Regular Non Additive Multimeasures Fundaments And Applications

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Regular Non Additive Multimeasures Fundaments And Applications

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Author : Alina Gavriluţ
language : en
Publisher: Springer Nature
Release Date : 2022-10-07

Regular Non Additive Multimeasures Fundaments And Applications written by Alina Gavriluţ and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-07 with Technology & Engineering categories.

This book is intended to be an exhaustive study on regularity and other properties of continuity for different types of non-additive multimeasures and with respect to different types of topologies. The book is addressed to graduate and postgraduate students, teachers and all researchers in mathematics, but not only. Since the notions and results offered by this book are closely related to various notions of the theory of probability, this book will be useful to a wider category of readers, using multivalued analysis techniques in areas such as control theory and optimization, economic mathematics, game theory, decision theory, etc. Measure and integration theory developed during the early years of the 20th century is one of the most important contributions to modern mathematical analysis, with important applications in many fields. In the last years, many classical problems from measure theory have been treated in the non-additive case and also extended in the set-valued case. The property of regularity is involved in many results of mathematical analysis, due to its applications in probability theory, stochastic processes, optimal control problems, dynamical systems, Markov chains, potential theory etc.

Atomicity Through Fractal Measure Theory

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Author : Alina Gavriluţ
language : en
Publisher: Springer Nature
Release Date : 2019-11-02

Atomicity Through Fractal Measure Theory written by Alina Gavriluţ and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-02 with Mathematics categories.

This book presents an exhaustive study of atomicity from a mathematics perspective in the framework of multi-valued non-additive measure theory. Applications to quantum physics and, more generally, to the fractal theory of the motion, are highlighted. The study details the atomicity problem through key concepts, such as the atom/pseudoatom, atomic/nonatomic measures, and different types of non-additive set-valued multifunctions. Additionally, applications of these concepts are brought to light in the study of the dynamics of complex systems. The first chapter prepares the basics for the next chapters. In the last chapter, applications of atomicity in quantum physics are developed and new concepts, such as the fractal atom are introduced. The mathematical perspective is presented first and the discussion moves on to connect measure theory and quantum physics through quantum measure theory. New avenues of research, such as fractal/multifractal measure theory with potential applications in life sciences, are opened.

Topics In Banach Space Integration

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Author : Stefan Schwabik
language : en
Publisher: World Scientific
Release Date : 2005

Topics In Banach Space Integration written by Stefan Schwabik and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

The relatively new concepts of the HenstockKurzweil and McShane integrals based on Riemann type sums are an interesting challenge in the study of integration of Banach space-valued functions. This timely book presents an overview of the concepts developed and results achieved during the past 15 years. The HenstockKurzweil and McShane integrals play the central role in the book. Various forms of the integration are introduced and compared from the viewpoint of their generality. Functional analysis is the main tool for presenting the theory of summation gauge integrals.

Topologies On Closed And Closed Convex Sets

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Author : Gerald Beer
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-10-31

Topologies On Closed And Closed Convex Sets written by Gerald Beer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-31 with Mathematics categories.

This monograph provides an introduction to the theory of topologies defined on the closed subsets of a metric space, and on the closed convex subsets of a normed linear space as well. A unifying theme is the relationship between topology and set convergence on the one hand, and set functionals on the other. The text includes for the first time anywhere an exposition of three topologies that over the past ten years have become fundamental tools in optimization, one-sided analysis, convex analysis, and the theory of multifunctions: the Wijsman topology, the Attouch--Wets topology, and the slice topology. Particular attention is given to topologies on lower semicontinuous functions, especially lower semicontinuous convex functions, as associated with their epigraphs. The interplay between convex duality and topology is carefully considered and a chapter on set-valued functions is included. The book contains over 350 exercises and is suitable as a graduate text. This book is of interest to those working in general topology, set-valued analysis, geometric functional analysis, optimization, convex analysis and mathematical economics.

Theory Of Random Sets

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Author : Ilya Molchanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-05-11

Theory Of Random Sets written by Ilya Molchanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-11 with Mathematics categories.

This is the first systematic exposition of random sets theory since Matheron (1975), with full proofs, exhaustive bibliographies and literature notes Interdisciplinary connections and applications of random sets are emphasized throughout the book An extensive bibliography in the book is available on the Web at http://liinwww.ira.uka.de/bibliography/math/random.closed.sets.html, and is accompanied by a search engine

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2005

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

Theory Of Random Sets

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Author : Ilya Molchanov
language : en
Publisher: Springer
Release Date : 2017-12-14

Theory Of Random Sets written by Ilya Molchanov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-14 with Mathematics categories.

This monograph, now in a thoroughly revised second edition, offers the latest research on random sets. It has been extended to include substantial developments achieved since 2005, some of them motivated by applications of random sets to econometrics and finance. The present volume builds on the foundations laid by Matheron and others, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference. It shows the various interdisciplinary relationships of random set theory within other parts of mathematics, and at the same time fixes terminology and notation that often vary in the literature, establishing it as a natural part of modern probability theory and providing a platform for future development. It is completely self-contained, systematic and exhaustive, with the full proofs that are necessary to gain insight. Aimed at research level, Theory of Random Sets will be an invaluable reference for probabilists; mathematicians working in convex and integral geometry, set-valued analysis, capacity and potential theory; mathematical statisticians in spatial statistics and uncertainty quantification; specialists in mathematical economics, econometrics, decision theory, and mathematical finance; and electronic and electrical engineers interested in image analysis.

Understanding The Well Being Of Lgbtqi Populations

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Author : National Academies of Sciences, Engineering, and Medicine
language : en
Publisher: National Academies Press
Release Date : 2021-01-23

Understanding The Well Being Of Lgbtqi Populations written by National Academies of Sciences, Engineering, and Medicine and has been published by National Academies Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-23 with Social Science categories.

The increase in prevalence and visibility of sexually gender diverse (SGD) populations illuminates the need for greater understanding of the ways in which current laws, systems, and programs affect their well-being. Individuals who identify as lesbian, gay, bisexual, asexual, transgender, non-binary, queer, or intersex, as well as those who express same-sex or -gender attractions or behaviors, will have experiences across their life course that differ from those of cisgender and heterosexual individuals. Characteristics such as age, race and ethnicity, and geographic location intersect to play a distinct role in the challenges and opportunities SGD people face. Understanding the Well-Being of LGBTQI+ Populations reviews the available evidence and identifies future research needs related to the well-being of SDG populations across the life course. This report focuses on eight domains of well-being; the effects of various laws and the legal system on SGD populations; the effects of various public policies and structural stigma; community and civic engagement; families and social relationships; education, including school climate and level of attainment; economic experiences (e.g., employment, compensation, and housing); physical and mental health; and health care access and gender-affirming interventions. The recommendations of Understanding the Well-Being of LGBTQI+ Populations aim to identify opportunities to advance understanding of how individuals experience sexuality and gender and how sexual orientation, gender identity, and intersex status affect SGD people over the life course.

Fractal Based Methods In Analysis

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Author : Herb Kunze
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-18

Fractal Based Methods In Analysis written by Herb Kunze and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-18 with Mathematics categories.

The idea of modeling the behaviour of phenomena at multiple scales has become a useful tool in both pure and applied mathematics. Fractal-based techniques lie at the heart of this area, as fractals are inherently multiscale objects; they very often describe nonlinear phenomena better than traditional mathematical models. In many cases they have been used for solving inverse problems arising in models described by systems of differential equations and dynamical systems. "Fractal-Based Methods in Analysis" draws together, for the first time in book form, methods and results from almost twenty years of research in this topic, including new viewpoints and results in many of the chapters. For each topic the theoretical framework is carefully explained using examples and applications. The second chapter on basic iterated function systems theory is designed to be used as the basis for a course and includes many exercises. This chapter, along with the three background appendices on topological and metric spaces, measure theory, and basic results from set-valued analysis, make the book suitable for self-study or as a source book for a graduate course. The other chapters illustrate many extensions and applications of fractal-based methods to different areas. This book is intended for graduate students and researchers in applied mathematics, engineering and social sciences. Herb Kunze is a professor of mathematics at the University of Guelph in Ontario. Davide La Torre is an associate professor of mathematics in the Department of Economics, Management and Quantitative Methods of the University of Milan. Franklin Mendivil is a professor of mathematics at Acadia University in Nova Scotia. Edward Vrscay is a professor in the department of Applied Mathematics at the University of Waterloo inOntario. The major focus of their research is on fractals and the applications of fractals.

The Science Of Self Control

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Author : Howard Rachlin
language : en
Publisher: Harvard University Press
Release Date : 2009-07-01

The Science Of Self Control written by Howard Rachlin and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-01 with Psychology categories.

This book proposes a new science of self-control based on principles of behavioral psychology and economics. Claiming that insight and self-knowledge are insufficient for controlling one’s behavior, Howard Rachlin argues that the only way to achieve such control—and ultimately happiness—is through the development of harmonious patterns of behavior.