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The material of the present book is an extension of a graduate
course given by the author at the University "Al.I. Cuza" Iasi and
is intended for stu dents and researchers interested in the
applications of optimal control and in mathematical biology. Age is
one of the most important parameters in the evolution of a bi
ological population. Even if for a very long period age structure
has been considered only in demography, nowadays it is fundamental
in epidemiology and ecology too. This is the first book devoted to
the control of continuous age structured populationdynamics.It
focuses on the basic properties ofthe solutions and on the control
of age structured population dynamics with or without diffusion.
The main goal of this work is to familiarize the reader with the
most important problems, approaches and results in the mathematical
theory of age-dependent models. Special attention is given to
optimal harvesting and to exact controllability problems, which are
very important from the econom ical or ecological points of view.
We use some new concepts and techniques in modern control theory
such as Clarke's generalized gradient, Ekeland's variational
principle, and Carleman estimates. The methods and techniques we
use can be applied to other control problems."
The material of the present book is an extension of a graduate
course given by the author at the University "Al.I. Cuza" Iasi and
is intended for stu dents and researchers interested in the
applications of optimal control and in mathematical biology. Age is
one of the most important parameters in the evolution of a bi
ological population. Even if for a very long period age structure
has been considered only in demography, nowadays it is fundamental
in epidemiology and ecology too. This is the first book devoted to
the control of continuous age structured populationdynamics.It
focuses on the basic properties ofthe solutions and on the control
of age structured population dynamics with or without diffusion.
The main goal of this work is to familiarize the reader with the
most important problems, approaches and results in the mathematical
theory of age-dependent models. Special attention is given to
optimal harvesting and to exact controllability problems, which are
very important from the econom ical or ecological points of view.
We use some new concepts and techniques in modern control theory
such as Clarke's generalized gradient, Ekeland's variational
principle, and Carleman estimates. The methods and techniques we
use can be applied to other control problems."
L.A.Zadeh introduced the notion of fuzzy sets which contributed to
the Mathematical study of uncertainty. The fuzzy concept has
invaded almost all branches of Mathematics ever since its
introduction. There has been a great deal of interest in the area
of fuzzy normed linear spaces. This book comprises of eleven
chapters and deals thoroughly with the theory of fuzzy n-normed
linear spaces and fuzzy n-inner product spaces including
convergence sequence, Cauchy sequence and completeness of fuzzy
n-normed linear spaces. The concepts of intuitionistic fuzzy
compact and bounded linear operators are explained in a fascinating
way. Cartesian products of fuzzy n-normed linear spaces and best
approximation sets are also discussed. Some fixed point theorems in
intuitionistic fuzzy n-normed linear space are proved and the
notion of interval valued fuzzy n-normed linear space is also
developed. This book will be of much use to learners and
researchers in this field.
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