Mathematical methods in engineering PDF
Preview Mathematical methods in engineering
MATHEMATICALMETHODS IN ENGINEERING Mathematical Methods in Engineering Edited by K. TA(cid:249) Çankaya University, Balgat-Ankara, Turkey J.A. TENREIRO MACHADO Institute of Engineering of Porto Porto, Portugal and D. BALEANU Çankaya University, Balgat-Ankara, Turkey AC.I.P. Catalogue record for this book is available from the Library of Congress. ISBN-10 1-4020-5677-X (HB) ISBN-13 978-1-4020-5677-2 (HB) ISBN-10 1-4020-5678-8 (e-book) ISBN-13 978-1-4020-5678-9 (e-book) Published by Springer, P.O. Box 17, 3300 AADordrecht, The Netherlands. www.springer.com Printed on acid-free paper All Rights Reserved © 2007 Springer No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Contents Preface ix Fractional mathematics Fractional calculus and regularized residue of infinite dimensional space 3 Asada Akira Fractional spaces generated by the positive differential and difference operators in a Banach space 13 Allaberen Ashyralyev Sub-diffusion equations of fractional order and their fundamental solutions 23 Francesco Mainardi, Antonio Mura, Gianni Pagnini and Rudolf Gorenflo Neutrices and generalized functions The composition and neutrix composition of distributions 59 Brian Fisher A review on the products of distributions 71 C.K. Li Some remarks on the incomplete gamma function 97 Emin O¨zc¸a˘g, I˙nci Ege, Ha¸smet Gu¨rc¸ay and Biljana Jolevska-Tuneska Boundary value problems One-dimensional wave propagation in functionally graded cylindrical layered media 111 Ibrahim Abu-Alshaikh v vi Contents Piecewise constant control of boundary value problem for linear impulsive differential systems 123 J.O. Alzabut On nonlocal boundary value problems for hyperbolic-parabolic equations 131 Allaberen Ashyralyev and Yildirim Ozdemir On asymptotical behavior of noises solution of Riccati equation arising in linear filtering with shifted noises 141 Agamirza E. Bashirov and Zeka Mazhar Isomorphism classes of ordinary elliptic curves over fields of characteristic 3 151 Murat Cenk and Ferruh O¨zbudak Hidden symmetries of two dimensional superintegrable systems 159 O¨zlem Defterli and Dumitru Baleanu A fourth order accurate difference-analytical method for solving Laplace’s boundary value problem with singularities 167 A.A. Dosiyev and S. Cival Buranay Modeling of PDE processes with finite dimensional non-autonomous ODE systems 177 Mehmet O¨nder Efe On solutions of discrete nonlinear elliptic boundary value problems 189 Gusein SH. Guseinov Some exact solutions of the (2 + 1)-dimensional Kadomtsev- Petviashvili equation 197 E.V. Krishnan Varadhan estimates without probability: lower bound 205 R´emi L´eandre Dirichlet problem for orthotropic bounded cylinder with combined boundary conditions 217 Raid Al-Momani and Khalid Al-Momani A numerical analysis of variational finite difference schemes for steady state heat conduction problems with discontinuous coefficients 223 Ebru Ozbilge Contents vii On the solution of a mathematical model of a viscoelastic bar 233 Arpad Taka´ci and Djurdjica Taka´ci Dynamics of wall bounded flow 243 Ozan Tu˘gluk and Hakan I. Tarman Applications of wavelets Wavelet transform for the simultaneous prediction of the colorants in food product 257 Hakan A. Akta¸s, Erdal Din¸c, Gu¨zide Pekcan, O¨zgu¨r U¨stu¨nda˘g and Aysegu¨l Ta¸s A review on the wavelet transform applications in analytical chemistry 265 Erdal Din¸c and Dumitru Baleanu Continuous wavelet analysis for the ratio signals of the absorption spectra of binary mixtures 285 Erdal Din¸c, Dumitru Baleanu and Kenan Ta¸s Improved incremental self-organizing map for the segmentation of ultrasound images 293 Zafer I˙¸scan, Zumray Dokur and Tamer O¨lmez An application of continuous wavelet transform to electrochemical signals for the quantitative analysis 303 I˙ncilay Su¨slu¨, Erdal Din¸c and Sacide Altin¨oz The threshold of compression in wavelet transform with Haar’s coefficients – numerical examples 315 Zlatko Udovicic Dynamical systems and control theory 3-D Computerized ionospheric tomography with random field priors 325 Orhan Arikan, Feza Arikan and Cemil B. Erol Comparison of fuzzy and Volterra series nonlinear system modeling approaches 335 Musa H. Asyali and Musa Alci Novel hardware-orientedalgorithms for TDOA positioning technique in cellular networks 347 E. Doukhnitch, M. Salamah and A. Sandouka viii Contents Unknown costs in a duopoly with differentiated products 359 Fernanda A. Ferreira, Fla´vio Ferreira and Alberto A. Pinto Bayesian price leadership 371 Fernanda A. Ferreira, Fla´vio Ferreira and Alberto A. Pinto Comparison of methodologies in river flow prediciton. The Paiva river case 381 Rui Gonc¸alves, Alberto Pinto and Francisco Calheiros A XY spin chain models on space curves and analogy with Kirchhoff rods 391 Georgi G. Grahovski and Rossen Dandoloff Approximate controllability of one-dimensional SDE driven by countably many Brownian motions 403 N.I. Mahmudov and M.M. Matar Synchronization between neuronal spiking activity and sub-threshold sinusoidal stimuli based on the FitzHugh-Nagumo model 415 Mahmut Ozer and Muhammet Uzuntarla A characterizationof the dynamics of Newton’s derivative 423 Mehmet O¨zer, A. Valaristos, Yasar Polatoglu, Gu¨rsel Hacibekiroglu, Antanas Cˇenys and A.N. Anagnostopoulos Dissipative solitons and nonlinear resonance dynamics in 2+1 dimensions 435 Oktay Pashaev Implementation of floating point arithmetics using an FPGA 445 Suhap Sahin, Adnan Kavak, Yasar Becerikli and H. Engin Demiray A method for the recovery of the electric field vibration inside vertical inhomogeneous anisotropic dielectrics 455 Valery Yakhno and Ali Sevimlican Author index 467 Preface This book contains some of the contributions under five main titles that are carefully selected according to the reports of referees, presented at the Inter- nationalSymposium, MME06MathematicalMethods in Engineering,heldin C¸ankaya University, Ankara, April 27–29,2006. The Symposium provided a setting for discussing recent developments in Fractional Mathematics, Neutrices and Generalized Functions, Boundary Value Problems, Applications of Wavelets, Dynamical Systems and Control Theory. ThemembersoftheorganizingcommitteewereDumitruBaleanu,Ronald A.DeVore,J.A.TenreiroMachado,AliH.NayfehandKenanTas(Chairman). LecturersoftheSymposiumwereOmP.Agrawal,BrianFisher,J.A.Tenreiro Machado, Francesco Mainardi, Hans J. Stetter. The editors of this book are grateful to the President of the board of trusteesofC¸ankayaUniversitySitkiAlp,totheRectorProf.Dr.ZiyaAkta¸sfor their continuous support of the Symposium activities. We are also obliged to theTUBITAK(TheScientificandTechnologicalResearchCouncilofTurkey) for their co-sponsorship. Wewouldliketothankalltherefereesandothercolleagueswhohelpedin preparingthisbookforpublication.Ourthanksarealsoduetoallparticipants for their contributions to the Symposium and to this book. TheOrganizingCommitteewishestoexpresstheirthankstoProf.Dr.Emel Dogramaci, Dean of the Faculty of Arts and Science and to the colleagues of theDepartmentofMathematicsandComputerScienceofC¸ankayaUniversity: A. Eris, F. Kumsel, M. Cenk, A. Bilgen, H. Baydar, Ozlem Defterli and A. Kabarcik who provided valuable work during the Symposium, and to our students: C. Acar, S. Arik, M.T. Dinc, K. Dogan, K.U. Aydin, R. Cebe, S. Ozsahin, B. Tasar, H. Hatipoglu, Y. Kaya,I.N. Ekim for their assistance. Our special thanks are due to Nathalie Jacobs and Anneke Pot from Springer-Verlag for their continuous help and work in connection with this book. Finally, we would like to express our gratitude to Isil Gence, web master of the Symposium. Ankara, August 8, 2006 Kenan Tas, J.A. Tenreiro Machado, Dumitru Baleanu Editors ix Fractional Mathematics
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