1st INTERNATIONAL EURASIAN CONFERENCE ON MATHEMATICAL SCIENCES … · 2018. 10. 9. · Professor...

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 TİKA 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 (Atatürk 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 GASİMOV (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 (Balıkesir 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 Gül 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. Hacısalihoğlu

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. Aydoğdu, R. Öztürk, E. Özkan, Y. Z. Flicker

9

A Combinatorial Discussion on Finite Dimensional Leavitt Path Algebras A. Koç, S. Esin, İ. Güloğlu, M. Kanuni

10

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

11

Zbërthimi në vlera singular I një matrice dhe zbatime A. Vrapi, F. Hoxha

12

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

13

𝑻𝑳-Vague Module D. Bayrak, S. Yamak

14

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

15


XXX

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

361

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

363

Some Examples of Crossed Modules T. S. Kuzpınarı

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. Tandoğan, Y. Pandır

367

A New Approach to the Trial Equation Method Y. Gürefe, Y. Pandır, E. Mısırlı

368

Elliptic Function Solutions of a Nonlinear Partial Differential Equation Y. Pandır, Y. Gürefe, E. Mısırlı

369

On Parallel Surfaces in Minkowski 3-Space Y. Ünlütürk, E. Özüsağlam

370

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

371

Participiants 373


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State Variables Computation Technique for Linear Systems by Using Block-Pulse

Functions

Saadettin Aksoy (1) and Hakan Kızmaz (2)

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

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

Abstract. State variables that determine a system’s dynamics should be known for

analysis and control of dynamical systems [1,2] Specifically, dynamic feedback for pole

placement is adaptive control applications [3]. Unfortunately, all of the state variables cannot

be measured in practice. As a result, use of a suitable state observer or estimator is

unavoidable in order to obtain immeasurable state variables. There exist variety of state

observers in the literature [4].

BPFs based the single-input single-output system identification has been studied by

Palasinamy and Bhattacharya [5] and Cheng and Hsu [6]. Also parameter estimation by using

block-pulse functions are studied by some people such as Kwong and Chen [7], Hsu and

Cheng [6].

In this study, a general algorithm that uses only input and output and output

measurements is proposed for state variables estimation of linear, time-invariant multi-input

multi-output systems. The proposed algorithm, which is simple in form and convenient for

computer usage is based on the BPFs and consist of three steps. In the first step, the feedback

gain matrix, G which will force the estimation error to go to zero in a short time, can be

determined by using a suitable method [4]. In the second step, input-output measurements and

unknown state vector are expressed in a block pulse series. Thus, we approximate the

continuous-time functions with a set of piecewise-constant functions. In this approximation,

the total numbers of steps in the interval is [0,T] is m, and it can be chosen as any positive

integer number. Finally, in the last step, the observer state equations are converted into

integral equations by integrating the terms on either side of the equations. Then, unknown

state estimation vector together with the block-pulse function approximation of known inputs

and outputs measurement vectors are substituted in the integral equation. After some algebraic

manipulations, state observer equation is transformed into a computationally convenient

algebraic form whose solution can be obtained easily by a computer program. Consequently,

resulting this recursive solution unknown state vector is easily calculated. Consequently,

resulting this recursive solution unknown state vector is easily calculated. Note that this

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algebraic solution form is rather convenient for computer usage and much computing time

and storage can be saved, and the recursive algorithms developed also make it possible to real

time state estimator for dynamic systems. The proposed estimation algorithm was

implemented in MATLAB and it was applied to different cases. Results obtained by the

proposed algorithm are in harmony with the real results.

Keywords. Orthogonal Functions, Block-Pulse Functions, Observers.

References

[1] Chi-Tsong CHEN, Linear System Theory and Design. USA: CBS Publishing, 1984.

[2] F. M. BRASCH and J. B. PEARSON, "Pole Placement Using Dynamic Compensators,"

IEEE Transactions on Automatic Control, vol. AC-15, pp. 34-43, 1970.

[3] K. J. ASTRÖM and B. WITTERMARK, Adaptive Control. USA: Addison Wesley

Publication Inc., 1989.

[4] O. REILLY, Observers for Linear Systems. London, UK: Academic Press, 1983.

[5] K. R. PALASINAMY and D. K. BHATTACHARYA, "System identifications via block-

pulse functions," International Journal of System Science, vol. 12, no. 5, pp. 643-647,

1981, DOI: 10.1080/00207728108963772.

[6] Bing CHENG and Ning-Show HSU, "Single-input-single-output system identification via

block-pulse functions," International Journal of Systems Science, vol. 13, no. 6, pp. 697-

702, 1982, DOI: 10.1080/00207728208926380.

[7] C. P. KWONG and C. F. CHEN, "Linear feedback system identification via block-pulse

functions," International Journal of System Science, vol. 12, no. 5, pp. 635-642, 1981,

DOI: 10.1080/00207728108963771.

362


241 Rsc. Assist. Bashkim Trupaj University of Prishtina 242 Rsc. Assist. Banu Pazar Varol Kocaeli University 243 Rsc. Assist. Behar Baxhaku University of Prishtina 244 Rsc. Assist. Bengi Yıldız Bilecik Seyh Edebali University 245 Rsc. Assist. Beste Madran Yeditepe University 246 Rsc. Assist. Burim Kamishi University of Prishtina 247 Rsc. Assist. Cansu Keskin Dumlupinar University 248 Rsc. Assist. Dilek Bayrak Karadeniz Teknik University 249 Rsc. Assist. Duygu Dönmez Demir Celal Bayar University 250 Rsc. Assist. Ece Yetkin Marmara University 251 Rsc. Assist. Edmond Aliaga University of Prishtina 252 Rsc. Assist. Elçin Gökmen Muğla Sıtkı Koçman University 253 Rsc. Assist. Elver Bajrami University of Prishtina 254 Rsc. Assist. Eray Yıldırım Sakarya University 255 Rsc. Assist. Esra Altıntaş Marmara University 256 Rsc. Assist. Fatih Temiz Yildiz Technical University 257 Rsc. Assist. Faton Merovci University of Prishtina 258 Rsc. Assist. Fisnik Aliaj University of Prishtina 259 Rsc. Assist. Gazmend Nafezi University of Prishtina 260 Rsc. Assist. Gönül Yazgan Sağ Gazi University 261 Rsc. Assist. Gül Güner Karadeniz Teknik University 262 Rsc. Assist. Gülsüm Biçer Aksaray University 263 Rsc. Assist. Hakan Kızmaz Sakarya University 264 Rsc. Assist. Hatice Parlatıcı Sakarya University 265 Rsc. Assist. Hatice Topcu Nevşehir University 266 Rsc. Assist. Hazim Misini University of Prishtina 267 Rsc. Assist. Hidayet Hüda Kösal Sakarya University 268 Rsc. Assist. İlkem Turhan Dumlupinar University 269 Rsc. Assist. İlknur Koca Gaziantep University 270 Rsc. Assist. İrfan Deli Kilis 7 Aralık University 271 Rsc. Assist. Kajtaz Bllaca University of Prishtina 272 Rsc. Assist. Kısmet Kasapoğlu Trakya University 273 Rsc. Assist. Kushtrim Podrimqaku University of Prishtina 274 Rsc. Assist. Mahmut Mak Ahi Evran University 275 Rsc. Assist. Mehmet Altay Ünal Ankara University 276 Rsc. Assist. Mehmet Fatih Karaaslan Yildiz Technical University 277 Rsc. Assist. Merve Görgülü Karamanoğlu Mehmetbey University 278 Rsc. Assist. Mesut Balıbey Tunceli University 279 Rsc. Assist. Nejla Gürefe Gazi University 280 Rsc. Assist. Nihat Yağmur Erzincan University 281 Rsc. Assist. Nurten Bayrak Yildiz Technical University 282 Rsc. Assist. Oğuzhan Bahadır Corum Hitit University 283 Rsc. Assist. Okan Kuzu Ahi Evran University 284 Rsc. Assist. Osman Zeki Okuyucu Bilecik Seyh Edebali University 285 Rsc. Assist. Önder Gökmen Yıldız Bilecik Seyh Edebali University 286 Rsc. Assist. Övgü Gürel Ankara University 287 Rsc. Assist. Pınar Güner Marmara University 288 Rsc. Assist. Seda Göktepe Yildiz Technical University 289 Rsc. Assist. Sefer Avdiaj University of Prishtina

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