Download or read book Quantitative Approximations written by George Anastassiou and published by CRC Press. This book was released on 2000-09-15 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few. For the first time in book form, Quantitative Approximations provides a thorough account of all of the significant developments in the area of contemporary quantitative mathematics. It offers readers the unique opportunity of approaching the field under the guidance of an expert. Among the book's outstanding features is the inclusion of the introductory chapter that summarizes the primary and most useful results. This section serves not only as a more detailed table of contents for those new to an area of application, but also as a quick reference for more seasoned researchers. The author describes all of the pertinent mathematical entities precisely and concretely. His approach and proofs are straightforward and constructive, making Quantitative Approximations accessible and valuable to researchers and graduate students alike.

Download or read book Quantitative Approximations written by George A. Anastassiou and published by Chapman and Hall/CRC. This book was released on 2000 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few. For the first time in book form, Quantitative Approximations provides a thorough account of all of the significant developments in the area of contemporary quantitative mathematics. It offers readers the unique opportunity of approaching the field under the guidance of an expert.Among the book's outstanding features is the inclusion of the introductory chapter that summarizes the primary and most useful results. This section serves not only as a more detailed table of contents for those new to an area of application, but also as a quick reference for more seasoned researchers.The author describes all of the pertinent mathematical entities precisely and concretely. His approach and proofs are straightforward and constructive, making Quantitative Approximations accessible and valuable to researchers and graduate students alike.

Download or read book Intelligent Comparisons II Operator Inequalities and Approximations written by George A. Anastassiou and published by Springer. This book was released on 2017-01-13 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This compact book focuses on self-adjoint operators’ well-known named inequalities and Korovkin approximation theory, both in a Hilbert space environment. It is the first book to study these aspects, and all chapters are self-contained and can be read independently. Further, each chapter includes an extensive list of references for further reading. The book’s results are expected to find applications in many areas of pure and applied mathematics. Given its concise format, it is especially suitable for use in related graduate classes and research projects. As such, the book offers a valuable resource for researchers and graduate students alike, as well as a key addition to all science and engineering libraries.

Download or read book Ordinary and Fractional Approximation by Non additive Integrals Choquet Shilkret and Sugeno Integral Approximators written by George A. Anastassiou and published by Springer. This book was released on 2018-12-07 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary and fractional approximations by non-additive integrals, especially by integral approximators of Choquet, Silkret and Sugeno types, are a new trend in approximation theory. These integrals are only subadditive and only the first two are positive linear, and they produce very fast and flexible approximations based on limited data. The author presents both the univariate and multivariate cases. The involved set functions are much weaker forms of the Lebesgue measure and they were conceived to fulfill the needs of economic theory and other applied sciences. The approaches presented here are original, and all chapters are self-contained and can be read independently. Moreover, the book’s findings are sure to find application in many areas of pure and applied mathematics, especially in approximation theory, numerical analysis and mathematical economics (both ordinary and fractional). Accordingly, it offers a unique resource for researchers, graduate students, and for coursework in the above-mentioned fields, and belongs in all science and engineering libraries.

Download or read book Intelligent Analysis Fractional Inequalities and Approximations Expanded written by George A. Anastassiou and published by Springer Nature. This book was released on 2020-01-15 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on computational and fractional analysis, two areas that are very important in their own right, and which are used in a broad variety of real-world applications. We start with the important Iyengar type inequalities and we continue with Choquet integral analytical inequalities, which are involved in major applications in economics. In turn, we address the local fractional derivatives of Riemann–Liouville type and related results including inequalities. We examine the case of low order Riemann–Liouville fractional derivatives and inequalities without initial conditions, together with related approximations. In the next section, we discuss quantitative complex approximation theory by operators and various important complex fractional inequalities. We also cover the conformable fractional approximation of Csiszar’s well-known f-divergence, and present conformable fractional self-adjoint operator inequalities. We continue by investigating new local fractional M-derivatives that share all the basic properties of ordinary derivatives. In closing, we discuss the new complex multivariate Taylor formula with integral remainder. Sharing results that can be applied in various areas of pure and applied mathematics, the book offers a valuable resource for researchers and graduate students, and can be used to support seminars in related fields.

Download or read book Cuts and Clouds written by Richard Dietz and published by Oxford University Press. This book was released on 2010-02-11 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vagueness is a deeply puzzling aspect of the relation between language and the world. Is it a feature of the way we represent reality in language, or a feature of reality itself? How can we reason with vague concepts? Cuts and Clouds presents the latest work towards an understanding of these puzzles about the nature and logic of vagueness.

Download or read book Intelligent Computations Abstract Fractional Calculus Inequalities Approximations written by George A. Anastassiou and published by Springer. This book was released on 2017-09-02 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief book presents the strong fractional analysis of Banach space valued functions of a real domain. The book’s results are abstract in nature: analytic inequalities, Korovkin approximation of functions and neural network approximation. The chapters are self-contained and can be read independently. This concise book is suitable for use in related graduate classes and many research projects. An extensive list of references is provided for each chapter. The book’s results are relevant for many areas of pure and applied mathematics. As such, it offers a unique resource for researchers, and a valuable addition to all science and engineering libraries.

Download or read book Microwave Imaging written by Matteo Pastorino and published by John Wiley & Sons. This book was released on 2010-04-27 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the most relevant theoretical and algorithmic aspects of modern microwave imaging approaches Microwave imaging—a technique used in sensing a given scene by means of interrogating microwaves—has recently proven its usefulness in providing excellent diagnostic capabilities in several areas, including civil and industrial engineering, nondestructive testing and evaluation, geophysical prospecting, and biomedical engineering. Microwave Imaging offers comprehensive descriptions of the most important techniques so far proposed for short-range microwave imaging—including reconstruction procedures and imaging systems and apparatus—enabling the reader to use microwaves for diagnostic purposes in a wide range of applications. This hands-on resource features: A review of the electromagnetic inverse scattering problem formulation, written from an engineering perspective and with notations The most effective reconstruction techniques based on diffracted waves, including time- and frequency-domain methods, as well as deterministic and stochastic space-domain procedures Currently proposed imaging apparatus, aimed at fast and accurate measurements of the scattered field data Insight on near field probes, microwave axial tomographs, and microwave cameras and scanners A discussion of practical applications with detailed descriptions and discussions of several specific examples (e.g., materials evaluation, crack detection, inspection of civil and industrial structures, subsurface detection, and medical applications) A look at emerging techniques and future trends Microwave Imaging is a practical resource for engineers, scientists, researchers, and professors in the fields of civil and industrial engineering, nondestructive testing and evaluation, geophysical prospecting, and biomedical engineering.

Download or read book Relativistic Fluid Dynamics In and Out of Equilibrium written by Paul Romatschke and published by Cambridge University Press. This book was released on 2019-05-09 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: The past decade has seen unprecedented developments in the understanding of relativistic fluid dynamics in and out of equilibrium, with connections to astrophysics, cosmology, string theory, quantum information, nuclear physics and condensed matter physics. Romatschke and Romatschke offer a powerful new framework for fluid dynamics, exploring its connections to kinetic theory, gauge/gravity duality and thermal quantum field theory. Numerical algorithms to solve the equations of motion of relativistic dissipative fluid dynamics as well as applications to various systems are discussed. In particular, the book contains a comprehensive review of the theory background necessary to apply fluid dynamics to simulate relativistic nuclear collisions, including comparisons of fluid simulation results to experimental data for relativistic lead-lead, proton-lead and proton-proton collisions at the Large Hadron Collider (LHC). The book is an excellent resource for students and researchers working in nuclear physics, astrophysics, cosmology, quantum many-body systems and string theory.

Download or read book Parametrized Deformed and General Neural Networks written by George A. Anastassiou and published by Springer Nature. This book was released on 2023-09-29 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we introduce the parametrized, deformed and general activation function of neural networks. The parametrized activation function kills much less neurons than the original one. The asymmetry of the brain is best expressed by deformed activation functions. Along with a great variety of activation functions, general activation functions are also engaged. Thus, in this book, all presented is original work by the author given at a very general level to cover a maximum number of different kinds of neural networks: giving ordinary, fractional, fuzzy and stochastic approximations. It presents here univariate, fractional and multivariate approximations. Iterated sequential multi-layer approximations are also studied. The functions under approximation and neural networks are Banach space valued.

Download or read book The Journal of Philosophy written by and published by . This book was released on 1916 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers topics in philosophy, psychology, and scientific methods. Vols. 31- include "A Bibliography of philosophy," 1933-

Download or read book The Journal of Philosophy Psychology and Scientific Methods written by and published by . This book was released on 1916 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Many Electron Approaches in Physics Chemistry and Mathematics written by Volker Bach and published by Springer. This book was released on 2014-07-01 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad description of the development and (computational) application of many-electron approaches from a multidisciplinary perspective. In the context of studying many-electron systems Computer Science, Chemistry, Mathematics and Physics are all intimately interconnected. However, beyond a handful of communities working at the interface between these disciplines, there is still a marked separation of subjects. This book seeks to offer a common platform for possible exchanges between the various fields and to introduce the reader to perspectives for potential further developments across the disciplines. The rapid advances of modern technology will inevitably require substantial improvements in the approaches currently used, which will in turn make exchanges between disciplines indispensable. In essence this book is one of the very first attempts at an interdisciplinary approach to the many-electron problem.

Download or read book Statistical Mechanics of Learning written by A. Engel and published by Cambridge University Press. This book was released on 2001-03-29 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learning is one of the things that humans do naturally, and it has always been a challenge for us to understand the process. Nowadays this challenge has another dimension as we try to build machines that are able to learn and to undertake tasks such as datamining, image processing and pattern recognition. We can formulate a simple framework, artificial neural networks, in which learning from examples may be described and understood. The contribution to this subject made over the last decade by researchers applying the techniques of statistical mechanics is the subject of this book. The authors provide a coherent account of various important concepts and techniques that are currently only found scattered in papers, supplement this with background material in mathematics and physics and include many examples and exercises to make a book that can be used with courses, or for self-teaching, or as a handy reference.

Download or read book 3D Multiscale Physiological Human written by Nadia Magnenat-Thalmann and published by Springer Science & Business Media. This book was released on 2013-12-23 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: 3D Multiscale Physiological Human aims to promote scientific exchange by bringing together overviews and examples of recent scientific and technological advancements across a wide range of research disciplines. As a result, the variety in methodologies and knowledge paradigms are contrasted, revealing potential gaps and opportunities for integration. Chapters have been contributed by selected authors in the relevant domains of tissue engineering, medical image acquisition and processing, visualization, modeling, computer aided diagnosis and knowledge management. The multi-scale and multi-disciplinary research aspects of articulations in humans are highlighted, with a particular emphasis on medical diagnosis and treatment of musculoskeletal diseases and related disorders. The need for multi-scale modalities and multi-disciplinary research is an emerging paradigm in the search for a better biological and medical understanding of the human musculoskeletal system. This is particularly motivated by the increasing socio-economic burden of disability and musculoskeletal diseases, especially in the increasing population of elderly people. Human movement is generated through a complex web of interactions between embedded physiological systems on different spatiotemporal scales, ranging from the molecular to the organ level. Much research is dedicated to the understanding of each of these systems, using methods and modalities tailored for each scale. Nevertheless, combining knowledge from different perspectives opens new venues of scientific thinking and stimulates innovation. Integration of this mosaic of multifaceted data across multiple scales and modalities requires further exploration of methods in simulations and visualization to obtain a comprehensive synthesis. However, this integrative approach cannot be achieved without a broad appreciation for the multiple research disciplines involved.

Download or read book Unsettled Thoughts written by Julia Staffel and published by Oxford University Press. This book was released on 2019-12-12 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: How should thinkers cope with uncertainty? What makes their degrees of belief rational, and how should they reason about uncertain matters? In epistemology, recent research has attempted to answer these questions by developing formal models of ideally rational credences. However, we know from psychological research that perfect rationality is unattainable for human thinkers—and so this raises the question of how rational ideals can apply to human thinkers. A popular reply is that the more a thinker's imperfectly rational credences approximate compliance with norms of ideal rationality, the better. But what exactly does this mean? Why is it better to be less irrational, if we can't ever be completely rational? And what does being closer to ideally rational amount to? If ideal models of rationality are supposed to help us understand the rationality of human, imperfect thinkers, we need answers to these questions. Unsettled Thoughts breaks new ground in the study of rationality in providing these answers: we can explain why it's better to be less irrational, because less irrational degrees of belief are generally more accurate and better at guiding our actions. Moreover, the way in which approximating ideal rationality is beneficial can be made formally precise by using a variety of distance measures that track the benefits of being more rational.

Download or read book Beyond Rationality written by Kenneth R. Hammond and published by Oxford University Press. This book was released on 2007-01-04 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hammond has changed the way academics think about decision making; with this book, he aims to show a larger audience why mistaken judgments happen, how to make better decisions, and how to understand the thought modes operating in the political process.