This book examines a system of parabolic-elliptic partial differential eq- tions proposed in mathematical biology, statistical mechanics, and chemical kinetics. In the context of biology, this system of equations describes the chemotactic feature of cellular slime molds and also the capillary formation of blood vessels in angiogenesis. There are several methods to derive this system. One is the biased random walk of the individual, and another is the reinforced random walk of one particle modelled on the cellular automaton. In the context of statistical mechanics or chemical kinetics, this...

Senba (Miyazaki U.) and Suzuki (Osaka U.) provide an introduction to applied mathematics in various disciplines. Topics include geometric objects, such as basic notions of vector analysis, curvature and extremals; calculus of variation including isoperimetric inequality, the direct and indirect methods, and numerical schemes; infinite dimensional a

The scope of the general equilibrium theory has been limited to the Walrasian tradition. This work proves the existence of a competitive equilibrium with increasing returns coming from externalities in a dynamic economy and a monopolistically competitive equilibrium with technologies exhibiting increasing returns coming from a large set-up cost.

This book provides a general introduction to applied analysis; vector analysis with physical motivation, calculus of variation, Fourier analysis, eigenfunction expansion, distribution, and so forth, including a catalogue of mathematical theories, such as basic analysis, topological spaces, complex function theory, real analysis, and abstract analysis. This book also uses fundamental ideas of applied mathematics to discuss recent developments in nonlinear science, such as mathematical modeling of reinforced random motion of particles, semiconductor device equation in applied physics, and...

The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.