Fuzzy Chaotic Systems

Fuzzy Chaotic Systems PDF

Author: Zhong Li

Publisher: Springer

Published: 2006-08-02

Total Pages: 300

ISBN-13: 3540332219

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This book presents the fundamental concepts of fuzzy logic and fuzzy control, chaos theory and chaos control. It also provides a definition of chaos on the metric space of fuzzy sets. The book raises many questions and generates a great potential to attract more attention to combine fuzzy systems with chaos theory. In this way it contains important seeds for future scientific research and engineering applications.

Boolean Algebras

Boolean Algebras PDF

Author: Roman Sikorski

Publisher: Springer

Published: 2013-11-11

Total Pages: 245

ISBN-13: 3662015072

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There are two aspects to the theory of Boolean algebras; the algebraic and the set-theoretical. A Boolean algebra can be considered as a special kind of algebraic ring, or as a generalization of the set-theoretical notion of a field of sets. Fundamental theorems in both of these directions are due to M. H. STONE, whose papers have opened a new era in the develop ment of this theory. This work treats the set-theoretical aspect, with little mention being made of the algebraic one. The book is composed of two chapters and an appendix. Chapter I is devoted to the study of Boolean algebras from the point of view of finite Boolean operations only; a greater part of its contents can be found in the books of BIRKHOFF [2J and HERMES [IJ. Chapter II seems to be the first systematic study of Boolean algebras with infinite Boolean operations. To understand Chapters I and II it suffices only to know fundamental notions from general set theory and set-theoretical topology. No know ledge of lattice theory or of abstract algebra is presumed. Less familiar topological theorems are recalled, and only a few examples use more advanced topological means; but these may be omitted. All theorems in both chapters are given with full proofs.

The Philosophy of Mathematics and Logic in the 1920s and 1930s in Poland

The Philosophy of Mathematics and Logic in the 1920s and 1930s in Poland PDF

Author: Roman Murawski

Publisher: Springer

Published: 2014-08-27

Total Pages: 235

ISBN-13: 3034808313

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The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s. It was a remarkable period in the history of Polish science, in particular in the history of Polish logic and mathematics. Therefore, it is justified to ask whether and to what extent the development of logic and mathematics was accompanied by a philosophical reflection. We try to answer those questions by analyzing both works of Polish logicians and mathematicians who have a philosophical temperament as well as their research practice. Works and philosophical views of the following Polish scientists will be analyzed: Wacław Sierpiński, Zygmunt Janiszewski, Stefan Mazurkiewicz, Stefan Banach Hugo Steinhaus, Eustachy Żylińsk and Leon Chwistek, Jan Łukasiewicz, Zygmunt Zawirski, Stanisław Leśniewski, Tadeusz Kotarbiński, Kazimierz Ajdukiewicz, Alfred Tarski, Andrzej Mostowski and Henryk Mehlberg, Jan Sleszyński, Stanisław Zaremba and Witold Wilkosz. To indicate the background of scientists being active in the 1920s and 1930s we consider in Chapter 1 some predecessors, in particular: Jan Śniadecki, Józef Maria Hoene-Wroński, Samuel Dickstein and Edward Stamm.

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