Orthogonal Decompositions And Integral Lattices

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Orthogonal Decompositions and Integral Lattices

Alexei Kostrikin,Pham Huu Tiep
Orthogonal Decompositions and Integral Lattices Book PDF

Author : Alexei Kostrikin,Pham Huu Tiep
Publisher : Walter de Gruyter
Page : 549 pages
File Size : 43,6 Mb
Release : 2011-06-01
Category : Mathematics
ISBN : 9783110901757

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Orthogonal Decompositions and Integral Lattices by Alexei Kostrikin,Pham Huu Tiep Pdf

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Groups, Difference Sets, and the Monster

K.T. Arasu,J.F. Dillon,K. Harada,S. Sehgal,R. Solomon
Groups Difference Sets and the Monster Book PDF

Author : K.T. Arasu,J.F. Dillon,K. Harada,S. Sehgal,R. Solomon
Publisher : Walter de Gruyter
Page : 477 pages
File Size : 55,7 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110893106

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Groups, Difference Sets, and the Monster by K.T. Arasu,J.F. Dillon,K. Harada,S. Sehgal,R. Solomon Pdf

This series is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.

Sphere Packings, Lattices and Groups

John Conway,Neil J. A. Sloane
Sphere Packings Lattices and Groups Book PDF

Author : John Conway,Neil J. A. Sloane
Publisher : Springer Science & Business Media
Page : 778 pages
File Size : 47,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475765687

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Sphere Packings, Lattices and Groups by John Conway,Neil J. A. Sloane Pdf

The third edition of this definitive and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also examine such related issues as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. There is also a description of the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analogue-to-digital conversion and data compression, n-dimensional crystallography, dual theory and superstring theory in physics. New and of special interest is a report on some recent developments in the field, and an updated and enlarged supplementary bibliography with over 800 items.

Lectures on Gaussian Integral Operators and Classical Groups

Yu. A. Neretin
Lectures on Gaussian Integral Operators and Classical Groups Book PDF

Author : Yu. A. Neretin
Publisher : European Mathematical Society
Page : 576 pages
File Size : 48,7 Mb
Release : 2011
Category : Geometry, Differential
ISBN : 3037190809

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Lectures on Gaussian Integral Operators and Classical Groups by Yu. A. Neretin Pdf

This book is an elementary self-contained introduction to some constructions of representation theory and related topics of differential geometry and analysis. Topics covered include the theory of various Fourier-like integral operators such as Segal-Bargmann transforms, Gaussian integral operators in $L^2$ and in the Fock space, integral operators with theta-kernels, the geometry of real and $p$-adic classical groups and symmetric spaces. The heart of the book is the Weil representation of the symplectic group (real and complex realizations, relations with theta-functions and modular forms, $p$-adic and adelic constructions) and representations in Hilbert spaces of holomorphic functions of several complex variables. This book is addressed to graduate students and researchers in representation theory, differential geometry, and operator theory. Prerequisites are standard university courses in linear algebra, functional analysis, and complex analysis.

Computer Algebra in Scientific Computing

Andreas Weber
Computer Algebra in Scientific Computing Book PDF

Author : Andreas Weber
Publisher : MDPI
Page : 160 pages
File Size : 40,8 Mb
Release : 2019-11-04
Category : Computers
ISBN : 9783039217304

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Computer Algebra in Scientific Computing by Andreas Weber Pdf

Although scientific computing is very often associated with numeric computations, the use of computer algebra methods in scientific computing has obtained considerable attention in the last two decades. Computer algebra methods are especially suitable for parametric analysis of the key properties of systems arising in scientific computing. The expression-based computational answers generally provided by these methods are very appealing as they directly relate properties to parameters and speed up testing and tuning of mathematical models through all their possible behaviors. This book contains 8 original research articles dealing with a broad range of topics, ranging from algorithms, data structures, and implementation techniques for high-performance sparse multivariate polynomial arithmetic over the integers and rational numbers over methods for certifying the isolated zeros of polynomial systems to computer algebra problems in quantum computing.

Galois Fields and Galois Rings Made Easy

Maurice Kibler
Galois Fields and Galois Rings Made Easy Book PDF

Author : Maurice Kibler
Publisher : Elsevier
Page : 270 pages
File Size : 49,5 Mb
Release : 2017-09-22
Category : Mathematics
ISBN : 9780081023518

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Galois Fields and Galois Rings Made Easy by Maurice Kibler Pdf

This book constitutes an elementary introduction to rings and fields, in particular Galois rings and Galois fields, with regard to their application to the theory of quantum information, a field at the crossroads of quantum physics, discrete mathematics and informatics. The existing literature on rings and fields is primarily mathematical. There are a great number of excellent books on the theory of rings and fields written by and for mathematicians, but these can be difficult for physicists and chemists to access. This book offers an introduction to rings and fields with numerous examples. It contains an application to the construction of mutually unbiased bases of pivotal importance in quantum information. It is intended for graduate and undergraduate students and researchers in physics, mathematical physics and quantum chemistry (especially in the domains of advanced quantum mechanics, quantum optics, quantum information theory, classical and quantum computing, and computer engineering). Although the book is not written for mathematicians, given the large number of examples discussed, it may also be of interest to undergraduate students in mathematics. Contains numerous examples that accompany the text Includes an important chapter on mutually unbiased bases Helps physicists and theoretical chemists understand this area of mathematics

The Finite Simple Groups

Robert Wilson
The Finite Simple Groups Book PDF

Author : Robert Wilson
Publisher : Springer Science & Business Media
Page : 310 pages
File Size : 44,5 Mb
Release : 2009-12-14
Category : Mathematics
ISBN : 9781848009875

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The Finite Simple Groups by Robert Wilson Pdf

Thisbookisintendedasanintroductiontoallthe?nitesimplegroups.During themonumentalstruggletoclassifythe?nitesimplegroups(andindeedsince), a huge amount of information about these groups has been accumulated. Conveyingthisinformationtothenextgenerationofstudentsandresearchers, not to mention those who might wish to apply this knowledge, has become a major challenge. With the publication of the two volumes by Aschbacher and Smith [12, 13] in 2004 we can reasonably regard the proof of the Classi?cation Theorem for Finite Simple Groups (usually abbreviated CFSG) as complete. Thus it is timely to attempt an overview of all the (non-abelian) ?nite simple groups in one volume. For expository purposes it is convenient to divide them into four basic types, namely the alternating, classical, exceptional and sporadic groups. The study of alternating groups soon develops into the theory of per- tation groups, which is well served by the classic text of Wielandt [170]and more modern treatments such as the comprehensive introduction by Dixon and Mortimer [53] and more specialised texts such as that of Cameron [19].

The Atlas of Finite Groups - Ten Years On

Robert Curtis
The Atlas of Finite Groups Ten Years On Book PDF

Author : Robert Curtis
Publisher : Cambridge University Press
Page : 315 pages
File Size : 48,6 Mb
Release : 1998-06-11
Category : Mathematics
ISBN : 9780521575874

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The Atlas of Finite Groups - Ten Years On by Robert Curtis Pdf

Proceedings containing twenty articles by leading experts in group theory and its applications.

Geometry of Quantum States

Ingemar Bengtsson,Karol Życzkowski
Geometry of Quantum States Book PDF

Author : Ingemar Bengtsson,Karol Życzkowski
Publisher : Cambridge University Press
Page : 637 pages
File Size : 45,9 Mb
Release : 2017-08-18
Category : Mathematics
ISBN : 9781107026254

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Geometry of Quantum States by Ingemar Bengtsson,Karol Życzkowski Pdf

This new edition describes the space of quantum states and the theory of quantum entanglement from a geometric perspective.

Embedding Problems in Symplectic Geometry

Felix Schlenk
Embedding Problems in Symplectic Geometry Book PDF

Author : Felix Schlenk
Publisher : Walter de Gruyter
Page : 261 pages
File Size : 49,5 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783110199697

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Embedding Problems in Symplectic Geometry by Felix Schlenk Pdf

Symplectic geometry is the geometry underlying Hamiltonian dynamics, and symplectic mappings arise as time-1-maps of Hamiltonian flows. The spectacular rigidity phenomena for symplectic mappings discovered in the last two decades show that certain things cannot be done by a symplectic mapping. For instance, Gromov's famous "non-squeezing'' theorem states that one cannot map a ball into a thinner cylinder by a symplectic embedding. The aim of this book is to show that certain other things can be done by symplectic mappings. This is achieved by various elementary and explicit symplectic embedding constructions, such as "folding", "wrapping'', and "lifting''. These constructions are carried out in detail and are used to solve some specific symplectic embedding problems. The exposition is self-contained and addressed to students and researchers interested in geometry or dynamics.

Character Theory of Finite Groups

Bertram Huppert
Character Theory of Finite Groups Book PDF

Author : Bertram Huppert
Publisher : Walter de Gruyter
Page : 625 pages
File Size : 54,6 Mb
Release : 2011-04-20
Category : Mathematics
ISBN : 9783110809237

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Character Theory of Finite Groups by Bertram Huppert Pdf

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Trigonometric Sums in Number Theory and Analysis

Gennady I. Arkhipov,Vladimir N. Chubarikov,Anatoly A. Karatsuba
Trigonometric Sums in Number Theory and Analysis Book PDF

Author : Gennady I. Arkhipov,Vladimir N. Chubarikov,Anatoly A. Karatsuba
Publisher : Walter de Gruyter
Page : 565 pages
File Size : 50,8 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783110197983

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Trigonometric Sums in Number Theory and Analysis by Gennady I. Arkhipov,Vladimir N. Chubarikov,Anatoly A. Karatsuba Pdf

The book presents the theory of multiple trigonometric sums constructed by the authors. Following a unified approach, the authors obtain estimates for these sums similar to the classical I. M. Vinogradov ́s estimates and use them to solve several problems in analytic number theory. They investigate trigonometric integrals, which are often encountered in physics, mathematical statistics, and analysis, and in addition they present purely arithmetic results concerning the solvability of equations in integers.

Finite Reductive Groups: Related Structures and Representations

Marc Cabanes
Finite Reductive Groups Related Structures and Representations Book PDF

Author : Marc Cabanes
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461241249

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Finite Reductive Groups: Related Structures and Representations by Marc Cabanes Pdf

Finite reductive groups and their representations lie at the heart of group theory. This volume treats linear representations of finite reductive groups and their modular aspects together with Hecke algebras, complex reflection groups, quantum groups, arithmetic groups, Lie groups, symmetric groups and general finite groups.

Compact Projective Planes

Helmut Salzmann,Dieter Betten,Theo Grundhöfer,Hermann Hähl,Rainer Löwen,Markus Stroppel
Compact Projective Planes Book PDF

Author : Helmut Salzmann,Dieter Betten,Theo Grundhöfer,Hermann Hähl,Rainer Löwen,Markus Stroppel
Publisher : Walter de Gruyter
Page : 705 pages
File Size : 50,7 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110876833

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Compact Projective Planes by Helmut Salzmann,Dieter Betten,Theo Grundhöfer,Hermann Hähl,Rainer Löwen,Markus Stroppel Pdf

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Automatic Sequences

von Friedrich Haeseler
Automatic Sequences Book PDF

Author : von Friedrich Haeseler
Publisher : Walter de Gruyter
Page : 200 pages
File Size : 51,5 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783110197969

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Automatic Sequences by von Friedrich Haeseler Pdf

Automatic sequences are sequences which are produced by a finite automaton. Although they are not random they may look as being random. They are complicated, in the sense of not being not ultimately periodic, they may look rather complicated, in the sense that it may not be easy to name the rule by which the sequence is generated, however there exists a rule which generates the sequence. The concept automatic sequences has special applications in algebra, number theory, finite automata and formal languages, combinatorics on words. The text deals with different aspects of automatic sequences, in particular: · a general introduction to automatic sequences · the basic (combinatorial) properties of automatic sequences · the algebraic approach to automatic sequences · geometric objects related to automatic sequences.