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Marginal and Functional Quantization of Stochastic Processes

Posted By: AvaxGenius

Date: 9 Dec 2023 06:09:24

Vector Quantization, a pioneering discretization method based on nearest neighbor search, emerged in the 1950s primarily in signal processing, electrical engineering, and information theory. Later in the 1960s, it evolved into an automatic classification technique for generating prototypes of extensive datasets. In modern terms, it can be recognized as a seminal contribution to unsupervised learning through the k-means clustering algorithm in data science.

Scienece Vector Quantization Quantization Signal transmission probability

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Hyponormal Quantization of Planar Domains: Exponential Transform in Dimension Two (Repost)

Posted By: AvaxGenius

Date: 29 Aug 2022 12:54:44

Hyponormal Quantization of Planar Domains: Exponential Transform in Dimension Two (Repost)

Hyponormal Quantization of Planar Domains: Exponential Transform in Dimension Two by Björn Gustafsson, Mihai Putinar
English | PDF | 2017 | 152 Pages | ISBN : 3319658093 | 2.2 MB

This book exploits the classification of a class of linear bounded operators with rank-one self-commutators in terms of their spectral parameter, known as the principal function. The resulting dictionary between two dimensional planar shapes with a degree of shade and Hilbert space operators turns out to be illuminating and beneficial for both sides. An exponential transform, essentially a Riesz potential at critical exponent, is at the heart of this novel framework; its best rational approximants unveil a new class of complex orthogonal polynomials whose asymptotic distribution of zeros is thoroughly studied in the text. Connections with areas of potential theory, approximation theory in the complex domain and fluid mechanics are established.

Science momentum problem orthogonal polynomial Complex Variable Operator Theory Potential Theory Numerical Analysis Quantization Hyponormal Quantization Mathematics

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Geometric Quantization and Quantum Mechanics

Posted By: AvaxGenius

Date: 20 Jun 2022 02:39:50

Geometric Quantization and Quantum Mechanics by Jȩdrzej Śniatycki
English | PDF | 1980 | 241 Pages | ISBN : 0387904697 | 19.4 MB

This book contains a revised and expanded version of the lecture notes of two seminar series given during the academic year 1976/77 at the Department of Mathematics and Statistics of the University of Calgary, and in the summer of 1978 at the Institute of Theoretical Physics of the Technical University Clausthal. The aim of the seminars was to present geometric quantization from the point of view· of its applica tions to quantum mechanics, and to introduce the quantum dynamics of various physical systems as the result of the geometric quantization of the classical dynamics of these systems.

Science Quantisierung Theoretical physics quantum mechanics Geometric Quantization Quantum Mechanics Mechanics Quantization Computational Physics

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Arithmetic and Geometry Around Quantization (Repost)

Posted By: AvaxGenius

Date: 24 Apr 2022 05:55:38

Arithmetic and Geometry Around Quantization (Repost)

Arithmetic and Geometry Around Quantization by Özgür Ceyhan
English | PDF | 2010 | 295 Pages | ISBN : 0817648305 | 3.9 MB

In recent decades, quantization has led to interesting applications in various mathematical branches. This volume, comprised of research and survey articles, discusses key topics, including symplectic and algebraic geometry, representation theory, quantum groups, the geometric Langlands program, quantum ergodicity, and non-commutative geometry. A wide range of topics related to quantization are covered, giving a glimpse of the broad subject. The articles are written by distinguished mathematicians in the field and reflect subsequent developments following the Arithmetic and Geometry around Quantization conference held in Istanbul.

Science algebra Geometry Arithmetic Quantization quantum invariants quantum groups Applications of Mathematics Algebra Mathematical Methods in Physics Quantum Physics Algebraic Geometry

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Quantum-Classical Correspondence: Dynamical Quantization and the Classical Limit

Posted By: AvaxGenius

Date: 3 Dec 2021 04:05:17

Quantum-Classical Correspondence: Dynamical Quantization and the Classical Limit by A. O. Bolivar
English | PDF | 2004 | 196 Pages | ISBN : 3540201467 | 15.2 MB

At what level of physical existence does "quantum behavior" begin? How does it develop from classical mechanics? This book addresses these questions and thereby sheds light on fundamental conceptual problems of quantum mechanics. Quantum-Classical Correspondence elucidates the problem by developing a procedure for quantizing stochastic systems (e.g. Brownian systems) described by Fokker-Planck equations.

Science Physics Classical limit Quantization stochastic process quantum mechanics classical mechanics Stochastic processes

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Collective Behavior in Complex Networked Systems under Imperfect Communication

Posted By: AvaxGenius

Date: 6 Jul 2021 13:32:50

This book aims to explain how collective behavior is formed via local interactions under imperfect communication in complex networked systems. It also presents some new distributed protocols or algorithms for complex networked systems to comply with bandwidth limitation and tolerate communication delays.