Problem Spaces

Author : Celia Lury
Publisher : John Wiley & Sons
Page : 256 pages
File Size : 44,8 Mb
Release : 2021-01-20
Category : Social Science
ISBN : 9781509507979

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Problem Spaces by Celia Lury Pdf

In this innovative book, Celia Lury argues that the time has come for us to explore the world not only with new methods, but with a new approach to methodology itself. Fundamental changes are taking place in how we produce knowledge, how we communicate it and, indeed, what we consider to be knowledge. These changes demand innovative and creative responses to research questions. Lury's rethinking of the nature of social inquiry starts by reconceptualizing the 'problem space'. Problems are not static or a 'given'; rather, they are created and continually recomposed as part of the methodological process itself. Following the line of thought that methods are practices that articulate as much as capture a social problem, Lury further develops the notion of compositional methodology to think through its implications. With remarkable fluency, the book draws into conversation a range of hot-button issues, both longstanding and novel, from observation, reflexivity, recursive measurement and feminist methodologies, to participation, context, datafication and platformization. Always with an eye to the methodological potential of new trends, the book provides a strong challenge to much received wisdom and argues that a combination of techniques can contribute to better understanding of the problem spaces we all inhabit.

Author : Celia Lury
Publisher : John Wiley & Sons
Page : 256 pages
File Size : 48,6 Mb
Release : 2020-11-10
Category : Social Science
ISBN : 9781509507955

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Problem Spaces by Celia Lury Pdf

In this innovative book, Celia Lury argues that the time has come for us to explore the world not only with new methods, but with a new approach to methodology itself. Fundamental changes are taking place in how we produce knowledge, how we communicate it and, indeed, what we consider to be knowledge. These changes demand innovative and creative responses to research questions. Lury's rethinking of the nature of social inquiry starts by reconceptualizing the 'problem space'. Problems are not static or a 'given'; rather, they are created and continually recomposed as part of the methodological process itself. Following the line of thought that methods are practices that articulate as much as capture a social problem, Lury further develops the notion of compositional methodology to think through its implications. With remarkable fluency, the book draws into conversation a range of hot-button issues, both longstanding and novel, from observation, reflexivity, recursive measurement and feminist methodologies, to participation, context, datafication and platformization. Always with an eye to the methodological potential of new trends, the book provides a strong challenge to much received wisdom and argues that a combination of techniques can contribute to better understanding of the problem spaces we all inhabit.

Author : Y. Roitberg
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401154109

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Elliptic Boundary Value Problems in the Spaces of Distributions by Y. Roitberg Pdf

This volume endeavours to summarise all available data on the theorems on isomorphisms and their ever increasing number of possible applications. It deals with the theory of solvability in generalised functions of general boundary-value problems for elliptic equations. In the early sixties, Lions and Magenes, and Berezansky, Krein and Roitberg established the theorems on complete collection of isomorphisms. Further progress of the theory was connected with proving the theorem on complete collection of isomorphisms for new classes of problems, and hence with the development of new methods to prove these theorems. The theorems on isomorphisms were first established for elliptic equations with normal boundary conditions. However, after the Noetherian property of elliptic problems was proved without assuming the normality of the boundary expressions, this became the natural way to consider the problems of establishing the theorems on isomorphisms for general elliptic problems. The present author's method of solving this problem enabled proof of the theorem on complete collection of isomorphisms for the operators generated by elliptic boundary-value problems for general systems of equations. Audience: This monograph will be of interest to mathematicians whose work involves partial differential equations, functional analysis, operator theory and the mathematics of mechanics.

Author : E. M. Polishchuk
Publisher : Walter de Gruyter GmbH & Co KG
Page : 164 pages
File Size : 45,8 Mb
Release : 2022-01-19
Category : Social Science
ISBN : 9783112471746

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Continual Means and Boundary Value Problems in Function Spaces by E. M. Polishchuk Pdf

Author : I. Cioranescu
Publisher : Springer Science & Business Media
Page : 284 pages
File Size : 55,5 Mb
Release : 1990-09-30
Category : Mathematics
ISBN : 0792309103

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Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems by I. Cioranescu Pdf

One service mathematics has rendered the 'Et moi, ...* si Javait so comment en revenir. je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com­ puter science .. .'; 'One service category theory has rendered mathematics .. .'. AIl arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Author : Mohammad Rostami
Publisher : CRC Press
Page : 220 pages
File Size : 49,8 Mb
Release : 2021-06-29
Category : Computers
ISBN : 9781000400571

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Transfer Learning through Embedding Spaces by Mohammad Rostami Pdf

Recent progress in artificial intelligence (AI) has revolutionized our everyday life. Many AI algorithms have reached human-level performance and AI agents are replacing humans in most professions. It is predicted that this trend will continue and 30% of work activities in 60% of current occupations will be automated. This success, however, is conditioned on availability of huge annotated datasets to training AI models. Data annotation is a time-consuming and expensive task which still is being performed by human workers. Learning efficiently from less data is a next step for making AI more similar to natural intelligence. Transfer learning has been suggested a remedy to relax the need for data annotation. The core idea in transfer learning is to transfer knowledge across similar tasks and use similarities and previously learned knowledge to learn more efficiently. In this book, we provide a brief background on transfer learning and then focus on the idea of transferring knowledge through intermediate embedding spaces. The idea is to couple and relate different learning through embedding spaces that encode task-level relations and similarities. We cover various machine learning scenarios and demonstrate that this idea can be used to overcome challenges of zero-shot learning, few-shot learning, domain adaptation, continual learning, lifelong learning, and collaborative learning.

Author : Joseph Albert Wolf
Publisher : American Mathematical Soc.
Page : 442 pages
File Size : 40,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852828

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Spaces of Constant Curvature by Joseph Albert Wolf Pdf

This book is the sixth edition of the classic Spaces of Constant Curvature, first published in 1967, with the previous (fifth) edition published in 1984. It illustrates the high degree of interplay between group theory and geometry. The reader will benefit from the very concise treatments of riemannian and pseudo-riemannian manifolds and their curvatures, of the representation theory of finite groups, and of indications of recent progress in discrete subgroups of Lie groups. Part I is a brief introduction to differentiable manifolds, covering spaces, and riemannian and pseudo-riemannian geometry. It also contains a certain amount of introductory material on symmetry groups and space forms, indicating the direction of the later chapters. Part II is an updated treatment of euclidean space form. Part III is Wolf's classic solution to the Clifford-Klein Spherical Space Form Problem. It starts with an exposition of the representation theory of finite groups. Part IV introduces riemannian symmetric spaces and extends considerations of spherical space forms to space forms of riemannian symmetric spaces. Finally, Part V examines space form problems on pseudo-riemannian symmetric spaces. At the end of Chapter 12 there is a new appendix describing some of the recent work on discrete subgroups of Lie groups with application to space forms of pseudo-riemannian symmetric spaces. Additional references have been added to this sixth edition as well.

Author : Krzysztof Jarosz
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 50,9 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821840610

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Function Spaces by Krzysztof Jarosz Pdf

This book consists of contributions by the participants of the Fifth Conference on Function Spaces, held at Southern Illinois University in May of 2006. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), $L{p $-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects. The goal of the conference was to bring together mathematicians interested in various problems related to function spaces and to facilitate the exchange of ideas between people working on similar problems. Hence, the majority of papers in this book are accessible to non-experts. Some articles contain expositions of known results and discuss open problems, others contain new results.

Author : A. Bayoumi
Publisher : Elsevier
Page : 304 pages
File Size : 42,9 Mb
Release : 2003-11-11
Category : Mathematics
ISBN : 9780080531922

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Foundations of Complex Analysis in Non Locally Convex Spaces by A. Bayoumi Pdf

All the existing books in Infinite Dimensional Complex Analysis focus on the problems of locally convex spaces. However, the theory without convexity condition is covered for the first time in this book. This shows that we are really working with a new, important and interesting field. Theory of functions and nonlinear analysis problems are widespread in the mathematical modeling of real world systems in a very broad range of applications. During the past three decades many new results from the author have helped to solve multiextreme problems arising from important situations, non-convex and non linear cases, in function theory. Foundations of Complex Analysis in Non Locally Convex Spaces is a comprehensive book that covers the fundamental theorems in Complex and Functional Analysis and presents much new material. The book includes generalized new forms of: Hahn-Banach Theorem, Multilinear maps, theory of polynomials, Fixed Point Theorems, p-extreme points and applications in Operations Research, Krein-Milman Theorem, Quasi-differential Calculus, Lagrange Mean-Value Theorems, Taylor series, Quasi-holomorphic and Quasi-analytic maps, Quasi-Analytic continuations, Fundamental Theorem of Calculus, Bolzano's Theorem, Mean-Value Theorem for Definite Integral, Bounding and weakly-bounding (limited) sets, Holomorphic Completions, and Levi problem. Each chapter contains illustrative examples to help the student and researcher to enhance his knowledge of theory of functions. The new concept of Quasi-differentiability introduced by the author represents the backbone of the theory of Holomorphy for non-locally convex spaces. In fact it is different but much stronger than the Frechet one. The book is intended not only for Post-Graduate (M.Sc.& Ph.D.) students and researchers in Complex and Functional Analysis, but for all Scientists in various disciplines whom need nonlinear or non-convex analysis and holomorphy methods without convexity conditions to model and solve problems. bull; The book contains new generalized versions of: i) Fundamental Theorem of Calculus, Lagrange Mean-Value Theorem in real and complex cases, Hahn-Banach Theorems, Bolzano Theorem, Krein-Milman Theorem, Mean value Theorem for Definite Integral, and many others. ii) Fixed Point Theorems of Bruower, Schauder and Kakutani's. bull; The book contains some applications in Operations research and non convex analysis as a consequence of the new concept p-Extreme points given by the author. bull; The book contains a complete theory for Taylor Series representations of the different types of holomorphic maps in F-spaces without convexity conditions. bull; The book contains a general new concept of differentiability stronger than the Frechet one. This implies a new Differentiable Calculus called Quasi-differential (or Bayoumi differential) Calculus. It is due to the author's discovery in 1995. bull; The book contains the theory of polynomials and Banach Stienhaus theorem in non convex spaces.

Author : N. U. Ahmed,Shian Wang
Publisher : Springer Nature
Page : 236 pages
File Size : 45,5 Mb
Release : 2023-09-12
Category : Mathematics
ISBN : 9783031372605

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Measure-Valued Solutions for Nonlinear Evolution Equations on Banach Spaces and Their Optimal Control by N. U. Ahmed,Shian Wang Pdf

This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces. Unlike traditional solutions, measure-valued solutions allow for a much broader class of abstract evolution equations to be addressed, providing a broader approach. The book presents extensive results on the existence of measure-valued solutions for differential equations that have no solutions in the usual sense. It covers a range of topics, including evolution equations with continuous/discontinuous vector fields, neutral evolution equations subject to vector measures as impulsive forces, stochastic evolution equations, and optimal control of evolution equations. The optimal control problems considered cover the existence of solutions, necessary conditions of optimality, and more, significantly complementing the existing literature. This book will be of great interest to researchers in functional analysis, partial differential equations, dynamic systems and their optimal control, and their applications, advancing previous research and providing a foundation for further exploration of the field.

Author : Sigurdur Helgason
Publisher : Academic Press
Page : 628 pages
File Size : 52,9 Mb
Release : 1979-02-09
Category : Mathematics
ISBN : 0080873960

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Differential Geometry, Lie Groups, and Symmetric Spaces by Sigurdur Helgason Pdf

The present book is intended as a textbook and reference work on three topics in the title. Together with a volume in progress on "Groups and Geometric Analysis" it supersedes my "Differential Geometry and Symmetric Spaces," published in 1962. Since that time several branches of the subject, particularly the function theory on symmetric spaces, have developed substantially. I felt that an expanded treatment might now be useful.

Author : Ilia Binder,Damir Kinzebulatov,Javad Mashreghi
Publisher : Springer Nature
Page : 487 pages
File Size : 41,6 Mb
Release : 2024-01-12
Category : Mathematics
ISBN : 9783031392702

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Function Spaces, Theory and Applications by Ilia Binder,Damir Kinzebulatov,Javad Mashreghi Pdf

The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They also have several essential applications in other fields of mathematics and engineering, e.g., robust control engineering, signal and image processing, and theory of communication. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins, e.g. the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b), have also been the center of attention in the past two decades. Studying the Hilbert spaces of analytic functions and the operators acting on them, as well as their applications in other parts of mathematics or engineering were the main subjects of this program. During the program, the world leading experts on function spaces gathered and discussed the new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains. With more than 250 hours of lectures by prominent mathematicians, a wide variety of topics were covered. More explicitly, there were mini-courses and workshops on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Blaschke Products and Inner Functions, Discrete and Continuous Semigroups of Composition Operators, The Corona Problem, Non-commutative Function Theory, Drury-Arveson Space, and Convergence of Scattering Data and Non-linear Fourier Transform. At the end of each week, there was a high profile colloquium talk on the current topic. The program also contained two semester-long advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions. The current volume features a more detailed version of some of the talks presented during the program.

Author : Mikhail Popov,Beata Randrianantoanina
Publisher : Walter de Gruyter
Page : 336 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783110263343

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Narrow Operators on Function Spaces and Vector Lattices by Mikhail Popov,Beata Randrianantoanina Pdf

Most classes of operators that are not isomorphic embeddings are characterized by some kind of a “smallness” condition. Narrow operators are those operators defined on function spaces that are “small” at {-1,0,1}-valued functions, e.g. compact operators are narrow. The original motivation to consider such operators came from theory of embeddings of Banach spaces, but since then they were also applied to the study of the Daugavet property and to other geometrical problems of functional analysis. The question of when a sum of two narrow operators is narrow, has led to deep developments of the theory of narrow operators, including an extension of the notion to vector lattices and investigations of connections to regular operators. Narrow operators were a subject of numerous investigations during the last 30 years. This monograph provides a comprehensive presentation putting them in context of modern theory. It gives an in depth systematic exposition of concepts related to and influenced by narrow operators, starting from basic results and building up to most recent developments. The authors include a complete bibliography and many attractive open problems.

Author : W. B. Vasantha Kandasamy,Florentin Smarandache,K. Amal
Publisher : Infinite Study
Page : 195 pages
File Size : 55,9 Mb
Release : 2012-01-01
Category : Computational linguistics
ISBN : 9781599731759

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Fuzzy Linguistic Topological Spaces by W. B. Vasantha Kandasamy,Florentin Smarandache,K. Amal Pdf

Author : Frank R. Deutsch
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468492989

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Best Approximation in Inner Product Spaces by Frank R. Deutsch Pdf

This is the first systematic study of best approximation theory in inner product spaces and, in particular, in Hilbert space. Geometric considerations play a prominent role in developing and understanding the theory. The only prerequisites for reading the book is some knowledge of advanced calculus and linear algebra.