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This book focuses on the latest approaches and methods in
fundamental mathematics and mechanics, and discusses the practical
application of abstract mathematical approaches, such as
differential geometry, and differential and difference equations in
solid mechanics, hydrodynamics, aerodynamics, optimization,
decision-making theory and control theory. Featuring selected
contributions to the open seminar series of Lomonosov Moscow State
University and Igor Sikorsky Kyiv Polytechnic Institute by
mathematicians from China, Germany, France, Italy, Spain, Russia,
Ukraine and the USA, the book will appeal to mathematicians and
engineers working at the interface of these fields
The book is devoted to the analysis of big data in order to extract
from these data hidden patterns necessary for making decisions
about the rational behavior of complex systems with the different
nature that generate this data. To solve these problems, a group of
new methods and tools is used, based on the self-organization of
computational processes, the use of crisp and fuzzy cluster
analysis methods, hybrid neural-fuzzy networks, and others. The
book solves various practical problems. In particular, for the
tasks of 3D image recognition and automatic speech recognition
large-scale neural networks with applications for Deep Learning
systems were used. Application of hybrid neuro-fuzzy networks for
analyzing stock markets was presented. The analysis of big
historical, economic and physical data revealed the hidden
Fibonacci pattern about the course of systemic world conflicts and
their connection with the Kondratieff big economic cycles and the
Schwabe-Wolf solar activity cycles. The book is useful for system
analysts and practitioners working with complex systems in various
spheres of human activity.
In this book international expert authors provide solutions for
modern fundamental problems including the complexity of computing
of critical points for set-valued mappings, the behaviour of
solutions of ordinary differential equations, partial differential
equations and difference equations, or the development of an
abstract theory of global attractors for multi-valued impulsive
dynamical systems. These abstract mathematical approaches are
applied to problem-solving in solid mechanics, hydro- and
aerodynamics, optimization, decision making theory and control
theory. This volume is therefore relevant to mathematicians as well
as engineers working at the interface of these fields.
The book focuses on the next fields of computer science:
combinatorial optimization, scheduling theory, decision theory, and
computer-aided production management systems. It also offers a
quick introduction into the theory of PSC-algorithms, which are a
new class of efficient methods for intractable problems of
combinatorial optimization. A PSC-algorithm is an algorithm which
includes: sufficient conditions of a feasible solution optimality
for which their checking can be implemented only at the stage of a
feasible solution construction, and this construction is carried
out by a polynomial algorithm (the first polynomial component of
the PSC-algorithm); an approximation algorithm with polynomial
complexity (the second polynomial component of the PSC-algorithm);
also, for NP-hard combinatorial optimization problems, an exact
subalgorithm if sufficient conditions were found, fulfilment of
which during the algorithm execution turns it into a polynomial
complexity algorithm. Practitioners and software developers will
find the book useful for implementing advanced methods of
production organization in the fields of planning (including
operative planning) and decision making. Scientists, graduate and
master students, or system engineers who are interested in problems
of combinatorial optimization, decision making with poorly
formalized overall goals, or a multiple regression construction
will benefit from this book.
Here, the authors present modern methods of analysis for nonlinear
systems which may occur in fields such as physics, chemistry,
biology, or economics. They concentrate on the following topics,
specific for such systems: (a) constructive existence results and
regularity theorems for all weak solutions; (b) convergence results
for solutions and their approximations; (c) uniform global behavior
of solutions in time; and (d) pointwise behavior of solutions for
autonomous problems with possible gaps by the phase variables. The
general methodology for the investigation of dissipative dynamical
systems with several applications including nonlinear parabolic
equations of divergent form, nonlinear stochastic equations of
parabolic type, unilateral problems, nonlinear PDEs on Riemannian
manifolds with or without boundary, contact problems as well as
particular examples is established. As such, the book is addressed
to a wide circle of mathematical, mechanical and engineering
readers.
The book focuses on the next fields of computer science:
combinatorial optimization, scheduling theory, decision theory, and
computer-aided production management systems. It also offers a
quick introduction into the theory of PSC-algorithms, which are a
new class of efficient methods for intractable problems of
combinatorial optimization. A PSC-algorithm is an algorithm which
includes: sufficient conditions of a feasible solution optimality
for which their checking can be implemented only at the stage of a
feasible solution construction, and this construction is carried
out by a polynomial algorithm (the first polynomial component of
the PSC-algorithm); an approximation algorithm with polynomial
complexity (the second polynomial component of the PSC-algorithm);
also, for NP-hard combinatorial optimization problems, an exact
subalgorithm if sufficient conditions were found, fulfilment of
which during the algorithm execution turns it into a polynomial
complexity algorithm. Practitioners and software developers will
find the book useful for implementing advanced methods of
production organization in the fields of planning (including
operative planning) and decision making. Scientists, graduate and
master students, or system engineers who are interested in problems
of combinatorial optimization, decision making with poorly
formalized overall goals, or a multiple regression construction
will benefit from this book.
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