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In this monograph, the authors develop a methodology that allows
one to construct and substantiate optimal and suboptimal algorithms
to solve problems in computational and applied mathematics.
Throughout the book, the authors explore well-known and proposed
algorithms with a view toward analyzing their quality and the range
of their efficiency. The concept of the approach taken is based on
several theories (of computations, of optimal algorithms, of
interpolation, interlination, and interflatation of functions, to
name several). Theoretical principles and practical aspects of
testing the quality of algorithms and applied software, are a major
component of the exposition. The computer technology in
construction of T-efficient algorithms for computing -solutions to
problems of computational and applied mathematics, is also
explored. The readership for this monograph is aimed at scientists,
postgraduate students, advanced students, and specialists dealing
with issues of developing algorithmic and software support for the
solution of problems of computational and applied mathematics.
This book opens new avenues in understanding mathematical models
within the context of a transition economy. The exposition lays out
the methods for combining different mathematical structures and
tools to effectively build the next model that will accurately
reflect real world economic processes. Mathematical modeling of
weather phenomena allows us to forecast certain essential weather
parameters without any possibility of changing them. By contrast,
modeling of transition economies gives us the freedom to not only
predict changes in important indexes of all types of economies, but
also to influence them more effectively in the desired direction.
Simply put: any economy, including a transitional one, can be
controlled. This book is useful to anyone who wants to increase
profits within their business, or improve the quality of their
family life and the economic area they live in. It is beneficial
for undergraduate and graduate students specializing in the fields
of Economic Informatics, Economic Cybernetics, Applied Mathematics
and Large Information Systems, as well as for professional
economists, and employees of state planning and statistical
organizations.
This work is devoted to the late Ukrainian computer scientist V. M.
Glushkov on the 90th anniversary of his birthday. Dr. Glushkov is
known for his contribution to the world computer science and
technology and this volume analyzes the ideas and paths of
development of informatics formulated by him and demonstrate their
important role in constructing computer technologies of basic
research in the fields of applied mathematics, theories of computer
programming and computing systems. A significant portion of the
monograph is devoted to the elucidation of new results obtained in
the field of mathematical modeling of complicated processes,
creation of new methods for solving and investigating optimization
problems in different statements and development of computer
technologies for investigations in the field of economy, biology,
medicine and information security in systems. The monograph will be
of particular interest to informatics specialists and experts using
methods of informatics and computer technologies to investigate
complicated processes of different natures and developing new
information technologies. It may also be useful for both graduate
students and postgraduates specializing in Computer Science.
This book opens new avenues in understanding mathematical models
within the context of a transition economy. The exposition lays out
the methods for combining different mathematical structures and
tools to effectively build the next model that will accurately
reflect real world economic processes. Mathematical modeling of
weather phenomena allows us to forecast certain essential weather
parameters without any possibility of changing them. By contrast,
modeling of transition economies gives us the freedom to not only
predict changes in important indexes of all types of economies, but
also to influence them more effectively in the desired direction.
Simply put: any economy, including a transitional one, can be
controlled. This book is useful to anyone who wants to increase
profits within their business, or improve the quality of their
family life and the economic area they live in. It is beneficial
for undergraduate and graduate students specializing in the fields
of Economic Informatics, Economic Cybernetics, Applied Mathematics
and Large Information Systems, as well as for professional
economists, and employees of state planning and statistical
organizations.
This work is devoted to the late Ukrainian computer scientist V. M.
Glushkov on the 90th anniversary of his birthday. Dr. Glushkov is
known for his contribution to the world computer science and
technology and this volume analyzes the ideas and paths of
development of informatics formulated by him and demonstrate their
important role in constructing computer technologies of basic
research in the fields of applied mathematics, theories of computer
programming and computing systems. A significant portion of the
monograph is devoted to the elucidation of new results obtained in
the field of mathematical modeling of complicated processes,
creation of new methods for solving and investigating optimization
problems in different statements and development of computer
technologies for investigations in the field of economy, biology,
medicine and information security in systems. The monograph will be
of particular interest to informatics specialists and experts using
methods of informatics and computer technologies to investigate
complicated processes of different natures and developing new
information technologies. It may also be useful for both graduate
students and postgraduates specializing in Computer Science.
This work presents lines of investigation and scientific
achievements of the Ukrainian school of optimization theory and
adjacent disciplines. These include the development of approaches
to mathematical theories, methodologies, methods, and application
systems for the solution of applied problems in economy, finances,
energy saving, agriculture, biology, genetics, environmental
protection, hardware and software engineering, information
protection, decision making, pattern recognition, self-adapting
control of complicated objects, personnel training, etc. The
methods developed include sequential analysis of variants,
nondifferential optimization, stochastic optimization, discrete
optimization, mathematical modeling, econometric modeling, solution
of extremum problems on graphs, construction of discrete images and
combinatorial recognition, etc. Some of these methods became well
known in the world's mathematical community and are now known as
classic methods.
At present, in order to resolve problems of ecology and to save
mineral resources for future population generations, it is quite
necessary to know how to maintain nature arrangement in an
efficient way. It is possible to achieve a rational nature
arrangement when analyzing solutions to problems concerned with
optimal control of distributed systems and with optimization of
modes in which main ground medium processes are functioning (motion
of liquids, generation of temperature fields, mechanical
deformation of multicomponent media). Such analysis becomes even
more difficult because of heterogeneity of the region that is
closest to the Earth surface, and thin inclusions/cracks in it
exert their essential influence onto a state and development of the
mentioned processes, especially in the cases of mining. Many
researchers, for instance, A.N. Tikhonov - A.A. Samarsky [121], L.
Luckner - W.M. Shestakow [65], Tien-Mo Shih, K.L. Johnson [47], E.
Sanchez-Palencia [94] and others stress that it is necessary to
consider how thin inclusions/cracks exert their influences onto
development of these processes, while such inclusions differ in
characteristics from main media to a considerable extent (moisture
permeability, permeability to heat, bulk density or shear strength
may be mentioned). Xll An influence exerted from thin interlayers
onto examined processes is taken into account sufficiently
adequately by means of various constraints, namely, by the
conjugation conditions [4, 8, 10, 15, 17-20, 22-26, 38, 44, 47, 52,
53, 68, 76, 77, 81, 83, 84, 90, 95, 96-100, 112-114, 117, 123].
At present, in order to resolve problems of ecology and to save
mineral resources for future population generations, it is quite
necessary to know how to maintain nature arrangement in an
efficient way. It is possible to achieve a rational nature
arrangement when analyzing solutions to problems concerned with
optimal control of distributed systems and with optimization of
modes in which main ground medium processes are functioning (motion
of liquids, generation of temperature fields, mechanical
deformation of multicomponent media). Such analysis becomes even
more difficult because of heterogeneity of the region that is
closest to the Earth surface, and thin inclusions/cracks in it
exert their essential influence onto a state and development of the
mentioned processes, especially in the cases of mining. Many
researchers, for instance, A.N. Tikhonov - A.A. Samarsky [121], L.
Luckner - W.M. Shestakow [65], Tien-Mo Shih, K.L. Johnson [47], E.
Sanchez-Palencia [94] and others stress that it is necessary to
consider how thin inclusions/cracks exert their influences onto
development of these processes, while such inclusions differ in
characteristics from main media to a considerable extent (moisture
permeability, permeability to heat, bulk density or shear strength
may be mentioned). Xll An influence exerted from thin interlayers
onto examined processes is taken into account sufficiently
adequately by means of various constraints, namely, by the
conjugation conditions [4, 8, 10, 15, 17-20, 22-26, 38, 44, 47, 52,
53, 68, 76, 77, 81, 83, 84, 90, 95, 96-100, 112-114, 117, 123].
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