Focused on recent advances, this book covers theoretical foundations as well as various applications. It presents modern mathematical modeling approaches to the qualitative and numerical analysis of solutions for complex engineering problems in physics, mechanics, biochemistry, geophysics, biology and climatology. Contributions by an international team of respected authors bridge the gap between abstract mathematical approaches, such as applied methods of modern analysis, algebra, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems on the one hand, and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. As such, the book will be of interest to mathematicians and engineers working at the interface of these fields.

This monograph is dedicated to the systematic presentation of main trends, technologies and methods of computational intelligence (CI). The book pays big attention to novel important CI technology- fuzzy logic (FL) systems and fuzzy neural networks (FNN). Different FNN including new class of FNN- cascade neo-fuzzy neural networks are considered and their training algorithms are described and analyzed. The applications of FNN to the forecast in macroeconomics and at stock markets are examined. The book presents the problem of portfolio optimization under uncertainty, the novel theory of fuzzy portfolio optimization free of drawbacks of classical model of Markovitz as well as an application for portfolios optimization at Ukrainian, Russian and American stock exchanges. The book also presents the problem of corporations bankruptcy risk forecasting under incomplete and fuzzy information, as well as new methods based on fuzzy sets theory and fuzzy neural networks and results of their application for bankruptcy risk forecasting are presented and compared with Altman method. This monograph also focuses on an inductive modeling method of self-organization - the so-called Group Method of Data Handling (GMDH) which enables to construct the structure of forecasting models almost automatically. The results of experimental investigations of GMDH for forecasting at stock exchanges are presented. The final chapters are devoted to theory and applications of evolutionary modeling (EM) and genetic algorithms. The distinguishing feature of this monograph is a great number of practical examples of CI technologies and methods application for solution of real problems in technology, economy and financial sphere, in particular forecasting, classification, pattern recognition, portfolio optimization, bankruptcy risk prediction under uncertainty which were developed by authors and published in this book for the first time. All CI methods and algorithms are presented from the general system approach and analysis of their properties, advantages and drawbacks that enables practitioners to choose the most adequate method for their own problems solution.

As in the previous volume on the topic, the authors close the gap between abstract mathematical approaches, such as applied methods of modern algebra and analysis, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems, on the one hand and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. Readers will also benefit from the presentation of modern mathematical modeling methods for the numerical solution of complicated engineering problems in biochemistry, geophysics, biology and climatology. This compilation will be of interest to mathematicians and engineers working at the interface of these fields. It presents selected works of the joint seminar series of Lomonosov Moscow State University and the Institute for Applied System Analysis at National Technical University of Ukraine “Kyiv Polytechnic Institute”. The authors come from Brazil, Germany, France, Mexico, Spain, Poland, Russia, Ukraine and the USA.

In this volume, the authors close the gap between abstract mathematical approaches, such as abstract algebra, number theory, nonlinear functional analysis, partial differential equations, methods of nonlinear and multi-valued analysis, on the one hand, and practical applications in nonlinear mechanics, decision making theory and control theory on the other. Readers will also benefit from the presentation of modern mathematical modeling methods for the numerical solution of complicated engineering problems in hydromechanics, geophysics and mechanics of continua. This compilation will be of interest to mathematicians and engineers working at the interface of these field. It presents selected works of the open seminar series of Lomonosov Moscow State University and the National Technical University of Ukraine “Kyiv Polytechnic Institute”. The authors come from Germany, Italy, Spain, Russia, Ukraine, and the USA.

Focused on recent advances, this book covers theoretical foundations as well as various applications. It presents modern mathematical modeling approaches to the qualitative and numerical analysis of solutions for complex engineering problems in physics, mechanics, biochemistry, geophysics, biology and climatology. Contributions by an international team of respected authors bridge the gap between abstract mathematical approaches, such as applied methods of modern analysis, algebra, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems on the one hand, and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. As such, the book will be of interest to mathematicians and engineers working at the interface of these fields.

This monograph is dedicated to the systematic presentation of main trends, technologies and methods of computational intelligence (CI). The book pays big attention to novel important CI technology- fuzzy logic (FL) systems and fuzzy neural networks (FNN). Different FNN including new class of FNN- cascade neo-fuzzy neural networks are considered and their training algorithms are described and analyzed. The applications of FNN to the forecast in macroeconomics and at stock markets are examined. The book presents the problem of portfolio optimization under uncertainty, the novel theory of fuzzy portfolio optimization free of drawbacks of classical model of Markovitz as well as an application for portfolios optimization at Ukrainian, Russian and American stock exchanges. The book also presents the problem of corporations bankruptcy risk forecasting under incomplete and fuzzy information, as well as new methods based on fuzzy sets theory and fuzzy neural networks and results of their application for bankruptcy risk forecasting are presented and compared with Altman method. This monograph also focuses on an inductive modeling method of self-organization - the so-called Group Method of Data Handling (GMDH) which enables to construct the structure of forecasting models almost automatically. The results of experimental investigations of GMDH for forecasting at stock exchanges are presented. The final chapters are devoted to theory and applications of evolutionary modeling (EM) and genetic algorithms. The distinguishing feature of this monograph is a great number of practical examples of CI technologies and methods application for solution of real problems in technology, economy and financial sphere, in particular forecasting, classification, pattern recognition, portfolio optimization, bankruptcy risk prediction under uncertainty which were developed by authors and published in this book for the first time. All CI methods and algorithms are presented from the general system approach and analysis of their properties, advantages and drawbacks that enables practitioners to choose the most adequate method for their own problems solution.

As in the previous volume on the topic, the authors close the gap between abstract mathematical approaches, such as applied methods of modern algebra and analysis, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems, on the one hand and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. Readers will also benefit from the presentation of modern mathematical modeling methods for the numerical solution of complicated engineering problems in biochemistry, geophysics, biology and climatology. This compilation will be of interest to mathematicians and engineers working at the interface of these fields. It presents selected works of the joint seminar series of Lomonosov Moscow State University and the Institute for Applied System Analysis at National Technical University of Ukraine "Kyiv Polytechnic Institute". The authors come from Brazil, Germany, France, Mexico, Spain, Poland, Russia, Ukraine and the USA.

In this volume, the authors close the gap between abstract mathematical approaches, such as abstract algebra, number theory, nonlinear functional analysis, partial differential equations, methods of nonlinear and multi-valued analysis, on the one hand, and practical applications in nonlinear mechanics, decision making theory and control theory on the other.

Readers will also benefit from the presentation of modern mathematical modeling methods for the numerical solution of complicated engineering problems in hydromechanics, geophysics and mechanics of continua. This compilation will be of interest to mathematicians and engineers working at the interface of these field. It presents selected works of the open seminar series of Lomonosov Moscow State University and the National Technical University of Ukraine Kyiv Polytechnic Institute . The authors come from Germany, Italy, Spain, Russia, Ukraine, and the USA."

Modern achievements in the intensively developing field of applied mathematics are presented in this monograph. In particular, it proposes a new approach to extremal problem theory for nonlinear operators, differential-operator equations and inclusions, and for variational inequalities in Banach spaces. An axiomatic study of nonlinear maps (including multi-valued ones) is given, and the properties of resolving operators for systems, consisting of operator and differential-operator equations, are stated in nonlinear-map terms. The solvability conditions and the properties of extremal problem solutions are obtained, while their weak expansions and necessary conditions of optimality in variational inequality form are formulated. In addition. the monograph proposes regularization methods and approximation schemes. This book is adressed to scientists, graduates and undergraduates who are interested in nonlinear analysis, control theory, system analysis and differential equations.

This book offers the foundations of system analysis as an applied scientific methodology assigned for the investigation of complex and highly interdisciplinary problems. It presents the basic definitions and the methodological and theoretical basis of formalization and solution processes in various subject domains. It describes in detail the methods of formalizing the system tasks and reducing them to a solvable form under real-world conditions.

Here, the authors present modern mathematical methods to solve problems of differential-operator inclusions and evolution variation inequalities which may occur in fields such as geophysics, aerohydrodynamics, or fluid dynamics. For the first time, they describe the detailed generalization of various approaches to the analysis of fundamentally nonlinear models and provide a toolbox of mathematical equations. These new mathematical methods can be applied to a broad spectrum of problems. Examples of these are phase changes, diffusion of electromagnetic, acoustic, vibro-, hydro- and seismoacoustic waves, or quantum mechanical effects. This is the second of two volumes dealing with the subject.

This book offers the foundations of system analysis as an applied scientific methodology assigned for the investigation of complex and highly interdisciplinary problems. It presents the basic definitions and the methodological and theoretical basis of formalization and solution processes in various subject domains. It describes in detail the methods of formalizing the system tasks and reducing them to a solvable form under real-world conditions.

Modern achievements in the intensively developing field of applied mathematics as applied to physical chemistry are presented in this monograph. In particular, it proposes a new approach to extremal problem theory for nonlinear operators, differential-operator equations and inclusions, and for variational inequalities in Banach spaces. An axiomatic study of nonlinear maps (including multi-valued ones) is given, and the properties of resolving operators for systems, consisting of operator and differential-operator equations, are stated in nonlinear-map terms. The solvability conditions and the properties of extremal problem solutions are obtained, while their weak expansions and necessary conditions of optimality in variational inequality form are formulated. In addition. the monograph proposes regularization methods and approximation schemes. This book is adressed to scientists, graduates and undergraduates who are interested in nonlinear analysis, control theory, system analysis and differential equations.

Here, the authors present modern mathematical methods to solve problems of differential-operator inclusions and evolution variation inequalities which may occur in fields such as geophysics, aerohydrodynamics, or fluid dynamics. For the first time, they describe the detailed generalization of various approaches to the analysis of fundamentally nonlinear models and provide a toolbox of mathematical equations. These new mathematical methods can be applied to a broad spectrum of problems. Examples of these are phase changes, diffusion of electromagnetic, acoustic, vibro-, hydro- and seismoacoustic waves, or quantum mechanical effects. This is the first of two volumes dealing with the subject.