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The subject of the book is the "know-how" of applied mathematical
modelling: how to construct specific models and adjust them to a
new engineering environment or more precise realistic assumptions;
how to analyze models for the purpose of investigating real life
phenomena; and how the models can extend our knowledge about a
specific engineering process. Two major sources of the book are the
stock of classic models and the authors' wide experience in the
field. The book provides a theoretical background to guide the
development of practical models and their investigation. It
considers general modelling techniques, explains basic underlying
physical laws and shows how to transform them into a set of
mathematical equations. The emphasis is placed on common features
of the modelling process in various applications as well as on
complications and generalizations of models. The book covers a
variety of applications: mechanical, acoustical, physical and
electrical, water transportation and contamination processes;
bioengineering and population control; production systems and
technical equipment renovation. Mathematical tools include partial
and ordinary differential equations, difference and integral
equations, the calculus of variations, optimal control, bifurcation
methods, and related subjects.
Modern economic growth is characterized by structural changes based
on the introduction of new technologies into economics. The
replacement and renova tion of technologies in industrial
environments undergoing technical change is clearly one of the key
aspects of economic development. The mathematical modeling of
evolutionary economics under technical change (TC) has been
rigorously considered by many authors during last decades. There is
a wide variety of economic approaches and models describing
different aspects of technical change. Among these are the models
of embodied technical progress [19], [35], [70], [129], endogenous
growth models [94], [102], the models of technological innovations
[31], [32], [41], and others. The perspective self organization
evolutionary approach is developed in [20], [38], [122], [123],
[124], [126], which unites the aspects of diffusion of new
technologies, technological and behavioral diversity of firms,
learning mechanisms, age-dependent effects, and other important
features of real-life economics. On the whole, an interest in
evolutionary economics has brought considerable progress in the
description and conceptualization of the sources, characteristics,
direction and effects of technical change [125]. However, the
modeling and control of technology lifetime under technical change
has received rather little attention in mathematical economics in
con trary to other aspects of technical progress. The lifetime of
technologies has rarely been formally treated as a part of more
general mathematical theory of economic dynamics. A problem which
is still to be resolved consists in establishing the rational
strategies of technologies' replacement under various assumptions
on the behavior of technical change.
The problems of interrelation between human economics and natural
environment include scientific, technical, economic, demographic,
social, political and other aspects that are studied by scientists
of many specialities. One of the important aspects in scientific
study of environmental and ecological problems is the development
of mathematical and computer tools for rational management of
economics and environment. This book introduces a wide range of
mathematical models in economics, ecology and environmental
sciences to a general mathematical audience with no in-depth
experience in this specific area. Areas covered are: controlled
economic growth and technological development, world dynamics,
environmental impact, resource extraction, air and water pollution
propagation, ecological population dynamics and exploitation. A
variety of known models are considered, from classical ones (Cobb
Douglass production function, Leontief input-output analysis, Solow
models of economic dynamics, Verhulst-Pearl and Lotka-Volterra
models of population dynamics, and others) to the models of world
dynamics and the models of water contamination propagation used
after Chemobyl nuclear catastrophe. Special attention is given to
modelling of hierarchical regional economic-ecological interaction
and technological change in the context of environmental impact.
Xlll XIV Construction of Mathematical Models ..."
Modern economic growth is characterized by structural changes based
on the introduction of new technologies into economics. The
replacement and renova tion of technologies in industrial
environments undergoing technical change is clearly one of the key
aspects of economic development. The mathematical modeling of
evolutionary economics under technical change (TC) has been
rigorously considered by many authors during last decades. There is
a wide variety of economic approaches and models describing
different aspects of technical change. Among these are the models
of embodied technical progress [19], [35], [70], [129], endogenous
growth models [94], [102], the models of technological innovations
[31], [32], [41], and others. The perspective self organization
evolutionary approach is developed in [20], [38], [122], [123],
[124], [126], which unites the aspects of diffusion of new
technologies, technological and behavioral diversity of firms,
learning mechanisms, age-dependent effects, and other important
features of real-life economics. On the whole, an interest in
evolutionary economics has brought considerable progress in the
description and conceptualization of the sources, characteristics,
direction and effects of technical change [125]. However, the
modeling and control of technology lifetime under technical change
has received rather little attention in mathematical economics in
con trary to other aspects of technical progress. The lifetime of
technologies has rarely been formally treated as a part of more
general mathematical theory of economic dynamics. A problem which
is still to be resolved consists in establishing the rational
strategies of technologies' replacement under various assumptions
on the behavior of technical change.
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