Due 2020-03-26
1st ed. 2020, X, 240 p. 1illus.
Softcover
ISBN 978-3-030-37704-5
Series : Lecture Notes in Mathematics
Important for applications in Mathematical Physics
Will be of interest to researchers in topological algebras
Suitable as a textbook for PhD courses
Includes an appendix on *-algebras useful for advanced masters students
This book offers a review of the theory of locally convex quasi *-algebras, authored by two of
its contributors over the last 25 years. Quasi *-algebras are partial algebraic structures that are
motivated by certain applications in Mathematical Physics. They arise in a natural way by
completing a *-algebra under a locally convex *-algebra topology, with respect to which the
multiplication is separately continuous. Among other things, the book presents an unbounded
representation theory of quasi *-algebras, together with an analysis of normed quasi *-
algebras, their spectral theory and a study of the structure of locally convex quasi *-algebras.
Special attention is given to the case where the locally convex quasi *-algebra is obtained by
completing a C*-algebra under a locally convex *-algebra topology, coarser than the C*-
topology. Introducing the subject to graduate students and researchers wishing to build on
their knowledge of the usual theory of Banach and/or locally convex algebras, this approach is
supported by basic results and a wide variety of examples
https://doi.org/10.1142/11651 | April 2020
Pages: 400
This volume provides a comprehensive introduction to the modern theory of differential-operator and kinetic models including Vlasov?Maxwell, Fredholm, Lyapunov?Schmidt branching equations to name a few. This book will bridge the gap in the considerable body of existing academic literature on the analytical methods used in studies of complex behavior of differential-operator equations and kinetic models. This monograph will be of interest to mathematicians, physicists and engineers interested in the theory of such non-standard systems.
Operator and Differential-Operator Equations
Theory of Linear Operators
Nonlinear Differential Equations near Branching Points
Nonlinear Systems Equilibrium Points: Stability, Branching, Blow-up
Irregular Systems of Equations with Partial Derivatives
Lyapunov Methods in the Bifurcation Theory
Bifurcation Points of Nonlinear Equations
General Existence Theorems for the Bifurcation Points
Asymptotics in a Neighborhood of a Bifurcation Point
Regularization of Computation of Solutions in a Branch Point Neighborhood
Iterations, Interlaced Equations and Lyapunov Majorants
Newton Diagrams
Interlaced and Potential BEQ
Vlasov?Maxwell System
Boundary Value Problem
Bifurcation of Solutions
Magnetic Insulation Problem
Graduate students and researchers interested in mathematical physics, differential
equations and mathematical modeling.
https://doi.org/10.1142/11644 | April 2020
Pages: 300
ISBN: 978-981-121-346-5 (hardcover)
ISBN: 978-981-121-349-6 (softcover)
Volume II is the second part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and "Golden" Paradigm of Modern Science. "Mathematics of Harmony" rises in its origin to the "harmonic ideas" of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the "Universe Harmony," the main conception of ancient Greek science, and implementation of this conception to modern science and education.
This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the "Mathematics of Harmony," a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).
The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
Foundations of the Constructive (Algorithmic) Measurement Theory
Principle of Asymmetry of Measurement and Fibonacci's Algorithms of Measurement
Evolution of Numeral Systems
Bergman's System and "Golden" Number Theory
The "Golden" Ternary Mirror-Symmetrical Arithmetic
Fibonacci p-Codes and Fibonacci Arithmetic for Mission-Critical Applications
Codes of the Golden p-proportions
Conclusions to the Volume II
High school, college and university students, teachers, professionals, scientists and investors interested in history of mathematics, Fibonacci numbers, golden section and their generalization.