Selection Theorems
Selection Theorems

Author:

Publisher:

Published: 2012

Total Pages: 0

ISBN-13:

DOWNLOAD EBOOK

The purpose of this paper is to provide a brief introduction to the theory of continuous selections. The theory of continuous selections was founded by E. Michael in his papers [2], [3], [4] and [5]. One of the most important and widely known selection theorems is the Convex-Valued Selection Theorem established by Michael [4], stating that every lower semi-continuous map from a paracompact space into a Banach space with closed convex values admits a continuous selection. The proof of the Convex-Valued Selection Theorem will be presented in Chapter 2 using two different approaches. In Chapter 3 we present another result obtained by Michael [2] called the Zero – Dimensional Selection Theorem. We structure our proofs in a similar manner as the proofs of the theorems found in[7].

A Course on Borel Sets
A Course on Borel Sets

Author: S.M. Srivastava

Publisher: Springer

Published: 2013-12-01

Total Pages: 271

ISBN-13: 3642854737

DOWNLOAD EBOOK

The roots of Borel sets go back to the work of Baire [8]. He was trying to come to grips with the abstract notion of a function introduced by Dirich let and Riemann. According to them, a function was to be an arbitrary correspondence between objects without giving any method or procedure by which the correspondence could be established. Since all the specific functions that one studied were determined by simple analytic expressions, Baire delineated those functions that can be constructed starting from con tinuous functions and iterating the operation 0/ pointwise limit on a se quence 0/ functions. These functions are now known as Baire functions. Lebesgue [65] and Borel [19] continued this work. In [19], Borel sets were defined for the first time. In his paper, Lebesgue made a systematic study of Baire functions and introduced many tools and techniques that are used even today. Among other results, he showed that Borel functions coincide with Baire functions. The study of Borel sets got an impetus from an error in Lebesgue's paper, which was spotted by Souslin. Lebesgue was trying to prove the following: Suppose / : )R2 -- R is a Baire function such that for every x, the equation /(x,y) = 0 has a. unique solution. Then y as a function 0/ x defined by the above equation is Baire.

Collected Papers
Collected Papers

Author: Robert J. Aumann

Publisher: MIT Press

Published: 2000

Total Pages: 806

ISBN-13: 9780262011549

DOWNLOAD EBOOK

Robert Aumann's career in game theory has spanned over research - from his doctoral dissertation in 1956 to papers as recent as January 1995. Threaded through all of Aumann's work (symbolized in his thesis on knots) is the study of relationships between different ideas, between different phenomena, and between ideas and phenomena. When you look closely at one scientific idea, writes Aumann, you find it hitched to all others. It is these hitches that I have tried to study.

Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications
Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications

Author: Olga Kosheleva

Publisher: Springer Nature

Published: 2020-02-28

Total Pages: 638

ISBN-13: 3030310418

DOWNLOAD EBOOK

Data processing has become essential to modern civilization. The original data for this processing comes from measurements or from experts, and both sources are subject to uncertainty. Traditionally, probabilistic methods have been used to process uncertainty. However, in many practical situations, we do not know the corresponding probabilities: in measurements, we often only know the upper bound on the measurement errors; this is known as interval uncertainty. In turn, expert estimates often include imprecise (fuzzy) words from natural language such as "small"; this is known as fuzzy uncertainty. In this book, leading specialists on interval, fuzzy, probabilistic uncertainty and their combination describe state-of-the-art developments in their research areas. Accordingly, the book offers a valuable guide for researchers and practitioners interested in data processing under uncertainty, and an introduction to the latest trends and techniques in this area, suitable for graduate students.

Hybrid Feedback Control
Hybrid Feedback Control

Author: Ricardo G. Sanfelice

Publisher: Princeton University Press

Published: 2021-01-12

Total Pages: 424

ISBN-13: 0691189536

DOWNLOAD EBOOK

A comprehensive introduction to hybrid control systems and design Hybrid control systems exhibit both discrete changes, or jumps, and continuous changes, or flow. An example of a hybrid control system is the automatic control of the temperature in a room: the temperature changes continuously, but the control algorithm toggles the heater on or off intermittently, triggering a discrete jump within the algorithm. Hybrid control systems feature widely across disciplines, including biology, computer science, and engineering, and examples range from the control of cellular responses to self-driving cars. Although classical control theory provides powerful tools for analyzing systems that exhibit either flow or jumps, it is ill-equipped to handle hybrid control systems. In Hybrid Feedback Control, Ricardo Sanfelice presents a self-contained introduction to hybrid control systems and develops new tools for their analysis and design. Hybrid behavior can occur in one or more subsystems of a feedback system, and Sanfelice offers a unified control theory framework, filling an important gap in the control theory literature. In addition to the theoretical framework, he includes a plethora of examples and exercises, a Matlab toolbox (as well as two open-source versions), and an insightful overview at the beginning of each chapter. Relevant to dynamical systems theory, applied mathematics, and computer science, Hybrid Feedback Control will be useful to students and researchers working on hybrid systems, cyber-physical systems, control, and automation.

The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities
The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities

Author: George Xian-Zhi Yuan

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 157

ISBN-13: 0821807471

DOWNLOAD EBOOK

This book provides a unified treatment for the study of the existence of equilibria of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities, which strongly depend on his infinite dimensional version of the classical Knaster, Kuratowski and Mazurkiewicz Lemma (KKM Lemma) in 1961. Studied are applications of general system versions of minimax inequalities and generalized quasi-variational inequalities, and random abstract economies and its applications to the system of random quasi-variational inequalities are given.

Convex Functions and Their Applications
Convex Functions and Their Applications

Author: Constantin P. Niculescu

Publisher: Springer

Published: 2018-06-08

Total Pages: 430

ISBN-13: 3319783378

DOWNLOAD EBOOK

Thorough introduction to an important area of mathematics Contains recent results Includes many exercises