Author : Bernhard Schmidt
Publisher : Springer
Page : 112 pages
File Size : 11,60 MB
Release : 2004-10-13
Category : Mathematics
ISBN : 3540457976
This monograph contributes to the existence theory of difference sets, cyclic irreducible codes and similar objects. The new method of field descent for cyclotomic integers of presribed absolute value is developed. Applications include the first substantial progress towards the Circulant Hadamard Matrix Conjecture and Ryser`s conjecture since decades. It is shown that there is no Barker sequence of length l with 13
Author : Alexander Pott
Publisher : Springer
Page : 185 pages
File Size : 20,55 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540491821
Difference sets are of central interest in finite geometry and design theory. One of the main techniques to investigate abelian difference sets is a discrete version of the classical Fourier transform (i.e., character theory) in connection with algebraic number theory. This approach is described using only basic knowledge of algebra and algebraic number theory. It contains not only most of our present knowledge about abelian difference sets, but also gives applications of character theory to projective planes with quasiregular collineation groups. Therefore, the book is of interest both to geometers and mathematicians working on difference sets. Moreover, the Fourier transform is important in more applied branches of discrete mathematics such as coding theory and shift register sequences.
Author : Marcus du Sautoy
Publisher : Springer Science & Business Media
Page : 217 pages
File Size : 47,7 MB
Release : 2008
Category : Mathematics
ISBN : 354074701X
Zeta functions have been a powerful tool in mathematics over the last two centuries. This book considers a new class of non-commutative zeta functions which encode the structure of the subgroup lattice in infinite groups. The book explores the analytic behaviour of these functions together with an investigation of functional equations. Many important examples of zeta functions are calculated and recorded providing an important data base of explicit examples and methods for calculation.
Author : Horst Herrlich
Publisher : Springer
Page : 207 pages
File Size : 33,57 MB
Release : 2006-07-21
Category : Mathematics
ISBN : 3540342680
AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom. It is shunned by some, used indiscriminately by others. This treatise shows paradigmatically that disasters happen without AC and they happen with AC. Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory.
Author : Jim Pitman
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 25,9 MB
Release : 2006-05-11
Category : Mathematics
ISBN : 354030990X
The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.
Author : David J. Green
Publisher : Springer Science & Business Media
Page : 156 pages
File Size : 19,67 MB
Release : 2003-11-18
Category : Mathematics
ISBN : 9783540203391
This monograph develops the Gröbner basis methods needed to perform efficient state of the art calculations in the cohomology of finite groups. Results obtained include the first counterexample to the conjecture that the ideal of essential classes squares to zero. The context is J. F. Carlson’s minimal resolutions approach to cohomology computations.
Author : Juan A. Navarro González
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 28,50 MB
Release : 2003-10-29
Category : Mathematics
ISBN : 9783540200727
The volume develops the foundations of differential geometry so as to include finite-dimensional spaces with singularities and nilpotent functions, at the same level as is standard in the elementary theory of schemes and analytic spaces. The theory of differentiable spaces is developed to the point of providing a handy tool including arbitrary base changes (hence fibred products, intersections and fibres of morphisms), infinitesimal neighbourhoods, sheaves of relative differentials, quotients by actions of compact Lie groups and a theory of sheaves of Fréchet modules paralleling the useful theory of quasi-coherent sheaves on schemes. These notes fit naturally in the theory of C^\infinity-rings and C^\infinity-schemes, as well as in the framework of Spallek’s C^\infinity-standard differentiable spaces, and they require a certain familiarity with commutative algebra, sheaf theory, rings of differentiable functions and Fréchet spaces.
Author : Michael Cowling
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 19,56 MB
Release : 2008-02-27
Category : Mathematics
ISBN : 3540768912
Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability. They further illustrate how representation theory is related to quantum computing; and much more. Taken together, this volume provides both a solid reference and deep insights on current research activity.
Author : Simeon Ball
Publisher : Cambridge University Press
Page : 299 pages
File Size : 40,77 MB
Release : 2015-07-02
Category : Mathematics
ISBN : 1107107997
A graduate-level introduction to finite geometry and its applications to other areas of combinatorics.
Author : Andras Telcs
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 34,72 MB
Release : 2006-05-17
Category : Mathematics
ISBN : 3540330275
Einstein proved that the mean square displacement of Brownian motion is proportional to time. He also proved that the diffusion constant depends on the mass and on the conductivity (sometimes referred to Einstein’s relation). The main aim of this book is to reveal similar connections between the physical and geometric properties of space and diffusion. This is done in the context of random walks in the absence of algebraic structure, local or global spatial symmetry or self-similarity. The author studies the heat diffusion at this general level and discusses the following topics: The multiplicative Einstein relation, Isoperimetric inequalities, Heat kernel estimates Elliptic and parabolic Harnack inequality.
