2nd INTERNATIONAL EURASIAN

CONFERENCE ON

MATHEMATICAL SCIENCES AND

APPLICATIONS

PROCEEDING BOOK

26-29 AUGUST 2013 SARAJEVO, BOSNIA and HERZEGOVINA

IV

HHONORARY COMMITTEE

Professor Muzaffer ELMAS (Sakarya University Rector)

Professor Özer ÇINAR (International University of Sarajevo Rector)

Professor Sezer Şener KOMSUOĞLU (Kocaeli University Rector)

Professor Azmi ÖZCAN (Bilecik Seyh Edebali University Rector)

V

SSCIENTIFIC COMMITTEE

Professor H. Hilmi HACISALİHOĞLU (Bilecik Şeyh Edebali University)

Professor Fikret ALIYEV (Bakü State University)

Professor İsmail KOCAYUSUFOĞLU (International University of Sarajevo)

Professor Nurlan M. TEMIRBEKOV(Rector, Ust-Kamenogorsk University)

Professor Harry MILLER (International University of Sarajevo)

Professor Ekrem SAVAŞ (İstanbul Commerce University)

Professor Ravi P. AGARWAL (Texas University)

Professor İrfan ŞİAP (Yıldız Technical University)

Professor Muharem AVDISPAHIC (International University of Sarajevo)

Professor Halis AYGÜN (Kocaeli University)

Professor Senada KALABUSIC (International University of Sarajevo)

Professor Mustafa KULENOVİC (University of Rhode Island)

Professor Müjgan TEZ (Marmara University)

Professor Mirna DZAMONJA (University of East Anglia)

Professor Branko CURGUS (Western Washington University)

Professor Baki KARLIĞA (Gazi University)

Professor Mirjana VUKOVIC (International University of Sarajevo)

Professor Mehmet CAN (International University of Sarajevo)

Professor Cihan ORHAN (Ankara University)

Professor Nargozy DANAEV (Al-Farabi Kazakh National University)

Professor Serpil PEHLİVAN (Süleyman Demirel University)

VI

Professor Josip PECARIC (University of Zagreb)

Professor J. Marshall ASH (DePaul University)

Professor Martin BUNTINAS (Loyola University)

Professor Jeff CONNOR (Ohio University)

Professor Kazım İLARSLAN (Kırıkkale University)

Professor Altay BORABAYEV (Kyrgyz National University)

Professor Billy E. RHOADES (Indiana University)

Professor Varga KALANTAROV (Koç University)

Professor Graham BENNETT (Indiana University)

Professor H. Hüseyin UĞURLU (Gazi University)

Professor Prasanna SAHOO (University of Louisville)

Professor Pascal WEIL (Universite Paris VII)

Professor Peter DANCHER (Plovdiv State University)

Professor A. Aziz ERGÜN (Akdeniz University)

Professor Paul HUMKE (St. Olaf University)

Professor Michael EVAN (Washington and Lee University)

Professor Boris GULAS (University of Zagreb)

Professor Levent KULA (Ahi Evran University)

Professor Gerasimos LADAS (University of Rhode Island)

Professor Neşet AYDIN (Çanakkale Onsekiz Mart University)

Professor Adam J. OSTASZEWSKI (London School of Economics and Political Science)

Professor Sait HALICIOĞLU (Ankara University)

Professor Nihal YILMAZ ÖZGÜR (Balikesir University)

VII

Professor Bayram ŞAHİN (İnönü University)

Professor Viorel BARBU (“Alexandru Ioan Cuza” University)

Professor Uğur DURSUN (İstanbul Technical University)

Professor Vladimir BALAN (University Politehnica of Bucharest)

Professor Abdullah ALTIN (Ankara University)

Professor Sotiris K. NTOUYAS (University of Ioannina)

Professor Mustafa ÇALIŞKAN (Gazi University)

Professor Fritz COLONİUS (University of Augsburg)

Professor Ömer AKIN (TOBB University of Economics and Technology)

Professor Themba DUBE (University of South Africa)

Professor Arif SALIMOV (Atatürk University)

Professor Vasyl USTIMENKO (University of Maria Curiwe Sklodowska)

Professor Emine MISIRLI (Ege University)

Professor Norbert HOUNKONNOU (University of Abomey-Calavi)

Professor Jawad ABULLAIL (King Fahd University of Petroleum and Minerals)

Professor Jerry Lloyd BONA (University of Illinois at Chicago)

Professor Enrique ZUAZUA (Basque Center for Applied Mathematics)

Professor A. Göksal AĞARĞÜN (Yıldız Technical University)

Professor Muhammad Aslam NOOR (COMSATS Institute of Information Tecnology)

Professor Wolfgang SPROESSİG (Technical University of Mining Academy Freiberg)

Professor Wieslaw PLESNIAK (Jagiellonian University)

Professor A. Ceylan ÇÖKEN (Süleyman Demirel University)

Professor Constantin UDRISTE (University Politehnica of Bucharest)

VIII

Professor Marcelo Moreira CAVALCANTI (State University of Maringa)

Professor Donal O'REGAN (National University of Ireland)

Professor Murat ALTUN (Uludağ University)

Professor Wojciech ZAJACZKOWSKI (Military University of Technology)

Professor Etibar PANAKHOV (Fırat University)

Professor Ali Bülent EKİN (Ankara University)

Professor Ali AKHMEDOV (Bakü State University)

IX

OORGANIZING COMMITTEE

Professor H. Hilmi HACISALİHOĞLU (Bilecik Seyh Edebali University)

Professor Murat TOSUN (Sakarya University)

Professor İsmail KOCAYUSUFOĞLU (International University of Sarajevo)

Professor Nuri KURUOĞLU (Bahcesehir University)

Professor Fikret ALİYEV (Baku Satate University)

Professor Halis AYGÜN (Kocaeli University)

Professor Mahmut ERGÜT (Firat University)

Professor Yusif GASİMOV (Baku Satate University)

Professor Yusuf YAYLI (Ankara University)

Professor İbrahim OKUR (Sakarya University)

Professor Harry MILLER (International University of Sarajevo)

Professor Levent KULA (Ahi Evran University)

Professor Kazim İLARSLAN (Kırıkkale University)

Professor Cengizhan MURATHAN (Uludağ University)

Professor Gabit X. MUKHAMEDIYEV

Associate Professor Florim ISUFI (University of Prishtina)

Associate Professor Soley ERSOY (Sakarya University)

Associate Professor Qendrim GASHI (University of Prishtina)

Associate Professor Mehmet Ali GÜNGÖR (Sakarya University)

X

Associate Professor Pepic MEDO (University of Sarajevo)

Associate Professor Hatice Gül İNCE İLARSLAN (Gazi University)

Associate Professor Huse FATKIC (International University of Sarajevo)

Associate Professor Mehmed NURKANOVIC (University of Tuzla)

Associate Professor Melek MASAL (Sakarya University)

Associate Professor Alica MILLER (University of Louisville)

Associate Professor Kamile ŞANLI KULA (Ahi Evran University)

Associate Professor Hamid KULOSMAN (University of Lousville)

Associate Professor Şevket GÜR (Sakarya University)

Assistant Professor Lejla MILLER (International University of Sarajevo)

Assistant Professor Murat SARDUVAN (Sakarya University)

Assistant Professor Emrah Evren KARA (Düzce University)

Assistant Professor Mahmut AKYİĞİT (Sakarya University)

Assistant Professor Ergin JABLE (University of Prishtina)

Assistant Professor Ercan MASAL (Sakarya University)

Assistant Professor Ayşe Zeynep AZAK (Sakarya University)

Assistant Professor Mehmet GÜNER (Sakarya University)

XI

SSECRETARIAT

Professor Murat TOSUN (Sakarya University)

Lecturer Muhsin ÇELİK (Sakarya University)

Lecturer Selman HIZAL (Sakarya University)

Lecturer Doğan ÜNAL (Sakarya University)

Research Assistant Hidayet Hüda KÖSAL (Sakarya University)

Research Assistant. Tülay SOYFİDAN (Sakarya University)

Research Assistant Hatice PARLATICI (Sakarya University)

XIII

CONTENTS

INVITED TALKS On Biharmonic Legendre Curves in S-Space Forms and Generalized Sasakian Space Forms 1 C. Özgür

Small Gaps between Primes 2 C. Y. Yıldırım

On Generalized Sequence Spaces via Modulus Function and A- Statistical Convergence 3 E. Savaş

Hidden Attractors in Dynamical Systems: Fundamental Problems and Applied Models 5 G. A. Leonov, N. V. Kuznetsov, S. M. Seledzhi

Parseval Frame Wavelets 8 H. Šikić

Geometric Modeling with Curves and Surfaces in Euclidean Spaces 11 K. Arslan

Two Pillars of Probability Theory 12 N. H. Bingham

Analogues of Some Tauberian Theorems for Bounded Variation 13 R. F. Patterson

Fuzzy Logic Control in Perspective A 50-Year History 14 R. Langari

Quaternionic and Clifford Analysis in Applications 15W. Sproessig

ALGEBRA

A New Study on Generalized Intuitionistic Fuzzy Subhyperalgebras of Boolean Hyperalgebras 16 B. A. Ersoy, S. Onar, K. Hila, B. Davvaz

Primitive Sets of nF R Lie Algebras 17 C. Eskal, N. Ekici

Crossed Modules of Commutative Algebras and Whiskered R-Algebroids 18 Ç. Ataseven, E. Ulualan

IECMSA-2013 2nd International Eurasian Conference on Mathematical Sciences and Applications

About one Method to Solve of Finite-Difference Equations of Incompressible Fluid in 436 Variables«Stream Function, Vorticity»N. T. Danaev, F. S. Аmenova

Spinor Frenet Equations in three Dimensional Lie Groups 438O. Z. Okuyucu, Ö. G. Yıldız , M. Tosun

Inextensible Flows of Curves in Lie Groups 439Ö. G. Yıldız, O. Z. Okuyucu

On Classification of Binary and Ternary Number Systems for Imaginary Quadratic Rings and 440 Their Applications P.S. Bogdanov, V.M. Chernov

Explicit Solution of Hydrogen Atom Equation via Fractional Calculus Operators 441R. Yılmazer, N. Çatalbaş, E. Baş

A Simple Approach for Estimation of Dynamic State Variable by Using Taylor Series 442 Approximation S. Aksoy, H. Kızmaz

State Variables Computational Technique for Linear Systems by Leguerre Series 444Approximation S. Aksoy, H. Kızmaz

On Some Combinatorial Identities Involving the Terms of Generalized Fibonacci and Lucas 446 SequencesS. Halıcı, Z. Akyüz

Weighted Quadrature Rules via Grüss Type Inequalities for Weighted LP Spaces 447S. Tipuric-Spuzevic, A. A. Aljinovic, J. Pecaric

Comparison Efficiency of Medium, Median and Geometric Medium at Evaluation of 448 Microbiological Analysis Results of Foods Ş. Uğuz, F. N. Çoksöyler

Constant Angle Spacelike Surface in de Sitter Space 449T. Mert, B. Karlığa

New Modified Trial Equation Method and its Application 451Y. A. Tandoğan, Y. Pandır

Some New Multiplicative Numerical Methods 452Y. Gürefe, E. Mısırlı

A Multiple Extended Trial Equation Method for Nonlinear Physical Problems 453Y. Pandır, Y. Gürefe, E. Mısırlı

Magnetic Curves on Sasakian Manifolds 454Z. Bozkurt, İ. Gök, F. N. Ekmekci, Y. Yaylı

Parameter Estimation Based Type-II Fuzzy Logic where the Independent Variables from 455 Pareto Distribution T. E. Dalkılıç, K. Ş. Kula, L. Kula

XXXVI

State Variables Computational Technique for Linear Systems by Leguerre Series

Approximation

Saadettin Aksoy1 and 2

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 required. Furthermore, estimation of state variables in real time is a very

important problem in adaptive control applications [3]. Unfortunately, all of the state variables

cannot be measured in practice. As a result, usage of a suitable state observer or estimator is

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

observers in the literature [4]. The gain matrix G, which is necessary for state observer, can be

calculated by using one of the methods such as Ackerman, Bass Gura etc. [4].

The Laguerre series are defined on the interval t [0, ) and have the orthogonal

property like the Walsh, Chebyshev and Legendre series [5,6]. The proposed algorithm uses

some important properties such as the operational matrix of integration for Laguerre vector

[7-9].

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

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

systems. The proposed algorithm is based on the Laguerre series approximation and has an

analog solution. Hence, it is not affected by rounding errors. As a consequence, accuracy is

not a function of the step size. The proposed method gives the approximate solution of the

estimation vector )t(x̂ as a function of time in the interval t [0, ).

The algorithm consists 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, is determined by using a

suitable method [4]. In the second step, the state and error equations are converted into

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

state and error vectors together with the Laguerre series approximation of known input

vectors are substituted in the integral equations. After some algebraic manipulations, the time

dependent terms on either side of the integral equations are removed. Finally, the nonlinear

equations are converted into a recursive form whose solution can be obtained easily by a

1Sakarya University, Sakarya, Turkey, saksoy@sakarya.edu.tr2Sakarya University, Sakarya, Turkey, hkizmaz@sakarya.edu.tr

computer program. Unknown series expansion coefficients for estimation of state variables

vector are easily calculated.

The proposed estimation algorithm was implemented in MATLABTM and it was

applied to different cases. Results obtained by the proposed algorithm are in harmony with the

real results.

Keywords. State estimation, Laguerre series, state observers.

References

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

[2] Brasch, F.M., and Pearson, J.B., Pole Placement Using Dynamic Compensators, IEEE Trans. Automatic Control, AC -15, 1970, pp. 34-43.

[3] Aström, K.J., and Wittermark, B., Adaptive Control, Addison–Wesley Pub. Inc., USA,1989.

[4] O. Reilly, J., Observers for Linear Systems, London Academic Press, London, 1983.

[5] G. Sansone, Orthogonal Functions, Interscience Publishers, Inc., New York, 1991.

[6] Cheng-Chilan Liu and Y. P. Shih, Analysis and Optimal Control of Time-Varying Systems Via Chebyshev Polynomials, Int. J. Control, Vol. 38, No. 5, 1983, pp. 1003-012.

[7] Hwang, C., and Shih, Y.P., Laguerre Operational Matrices for Fractional Calculus and Applications, Int. J. Control, Vol. 34, No. 3, 1981, pp. 577-584.

[8] Chyi Hwang and Y. P. Shih, Parameter Identification Via Laguerre Polynomials, Int. J. Systems Sci., Vol. 13, No. 2, 1982, pp. 209-217.

[9] M. H. Perng, Laguerre Polynomials analysis in Optimal Control Systems Incorporating Observers, Int. J. Control, Vol. 44, No. 1, 1986, pp. 43-48.

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PARTICIPANTS

1 Prof. Dr. Abdullah Aziz Ergin Akdeniz University2 Prof. Dr. Ataturk University3 Prof. Dr. Aibat Rafhatuly Yeshkeyev Karaganda State University Named After E. A. Buketov4 Prof. Dr. Ants Aasma Tallinn University of Technology5 Prof. Dr. Arif Salimov Ataturk University6 Prof. Dr. Auzhan Sakabekov Kazakh-British Technical University7 Prof. Dr. Gazi University8 Prof. Dr. Pamukkale University9 Prof. Dr. Ankara University10 Prof. Dr. Azer Hanmehmetli Hacettepe University11 Prof. Dr. Azmi Özcan Bilecik Seyh Edebali University12 Prof. Dr. Gazi University13 Prof. Dr. Inonu University14 Prof. Dr. Bilal Altay Inonu University15 Prof. Dr. Bogazici University16 Prof. Dr. Cengizhan Murathan Uludag University17 Prof. Dr. Cihan Orhan Ankara University18 Prof. Dr. Cihan Özgür Balikesir Üniversitesi19 Prof. Dr. Istanbul Commerce University,20 Prof. Dr. Hacettepe University21 Prof. Dr. Ege University22 Prof. Dr. Erol Balkanay23 Prof. Dr. Essin Turhan24 Prof. Dr. Etibar Panakhov25 Prof. Dr. F. Nafi Çoksöyler Yuzuncu Yil University26 Prof. Dr. Fethi Çallialp Dogus University27 Prof. Dr. Gennady A. Leonov State University Of Saint-Petersburg28 Prof. Dr. Ankara University29 Prof. Dr. Bilecik Seyh Edebali University30 Prof. Dr. Halit Orhan Ataturk University31 Prof. Dr. Harry I. Miller International University of Sarajevo32 Prof. Dr. Trakya Üniversitesi33 Prof. Dr. Mevlana University34 Prof. Dr. Hrvoje Sikic University Of Zagreb35 Prof. Dr. Yildiz Technical University36 Prof. Dr. Jenaliyev T. Muvasharkhan Inst. of Math. and Math. Modeling37 Prof. Dr. Juergen Batt Munich University38 Prof. Dr. Kadri Arslan Uludag University39 Prof. Dr. Kirikkale University40 Prof. Dr. Kazim Hasanov Baku State University41 Prof. Dr. Kil Hyun Kwon Korea Advanced Institute of Science and Technology42 Prof. Dr. Latifa Agamalieva Baku State University43 Prof. Dr. Laura Ventura Department Of Statistics, University of Padova44 Prof. Dr. Leili Kussainova L.N. Gumilyov Eurasian National University45 Prof. Dr. Levent Kula Ahi Evran University46 Prof. Dr. Lubica Hola Math. Inst. Slovak Academy of Sciences47 Prof. Dr. Mahmut Ergüt Firat University48 Prof. Dr. Maksat N. Kalimoldayev Inst. of Problems of Informatics and Control49 Prof. Dr. Mao-Ting Chien Soochow University50 Prof. Dr. Mikail Et Firat University

321 Rsc. Assist. Middle East Technical University322 Rsc. Assist. Elçin Gökmen Mugla Sitki Kocman University323 Rsc. Assist. Marmara University324 Rsc. Assist. Ankara University325 Rsc. Assist. Faik Gürsoy Yildiz Technical University326 Rsc. Assist. Fatma Gökçelik Ankara University327 Rsc. Assist. Uludag University328 Rsc. Assist. Fatma Peker Erciyes University329 Rsc. Assist. Fatmanur Gürsoy Yildiz Technical University330 Rsc. Assist. Erciyes University331 Rsc. Assist. Gökhan Çelebi Anadolu University332 Rsc. Assist. Mugla Sitki Kocman University333 Rsc. Assist. Gülden Altay Firat University334 Rsc. Assist. Gülseli Burak Pamukkale University335 Rsc. Assist. Suleyman Demirel University336 Rsc. Assist. Ankara University337 Rsc. Assist. Sakarya University338 Rsc. Assist. Yildiz Technical University339 Rsc. Assist. Hatice Aslan Firat University340 Rsc. Assist. Sakarya University341 Rsc. Assist. Hidayet Hüda Kösal Sakarya University342 Rsc. Assist. Hüseyin Albayrak Suleyman Demirel University343 Rsc. Assist. Erzurum Technical University344 Rsc. Assist. Yildiz Technical University345 Rsc. Assist. Ankara University346 Rsc. Assist. Uludag University347 Rsc. Assist. Kadir Emir Osmangazi University348 Rsc. Assist. Kadirhan Polat Ataturk University349 Rsc. Assist. Kadriye Aydemir Gaziosmanpasa University350 Rsc. Assist. Bilecik Seyh Edebali University351 Rsc. Assist. Dumlupinar University352 Rsc. Assist. Mehmet Fatih Karaaslan Yildiz Technical University353 Rsc. Assist. Mehmet Gülbahar Inonu University354 Rsc. Assist. Mehmet Ünver Ankara University355 Rsc. Assist. Ankara University356 Rsc. Assist. Necmettin Erbakan University357 Rsc. Assist. Ataturk University358 Rsc. Assist. Yildiz Technical University359 Rsc. Assist. Müzeyyen Ertürk Yildiz Technical University360 Rsc. Assist. Naime Tozlu Nigde University361 Rsc. Assist. Nazan Çakmak Mugla Sitki Kocman University362 Rsc. Assist. Nejla Gürefe Gazi University363 Rsc. Assist. Mehmet Akif Ersoy University364 Rsc. Assist. Selcuk University365 Rsc. Assist. Erzincan University366 Rsc. Assist. Nilüfer Köse Anadolu University367 Rsc. Assist. Nurten Bayrak Gürses Yildiz Technical University368 Rsc. Assist. Yuzuncu Yil University369 Rsc. Assist. Bilecik Seyh Edebali University370 Rsc. Assist. Özlem Öksüzer Ankara University371 Rsc. Assist. Celal Bayar University372 Rsc. Assist. Rabia Çakan Ataturk University373 Rsc. Assist. Ramazan Ekmekçi Canakkale Onsekiz Mart University374 Rsc. Assist. Rukiye Öztürk Ataturk University

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