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Operator Relations Characterizing Derivatives
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Book Synopsis Operator Relations Characterizing Derivatives by : Hermann König
Download or read book Operator Relations Characterizing Derivatives written by Hermann König and published by Springer. This book was released on 2018-10-03 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops an operator viewpoint for functional equations in classical function spaces of analysis, thus filling a void in the mathematical literature. Major constructions or operations in analysis are often characterized by some elementary properties, relations or equations which they satisfy. The authors present recent results on the problem to what extent the derivative is characterized by equations such as the Leibniz rule or the Chain rule operator equation in Ck-spaces. By localization, these operator equations turn into specific functional equations which the authors then solve. The second derivative, Sturm-Liouville operators and the Laplacian motivate the study of certain "second-order" operator equations. Additionally, the authors determine the general solution of these operator equations under weak assumptions of non-degeneration. In their approach, operators are not required to be linear, and the authors also try to avoid continuity conditions. The Leibniz rule, the Chain rule and its extensions turn out to be stable under perturbations and relaxations of assumptions on the form of the operators. The results yield an algebraic understanding of first- and second-order differential operators. Because the authors have chosen to characterize the derivative by algebraic relations, the rich operator-type structure behind the fundamental notion of the derivative and its relatives in analysis is discovered and explored. The book does not require any specific knowledge of functional equations. All needed results are presented and proven and the book is addressed to a general mathematical audience.
Book Synopsis Operator Relations Characterizing Derivatives by : Hermann Kèonig
Download or read book Operator Relations Characterizing Derivatives written by Hermann Kèonig and published by . This book was released on 2018 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops an operator viewpoint for functional equations in classical function spaces of analysis, thus filling a void in the mathematical literature. Major constructions or operations in analysis are often characterized by some elementary properties, relations or equations which they satisfy. The authors present recent results on the problem to what extent the derivative is characterized by equations such as the Leibniz rule or the Chain rule operator equation in C^k-spaces. By localization, these operator equations turn into specific functional equations which the authors then solve. The second derivative, Sturm-Liouville operators and the Laplacian motivate the study of certain "second-order" operator equations. Additionally, the authors determine the general solution of these operator equations under weak assumptions of non-degeneration. In their approach, operators are not required to be linear, and the authors also try to avoid continuity conditions. The Leibniz rule, the Chain rule and its extensions turn out to be stable under perturbations and relaxations of assumptions on the form of the operators. The results yield an algebraic understanding of first- and second-order differential operators. Because the authors have chosen to characterize the derivative by algebraic relations, the rich operator-type structure behind the fundamental notion of the derivative and its relatives in analysis is discovered and explored. The book does not require any specific knowledge of functional equations. All needed results are presented and proven and the book is addressed to a general mathematical audience.
Book Synopsis From Fields to Strings by : Misha Shifman
Download or read book From Fields to Strings written by Misha Shifman and published by World Scientific. This book was released on 2005 with total page 868 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Foundations Of The Hyperunified Field Theory by : Yue-liang Wu
Download or read book Foundations Of The Hyperunified Field Theory written by Yue-liang Wu and published by World Scientific. This book was released on 2022-09-28 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quest for the unification of fundamental interactions has become the most challenging frontier of sciences in the 21st century. This book presents a detailed analysis and systematic investigation of the foundations of the hyperunified field theory (HUFT) in light of the path integral formulation with the least action principle. Alternative to other unification theories, the starting point of HUFT is initiated from a simple notion that the universe is made of the fundamental building block which is always moving and obeys the basic rule. Such a rule is delved into in this book by proposing the maximum locally entangled-qubits motion principle together with the scaling and gauge invariance principle. These two basic guiding principles are demonstrated to lay the foundations of HUFT, which enable enables us to discuss a series of long-standing fundamental questions, such as: why does the fundamental building block of nature appear as an entangled qubit-spinor field? what brings about the fundamental symmetry of nature? how does the inhomogeneous hyperspin gauge symmetry govern all basic forces? what is the nature of gravity and space-time? how can the space-time dimension and qubit-spinor field be categorized? why do we live in a universe with only four-dimensional space-time? why are there more than one family of leptons and quarks? how does the early universe evolve to be inflationary? what is the nature of dark matter and dark energy?Foundations of the Hyperunified Field Theory will be of great interest to graduate and senior undergraduate students, junior and senior researchers in theoretical physics, quantum field theory, particle physics, gravitational theory, cosmology, as well as mathematical physics and general physics.
Book Synopsis Characterization of Distributions by the Method of Intensively Monotone Operators by : A.V. Kakosyan
Download or read book Characterization of Distributions by the Method of Intensively Monotone Operators written by A.V. Kakosyan and published by Springer. This book was released on 2007-01-05 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scalar and Asymptotic Scalar Derivatives by : George Isac
Download or read book Scalar and Asymptotic Scalar Derivatives written by George Isac and published by Springer Science & Business Media. This book was released on 2008-05-21 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This extremely useful book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to some problems in nonlinear analysis, Riemannian geometry and applied mathematics. The theoretical results are developed in particular with respect to the study of complementarity problems, monotonicity of nonlinear mappings and the non-gradient type monotonicity on Riemannian manifolds. The text is intended for researchers and graduate students working in the fields of nonlinear analysis, Riemannian geometry and applied mathematics.
Book Synopsis Recent Trends in Operator Theory and Partial Differential Equations by : Vladimir Maz'ya
Download or read book Recent Trends in Operator Theory and Partial Differential Equations written by Vladimir Maz'ya and published by Birkhäuser. This book was released on 2017-02-23 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz, Wiener-Hopf, and pseudodifferential operators, boundary value problems, operator theory, approximation theory, and reflects the broad spectrum of Roland Duduchava's research. The book is addressed to a wide audience of pure and applied mathematicians.
Book Synopsis Fractional Derivative Modeling in Mechanics and Engineering by : Wen Chen
Download or read book Fractional Derivative Modeling in Mechanics and Engineering written by Wen Chen and published by Springer Nature. This book was released on 2022-02-26 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook highlights the theory of fractional calculus and its wide applications in mechanics and engineering. It describes in details the research findings in using fractional calculus methods for modeling and numerical simulation of complex mechanical behavior. It covers the mathematical basis of fractional calculus, the relationship between fractal and fractional calculus, unconventional statistics and anomalous diffusion, typical applications of fractional calculus, and the numerical solution of the fractional differential equation. It also includes latest findings, such as variable order derivative, distributed order derivative and its applications. Different from other textbooks in this subject, the book avoids lengthy mathematical demonstrations, and presents the theories in close connection to the applications in an easily readable manner. This textbook is intended for students, researchers and professionals in applied physics, engineering mechanics, and applied mathematics. It is also of high reference value for those in environmental mechanics, geotechnical mechanics, biomechanics, and rheology.
Book Synopsis Geometric Analysis of Nonlinear Partial Differential Equations by : Valentin Lychagin
Download or read book Geometric Analysis of Nonlinear Partial Differential Equations written by Valentin Lychagin and published by MDPI. This book was released on 2021-09-03 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of twelve papers that reflect the state of the art of nonlinear differential equations in modern geometrical theory. It comprises miscellaneous topics of the local and nonlocal geometry of differential equations and the applications of the corresponding methods in hydrodynamics, symplectic geometry, optimal investment theory, etc. The contents will be useful for all the readers whose professional interests are related to nonlinear PDEs and differential geometry, both in theoretical and applied aspects.
Book Synopsis Face Recognition in Adverse Conditions by : De Marsico, Maria
Download or read book Face Recognition in Adverse Conditions written by De Marsico, Maria and published by IGI Global. This book was released on 2014-04-30 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Facial recognition software has improved by leaps and bounds over the past few decades, with error rates decreasing significantly within the past ten years. Though this is true, conditions such as poor lighting, obstructions, and profile-only angles have continued to persist in preventing wholly accurate readings. Face Recognition in Adverse Conditions examines how the field of facial recognition takes these adverse conditions into account when designing more effective applications by discussing facial recognition under real world PIE variations, current applications, and the future of the field of facial recognition research. The work is intended for academics, engineers, and researchers specializing in the field of facial recognition.
Book Synopsis Seismic Attributes for Prospect Identification and Reservoir Characterization by : Satinder Chopra
Download or read book Seismic Attributes for Prospect Identification and Reservoir Characterization written by Satinder Chopra and published by SEG Books. This book was released on 2007 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing the physical basis, mathematical implementation, and geologic expression of modern volumetric attributes including coherence, dip/azimuth, curvature, amplitude gradients, seismic textures, and spectral decomposition, the authors demonstrate the importance of effective colour display and sensitivity to seismic acquisition and processing.
Book Synopsis Particle Characterization: Light Scattering Methods by : Renliang Xu
Download or read book Particle Characterization: Light Scattering Methods written by Renliang Xu and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Particle characterization is an important component in product research and development, manufacture, and quality control of particulate materials and an important tool in the frontier of sciences, such as in biotechnology and nanotechnology. This book systematically describes one major branch of modern particle characterization technology - the light scattering methods. This is the first monograph in particle science and technology covering the principles, instrumentation, data interpretation, applications, and latest experimental development in laser diffraction, optical particle counting, photon correlation spectroscopy, and electrophoretic light scattering. In addition, a summary of all major particle sizing and other characterization methods, basic statistics and sample preparation techniques used in particle characterization, as well as almost 500 latest references are provided. The book is a must for industrial users of light scattering techniques characterizing a variety of particulate systems and for undergraduate or graduate students who want to learn how to use light scattering to study particular materials, in chemical engineering, material sciences, physical chemistry and other related fields.
Book Synopsis Unbounded Weighted Composition Operators in L2-Spaces by : Piotr Budzyński
Download or read book Unbounded Weighted Composition Operators in L2-Spaces written by Piotr Budzyński and published by Springer. This book was released on 2018-05-28 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book establishes the foundations of the theory of bounded and unbounded weighted composition operators in L2-spaces. It develops the theory in full generality, meaning that the corresponding composition operators are not assumed to be well defined. A variety of seminormality properties of unbounded weighted composition operators are characterized. The first-ever criteria for subnormality of unbounded weighted composition operators are provided and the subtle interplay between the classical moment problem, graph theory and the injectivity problem for weighted composition operators is revealed. The relationships between weighted composition operators and the corresponding multiplication and composition operators are investigated. The optimality of the obtained results is illustrated by a variety of examples, including those of discrete and continuous types. The book is primarily aimed at researchers in single or multivariable operator theory.
Book Synopsis Advances in Harmonic Analysis and Operator Theory by : Alexandre Almeida
Download or read book Advances in Harmonic Analysis and Operator Theory written by Alexandre Almeida and published by Springer Science & Business Media. This book was released on 2013-01-31 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Professor Stefan Samko on the occasion of his seventieth birthday. The contributions display the range of his scientific interests in harmonic analysis and operator theory. Particular attention is paid to fractional integrals and derivatives, singular, hypersingular and potential operators in variable exponent spaces, pseudodifferential operators in various modern function and distribution spaces, as well as related applications, to mention but a few. Most contributions were firstly presented in two conferences at Lisbon and Aveiro, Portugal, in June‒July 2011.
Book Synopsis Reservoir Characterization, Modeling and Quantitative Interpretation by : Shib Sankar Ganguli
Download or read book Reservoir Characterization, Modeling and Quantitative Interpretation written by Shib Sankar Ganguli and published by Elsevier. This book was released on 2023-10-27 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reservoir Characterization, Modeling and Quantitative Interpretation: Recent Workflows to Emerging Technologies offers a wide spectrum of reservoir characterization techniques and technologies, focusing on the latest breakthroughs and most efficient methodologies in hydrocarbon exploration and development. Topics covered include 4D seismic technologies, AVAz inversion, fracture characterization, multiscale imaging technologies, static and dynamic reservoir characterization, among others. The content is delivered through an inductive approach, which will help readers gain comprehensive insights on advanced practices and be able to relate them to other subareas of reservoir characterization, including CO2 storage and data-driven modeling. This will be especially useful for field scientists in collecting and analyzing field data, prospect evaluation, developing reservoir models, and adopting new technologies to mitigate exploration risk. They will be able to solve the practical and challenging problems faced in the field of reservoir characterization, as it will offer systematic industrial workflows covering every aspect of this branch of Earth Science, including subsurface geoscientific perspectives of carbon geosequestration. This resource is a 21st Century guide for exploration geologists, geoscience students at postgraduate level and above, and petrophysicists working in the oil and gas industry. Covers the latest and most effective technologies in reservoir characterization, including Avo analysis, AVAz inversion, wave field separation and Machine Learning techniques Provides a balanced blend of both theoretical and practical approaches for solving challenges in reservoir characterization Includes detailed industry-standard practical workflows, along with code structures for algorithms and practice exercises
Download or read book Discrete Calculus written by Leo J. Grady and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Many example applications from several fields of computational science are provided.
Book Synopsis Scaling, Fractals and Wavelets by : Patrice Abry
Download or read book Scaling, Fractals and Wavelets written by Patrice Abry and published by John Wiley & Sons. This book was released on 2013-03-01 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scaling is a mathematical transformation that enlarges or diminishes objects. The technique is used in a variety of areas, including finance and image processing. This book is organized around the notions of scaling phenomena and scale invariance. The various stochastic models commonly used to describe scaling — self-similarity, long-range dependence and multi-fractals — are introduced. These models are compared and related to one another. Next, fractional integration, a mathematical tool closely related to the notion of scale invariance, is discussed, and stochastic processes with prescribed scaling properties (self-similar processes, locally self-similar processes, fractionally filtered processes, iterated function systems) are defined. A number of applications where the scaling paradigm proved fruitful are detailed: image processing, financial and stock market fluctuations, geophysics, scale relativity, and fractal time-space.
