Books in the Grundlehren der mathematischen Wissenschaften series

The publication of the first edition of Lagerungen in der Ebene, auf der Kugel und im Raum in 1953 marked the birth of discrete geometry. Since then, the book has had a profound and lasting influence on the development of the field. It included many open problems and conjectures, often accompanied by suggestions for their resolution. A good number of new results were surveyed by László Fejes Tóth in his Notes to the 2nd edition.The present version of Lagerungen makes this classic monograph available in English for the first time, with updated Notes, completed by extensive surveys of the state of the art. More precisely, this book consists of: a corrected English translation of the original Lagerungen,the revised and updated Notes on the original text, eight self-contained chapters surveying additional topics in detail. The English edition provides a comprehensive update to an enduring classic. Combining the lucid exposition of the original text with extensive new material, it will be a valuable resource for researchers in discrete geometry for decades to come.

Automatic computing has undergone drastic changes since the pioneering days of the early Fifties, one of the most obvious being that today the majority of computer programs are no longer written in machine code but in some programming language like FORTRAN or ALGOL.

The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves.

This book reviews higher dimensional Nevanlinna theory and its relationship with Diophantine approximation theory. Coverage builds up from the classical theory of meromorphic functions on the complex plane with full proofs, to the current state of research.

This book deals with condition as a main aspect in the understanding of the performance-regarding both stability and complexity-of numerical algorithms. It offers partial solutions for Smale's 17th problem.

Lehner University of Pittsburgh, Pittsburgh, PA 15213 and National Bureau of Standards, Washington, DC 20234, U.S.A. Bernoulli polynomials and Bernoulli numbers ....... Zeros of the Bernoulli polynomials ............................. A multiplication formula for the Bernoulli polynomials ...........

This presentation of the theory of hyperbolic conservation laws illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory.

The field of optimal transport has made breathtaking forays into various other domains of mathematics. This book presents a broad overview of this area. PhD students or researchers can read the entire book without any prior knowledge of the field.

A monograph that deals with countable state Markov chains in both discrete time (Part I) and continuous time (Part II). [...]. It includes much of Kai Lai's fundamental work.

But other subjects also play an important role: homology theory, fibration theory (and characteristic classes in particular), and also branches of mathematics that are not directly a part of topology, but which use topological methods in an essential way: for example, the theory of indices of elliptic operators and the theory of complex manifolds.

Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem.

The Local Langlands Conjecture for GL(2) contributes an unprecedented text to the so-called Langlands theory. It presupposes no special knowledge beyond the beginnings of the representation theory of finite groups and the structure theory of local fields.

From the reviews: "The account is quite detailed and is written in a manner that will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations....

A 1988 classic, covering Two-dimensional Surfaces; Domains on the Plane and on Surfaces; Brunn-Minkowski Inequality and Classical Isoperimetric Inequality; Isoperimetric Inequalities for Various Definitions of Area; and Inequalities Involving Mean Curvature.

Sheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations.

The expanded second edition of this book reflects new developments including the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems and the Neistadt theory.

This book has been long awaited in the "interacting particle systems" community. Begun by Claude Kipnis before his untimely death, it was completed by Claudio Landim, his most brilliant student and collaborator. It presents the techniques used in the proof of the hydrodynamic behavior of interacting particle systems.

In the present book, we have put together the basic theory of the units and cuspidal divisor class group in the modular function fields, developed over the past few years. Then r(N)\i) 2 is complex analytic isomorphic to an affine curve YeN), whose compactifi cation is called the modular curve X(N).

This book covers the fundamentals of convex analysis, a refinement of standard calculus with equalities and approximations replaced by inequalities. Reviews minimization algorithms, which provide immediate application to optimization and operations research.

these general notions are useful in con structing travelling waves for systems of nonlinear equations. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves.

Coupled with its sequel, this book gives a connected, unified exposition of Approximation Theory for functions of one real variable. It describes spaces of functions such as Sobolev, Lipschitz, Besov rearrangement-invariant function spaces and interpolation of operators.

From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control.

In recent years there has been enormous activity in the theory of algebraic curves. Our goal is to give a comprehensive and self-contained account of the extrinsic geometry of algebraic curves, which in our opinion constitutes the main geometric core of the recent advances in curve theory.

The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.

It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. New material is introduced here on duality theorems for unramified and tamely ramified extensions as well as a careful analysis of 2-extensions of real number fields.

This two-volume treatise is a standard reference in the field. It pays special attention to the historical aspects and the origins partly in applied problems-such as those of geometric optics-of parts of the theory.