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Nonlinear Algebraic Analysis and Applications 
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Hb       350pp     2004

Proceedings of The International Conference on Generalized Functions (ICGF 2000)



A.Delcroix, M.Hasler, J-A.Marti, V.Valmorin

University of French West Indies

This volume is a collection of refereed and edited papers originally presented at the International Conference on Generalized Functions (ICGF 2000) and provides a useful source of reference for graduates and researchers in mathematics and applied subjects. The papers are presented in four sections:

Section I: Theoretical Structures collects different viewpoints of algebraic and topological aspects  of generalized functions

Section II: Integral and Partial Differential Equations includes:

-results of existence, uniqueness and stability

-asymptotic methods

-analysis and propagation of singularities

Section III: Geometry and Applications includes work on the manifold structure of generalized functions

Section IV: Application to Numerical Analysis covers numerical algorithms



978-1-904868-31-2

A Short Course in Differential Geometry and Topology 
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Hb       350pp      2008

A.T.Fomenko and A.S.Mishchenko

Moscow State University, Russia

 

This volume is intended for graduate and research students in mathematics and physics. It covers general topology, nonlinear co-ordinate systems, theory of smooth manifolds, theory of curves and surfaces, transformation groups, tensor analysis and Riemannian geometry, theory of integration and homologies, fundamental groups and variational principles in Riemannian geometry. The text is presented in a form that is easily accessible to students and is supplemented by a large number of examples, problems, drawings and appendices.



978-1-904868-32-3

Selected Problems in Differential Geometry and Topology 
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Hb       350pp      2013

A.T.Fomenko, A.S.Mischenko and Y.P.Solovyev

Moscow State University, Russia

 

This volume is intended as a supplementary text for a course on differential geometry and topology and other courses in mathematics, physics and mechanics for graduate students specializing in mathematics and applied fields.  The volume is divided into two parts. Part I includes problems prescribed in standard courses of geometry and topology. Part II contains problems intended for a more profound grasp of modern geometry and its applications.



978-1-904868-33-9

Handbook of Mellin Transforms 
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800pp  Hbk     2014

 



A.A.Kilbas and A.A.Prudnikov, Belarusian State University, Minsk

 

This volume presents the tables of formulae for the evaluation of Mellin Transforms of elementary and special functions. The Handbook includes some formulae obtained by the authors and published for the first time. The tables are prefaced by a summary of notation for special functions and certain constants. The appendix  contains some properties of the Mellin transform and applications.  The results in tables are important for applications in different areas of mathematics, physics, mechanics, engineering, chemistry, biology and other applied sciences. The Handbook is a useful source of reference for graduate students and researchers.



978-1-904868-40-8

Topological Methods in the Theory of Integrable Systems 
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300pp  Hbk   2006

A.V.Bolsinov,  A.T.Fomenko and A.A.Oshemkov, Moscow State University, Russia

 

This volume comprises selected papers on the subject of the topology of integrable systems theory which studies their qualitative properties, singularities and topological invariants. The aim of this volume is to develop the classification theory for integrable systems with two degrees of freedom which would allow for distinguishing such systems up to two natural equivalence relations. The first one is the equivalence of the associated foliations into Liouville tori. The second is the usual orbital equivalence. Also, general methods of classification theory are applied to the classical integrable problems in rigid body dynamics. In addition,  integrable geodesic flows on two-dimensional surfaces are analysed from the viewpoint of the topology of integrable systems.  

978-1-904868-42-8

Theory of Set Differential Equations in Metric Spaces 
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250pp  Hbk    2005

V.Lakshnikantham, T.Gnana Bhaskar and J.Vasundhara Devi, Florida Institute of Technology, USA

 

The aim of this volume is to describe the theory of set differential equations (SDEs) as an independent discipline. It incorporates the recent general theory of set differential equations, discusses the interconnections between set differential equations and fuzzy differential equations  and uses both smooth and nonsmooth analysis for investigation. The study of SDEs is a rapidly growing area of mathematics and this volume provides a timely introduction to a subject that follows the present trend of studying analysis and differential equations in metric spaces. It is a useful reference text for postgraduates and researchers/nonlinear analysts, engineering and computational scientists working in fuzzy systems.

978-1-904868-46-0

The Origin and History of Mathematics 
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180pp  Pbk    2005

V.Lakshnikantham, S.Leela and J.Vasundhara Devi, Florida Institute of Technology, USA

 

This is the first book on the history of mathematics that attempts to report the immense mathematical activity and contribution of Bharat (greater India) which has been ignored in existing books. This volume also provides the true origin of mathematical knowledge correcting the existing historical distortions and rectifies the chronology of important early mathematicians of India so that priority of discovery can be properly attributed and acknowledged. The authors stress the work of the fourteenth century Indian astronomer and mathematician, Madhava, who discovered the limiting process to infinity before Newton and Leibnitz.  In this book the authors introduce a balanced view of the origin and history of mathematics by incorporating the extensive mathematical knowledge relative to the origin and continuity of mathematical research so as to present the true facts of history.

978-1-904868-47-9

Numerical Algorithms in Scientific Computing 
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2009 200pp  Pbk

X-S. Yang, University of Cambridge, UK

This book is structured in three parts: Part I: Basic Algorithms Part II: Conventional Algorithms: Part III: Unconventional Algorithms. It introduces all major numerical algorithms used in modern scientific computing with the emphasis on worked examples to show how each algorithm works. Topics include root-finding algorithms, numerical integration, solution of linear systems, interpolation, numerical solutions of ordinary differential equations and partial differential equations, cellular automata, statistical modelling, random number generation, Monte Carlo methods, function optimization and unconventional metaheuristic algorithms such as ant algorithms, harmony search and firefly algorithms. The book is intended as a text book or supplementary text and will provide a useful source of reference for students and researchers.



978-1-904868-66-8

Theory of Fractional Dynamic Systems 
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176pp   Hbk               2009

V. Lakshmikantham, S. Leela, J. Vasundhara Devi, Florida Institute of Technology, USA

This is the first book that attempts to describe the theory of fractional differential equations as an independent discipline. It incorporates the recent upsurge in the general theory of fractional differential equations, shows the interconnection between fractional differential equations and classical differential equations of integer order derivatives and uses both smooth and nonsmooth analysis for investigation. It is a timely introduction to the study of fractional differential equations that follows the classical approach and to compare and contrast the differences as well as intricacies that result in the development. It is a useful reference text for post graduates and researchers/nonlinear analysts, and engineering and computational scientists working in real world problems where fractional derivatives are involved in their modeling.



978-1-904868-64-4

The Legacy of A.Y. Khintchine's Work in Probability Theory 
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280pp   Hbk               2011

S. Rogosin, State University of Belarus, Minsk and F. Mainardi, University of Bologna, Italy

This volume describes and highlights the role of the work of the well-known Russian mathematician, Alexander Yakovlevich Khintchine (1894-1959), in the early development of modern Probability Theory. The authors present the English translations of many of the key papers and monographs by Khintchine, supplemented by comments and notes. Several important results of Khintchine’s work were previously inaccessible and so this volume provides a useful reference text for students and researchers working in this area of mathematics.



978-1-904868-65-1

Analytic Methods of Analysis and Differential Equations: AMADE 2003 
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300pp   Pbk     2006

A.A.Kilbas and S.V.Rogosin, Belarusian State University, Minsk

 

The third international conference of AMADE was held in Minsk, Belarus in September 2003 and covered key topics including integral transforms and special functions; differential equations and their applications; integral, difference, functional equations and fractional calculus; real and complex analysis. This volume comprises selected papers presented at this conference and provides a useful reference for graduates and researchers working in these areas of mathematics.

978-1-904868-41-X

Analytic Methods of Analysis and Differential Equations: AMADE 2006 
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300pp   Pbk               2008

A. A. Kilbas and S. V. Rogosin, Belarusian State University, Minsk

The fourth international conference of AMADE was held in Minsk in September 2006 and covered key topics including real and complex analysis, ordinary and partial differential equations, fractional calculus and functional equations, operator theory, potential theory as well as their applications. This volume comprises selected papers presented at the conference and provides a useful reference for graduates and researchers working in these areas of mathematics.



978-1-904868-60-6

Analytic Methods of Analysis and Differential Equations: AMADE 2009 
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2011   290pp             Pbk

Edited by A.A.Kilbas and S.V.Rogosin, State University of Belarus, Minsk

 

The fifth international conference of AMADE was held in September 2009 in Minsk, Belarus and covered key topics including integral transforms and special functions; differential equations; integral, difference, functional equations and fractional calculus; real and complex analysis; applied questions of analysis and difference equations; modern problems of mechanics. This volume comprises selected papers presented at the conference and provides a useful reference for graduates and researchers working in these areas of mathematics.



978-1-908106-13-1

Nonlinear Problems in Aviation & Aerospace ICNPAA 2002 
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Pb        550pp              2003

Edited by S.Sivasundaram, Embry-Riddle Aeronautical University, Daytona Beach, USA

 

The fourth international conference on Nonlinear Problems in Aviation and Aerospace was held in Florida Institute of Technology, USA in May 2002. This proceedings publication includes keynote addresses, invited lectures and contributed papers presented at the conference. In recent years aviation and aerospace non-linear (not necessarily linear) phenomena have stimulated cooperation between scientists from several disciplines. The developments in computer technology have also allowed for solutions of nonlinear problems. The publication includes presentations on guidance, stability and control, computational structures, multidisciplinary design, computational fluids, optimisation, reliability, validation and verification, neural networks, neuro-fuzzy control, nonlinear mechanical systems, advances in nonlinear dynamics, soft computing, modelling and simulation, intelligent control, high performance computing, structural dynamics, aero acoustics, hybrid systems and nonlinear dynamical systems.



0-9526643-3-X

Mathematical Problems in Engineering and Aerospace Sciences: ICNPAA 2004 
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800pp  Pbk    2005

S.Sivasundaram, Embry Riddle Aeronautical University, Daytona Beach, USA

 

The fifth international conference on Mathematical Problems in Engineering and Aerospace Sciences was held at University of Timisoara, Romania in June 2004. This proceedings publication includes keynote addresses, invited lectures and contributed papers presented at the conference. Mathematical problems in engineering and aerospace science have stimulated cooperation among scientists from several disciplines and developments in computer technology have led to solutions of mathematical problems. The publication includes papers on aeroacoustics, aerodynamics, computational fluid dynamics, air traffic control design, nonlinear filtering, atmospheric flight mechanics, propulsion and combustion, navigation, guidance, stability and control, neural networks, optimization, computer security and cryptography.

978-1-904868-48-7

Mathematical Problems in Engineering and Aerospace Sciences: ICNPAA 2006  
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860pp  Pbk   2007

S. Sivasundaram (ed) Embry Riddle Aeronautical University, Daytona Beach, USA

The Sixth International Conference on Mathematical Problems in Engineering and Aerospace Sciences was held at Budapest University of Technology and Economics, in June 2006. This proceedings publication reports on new ideas and research directions in engineering and aerospace sciences and comprises keynote addresses, invited lectures, and contributed papers. The volume includes papers on new trends and applications in transform theory, nonlinear flight dynamics problems: algorithm and software tools, stability in nonlinear sciences, multi disciplinary optimization, boundary value problems, optimization and simulation, air transport, operation and management, unmanned aircraft vehicles, numerical methods, region of attraction and its application to control theory, computational fluid dynamics, modeling and control in aerospace problems, fuzzy and intelligent control, unsteady flight control, reentry vehicles, stability and control, nonlinear mechanical systems.



978-1-904868-56-9

Mathematical Problems in Engineering and Aerospace Sciences: ICNPAA 2008 
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950pp  Pbk   2009

S. Sivasundaram (ed) Embry Riddle Aeronautical University, Daytona Beach, USA

The Seventh International Conference on Mathematical Problems in Engineering Aerospace and Sciences was held Genoa, in June 2008. This proceedings publication reports on new ideas and research directions in engineering and aerospace sciences and comprises keynote addresses, invited lectures, and contributed papers. The volume includes papers on new trends and applications in transform theory, nonlinear flight dynamics problems: algorithm and software tools, stability in nonlinear sciences, multi disciplinary optimization, boundary value problems, optimization and simulation, air transport, operation and management, unmanned aircraft vehicles, numerical methods, region of attraction and its application to control theory, computational fluid dynamics, modeling and control in aerospace problems, fuzzy and intelligent control, unsteady flight control, reentry vehicles, stability and control, nonlinear mechanical systems.



978-1-904868-70-5

Mathematical Problems in Engineering and Aerospace Sciences: ICNPAA 2008 CD 
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2010

S. Sivasundaram (ed) Embry Riddle Aeronautical University, Daytona Beach, USA

The complete contents now available on CD.



978-1-904868-80-4

Proceedings Of International Conference On Topology And Its Applications (ICTA 2011) 
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2012 250pp Pbk 



Alexander V.Arhangel’skii, Moiz ud Din Khan, Ljubisa D.R.Kocinac (eds)

ICTA 2011 was held in July 2011 in Islamabad, Pakistan. The aim of the conference was to review and explore some of the recent achievements in topology and to provide an opportunity for scientific exchange and interaction between scientists who work on different aspects and applications of topology. Topics include: Set Theory and Set-Theoretic Topology; General Topology; Algebraic Topology, Geometric Topology, Symplectic Topology; Continuum Theory; Asymmetric Topology; Symmetric Topology; Categorical, Point-free or Constructive Aspects of Topology; Topology on Lattices; History of Topology; Computational Topology; Applications of Topology. This volume will provide a useful reference for graduates and researchers working in this area of mathematics.

 



978-1-908106-17-9

Theory of Differential Equations in Cones 
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170pp   Hbk               2011

 

V. Lakshmikantham, Florida Institute of Technology, USA

S. Leela, State University of New York at Geneseo, USA

A.S. Vatsala, University of Louisiana at Lafayette, USA

 

This volume deals essentially with the theory of differential equations in arbitrary cones and demonstrates that developing Lyapunov method in cones greatly enhances the power of that method.  It also presents theoretical approximation methods in terms of oder relations induced by cones and shows that utilizing cones in investigating the theory of several dynamic systems is significantly more useful.

 

The monograph provides a timely introduction to the study of the theory of differential equations in cones and is a useful source of reference for graduates and researchers working in this developing area of mathematics.



978-1-904868-96-5

Pi, Epsilon, Phi, With MATLAB: Random and Rational Sequences with Scope in Supercomputing Era  
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Format: Paperback Hardback + £10.00
300pp  Hbk   2012

 

S. K. Sen and R. P. Agarwal, Department of Mathematical Sciences, Florida Institute of Technology, USA

The authors present some characters of three famous irrational numbers: pi (the area of the circle of unit radius), Epsilon (the exponential function with argument 1) and Phi (the golden ratio), along with their formulas and their variable precision computations in Matlab. They also explore the possible use and efficacy of each of these numbers as random sequence sources for solving real world problems specifically in the ultra-high speed computing era. In addition, algorithms are described for the best absolute rational approximation of these numbers and their usage in error-free computations. The concerned programs/commands are included, written in high level, user friendly, and globally available programming language Matlab. This volume is intended to be a useful reference book for students of engineering and science courses that involve numerical computations including error-free computations and those underlying evolutionary approaches/genetic and randomized algorithms for optimization and for other applications.



History of the Mathematical Sciences II  
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250pp   Hbk               2011

 

B. S. Yadav and S. L. Singh, Indian Society of Mathematics

The international conference on History of the Mathematical Sciences was organized by the Indian Society for History of Mathematics and the G. B. Pant University of Agriculture and Technology, Pant Nagar in December 2007. This volume comprises selected papers, presented at the conference, on topics relating to periods in history from Vedic times to the nineteenth and twentieth centuries and covering many cultures. Contents include:

- Lagrange’s strategy for solving algebraic equation – Anjing QU

- Evolution of the idea of Abstract Groups – Mingli Deng, Xianfen Wang

- Selection principles: history and recent development – L. D. R. Kocinac

- Karamata’s proofs of Pappus-Pascal and Desargues theorems – A. M. Nikolic

- Artin’s theory of braids and algebraization of topology – B. S. Yadav

- Turning an algebraic identity into an infinite series – K. Mahesh, R.Venketeswara Pai and K. Ramasubramanian



978-1-904868-94-1

Approximation By Singular Integrals 
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2012 250pp Hbk



G. Anastassiou and R. Mezei, University of Memphis, USA

This monograph is the first one to deal exclusively with the study of the approximation of singular integrals to the identity-unit operator. The authors study quantitatively the basic approximation properties of the general Picard, Gauss-Weierstrass and Poisson-Cauchy singular integral operators over the real line, which are not positive linear operators. In particular the authors study the rate of convergence of these operators to the unit operator, as well as the related simultaneous approximation and the global smoothness preservation property of these operators. The corresponding general approximation theory of general singular integral operators is presented with many applications to the trigonometric singular integral. For the convenience of the reader, the chapters of this book are written in a self-contained style. This monograph is intended for researchers, graduate students working in many areas of pure and applied mathematics, including mathematical analysis, probability, statistics, ordinary and partial differential equations.

 



978-1-908106-19-3

Topics In Complex Approximation 
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2012 250pp Hbk 



G. Anastassiou, University of Memphis, USA

In this monograph we study quantitatively the order of simultaneous approximation and Voronovskaja type asymptotic results for complex Bernstein-Schurer, Kantorovich-Schurer and Bernstein-Durrmeyer polynomials related to analytic functions on compact disks. In this way the overconvergence phenomenon for Bernstein-Schurer and Bernstein-Durrmeyer polynomials is revealed. We continue with explicit quantitative estimates for the overconvergence in the complex plane of the partial sums of the Fourier-type expansions on [-1, 1] with respect to Chebyshev and Legendre orthogonal polynomials. Furthermore we obtain quantitative estimates in the overconvergence phenomenon for the classical and generalized singular integrals of Gauss-Weierstrass, Poisson-Cauchy and Picard on a strip. Furthermore we present Jackson type approximation results by generalizations of multi-complex Picard, Poisson-Cauchy and Gauss-Weierstrass singular integrals in terms of higher order moduli of smoothness on polydisks. It follows quantitative estimates in the overconvergence phenomenon on polystrips, for the weighted and non-weighted cases, for generalized multicomplex singular integrals of Picard, Poisson-Cauchy and Gauss-Weierstrass types. We establish basic results concerning the best approximation of vector-valued functions by generalized polynomials. The overconvergence of singular integrals is presented for the first time in book form. This monograph is intended for researchers, graduate students working in many areas of pure and applied mathematics.

 



978-1-908106-21-6

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