This book offers a self-contained introduction to the theory of guiding functions methods, which can be used to study the existence of periodic solutions and their bifurcations in ordinary differential equations, differential inclusions and in control theory. It starts with the basic concepts of nonlinear and multivalued analysis, describes the classical aspects of the method of guiding functions, and then presents recent findings only available in the research literature. It describes essential applications in control theory, the theory of bifurcations, and physics, making it a valuable resource not only for “pure” mathematicians, but also for students and researchers working in applied mathematics, the engineering sciences and physics.
This book offers a self-contained introduction to the theory of guiding functions methods, which can be used to study the existence of periodic solutions and their bifurcations in ordinary differential equations, differential inclusions and in control theory. It starts with the basic concepts of nonlinear and multivalued analysis, describes the classical aspects of the method of guiding functions, and then presents recent findings only available in the research literature. It describes essential applications in control theory, the theory of bifurcations, and physics, making it a valuable resource not only for “pure” mathematicians, but also for students and researchers working in applied mathematics, the engineering sciences and physics.
This textbook is intended for practical, laboratory sessions associated with the course of quantum computing and quantum algorithms, as well as for self-study. It contains basic theoretical concepts and methods for solving basic types of problems and gives an overview of basic qubit operations, entangled states, quantum circuits, implementing functions, quantum Fourier transform, phase estimation, etc. The book serves as a basis for the application of new information technologies in education and corporate technical training: theoretical material and examples of practical problems, as well as exercises with, in most cases, detailed solutions, have relation to information technologies. A large number of detailed examples serve to better develop professional competencies in computer science.
This book focuses on the effect the composition of rubbers and the conditions of their processing have on low-temperature resistance. It considers the nature and development of two physical processes, glass transition and crystallization, determining low-temperature behavior of elastomers. The book addresses the effects of deformation, pressure, and temperature on these processes. It discusses the contribution of different factors in frost-resistance of elastomeric materials and articles and the possibility of increasing frost-resistance by optimization of composition and design.
This volume in the book series New Concepts in Polymer Science deals with the damaging effects, which microorganisms such as bacteria, fungi, etc. can have on a range of materials in machinery. The book aims to provide theoretical notions about the mechanisms of material damaging by microorganisms under operation conditions as well as to give recommendations for protection of technical articles and machinery.This monograph consists of the following topics: finding of kinetic regularities, analytical models and quantitative indices for stages material biodamaging; study of influence of properties of materials, features of microorganisms, temperature, humidity and other factors on interaction between a material and a biodestructor; and, compilation of guidelines to determine and forecast biological resistance (bioresistance) of materials, development of means and methods for their protection as well as estimates of their efficiency.This monograph will be of value and interest to researchers and engineers working in fields in which materials are subject to active microbiological aging and destruction.
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