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Usco And Quasicontinuous Mappings


Usco And Quasicontinuous Mappings
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Usco And Quasicontinuous Mappings


Usco And Quasicontinuous Mappings
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Author : L’ubica Holá
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-10-25

Usco And Quasicontinuous Mappings written by L’ubica Holá and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-25 with Mathematics categories.


This book presents two natural generalizations of continuous mappings, namely usco and quasicontinuous mappings. The first class considers set-valued mappings, the second class relaxes the definition of continuity. Both these topological concepts stem naturally from basic mathematical considerations and have numerous applications that are covered in detail.



Usco And Quasicontinuous Mappings


Usco And Quasicontinuous Mappings
DOWNLOAD
Author : L’ubica Holá
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-10-25

Usco And Quasicontinuous Mappings written by L’ubica Holá and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-25 with Mathematics categories.


This book presents two natural generalizations of continuous mappings, namely usco and quasicontinuous mappings. The first class considers set-valued mappings, the second class relaxes the definition of continuity. Both these topological concepts stem naturally from basic mathematical considerations and have numerous applications that are covered in detail.



Advances In Topology And Their Interdisciplinary Applications


Advances In Topology And Their Interdisciplinary Applications
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Author : Santanu Acharjee
language : en
Publisher: Springer Nature
Release Date : 2023-05-09

Advances In Topology And Their Interdisciplinary Applications written by Santanu Acharjee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-09 with Mathematics categories.


This book contains selected chapters on recent research in topology. It bridges the gap between recent trends of topological theories and their applications in areas like social sciences, natural sciences, soft computing, economics, theoretical chemistry, cryptography, pattern recognitions and granular computing. There are 14 chapters, including two chapters on mathematical economics from the perspective of topology. The book discusses topics on function spaces, relator space, preorder, quasi-uniformities, bitopological dynamical systems, b-metric spaces and related fixed point theory. This book is useful to researchers, experts and scientists in studying the cutting-edge research in topology and related areas and helps them applying topology in solving real-life problems the society and science are facing these days.



Separate And Joint Continuity


Separate And Joint Continuity
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Author : Jiling Cao
language : en
Publisher: CRC Press
Release Date : 2024-07-09

Separate And Joint Continuity written by Jiling Cao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-09 with Mathematics categories.


Separate and Joint Continuity presents and summarises the main ideas and theorems that have been developed on this topic, which lies at the interface between General Topology and Functional Analysis (and the geometry of Banach spaces in particular). The book offers detailed, self-contained proofs of many of the key results. Although the development of this area has now slowed to a point where an authoritative book can be written, many important and significant problems remain open, and it is hoped that this book may serve as a springboard for future and emerging researchers into this area. Furthermore, it is the strong belief of the authors that this area of research is ripe for exploitation. That is to say, it is their belief that many of the results contained in this monograph can, and should be, applied to other areas of mathematics. It is hoped that this monograph may provide an easily accessible entry point to the main results on separate and joint continuity for mathematicians who are not directly working in this field, but who may be able to exploit some of the deep results that have been developed over the past 125 years. Features Provides detailed, self-contained proofs of many of the key results in the area Suitable for researchers and postgraduates in topology and functional analysis Is the first book to offer a detailed and up-to-date summary of the main ideas and theorems on this topic



Optimal Input Signals For Parameter Estimation


Optimal Input Signals For Parameter Estimation
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Author : Ewaryst Rafajłowicz
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-03-07

Optimal Input Signals For Parameter Estimation written by Ewaryst Rafajłowicz and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-07 with History categories.


The aim of this book is to provide methods and algorithms for the optimization of input signals so as to estimate parameters in systems described by PDE’s as accurate as possible under given constraints. The optimality conditions have their background in the optimal experiment design theory for regression functions and in simple but useful results on the dependence of eigenvalues of partial differential operators on their parameters. Examples are provided that reveal sometimes intriguing geometry of spatiotemporal input signals and responses to them. An introduction to optimal experimental design for parameter estimation of regression functions is provided. The emphasis is on functions having a tensor product (Kronecker) structure that is compatible with eigenfunctions of many partial differential operators. New optimality conditions in the time domain and computational algorithms are derived for D-optimal input signals when parameters of ordinary differential equations are estimated. They are used as building blocks for constructing D-optimal spatio-temporal inputs for systems described by linear partial differential equations of the parabolic and hyperbolic types with constant parameters. Optimality conditions for spatially distributed signals are also obtained for equations of elliptic type in those cases where their eigenfunctions do not depend on unknown constant parameters. These conditions and the resulting algorithms are interesting in their own right and, moreover, they are second building blocks for optimality of spatio-temporal signals. A discussion of the generalizability and possible applications of the results obtained is presented.



Unity Of Logic And Computation


Unity Of Logic And Computation
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Author : Gianluca Della Vedova
language : en
Publisher: Springer Nature
Release Date : 2023-07-18

Unity Of Logic And Computation written by Gianluca Della Vedova and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-18 with Computers categories.


This book constitutes the refereed proceedings of the 19th International Conference on Unity of Logic and Computation, CiE 2023, held in Batumi, Georgia, during July 24–28, 2023. The 23 full papers and 13 invited papers included in this book were carefully reviewed and selected from 51 submissions. They were organized in topical sections as follows: ​Degree theory; Proof Theory; Computability; Algorithmic Randomness; Computational Complexity; Interactive proofs; and Combinatorial approaches.



Topological Groups And The Pontryagin Van Kampen Duality


Topological Groups And The Pontryagin Van Kampen Duality
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Author : Lydia Außenhofer
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-11-22

Topological Groups And The Pontryagin Van Kampen Duality written by Lydia Außenhofer and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-22 with Mathematics categories.


This book provides an introduction to topological groups and the structure theory of locally compact abelian groups, with a special emphasis on Pontryagin-van Kampen duality, including a completely self-contained elementary proof of the duality theorem. Further related topics and applications are treated in separate chapters and in the appendix.



Noncommutative Geometry


Noncommutative Geometry
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Author : Igor V. Nikolaev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-07-18

Noncommutative Geometry written by Igor V. Nikolaev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-18 with Mathematics categories.


Noncommutative geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. This book covers the key concepts of noncommutative geometry and its applications in topology, algebraic geometry, and number theory. Our presentation is accessible to the graduate students as well as nonexperts in the field. The second edition includes two new chapters on arithmetic topology and quantum arithmetic.



Measure Theory And Nonlinear Evolution Equations


Measure Theory And Nonlinear Evolution Equations
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Author : Flavia Smarrazzo
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-04-19

Measure Theory And Nonlinear Evolution Equations written by Flavia Smarrazzo and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-19 with Mathematics categories.


This text on measure theory with applications to partial differential equations covers general measure theory, Lebesgue spaces of real-valued and vector-valued functions, different notions of measurability for the latter, weak convergence of functions and measures, Radon and Young measures, capacity. A comprehensive discussion of applications to quasilinear parabolic and hyperbolic problems is provided.



Pointwise Variable Anisotropic Function Spaces On Rn


Pointwise Variable Anisotropic Function Spaces On Rn
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Author : Shai Dekel
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-04-04

Pointwise Variable Anisotropic Function Spaces On Rn written by Shai Dekel and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-04 with Mathematics categories.


Spaces of homogeneous type were introduced as a generalization to the Euclidean space and serve as a suffi cient setting in which one can generalize the classical isotropic Harmonic analysis and function space theory. This setting is sometimes too general, and the theory is limited. Here, we present a set of fl exible ellipsoid covers of Rn that replace the Euclidean balls and support a generalization of the theory with fewer limitations.