This book considers the Cauchy problem for a system of ordinary differential equations with a small parameter, filling in areas that have not been extensively covered in the existing literature. The well-known types of equations, such as the regularly perturbed Cauchy problem and the Tikhonov problem, are dealt with, but new ones are also treated, such as the quasiregular Cauchy problem, and the Cauchy problem with double singularity. For each type of problem, series are constructed which generalise the well-known series of Poincare and Vasilyeva-Imanaliyev. It is shown that these series are...
This book considers the Cauchy problem for a system of ordinary differential equations with a small parameter, filling in areas that have not been ext...
Boolean Algebras in Analysis consists of two parts. The first concerns the general theory at the beginner's level. Presenting classical theorems, the book describes the topologies and uniform structures of Boolean algebras, the basics of complete Boolean algebras and their continuous homomorphisms, as well as lifting theory. The first part also includes an introductory chapter describing the elementary to the theory.
The second part deals at a graduate level with the metric theory of Boolean algebras at a graduate level. The covered topics include measure algebras,...
Boolean Algebras in Analysis consists of two parts. The first concerns the general theory at the beginner's level. Presenting clas...
Algebras of bounded operators are familiar, either as C*-algebras or as von Neumann algebras. A first generalization is the notion of algebras of unbounded operators (O*-algebras), mostly developed by the Leipzig school and in Japan (for a review, we refer to the monographs of K. Schmudgen 1990] and A. Inoue 1998]). This volume goes one step further, by considering systematically partial *-algebras of unbounded operators (partial O*-algebras) and the underlying algebraic structure, namely, partial *-algebras. It is the first textbook on...
Algebras of bounded operators are familiar, either as C*-algebras or as von Neumann algebras. A first generalization is the notion of algeb...
This book is the first to systematically explore the classification and function theory of complex homogeneous bounded domains. The Siegel domains are discussed in detail, and proofs are presented. Using the normal Siegel domains to realize the homogeneous bounded domains, we can obtain more property of the geometry and the function theory on homogeneous bounded domains.
This book is the first to systematically explore the classification and function theory of complex homogeneous bounded domains. The Siegel domains ...
Supermanifolds and Supergroups explains the basic ingredients of super manifolds and super Lie groups. It starts with super linear algebra and follows with a treatment of super smooth functions and the basic definition of a super manifold. When discussing the tangent bundle, integration of vector fields is treated as well as the machinery of differential forms. For super Lie groups the standard results are shown, including the construction of a super Lie group for any super Lie algebra. The last chapter is entirely devoted to super connections.
The book requires...
Supermanifolds and Supergroups explains the basic ingredients of super manifolds and super Lie groups. It starts with super linear...
This book describes a new and original formalism based on mirror symmetries of Lie groups, Lie algebras and Homogeneous spaces. Special systems of mirrors are used for classification purposes and as an instrument for studies of Homogeneous spaces. Tri-symmetric and arbitrary Riemannian Homogeneous spaces can also be researched in this way.
The book should be of particular interest to researchers in Lie Groups, Lie Algebras, Differential Geometry and their applications but it should also prove useful for other postgraduate and advanced graduate students in mathematics.
This book describes a new and original formalism based on mirror symmetries of Lie groups, Lie algebras and Homogeneous spaces. Special systems of ...
This volume presents a unified approach to constructing iterative methods for solving irregular operator equations and provides rigorous theoretical analysis for several classes of these methods. The analysis of methods includes convergence theorems as well as necessary and sufficient conditions for their convergence at a given rate. The principal groups of methods studied in the book are iterative processes based on the technique of universal linear approximations, stable gradient-type processes, and methods of stable continuous approximations. Compared to existing monographs and...
This volume presents a unified approach to constructing iterative methods for solving irregular operator equations and provides rigorous theoretica...
L inj enuit m eme d un regard neuf (celui de la science l est toujours) peut parfois clairer d un jour nouveau d anciens probl emes. J.Monod 77, p. 13] his book is intended as a comprehensive introduction to the theory of T principalsheaves andtheirconnections inthesettingofAbstractDi?- ential Geometry (ADG), the latter being initiated by A. Mallios sGeometry of Vector Sheaves 62]. Based on sheaf-theoretic methods and sheaf - homology, the presentGeometry of Principal Sheaves embodies the classical theory of connections on principal and vector bundles, and connections on vector sheaves,...
L inj enuit m eme d un regard neuf (celui de la science l est toujours) peut parfois clairer d un jour nouveau d anciens probl emes. J.Monod 77, p. 1...
The theory of foliations of manifolds was created in the forties of the last century by Ch. Ehresmann and G. Reeb ER44]. Since then, the subject has enjoyed a rapid development and thousands of papers investigating foliations have appeared. A list of papers and preprints on foliations up to 1995 can be found in Tondeur Ton97]. Due to the great interest of topologists and geometers in this rapidly ev- ving theory, many books on foliations have also been published one after the other. We mention, for example, the books written by: I. Tamura Tam76], G. Hector and U. Hirsch HH83], B. Reinhart...
The theory of foliations of manifolds was created in the forties of the last century by Ch. Ehresmann and G. Reeb ER44]. Since then, the subject has ...
