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- national Symposium, MME06 Mathematical Methods in Engineering, held in 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.

This book defines the wide application of the art of modelling. The main emphasis is on the imaging of dynamic processes which are analysed and subdivided into their atomic constituents by means of systems analysis. The cyclic structure and the stages of models set-up are explained. The evaluation of a models quality is regarded as a stochastic process. The aspects of grade used in different fields of sciences are brought into perspective. Thus, a quantitative concept of validity on the basis of conditional degrees of rational belief can be developed.

The performance of a nonlinear programming algorithm can only be ascertained by numerical experiments requiring the collection and implementation of test examples in dependence upon the desired performance criterium. This book should be considered as an assis­ tance for a test designer since it presents an extensive collec­ tion of nonlinear programming problems which have been used in the past to test or compare optimization programs. He will be in­ formed about the optimal solution, about the structure of the problem in the neighbourhood of the solution, and, in addition, about the usage of the corresp,onding FORTRAN subroutines if he is interested in obtaining them -ofi a magnetic tape. Chapter I shows how the test examples are documented. In par­ ticular, the evaluation of computable information about the solu­ tion of a problem is outlined.

Contemporary epistemological and cognitive studies, as well as recent trends in computer science and game theory have revealed an increasingly important and intimate relationship between Information, Interaction, and Agency.

Agent-Based Computer Simulation of Dichotomous Economic Growth reports a project in agent-based computer stimulation of processes of economic growth in a population of boundedly rational learning agents.

The most powerful computers in the world are not only used for scientific research, defence, and business, but also in game playing. Computer games are a multi-billion dollar industry. Recent advances in computational intelligence paradigms have generated tremendous interest among researchers in the theory and implementation of games. Game theory is a branch of operational research dealing with decision theory in a competitive situation. Game theory involves the mathematical calculations and heuristics to optimize the efficient lines of play. This book presents a sample of the most recent research on the application of computational intelligence techniques in games.

This book is a collection of 20 chapters on chosen topics from cross-section and panel data econometrics. It explores both theoretical and practical aspects of selected cutting-edge techniques which are gaining popularity among applied econometricians, while following the motto of “keeping things simple”. Each chapter gives a basic introduction to one such method, directs readers to supplementary references, and shows an application. The book takes into account that—A: The field of econometrics is evolving very fast and leading textbooks are trying to cover some of the recent developments in revised editions. This book offers basic introduction to state-of-the-art techniques and recent advances in econometric models with detailed applications from various developing and developed countries. B: An applied researcher or practitioner may prefer reference books with a simple introduction to an advanced econometric method or model with no theorems but with a longer discussion on empirical application. Thus, an applied econometrics textbook covering these cutting-edge methods is highly warranted; a void this book attempts to fills.

This work is a revised and enlarged edition of a book with the same title published in Romanian by the Publishing House of the Romanian Academy in 1989. It grew out of lecture notes for a graduate course given by the author at the University if Ia~i and was initially intended for students and readers primarily interested in applications of optimal control of ordinary differential equations. In this vision the book had to contain an elementary description of the Pontryagin maximum principle and a large number of examples and applications from various fields of science. The evolution of control science in the last decades has shown that its meth­ ods and tools are drawn from a large spectrum of mathematical results which go beyond the classical theory of ordinary differential equations and real analy­ ses. Mathematical areas such as functional analysis, topology, partial differential equations and infinite dimensional dynamical systems, geometry, played and will continue to play an increasing role in the development of the control sciences. On the other hand, control problems is a rich source of deep mathematical problems. Any presentation of control theory which for the sake of accessibility ignores these facts is incomplete and unable to attain its goals.

This book presents the best papers from the 4th International Conference on Mathematical Research for Blockchain Economy (MARBLE) 2023, held in London, UK. While most blockchain conferences and forums are dedicated to business applications, product development, or Initial Coin Offering (ICO) launches, this conference focused on the mathematics behind blockchain to bridge the gap between practice and theory.

Over the course of a scientific career spanning more than fifty years, Alex Grossmann (1930-2019) made many important contributions to a wide range of areas including, among others, mathematics, numerical analysis, physics, genetics, and biology. His lasting influence can be seen not only in his research and numerous publications, but also through the relationships he cultivated with his collaborators and students. This edited volume features chapters written by some of these colleagues, as well as researchers whom Grossmann’s work and way of thinking has impacted in a decisive way.

Eva Maria Hickmann legt den Fokus auf eine didaktisch und gleichzeitig mathematisch präzise Darstellung über Differentialgleichungen als zentraler Baustein der Physik zur Beschreibung von Zuständen und Bewegungen. Die Autorin stellt die relevanten Lösungsmethoden anhand des harmonischen Oszillators, der Wellengleichung sowie der Korteweg-de-Vries-Gleichung vor. Dabei wird großer Wert auf die Vollständigkeit der Zwischenschritte gelegt, so dass diese Arbeit auch für Studierende und Lehrpersonen im Selbststudium verständlich ist.

The Eleventh International Transport Theory Conference and Symposium in honor of the sixty-fifth birthday of Kenneth Case and the sixtieth birthday of Paul Zweifel was held in Blacksburg, Virginia, during May 22-26, 1989, on the campus of Virginia Polytechnic Institute and State University (Virginia Tech). This volume consists of a selection of the invited papers delivered at the Conference, and represents a cross section of the research currently being carried out in the field of transport theory. The volume is divided into two sections. The Symposium lectures are intended each to summarize an important aspect of transport theory, as well as to present timely new results of the author's research interest. The Conference lectures are contributions of each author on his current research.

The author would like to acknowledge his obligation to all his (;Olleagues and friends at the Institute of Mathematical Sciences of New York University for their stimulation and criticism which have contributed to the writing of this tract. The author also wishes to thank Aughtum S. Howard for permission to include results from her unpublished dissertation, Larkin Joyner for drawing the figures, Interscience Publishers for their cooperation and support, and particularly Lipman Bers, who suggested the publication in its present form.

The whole picture of Mathematical Modeling is systematically and thoroughly explained in this text for undergraduate and graduate students of mathematics, engineering, economics, finance, biology, chemistry, and physics. This textbook gives an overview of the spectrum of modeling techniques, deterministic and stochastic methods, and first-principle and empirical solutions.

The triumphant vindication of bold theories-are these not the pride and justification of our life's work? -Sherlock Holmes, The Valley of Fear Sir Arthur Conan Doyle The main purpose of our book is to present and explain mathematical methods for obtaining approximate analytical solutions to differential and difference equations that cannot be solved exactly. Our objective is to help young and also establiShed scientists and engineers to build the skills necessary to analyze equations that they encounter in their work. Our presentation is aimed at developing the insights and techniques that are most useful for attacking new problems.