Fuzzy Logic in Chemistry

Academic Press
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Fuzzy Logic has gained increasing acceptance as a way to deal with complexity and uncertainty in many areas of science and engineering. This book is the first to address its practical applications to chemical systems. Ten distinguished authors discuss the role of fuzzy logic in the characterization of a variety of chemical concepts, including chirality, quantum systems, molecular engineering and design, and hierarchical classification methods. Fuzzy Logic in Chemistry will appeal to both students and professionals who are seeking to learn more about theory and applications in an area of growing importance to the physical sciences.
  • The first book on the applications of fuzzy logic in chemistry
  • Covers a topic relevant to many disciplines, including molecular design
  • Discusses applications of fuzzy logic to the physical sciences, a rapidly growing area
  • Features chapters from highly distinguished authors in the physical sciences
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Additional Information

Academic Press
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Published on
Apr 18, 1997
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Mathematics / Set Theory
Science / Chemistry / General
Science / Chemistry / Physical & Theoretical
Science / Physics / General
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Content Protection
This content is DRM protected.
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Available on Android devices
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Eligible for Family Library

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An In-Depth View of Hardware Issues, Programming Practices, and Implementation of Key Methods

Exploring the challenges of parallel programming from the perspective of quantum chemists, Parallel Computing in Quantum Chemistry thoroughly covers topics relevant to designing and implementing parallel quantum chemistry programs.

Focusing on good parallel program design and performance analysis, the first part of the book deals with parallel computer architectures and parallel computing concepts and terminology. The authors discuss trends in hardware, methods, and algorithms; parallel computer architectures and the overall system view of a parallel computer; message-passing; parallelization via multi-threading; measures for predicting and assessing the performance of parallel algorithms; and fundamental issues of designing and implementing parallel programs.

The second part contains detailed discussions and performance analyses of parallel algorithms for a number of important and widely used quantum chemistry procedures and methods. The book presents schemes for the parallel computation of two-electron integrals, details the Hartree–Fock procedure, considers the parallel computation of second-order Møller–Plesset energies, and examines the difficulties of parallelizing local correlation methods.

Through a solid assessment of parallel computing hardware issues, parallel programming practices, and implementation of key methods, this invaluable book enables readers to develop efficient quantum chemistry software capable of utilizing large-scale parallel computers.

Molecular surface science has made enormous progress in the past 30 years. The development can be characterized by a revolution in fundamental knowledge obtained from simple model systems and by an explosion in the number of experimental techniques. The last 10 years has seen an equally rapid development of quantum mechanical modeling of surface processes using Density Functional Theory (DFT).

Chemical Bonding at Surfaces and Interfaces focuses on phenomena and concepts rather than on experimental or theoretical techniques. The aim is to provide the common basis for describing the interaction of atoms and molecules with surfaces and this to be used very broadly in science and technology.

The book begins with an overview of structural information on surface adsorbates and discusses the structure of a number of important chemisorption systems. Chapter 2 describes in detail the chemical bond between atoms or molecules and a metal surface in the observed surface structures. A detailed description of experimental information on the dynamics of bond-formation and bond-breaking at surfaces make up Chapter 3. Followed by an in-depth analysis of aspects of heterogeneous catalysis based on the d-band model. In Chapter 5 adsorption and chemistry on the enormously important Si and Ge semiconductor surfaces are covered. In the remaining two Chapters the book moves on from solid-gas interfaces and looks at solid-liquid interface processes. In the final chapter an overview is given of the environmentally important chemical processes occurring on mineral and oxide surfaces in contact with water and electrolytes.

Gives examples of how modern theoretical DFT techniques can be used to design heterogeneous catalystsThis book suits the rapid introduction of methods and concepts from surface science into a broad range of scientific disciplines where the interaction between a solid and the surrounding gas or liquid phase is an essential componentShows how insight into chemical bonding at surfaces can be applied to a range of scientific problems in heterogeneous catalysis, electrochemistry, environmental science and semiconductor processingProvides both the fundamental perspective and an overview of chemical bonding in terms of structure, electronic structure and dynamics of bond rearrangements at surfaces
Set Theory and Logic is the result of a course of lectures for advanced undergraduates, developed at Oberlin College for the purpose of introducing students to the conceptual foundations of mathematics. Mathematics, specifically the real number system, is approached as a unity whose operations can be logically ordered through axioms. One of the most complex and essential of modern mathematical innovations, the theory of sets (crucial to quantum mechanics and other sciences), is introduced in a most careful concept manner, aiming for the maximum in clarity and stimulation for further study in set logic.
Contents include: Sets and Relations — Cantor's concept of a set, etc.
Natural Number Sequence — Zorn's Lemma, etc.
Extension of Natural Numbers to Real Numbers
Logic — the Statement and Predicate Calculus, etc.
Informal Axiomatic Mathematics
Boolean AlgebraInformal Axiomatic Set TheorySeveral Algebraic Theories — Rings, Integral Domains, Fields, etc.
First-Order Theories — Metamathematics, etc.
Symbolic logic does not figure significantly until the final chapter. The main theme of the book is mathematics as a system seen through the elaboration of real numbers; set theory and logic are seen s efficient tools in constructing axioms necessary to the system.
Mathematics students at the undergraduate level, and those who seek a rigorous but not unnecessarily technical introduction to mathematical concepts, will welcome the return to print of this most lucid work.
"Professor Stoll . . . has given us one of the best introductory texts we have seen." — Cosmos.
"In the reviewer's opinion, this is an excellent book, and in addition to its use as a textbook (it contains a wealth of exercises and examples) can be recommended to all who wish an introduction to mathematical logic less technical than standard treatises (to which it can also serve as preliminary reading)." — Mathematical Reviews.
One of the most pressingproblems of mathematics over the last hundred years has been the question: What is a number? One of the most impressive answers has been the axiomatic development of set theory. The question raised is: "Exactly what assumptions, beyond those of elementary logic, are required as a basis for modern mathematics?" Answering this question by means of the Zermelo-Fraenkel system, Professor Suppes' coverage is the best treatment of axiomatic set theory for the mathematics student on the upper undergraduate or graduate level.
The opening chapter covers the basic paradoxes and the history of set theory and provides a motivation for the study. The second and third chapters cover the basic definitions and axioms and the theory of relations and functions. Beginning with the fourth chapter, equipollence, finite sets and cardinal numbers are dealt with. Chapter five continues the development with finite ordinals and denumerable sets. Chapter six, on rational numbers and real numbers, has been arranged so that it can be omitted without loss of continuity. In chapter seven, transfinite induction and ordinal arithmetic are introduced and the system of axioms is revised. The final chapter deals with the axiom of choice. Throughout, emphasis is on axioms and theorems; proofs are informal. Exercises supplement the text. Much coverage is given to intuitive ideas as well as to comparative development of other systems of set theory. Although a degree of mathematical sophistication is necessary, especially for the final two chapters, no previous work in mathematical logic or set theory is required.
For the student of mathematics, set theory is necessary for the proper understanding of the foundations of mathematics. Professor Suppes in Axiomatic Set Theory provides a very clear and well-developed approach. For those with more than a classroom interest in set theory, the historical references and the coverage of the rationale behind the axioms will provide a strong background to the major developments in the field. 1960 edition.
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