Uncertainty Principles On Riemannian Manifolds

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Uncertainty Principles on Riemannian Manifolds

Author : Wolfgang Erb
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832527443
Total Pages : 174 pages
Book Rating : 4.8/5 (325 download)

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Book Synopsis Uncertainty Principles on Riemannian Manifolds by : Wolfgang Erb

Download or read book Uncertainty Principles on Riemannian Manifolds written by Wolfgang Erb and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, the Heisenberg-Pauli-Weyl uncertainty principle on the real line and the Breitenberger uncertainty on the unit circle are generalized to Riemannian manifolds. The proof of these generalized uncertainty principles is based on an operator theoretic approach involving the commutator of two operators on a Hilbert space. As a momentum operator, a special differential-difference operator is constructed which plays the role of a generalized root of the radial part of the Laplace-Beltrami operator. Further, it is shown that the resulting uncertainty inequalities are sharp. In the final part of the thesis, these uncertainty principles are used to analyze the space-frequency behavior of polynomial kernels on compact symmetric spaces and to construct polynomials that are optimally localized in space with respect to the position variance of the uncertainty principle.

Geometric Analysis on the Heisenberg Group and Its Generalizations

Author : Ovidiu Calin
Publisher : American Mathematical Soc.
ISBN 13 : 0821846884
Total Pages : 258 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometric Analysis on the Heisenberg Group and Its Generalizations by : Ovidiu Calin

Download or read book Geometric Analysis on the Heisenberg Group and Its Generalizations written by Ovidiu Calin and published by American Mathematical Soc.. This book was released on 2008-06-30 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Differential Heterogenesis

Author : Alessandro Sarti
Publisher : Springer Nature
ISBN 13 : 3030977978
Total Pages : 222 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Differential Heterogenesis by : Alessandro Sarti

Download or read book Differential Heterogenesis written by Alessandro Sarti and published by Springer Nature. This book was released on 2022-07-15 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes about unlike usual differential dynamics common in mathematical physics, heterogenesis is based on the assemblage of differential constraints that are different from point to point. The construction of differential assemblages will be introduced in the present study from the mathematical point of view, outlining the heterogeneity of the differential constraints and of the associated phase spaces, that are continuously changing in space and time. If homogeneous constraints well describe a form of swarm intelligence or crowd behaviour, it reduces dynamics to automatisms, by excluding any form of imaginative and creative aspect. With this study we aim to problematize the procedure of homogeneization that is dominant in life and social science and to outline the dynamical heterogeneity of life and its affective, semiotic, social, historical aspects. Particularly, the use of sub-Riemannian geometry instead of Riemannian one allows to introduce disjointed and autonomous areas in the virtual plane. Our purpose is to free up the dynamic becoming from any form of unitary and totalizing symmetry and to develop forms, action, thought by means of proliferation, juxtaposition, and disjunction devices. After stating the concept of differential heterogenesis with the language of contemporary mathematics, we will face the problem of the emergence of the semiotic function, recalling the limitation of classical approaches (Hjelmslev, Saussure, Husserl) and proposing a possible genesis of it from the heterogenetic flow previously defined. We consider the conditions under which this process can be polarized to constitute different planes of Content (C) and Expression (E), each one equipped with its own formed substances. A possible (but not unique) process of polarization is constructed by means of spectral analysis, that is introduced to individuate E/C planes and their evolution. The heterogenetic flow, solution of differential assemblages, gives rise to forms that are projected onto the planes, offering a first referring system for the flow, that constitutes a first degree of semiosis.

Stochastic Processes and Functional Analysis

Author : Randall J. Swift
Publisher : American Mathematical Society
ISBN 13 : 1470459825
Total Pages : 248 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Stochastic Processes and Functional Analysis by : Randall J. Swift

Download or read book Stochastic Processes and Functional Analysis written by Randall J. Swift and published by American Mathematical Society. This book was released on 2021-11-22 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Celebrating M. M. Rao's Many Mathematical Contributions as he Turns 90 Years Old, held from November 9–10, 2019, at the University of California, Riverside, California. The articles show the effectiveness of abstract analysis for solving fundamental problems of stochastic theory, specifically the use of functional analytic methods for elucidating stochastic processes and their applications. The volume also includes a biography of M. M. Rao and the list of his publications.

Dictionary of Scientific Principles

Author : Stephen Marvin
Publisher : John Wiley & Sons
ISBN 13 : 047014680X
Total Pages : 176 pages
Book Rating : 4.4/5 (71 download)

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Book Synopsis Dictionary of Scientific Principles by : Stephen Marvin

Download or read book Dictionary of Scientific Principles written by Stephen Marvin and published by John Wiley & Sons. This book was released on 2011-01-04 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dictionary of Scientific Principles presents a unique and timeless collection of (almost) all known rules or laws commonly called principles, identified throughout the history of scientific development, their definition, and use. Exploring a broad range of disciplines, the book first lists more than 2,000 principles organized in a standard alphabetical order, then provides a list of subject headings for which related principles are identified. A staple addition to every library, the dictionary will also be of interest to scientists and general readers.

Chaos Theory

Author : Ioannis Dimotikalis
Publisher : World Scientific
ISBN 13 : 9814350346
Total Pages : 467 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Chaos Theory by : Ioannis Dimotikalis

Download or read book Chaos Theory written by Ioannis Dimotikalis and published by World Scientific. This book was released on 2011 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithmic sound composition using coupled cellular automata / Jaime Serquera and Eduardo R. Miranda -- Efficient large-scale forcing in finite-difference simulations of steady isotropic turbulence / Ryo Onishi, Yuya Baba and Keiko Takahashi -- Rendering statistical significance of information flow measures / Angeliki Papana and Dimitris Kugiumtzis. Complexity theory and physical unification : from microscopic to macroscopic level / G.P. Pavlos [und weitere] -- Regular variation, Paretian distributions, and the interplay of light and heavy tails in the fractality of asymptotic models / Dinis D. Pestana, Sandra M. Aleixo and J. Leonel Rocha -- Tools for investigation of dynamics of DC-DC converters within Matlab/Simulink / Dmitry Pikulin -- Chaos as compositional order / Eleri Angharad Pound -- Beta(p, q)-Cantor sets - determinism and randomness / J. Leonel Rocha, Sandra M. Aleixo and Dinis D. Pestana -- Predicting chaos with second method of Lyapunov / Vladimir B. Ryabov -- Analysis of homoclinic bifurcation in Duffing oscillator under two-frequency excitation : peculiarity of using Melnikov method in combination with averaging technique / Vladimir Ryabov and Kenta Fukushima -- Exploring life expectancy limits : first exit time modeling, parameter analysis and forecasts / Christos H. Skiadas and Charilaos Skiadas -- Composing chaotic music from the letter m / Anastasios D. Sotiropoulos -- On the timbre of chaotic algorithmic sounds / Dimitrios A. Sotiropoulos, Anastasios D. Sotiropoulos and Vaggelis D. Sotiropoulos -- The rainbow effect on composing chaotic algorithmic music / Vaggelis D. Sotiropoulos -- A highly chaotic attractor for a dual-channel single-attractor, private communication system / Banlue Srisuchinwong and Buncha Munmuangsaen -- Manifestation of chaos in collective models of nuclei / Pavel Stransky [und weitere] -- Importance of the chaos for computational processes of collective intelligence in social structures / Tadeusz (Ted) Szuba -- Complex signal generators based on capacitors and on piezoelectric loads / Horia-Nicolai L. Teodorescu and Victor P. Cojocaru -- Drift waves' synchronization by using an external signal. The stabilization of a chaotic plasma turbulence / C.L. Xaplanteris and E. Filippaki -- Chaos game technique as a tool for the analysis of natural geomorphological features / G. Zibret and T. Verbovsek -- Dynamics of a steel turning process / Grzegorz Litak and Rafal Rusinek

On Some Aspects of Oscillation Theory and Geometry

Author : Bruno Bianchini
Publisher : American Mathematical Soc.
ISBN 13 : 0821887998
Total Pages : 208 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis On Some Aspects of Oscillation Theory and Geometry by : Bruno Bianchini

Download or read book On Some Aspects of Oscillation Theory and Geometry written by Bruno Bianchini and published by American Mathematical Soc.. This book was released on 2013-08-23 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this paper is to analyze some of the relationships between oscillation theory for linear ordinary differential equations on the real line (shortly, ODE) and the geometry of complete Riemannian manifolds. With this motivation the authors prove some new results in both directions, ranging from oscillation and nonoscillation conditions for ODE's that improve on classical criteria, to estimates in the spectral theory of some geometric differential operator on Riemannian manifolds with related topological and geometric applications. To keep their investigation basically self-contained, the authors also collect some, more or less known, material which often appears in the literature in various forms and for which they give, in some instances, new proofs according to their specific point of view.

Algorithmic Advances in Riemannian Geometry and Applications

Author : Hà Quang Minh
Publisher : Springer
ISBN 13 : 3319450263
Total Pages : 216 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Algorithmic Advances in Riemannian Geometry and Applications by : Hà Quang Minh

Download or read book Algorithmic Advances in Riemannian Geometry and Applications written by Hà Quang Minh and published by Springer. This book was released on 2016-10-05 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a selection of the most recent algorithmic advances in Riemannian geometry in the context of machine learning, statistics, optimization, computer vision, and related fields. The unifying theme of the different chapters in the book is the exploitation of the geometry of data using the mathematical machinery of Riemannian geometry. As demonstrated by all the chapters in the book, when the data is intrinsically non-Euclidean, the utilization of this geometrical information can lead to better algorithms that can capture more accurately the structures inherent in the data, leading ultimately to better empirical performance. This book is not intended to be an encyclopedic compilation of the applications of Riemannian geometry. Instead, it focuses on several important research directions that are currently actively pursued by researchers in the field. These include statistical modeling and analysis on manifolds,optimization on manifolds, Riemannian manifolds and kernel methods, and dictionary learning and sparse coding on manifolds. Examples of applications include novel algorithms for Monte Carlo sampling and Gaussian Mixture Model fitting, 3D brain image analysis,image classification, action recognition, and motion tracking.

Frames and Other Bases in Abstract and Function Spaces

Author : Isaac Pesenson
Publisher : Birkhäuser
ISBN 13 : 3319555502
Total Pages : 437 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Frames and Other Bases in Abstract and Function Spaces by : Isaac Pesenson

Download or read book Frames and Other Bases in Abstract and Function Spaces written by Isaac Pesenson and published by Birkhäuser. This book was released on 2017-06-11 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume I is organized around the theme of frames and other bases in abstract and function spaces, covering topics such as: The advanced development of frames, including Sigma-Delta quantization for fusion frames, localization of frames, and frame conditioning, as well as applications to distributed sensor networks, Galerkin-like representation of operators, scaling on graphs, and dynamical sampling. A systematic approach to shearlets with applications to wavefront sets and function spaces. Prolate and generalized prolate functions, spherical Gauss-Laguerre basis functions, and radial basis functions. Kernel methods, wavelets, and frames on compact and non-compact manifolds.

Sub-Riemannian Geometry

Author : Ovidiu Calin
Publisher : Cambridge University Press
ISBN 13 : 0521897300
Total Pages : 371 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Sub-Riemannian Geometry by : Ovidiu Calin

Download or read book Sub-Riemannian Geometry written by Ovidiu Calin and published by Cambridge University Press. This book was released on 2009-04-20 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive text and reference on sub-Riemannian and Heisenberg manifolds using a novel and robust variational approach.

Diffusion, Quantum Theory, and Radically Elementary Mathematics. (MN-47)

Author : William G. Faris
Publisher : Princeton University Press
ISBN 13 : 1400865255
Total Pages : 257 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Diffusion, Quantum Theory, and Radically Elementary Mathematics. (MN-47) by : William G. Faris

Download or read book Diffusion, Quantum Theory, and Radically Elementary Mathematics. (MN-47) written by William G. Faris and published by Princeton University Press. This book was released on 2014-09-08 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes.

Heat Kernels and Spectral Theory

Author : E. B. Davies
Publisher : Cambridge University Press
ISBN 13 : 9780521409971
Total Pages : 212 pages
Book Rating : 4.4/5 (99 download)

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Book Synopsis Heat Kernels and Spectral Theory by : E. B. Davies

Download or read book Heat Kernels and Spectral Theory written by E. B. Davies and published by Cambridge University Press. This book was released on 1989 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heat Kernels and Spectral Theory investigates the theory of second-order elliptic operators.

Evolutionary Computation

Author : Gai-Ge Wang
Publisher : MDPI
ISBN 13 : 3039219286
Total Pages : 424 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Evolutionary Computation by : Gai-Ge Wang

Download or read book Evolutionary Computation written by Gai-Ge Wang and published by MDPI. This book was released on 2019-11-28 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational intelligence is a general term for a class of algorithms designed by nature's wisdom and human intelligence. Computer scientists have proposed many computational intelligence algorithms with heuristic features. These algorithms either mimic the evolutionary processes of the biological world, mimic the physiological structure and bodily functions of the organism, imitate the behavior of the animal's group, mimic the characteristics of human thought, language, and memory processes, or mimic the physical phenomena of nature, hoping to simulate the wisdom of nature and humanity enables an optimal solution to the problem and solves an acceptable solution in an acceptable time. Computational intelligent algorithms have received extensive attention at home and abroad, and have become an important research direction of artificial intelligence and computer science. This book will introduce the application of intelligent optimization algorithms in detail from the aspects of computational intelligence, job shop scheduling problems, multi-objective optimization problems, and machine learning

Analysis and Applications

Author : H. P. Dikshit
Publisher : CRC Press
ISBN 13 : 9780849317217
Total Pages : 320 pages
Book Rating : 4.3/5 (172 download)

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Book Synopsis Analysis and Applications by : H. P. Dikshit

Download or read book Analysis and Applications written by H. P. Dikshit and published by CRC Press. This book was released on 2003-01-29 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis and its applications have been major areas for research in mathematics and allied fields. The fast growing power of computation has made a significant and useful impact in these areas. This has lead to computational analysis and the emergence of fields like Bezier-Bernstein methods for computer-aided geometric design, constructive approximation and wavelets, and even computational harmonic analysis. Analysis and Applications consists of research articles, including a few survey articles, by eminent mathematicians projecting trends in constructive and computational approximation, summability theory, optimal control and theory and applications of function spaces and wavelets.

Quantum Probability and Applications to the Quantum Theory of Irreversible Processes

Author : L. Accardi
Publisher : Springer
ISBN 13 : 3540387986
Total Pages : 417 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Quantum Probability and Applications to the Quantum Theory of Irreversible Processes by : L. Accardi

Download or read book Quantum Probability and Applications to the Quantum Theory of Irreversible Processes written by L. Accardi and published by Springer. This book was released on 2006-11-14 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to the Theory of Valuations

Author : Semyon Alesker
Publisher : American Mathematical Soc.
ISBN 13 : 1470443597
Total Pages : 93 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Introduction to the Theory of Valuations by : Semyon Alesker

Download or read book Introduction to the Theory of Valuations written by Semyon Alesker and published by American Mathematical Soc.. This book was released on 2018-06-27 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of valuations on convex sets is a classical part of convex geometry which goes back at least to the positive solution of the third Hilbert problem by M. Dehn in 1900. Since then the theory has undergone a multifaceted development. The author discusses some of Hadwiger's results on valuations on convex compact sets that are continuous in the Hausdorff metric. The book also discusses the Klain-Schneider theorem as well as the proof of McMullen's conjecture, which led subsequently to many further applications and advances in the theory. The last section gives an overview of more recent developments in the theory of translation-invariant continuous valuations, some of which turn out to be useful in integral geometry. This book grew out of lectures that were given in August 2015 at Kent State University in the framework of the NSF CBMS conference “Introduction to the Theory of Valuations on Convex Sets”. Only a basic background in general convexity is assumed.

Lectures on Field Theory and Topology

Author : Daniel S. Freed
Publisher : American Mathematical Soc.
ISBN 13 : 1470452065
Total Pages : 202 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Lectures on Field Theory and Topology by : Daniel S. Freed

Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2019-08-23 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.