Books in the Mathematics and its Applications series

The fields of Artificial Intelligence and Machine Learning have grown dramatically in recent years, with an increasingly impressive spectrum of successful applications. This book represents a key reference for anybody interested in the intersection between Mathematics and AI/ML and provides an overview of the current research streams.

Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand the real-life problems. The applications can be applied to engineering and science disciplines.

This book covers contemporary topics of mathematical analysis in the form of new ideas, methods, techniques, algorithms, as well as applications of tools in various engineering and scientific fields. It discusses various problems and offers ways to create models to solve those problems.

Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics;

This book covers applications of fractional calculus used for medical and health science.

Integration in infinitely dimensional spaces (continual integration) is a powerful mathematical tool which is widely used in a number of fields of modern mathematics, such as analysis, the theory of differential and integral equations, probability theory and the theory of random processes.

Within that conceptual framework, we then trace the development and sophistication of our clinical research, presenting for the first time in a single work a complete consideration of the rationale, methods, and results of the study of Individualized Be havior Therapy (IBT) for alcoholics.

The purpose of this book is to give a comprehensive introduction to the theory of spline functions, together with some applications to various fields, emphasizing the significance of the relationship between the general theory and its applications.

The other restricts its area of interest to certain families of equations and studies in maximal details phenomena which characterize only those equations. Among them we find third and fourth order equations, self adjoint equations, etc.

Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics;

Integration in infinitely dimensional spaces (continual integration) is a powerful mathematical tool which is widely used in a number of fields of modern mathematics, such as analysis, the theory of differential and integral equations, probability theory and the theory of random processes.

Exponential Fitting is a procedure for an efficient numerical approach of functions consisting of weighted sums of exponential, trigonometric or hyperbolic functions with slowly varying weight functions.

However, they possess enough hyperbolicity to enable us to use shadowing ideas to give computer-assisted proofs that computed orbits of such systems can be shadowed by true orbits for long periods of time, that they possess periodic orbits of long periods and that it is really true that they are chaotic.

From a modelling point of view, it is more realistic to model a phenomenon by a dynamic system which incorporates both continuous and discrete times, namely, time as an arbitrary closed set of reals called time-scale or measure chain.

Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics;

Devoted to the basic notions of vector bundles and their applications. This book explains important notions and geometric constructions connected with the theory of vector bundles. It contains illustrations and applications to various problems in mathematics and sciences. It is intended for graduate students from pure and applied mathematics.

Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics;

The other restricts its area of interest to certain families of equations and studies in maximal details phenomena which characterize only those equations. Among them we find third and fourth order equations, self adjoint equations, etc.