Spectral Theory Of Non Commutative Harmonic Oscillators An Introduction

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Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction

Alberto Parmeggiani
Spectral Theory of Non Commutative Harmonic Oscillators An Introduction Book PDF

Author : Alberto Parmeggiani
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 46,9 Mb
Release : 2010-04-22
Category : Mathematics
ISBN : 9783642119217

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Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction by Alberto Parmeggiani Pdf

This volume describes the spectral theory of the Weyl quantization of systems of polynomials in phase-space variables, modelled after the harmonic oscillator. The main technique used is pseudodifferential calculus, including global and semiclassical variants. The main results concern the meromorphic continuation of the spectral zeta function associated with the spectrum, and the localization (and the multiplicity) of the eigenvalues of such systems, described in terms of “classical” invariants (such as the periods of the periodic trajectories of the bicharacteristic flow associated with the eiganvalues of the symbol). The book utilizes techniques that are very powerful and flexible and presents an approach that could also be used for a variety of other problems. It also features expositions on different results throughout the literature.

Noncommutative Geometry and Physics 3

Giuseppe Dito,Motoko Kotani,Yoshiaki Maeda
Noncommutative Geometry and Physics 3 Book PDF

Author : Giuseppe Dito,Motoko Kotani,Yoshiaki Maeda
Publisher : World Scientific
Page : 537 pages
File Size : 44,9 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814425018

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Noncommutative Geometry and Physics 3 by Giuseppe Dito,Motoko Kotani,Yoshiaki Maeda Pdf

Noncommutative differential geometry has many actual and potential applications to several domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field.

International Symposium on Mathematics, Quantum Theory, and Cryptography

Tsuyoshi Takagi,Masato Wakayama,Keisuke Tanaka,Noboru Kunihiro,Kazufumi Kimoto,Yasuhiko Ikematsu
International Symposium on Mathematics Quantum Theory and Cryptography Book PDF

Author : Tsuyoshi Takagi,Masato Wakayama,Keisuke Tanaka,Noboru Kunihiro,Kazufumi Kimoto,Yasuhiko Ikematsu
Publisher : Springer Nature
Page : 275 pages
File Size : 45,8 Mb
Release : 2020-10-22
Category : Technology & Engineering
ISBN : 9789811551918

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International Symposium on Mathematics, Quantum Theory, and Cryptography by Tsuyoshi Takagi,Masato Wakayama,Keisuke Tanaka,Noboru Kunihiro,Kazufumi Kimoto,Yasuhiko Ikematsu Pdf

This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography.

A Mathematical Approach to Research Problems of Science and Technology

Ryuei Nishii,Shin-ichiro Ei,Miyuki Koiso,Hiroyuki Ochiai,Kanzo Okada,Shingo Saito,Tomoyuki Shirai
A Mathematical Approach to Research Problems of Science and Technology Book PDF

Author : Ryuei Nishii,Shin-ichiro Ei,Miyuki Koiso,Hiroyuki Ochiai,Kanzo Okada,Shingo Saito,Tomoyuki Shirai
Publisher : Springer
Page : 507 pages
File Size : 44,8 Mb
Release : 2014-07-14
Category : Technology & Engineering
ISBN : 9784431550600

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A Mathematical Approach to Research Problems of Science and Technology by Ryuei Nishii,Shin-ichiro Ei,Miyuki Koiso,Hiroyuki Ochiai,Kanzo Okada,Shingo Saito,Tomoyuki Shirai Pdf

This book deals with one of the most novel advances in mathematical modeling for applied scientific technology, including computer graphics, public-key encryption, data visualization, statistical data analysis, symbolic calculation, encryption, error correcting codes, and risk management. It also shows that mathematics can be used to solve problems from nature, e.g., slime mold algorithms. One of the unique features of this book is that it shows readers how to use pure and applied mathematics, especially those mathematical theory/techniques developed in the twentieth century, and developing now, to solve applied problems in several fields of industry. Each chapter includes clues on how to use "mathematics" to solve concrete problems faced in industry as well as practical applications. The target audience is not limited to researchers working in applied mathematics and includes those in engineering, material sciences, economics, and life sciences.

Casimir Force, Casimir Operators and the Riemann Hypothesis

Gerrit Dijk,Masato Wakayama
Casimir Force Casimir Operators and the Riemann Hypothesis Book PDF

Author : Gerrit Dijk,Masato Wakayama
Publisher : Walter de Gruyter
Page : 295 pages
File Size : 45,5 Mb
Release : 2010-10-19
Category : Mathematics
ISBN : 9783110226133

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Casimir Force, Casimir Operators and the Riemann Hypothesis by Gerrit Dijk,Masato Wakayama Pdf

This volume contains the proceedings of the conference "Casimir Force, Casimir Operators and the Riemann Hypothesis – Mathematics for Innovation in Industry and Science" held in November 2009 in Fukuoka (Japan). The motive for the conference was the celebration of the 100th birthday of Casimir and the 150th birthday of the Riemann hypothesis. The conference focused on the following topics: Casimir operators in harmonic analysis and representation theory Number theory, in particular zeta functions and cryptography Casimir force in physics and its relation with nano-science Mathematical biology Importance of mathematics for innovation in industry The latter topic was inspired both by the call for innovation in industry worldwide and by the fact that Casimir, who was the director of Philips research for a long time in his career, had an outspoken opinion on the importance of fundamental science for industry. These proceedings are of interest both to research mathematicians and to those interested in the role science, and in particular mathematics, can play in innovation in industry.

Mathematical Modelling for Next-Generation Cryptography

Tsuyoshi Takagi,Masato Wakayama,Keisuke Tanaka,Noboru Kunihiro,Kazufumi Kimoto,Dung Hoang Duong
Mathematical Modelling for Next Generation Cryptography Book PDF

Author : Tsuyoshi Takagi,Masato Wakayama,Keisuke Tanaka,Noboru Kunihiro,Kazufumi Kimoto,Dung Hoang Duong
Publisher : Springer
Page : 368 pages
File Size : 48,5 Mb
Release : 2017-07-25
Category : Computers
ISBN : 9789811050657

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Mathematical Modelling for Next-Generation Cryptography by Tsuyoshi Takagi,Masato Wakayama,Keisuke Tanaka,Noboru Kunihiro,Kazufumi Kimoto,Dung Hoang Duong Pdf

This book presents the mathematical background underlying security modeling in the context of next-generation cryptography. By introducing new mathematical results in order to strengthen information security, while simultaneously presenting fresh insights and developing the respective areas of mathematics, it is the first-ever book to focus on areas that have not yet been fully exploited for cryptographic applications such as representation theory and mathematical physics, among others. Recent advances in cryptanalysis, brought about in particular by quantum computation and physical attacks on cryptographic devices, such as side-channel analysis or power analysis, have revealed the growing security risks for state-of-the-art cryptographic schemes. To address these risks, high-performance, next-generation cryptosystems must be studied, which requires the further development of the mathematical background of modern cryptography. More specifically, in order to avoid the security risks posed by adversaries with advanced attack capabilities, cryptosystems must be upgraded, which in turn relies on a wide range of mathematical theories. This book is suitable for use in an advanced graduate course in mathematical cryptography, while also offering a valuable reference guide for experts.

Topics in Algebraic and Topological K-Theory

Paul Frank Baum,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën
Topics in Algebraic and Topological K Theory Book PDF

Author : Paul Frank Baum,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 51,6 Mb
Release : 2010-11-05
Category : Mathematics
ISBN : 9783642157073

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Topics in Algebraic and Topological K-Theory by Paul Frank Baum,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën Pdf

This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.

Blow-up Theories for Semilinear Parabolic Equations

Bei Hu
Blow up Theories for Semilinear Parabolic Equations Book PDF

Author : Bei Hu
Publisher : Springer Science & Business Media
Page : 137 pages
File Size : 51,7 Mb
Release : 2011-03-23
Category : Mathematics
ISBN : 9783642184598

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Blow-up Theories for Semilinear Parabolic Equations by Bei Hu Pdf

There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.

Lévy Matters I

Thomas Duquesne,Oleg Reichmann,Ken-iti Sato,Christoph Schwab
L vy Matters I Book PDF

Author : Thomas Duquesne,Oleg Reichmann,Ken-iti Sato,Christoph Schwab
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 47,8 Mb
Release : 2010-09-05
Category : Mathematics
ISBN : 9783642140068

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Lévy Matters I by Thomas Duquesne,Oleg Reichmann,Ken-iti Sato,Christoph Schwab Pdf

Focusing on the breadth of the topic, this volume explores Lévy processes and applications, and presents the state-of-the-art in this evolving area of study. These expository articles help to disseminate important theoretical and applied research to those studying the field.

Computational Approach to Riemann Surfaces

Alexander I. Bobenko
Computational Approach to Riemann Surfaces Book PDF

Author : Alexander I. Bobenko
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 42,5 Mb
Release : 2011-02-12
Category : Mathematics
ISBN : 9783642174124

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Computational Approach to Riemann Surfaces by Alexander I. Bobenko Pdf

This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.

Random Perturbation of PDEs and Fluid Dynamic Models

Franco Flandoli
Random Perturbation of PDEs and Fluid Dynamic Models Book PDF

Author : Franco Flandoli
Publisher : Springer Science & Business Media
Page : 187 pages
File Size : 44,8 Mb
Release : 2011-03-11
Category : Mathematics
ISBN : 9783642182303

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Random Perturbation of PDEs and Fluid Dynamic Models by Franco Flandoli Pdf

This volume explores the random perturbation of PDEs and fluid dynamic models. The text describes the role of additive and bilinear multiplicative noise, and includes examples of abstract parabolic evolution equations.

Séminaire de Probabilités XLIII

Catherine Donati Martin,Antoine Lejay,Alain Rouault
S minaire de Probabilit s XLIII Book PDF

Author : Catherine Donati Martin,Antoine Lejay,Alain Rouault
Publisher : Springer Science & Business Media
Page : 511 pages
File Size : 44,8 Mb
Release : 2010-10-28
Category : Mathematics
ISBN : 9783642152160

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Séminaire de Probabilités XLIII by Catherine Donati Martin,Antoine Lejay,Alain Rouault Pdf

This is a new volume of the Séminaire de Probabilités which is now in its 43rd year. Following the tradition, this volume contains about 20 original research and survey articles on topics related to stochastic analysis. It contains an advanced course of J. Picard on the representation formulae for fractional Brownian motion. The regular chapters cover a wide range of themes, such as stochastic calculus and stochastic differential equations, stochastic differential geometry, filtrations, analysis on Wiener space, random matrices and free probability, as well as mathematical finance. Some of the contributions were presented at the Journées de Probabilités held in Poitiers in June 2009.

Topological Complexity of Smooth Random Functions

Robert Adler,Jonathan E. Taylor
Topological Complexity of Smooth Random Functions Book PDF

Author : Robert Adler,Jonathan E. Taylor
Publisher : Springer Science & Business Media
Page : 135 pages
File Size : 48,8 Mb
Release : 2011-05-18
Category : Mathematics
ISBN : 9783642195792

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Topological Complexity of Smooth Random Functions by Robert Adler,Jonathan E. Taylor Pdf

These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.

Lebesgue and Sobolev Spaces with Variable Exponents

Lars Diening
Lebesgue and Sobolev Spaces with Variable Exponents Book PDF

Author : Lars Diening
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 55,5 Mb
Release : 2011-03-31
Category : Mathematics
ISBN : 9783642183621

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Lebesgue and Sobolev Spaces with Variable Exponents by Lars Diening Pdf

The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.

The Ricci Flow in Riemannian Geometry

Ben Andrews,Christopher Hopper
The Ricci Flow in Riemannian Geometry Book PDF

Author : Ben Andrews,Christopher Hopper
Publisher : Springer Science & Business Media
Page : 306 pages
File Size : 49,9 Mb
Release : 2011
Category : Mathematics
ISBN : 9783642162855

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The Ricci Flow in Riemannian Geometry by Ben Andrews,Christopher Hopper Pdf

This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.