximal Elements and Prime elements in Lattice Modules,

Damascus University for Basic Sciences 19, 9 -20:

[4] H. Ansari-Toroghy, F. Farshadifar, On Multiplication and comultiplication modules,Acta

Mathematica Scientia 2011,31B(2),694 - 700:

[5] H. Ansari-Toroghy, F. Farshadifar, On comultiplication modules, Korean Ann. Math. 25

(2008), no. 1-2, 57 - 66:

[6] F.Callialp, U.Tekir, Multiplication lattice modules, Iranian Journal of Science &

Technology (2011);no.4, 309 - 313:

20


On Closed Submodules of a Finite Rank Free Module over a Complete DVR

Hanni Garminia (1), Gantina Rahmaputri (2) and Pudji Astuti (3)

(1) Institut Teknologi Bandung, Bandung, Indonesia, [email protected],

(2) Institut Teknologi Bandung, Bandung, Indonesia, [email protected]

(3) Institut Teknologi Bandung, Bandung, Indonesia, [email protected]

Abstract. Fuhrmann [1] introduced the complete notion of a subspace of formal series

in term of an algebraic condition connected to certain projection. In this paper we show that

this algebraic condition can be adapted to obtain a characterization of closed submodules of

a finite rank free module over a complete discrete valuation domain (DVR).

Keywords. Complete discrete valuation domain, closed submodule, exact sequence,

p-adic topology, projection.

References

[1] P.A. Fuhrmann, A Study of Behaviors, Linear Algebra and Its Appl, 351-352, 303-380,

2002.

21


Commutative and Normal Groups on Soft Sets

rfan imek (1), Naim aman (2), Kenan Kaygsz (3) and rfan Deli (4)

(1) Gaziosmanpasa University, Tokat, Turkey, [email protected]



(4) University of 7 Aralik, Kilis, Turkey, [email protected]

Abstract. Soft set theory introduced by Molodtsov in 1999 in order to deal with

uncertainties. In this work, we define commutative and normalizer groups on the soft sets.

We then investigate their related properties by inspiring the group theory.

Keywords. Soft sets, normalizer, soft groups, soft int-groups, commutative soft int-

groups, normal soft int-group.

AMS 2010. 20D15, 20D35, 20F18

References

[1] Ali, M.I., Feng, F., Liu, X., Min W.K., and Shabir, M., On some new operations in soft set theory, Computers and Mathematics with Applications 57, 1547-1553, 2009.

[2] aman N. and Enginolu, S., Soft set theory and uni-int decision making, European Journal of Operational Research 207, 848-855, 2010.

[3] Molodtsov, D.A., Soft set theory-first results, Computers and Mathematics with Applications 37, 19-31, 1999.

[4] Akgl, M., Some properties of soft groups, J. Math. Anal. Appl. 133, 93-100. 29, 1988.

[5] Akta, H. and aman, N., Soft sets and soft groups, Inform. Sci. 177, 2726-2735 2007.

[6] Kaygsz, K., On soft int-groups, Ann. Fuzzy Math. Inform., in press.

[7] Kaygsz, K., Normal soft int-groups, submitted.

22


mailto:[email protected]:[email protected]:[email protected]:[email protected]

On topological Structure on Ternary Semihyperrings

Kostaq Hila (1) and Armend Sh. Shabani (2)

(1) University of Gjirokastra, Gjirokastra, Albania, [email protected]

(2) University of Prishtina, Prishtin, Kosova, [email protected]

Abstract. This paper deals with the topological structure of a class of algebraic hyperstructures called ternary semihyperrings, which are a generalization of semirings and ternary semirings. In this paper we introduce a class of hyperideals in ternary semihyperrings called prime k-hyperideal. Considering and investigating properties of the collection A of all proper prime k-hyperideals of a ternary semihyperring H, we construct a topology A on A by means of closure operator defined in terms of intersection and inclusion relation among these hyperideals of ternary semihyperring H. The topological space (A, A ) is called the structure space of the ternary semihyperring H. We study a several principal topological axioms and properties in this structure space of ternary semihyperring such as separation axioms, compactness etc.

Keywords. Ternary semihyperring; Prime k-hyperideal; k-Noetherian ternary semihyperring; Hull-Kernel topology; Structure space. AMS 2010. 16Y99, 20N20, 17A30.

References

[1] R. Ameri and H. Hedayati, On k-hyperideals of semihyperrings, J. Discrete Math. Sci. Cryptogr.10 (2007), 41-54.

[2] M. R. Adhikari, M. K. Das, Structure spaces of semirings, Bull. Cal. Math. Soc. 86 (1994), 313-317.

[3] A.P. Pojidaev, Enveloping algebras of Fillipov algebras, Comm. Algebra 31 (2003) 883-900.

[4] A. Cayley, Comb. Math. J. 4(1) (1845).

[5] P. Bonansinga and P. Corsini, On semihypergroup and hypergroup homomorphisms, Boll. Un. Mat. Ital. B (6) 1(2) (1982), 717-727.

[6] G. L. Booth and N. J. Groendwald, On uniformly strongly prime - rings, Bull. Austral.Math. Soc. Vol 37 (1988), 437-445.

[7] S. Chattopadhyay and S. Kar, On structure space of - semigroups, Acta Univ. Palacki.Olomuc., Fac. rer. nat., Mathematica 47 (2008), 37-46.

[8] P. Corsini, Prolegomena of hypergroup theory, Second edition, Aviani editor, 1993.

23



N-dimensional (, )-fuzzy ideals of hemirings

Muhammad Aslam (1) and Saleem Abdullah (2)

(1) Quaid-I-Azam University, Islamabad, Pakistan, [email protected]

(2) Quaid-I-Azam University, Islamabad, Pakistan, [email protected]

Abstract. In this paper, we introduce the notion of N-dimensional (, )-fuzzy ideals

in hemirings by using N-dimensional fuzzy point and N-dimensional fuzzy set,. Moreover we

introduced N-dimensional (, )-fuzzy h-ideals in hemirings. We give some characterization

Theorems of N-dimensional (, )-fuzzy h-ideals in hemirings. N-dimensional (, )-fuzzy

ideals in hemirings is most generalization of N-dimensional fuzzy ideals in hemirings and (,

)-fuzzy ideals in hemirings. We also define N-dimensional prime (, )-fuzzy ideals in

hemirings.

Keywords. Hemiring. N-dimensional fuzzy set, N-dimensional (, )-fuzzy h-ideals

24


Test Rank of the Lie Algebra '/ ,F R F

Nazar ahin l (1) and Naime Ekici (2)



Abstract. Let F be a free Lie algebra of rank 2n and R be a fully invariant ideal

of F . We show that the test rank of the Lie algebra '/ ,F R F is equal to 1 when n is even

and less than or equal to 2 when n is odd.

Keywords. Free Lie algebras, Test sets, Test rank.

AMS 2010. 17B01, 17B40.

References

[1] Esmerligil, Z., Ekici, N., Test sets and test rank of a free metabelian Liealgebra. Comm.

Algebra, 31, 11, 5581-5589, 2003.

[2] Esmerligil, Z., Kahyalar, D., Ekici, E., Test rank of F/R Lie algebras. Internat. J. Algebra

Comput., 16, 4, 817-825, 2006.

[3] Fox, R. H., Free differential calculus. I. Derivations in free group rings. Ann. Math. 2, 57,

547-560, 1995.

[4] Mikhalev, A. A., Yu, J. T., Primitive, almost primitive, test and -primitive elements of

free algebras with the Nielsen-Schreier property, J. Algebra, 228, 603-623, 2000.

[5] Mikhalev, A. A., Umirbaev, U. U., Yu, J. T., Generic, almost primitive and test elements

of free Lie algebras, Proc. Amer. Math. Soc., 130, 5, 1303-1310, 2001.

[6] Shpilrain, V., On generators of L/ 2R Lie algebras, Proc. Amer. Math. Soc., 119, 4, 1039-

1043, 1993.

[7] Shpilrain, V., On the rank of an element of a free Lie algebra, Proc. Amer. Math. Soc.,

123, 5, 1303-1307, 1995.

25



[8] Temizyrek, A., Ekici, E., A particular test element of a free solvable Lie algebra of rank

two, Rocky Mountain J. Math., 37, 4, 1315-1326, 2007.

[9] Timoshenko, E. I., Test sets in free metabelian Lie algebras, Siberian Math. J., 43, 6,

1135-1140, 2002.

[10] Timoshenko, E. I., Shevelin, M. A., Computing the test rank of a free solvable Lie

algebra, Siberian Math. J., 49, 6, 1131-1135, 2008.

[11] Umirbaev, U. U., Approximation of free Lie algebras relative to inclusion, Monoids,

Rings and Algebras, Uchen. Zap. Tartu Univ., 878, 142-145, 1990.

[12] Umirbaev, U. U., Partial derivatives and endomorphisms of some relatively free Lie

algebras, Sibirsk. Mat. Zh., 42, 3, 720-723, 2001.

[13] Yagzhev, A. V., Endomorphisms of free algebras, Sibirsk. Math. Zh.21, 181-192;

English Transl. Siberian Math. J., 21, 133-141, 1980.

26


Pullback for Simplicial Lie algebras

zgn Grmen Alansal

Dumlupinar University, Kutahya, Turkey, [email protected]

Abstract. Pullback simplicial object had been defined by Glenn [4]. In this work we

consider this object for lie algebra case.

Keywords. Simplicial algebra, Pullback object, Crossed module.

AMS 2010. 13G05, 18G50, 20J05.

References

[1] Brown, R., Topology, Ellis Horwood Series in Mathematics and its applications Ellis

Horwood, Ltd. p. 460. 1988.

[2] Brown, R., Higgins, P., On the Connection between the Second Relative Homotopy

Groups of some Related Spaces, Proc. LondonMath. Soc.,3, 36, 193-212. 1978.

[3] Curtis, E. B.,Simplicial Homotopy Theory, Adv in Math 6, 107-209 1971.

[4] Glenn P.G., Realization of Cohomology Classes in arbitrary exact categories, Journal of

pure and applied Algebra 25, 33-105, 1982.

27


Induced Inner Product on a Quotient Tensor Product Space

Pudji Astuti

Institut Teknologi Bandung, Bandung, Indonesia, [email protected]

Abstract. The concept of generalized n-inner product was introduced by Trenevsky

and Maleski [6] as a generalization of an n-inner product by Misiak [3]. Following this

intro-duction, a number of results concerning the structure and properties of generalized n-

inner product spaces can be found in literature (see [1], [2] and [4]).

A standard generalized n-inner product is a generalized n-inner product induced by an inner

product [6]. In this presentation we show that one can develop an inner product on a quotient

tensor product space [5] induced by any standard generalized n-inner product. As a result,

the study of any alternating multilinear functional on a standard generalized n-inner product

space can be lifted to the study of the corresponding linear functional on the induced inner

product space.

Keywords. Inner products, generalized n-inner products, tensor products.

AMS 2010. 46C05, 15A69.

References

[1] R. Chugh and S. Lather, On Generalized n-inner product spaces, Navi Sad J. Math.,

41(2011) 73-80.

[2] R. Chugh and Sushma, Some results in Generalized n-inner product spaces, Internat.

Math. Forum, 4(2009) 1013-1020.

[3] A. Misiak, n-inner product spaces, Math. Nachr, 140 (1989) 200-319.

[4] B.S. Reddy, Some Properties in Generalized n-inner product spaces, Int. Journal of Math.

Analysis, 4(2010) 2229-2234.

[5] S. Roman, Advanced Linear Algebra, third ed., Springer, 2008.

[6] K. Trenevsky and R. Maleski, On generalized n-inner product and the corres-ponding

Cauchy-Schwarz inequality, J. Inequal. Pure and Appl. Math., 7 Art. 57 (2006).

28


Normality and Quadraticity for Special Ample Line Bundles on Toric Varieties Arising

from Root Systems

Qndrim R. Gashi (1) and Travis Schedler (2)


(2) MIT, Cambridge (MA), USA, [email protected]

Abstract. We prove that special ample line bundles on toric varieties arising from root

systems are projectively normal. Here the maximal cones of the fans correspond to the Weyl

chambers, and special means that the bundle is torus-equivariant such that the character of the

line bundle that corresponds to a maximal Weyl chamber is dominant with respect to that

chamber. Moreover, we prove that the associated semigroup algebras are quadratic

AMS 2010. 00B05, 14M25, 05E15

29


The Square Terms in Generalized Fibonacci Sequence

Refik Keskin (1) and Zafer iar (2)

(1) Sakarya University, Sakarya, TURKEY, [email protected]

(2) Bilecik Seyh Edebali University, Bilecik, TURKEY, [email protected]

Abstract. Let P and Q be nonzero integers. Generalized Fibonacci sequence { }nU and Lucas sequence { }nV are defined by ,00 =U 11 =U and 11 + += nnn QUPUU for 1n and

,20 =V PV =1 and 11 + += nnn QVPVV for 1n , respectively. In this paper, we assume that

1=Q . We solve the equations 2xUU mn = , 22 xUU mn = ,

23 xUU mn = and 26 xUU mn =

when P is even and mn 2 . Moreover, we solve the equations 23 xUU mn = and 26 xUU mn = when P is odd.

Keywords. Generalized Fibonacci numbers; Generalized Lucas numbers;

Congruences.

AMS 2010. 11B37, 11B39.

References

[1] R. Keskin and Z. Yosma, Some new identities concerning generalized Fibonacci and

Lucas numbers (Accepted for publication).

[2] M. Mignotte and A. Peth, Sur les carres dans certanies suites de Lucas, Journal de

Theorie des nombers de Bordeaux, 5 no. 2 (1993), 333--341.

[3] K. Nakamula and A. Peth, Squares in binary recurrence sequences, Number Theory:

Diophantine, computational and algebraic aspects; proceedings of the international

conference, de Gruyter, 1998, 409--421.

[4] P. Ribenboim and W. L. McDaniel, On Lucas sequence terms of the form kx, Number

Theory: proceedings of the Turku symposium on Number Theory in memory of Kustaa Inkeri

(Turku, 1999), de Gruyter, Berlin, 2001, 293--303.

30


Generalized Fuzzy Bi-hyperideals in Semihypergroups

Saleem Abdullah (1) and Kostaq Hila (2)

(1) Quaid-i-Azam University, Islamabad, Pakistan, [email protected]

(2) Gijrokastera University, Gijrokastera, Albania, [email protected]

Abstract. In this paper we introduced interval valued ( ), -fuzzy bi-hyperideal in

semihypergroups which is a generalization of fuzzy hyperideals and ( ), -fuzzy bi-

hyperideal in semihypergroups, where { }, , , ,q q q with q . So we can

easily construct twelve different types of interval valued fuzzy hyperideals in

semihypergroups. Using the idea of a quasi-coincidence of an interval valued fuzzy point

with a interval valued fuzzy set, the concept of an ( ), -fuzzy bi-hyperideal in

semihypergroups is introduced and some interesting characterizations theorems are obtained.

A special attention in given to ( ), q -fuzzy bi-hyperideals. We prove that for a

semihypergroups S . Let A be an interval valued fuzzy subset of S . Then, A is an

interval valued ( , )q -fuzzy bi-hyperideal of if and only if t

A is a bi-hyperideal

of S for all (0,1]t D , where : { | }.ttA x S x qA =

Keywords. Fuzzy algebra; semihypergroups; quasi-coincidence; ( , ) -fuzzy bi-

hyperideal, ( , )q -fuzzy bi-hyperideals.

AMS 2010. 53A40, 20M15.

References

[1] L. A. Zadeh, Fuzzy Sets, Inform. and Control, 8 (1965) 338-353.

[2] B. Davvaz, Fuzzy hyperideals in semihypergroups, Italian J. Pure and Appl. Math. no. 8, (2000), 67-74.

[3] B. Davvaz, Strong Regularity and Fuzzy Strong Regularity in Semihypergroups., Korean J.Comput. & Appl. Math. Vol. 7 ,No 1, (2000), 205-213.

[4] Tosun, M., Kuruolu, N., On B. Davvaz: (,q)-fuzzy subnearrings and ideals, Soft Comput, 10:(2006),206-211.

[5] Yaglom, I. M., A simple non-Euclidean geometry and its physical basis, Springer- Verlag, New-York, 1979.

31


Some Relations on Extending Modules

Semra Doruz

Adnan Menderes University, Aydin, Turkey, [email protected]

Abstract. In the development of extending module theory, behaviour of closed and

complement submodules take an important place. In this work all rece

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