Bøger i Encyclopaedia of Mathematical Sciences serien

This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors.

From the reviews of the first edition:"... Here ... a wealth of material is displayed for us, too much to even indicate in a review. ... Your reviewer was very impressed by the contents of both volumes (EMS 2 and 4), recommending them without any restriction." Mededelingen van het Wiskundig genootshap 1992

Together with Theory of Operator Algebras I and III, this book presents the theory of von Neumann algebras and non-commutative integration focusing on the group of automorphisms and the structure analysis.

Equivariant embeddings are essential tools in solving a variety of problems relating to homogenous spaces in linear algebraic groups. This volume classifies these embeddings using a 'combinatorial' data framework, with a special focus on spherical varieties.

This book presents a survey of the theory of general linear partial differential equations and, in particular, of equations with constant coefficients. It is written for researchers and graduate students in mathematics and theoretical physics.

A brilliant and coherent summation of both the modern state and the trends of continuing development in various branches of number theory. Illuminated by elementary problems, the central ideas of modern theories are laid bare.

From the reviews of the first edition:"... Here ... a wealth of material is displayed for us, too much to even indicate in a review. ... Your reviewer was very impressed by the contents of both volumes (EMS 2 and 4), recommending them without any restriction." Mededelingen van het Wiskundig genootshap 1992

From the reviews: "These three bulky volumes [EMS 124, 125, 127] [...] provide an introduction to this rapidly developing theory. [...] These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of mathematics. Acta Scientiarum Mathematicarum

Wholeheartedly recommended to every student and user of mathematics, this is an extremely original and highly informative essay on algebra and its place in modern mathematics and science.

This book discusses knotted surfaces in 4-dimensional space and surveys many of the known results, including knotted surface diagrams, constructions of knotted surfaces, classically defined invariants, and new invariants defined via quandle homology theory.

This book contains two surveys on important topics in complex analysis. It addresses graduate students and researchers in complex analysis.

In the Part at hand the authors undertake to give a presentation of the historical development of the theory of imbedding of function spaces, of the internal as well as the externals motives which have stimulated it, and of the current state of art in the field, in particular, what regards the methods employed today.

This volume is devoted to the "hyperbolic theory" of dynamical systems (DS), that is, the theory of smooth DS's with hyperbolic behaviour of the tra jectories (generally speaking, not the individual trajectories, but trajectories filling out more or less "significant" subsets in the phase space.

Devoted to finite-dimensional deterministic control systems governed by smooth ordinary differential equations, this book treats Mathematical Control Theory from a geometric viewpoint. Covers controllability, state and feedback equivalence and optimal control.

Two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory, by well-known experts in the fields. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics.

This two-part EMS volume provides a succinct summary of complex algebraic geometry, coupled with a lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties. An excellent companion to the older classics on the subject.

A two-part monograph covering recent research in an important field, previously scattered in numerous journals, including the latest results in the theory of mixed problems for hyperbolic operators. The book is hence of immense value to graduate students and researchers in partial differential equations and theoretical physics.

Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Catastrophe theory is accurately described as singularity theory and its (genuine) applications.

By definition, diophantine problems concern the solutions of equations in integers, or rational numbers, or various generalizations, such as finitely generated rings over Z or finitely generated fields over Q.

This volume is the first in the series devoted to the commutative harmonic analysis, a fundamental part of the contemporary mathematics.

Thus, m the space of states (phase space) is a subset M of an Euclidean space M . For continuous time systems, the evolution rule may be a differential eq- tion: to each state x G M one associates the speed and direction in which the system is going to evolve from that state.

Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest.

In sum, the volume under review is the first quarter of an important work that surveys an active branch of modern mathematics. it will be an invaluable reference and a companion to modern courses on several complex variables."

From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject.

A very clear account of the subject from the viewpoints of elementary geometry, Riemannian geometry and group theory - a book with no rival in the literature. Mostly accessible to first-year students in mathematics, the book also includes very recent results which will be of interest to researchers in this field.

[Gabriel and Roiter] are pioneers in this subject and they have included proofs for statements which in their opinions are elementary, those which will help further understanding and those which are scarcely available elsewhere. They attempt to take us up to the point where we can find our way in the original literature.

Contributions by three authors treat aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different points of view. Cyclic theory is the natural setting for a variety of general abstract index theorems.

This book covers the modular invariant theory of finite groups. It details techniques for the computation of invariants for many modular representations of finite groups, especially the cyclic group of prime order, and includes many examples.

This newly translated addition to the literature provides a comprehensive treatment of the fundamentals of geophysical hydrodynamics -as expressed in Dolzhansky's four decades of ground-breaking work at the Moscow Institute of Physics and Technology.