Mathematical Logic

An Introduction to Model Theory

Author: A. Lightstone

Publisher: Springer Science & Business Media

ISBN: 1461587506

Category: Mathematics

Page: 338

View: 6334

Before his death in March, 1976, A. H. Lightstone delivered the manu script for this book to Plenum Press. Because he died before the editorial work on the manuscript was completed, I agreed (in the fall of 1976) to serve as a surrogate author and to see the project through to completion. I have changed the manuscript as little as possible, altering certain passages to correct oversights. But the alterations are minor; this is Lightstone's book. H. B. Enderton vii Preface This is a treatment of the predicate calculus in a form that serves as a foundation for nonstandard analysis. Classically, the predicates and variables of the predicate calculus are kept distinct, inasmuch as no variable is also a predicate; moreover, each predicate is assigned an order, a unique natural number that indicates the length of each tuple to which the predicate can be prefixed. These restrictions are dropped here, in order to develop a flexible, expressive language capable of exploiting the potential of nonstandard analysis. To assist the reader in grasping the basic ideas of logic, we begin in Part I by presenting the propositional calculus and statement systems. This provides a relatively simple setting in which to grapple with the some times foreign ideas of mathematical logic. These ideas are repeated in Part II, where the predicate calculus and semantical systems are studied.

Applied Mathematics in Aerospace Science and Engineering

Author: Angelo Miele,Attilio Salvetti

Publisher: Springer Science & Business Media

ISBN: 147579259X

Category: Technology & Engineering

Page: 514

View: 4553

This book contains the proceedings ofthe meeting on "Applied Mathematics in the Aerospace Field," held in Erice, Sicily, Italy from September 3 to September 10, 1991. The occasion of the meeting was the 12th Course of the School of Mathematics "Guido Stampacchia," directed by Professor Franco Giannessi of the University of Pisa. The school is affiliated with the International Center for Scientific Culture "Ettore Majorana," which is directed by Professor Antonino Zichichi of the University of Bologna. The objective of the course was to give a perspective on the state-of the-art and research trends concerning the application of mathematics to aerospace science and engineering. The course was structured with invited lectures and seminars concerning fundamental aspects of differential equa tions, mathematical programming, optimal control, numerical methods, per turbation methods, and variational methods occurring in flight mechanics, astrodynamics, guidance, control, aircraft design, fluid mechanics, rarefied gas dynamics, and solid mechanics. The book includes 20 chapters by 23 contributors from the United States, Germany, and Italy and is intended to be an important reference work on the application of mathematics to the aerospace field. It reflects the belief of the course directors that strong interaction between mathematics and engineering is beneficial, indeed essential, to progresses in both areas.

Applied Mathematics

An Intellectual Orientation

Author: F. J. Murray

Publisher: Springer Science & Business Media

ISBN: 1468433121

Category: Juvenile Nonfiction

Page: 225

View: 2428

The primary objective of the course presented here is orientation for those interested in applying mathematics, but the course should also be of value or in using math to those interested in mathematical research and teaching ematics in some other professional context. The course should be suitable for college seniors and graduate students, as well as for college juniors who have had mathematics beyond the basic calculus sequence. Maturity is more significant than any formal prerequisite. The presentation involves a number of topics that are significant for applied mathematics but that normally do not appear in the curriculum or are depicted from an entirely different point of view. These topics include engineering simulations, the experience patterns of the exact sciences, the conceptual nature of pure mathematics and its relation to applied mathe matics, the historical development of mathematics, the associated conceptual aspects of the exact sciences, and the metaphysical implications of mathe matical scientific theories. We will associate topics in mathematics with areas of application. This presentation corresponds to a certain logical structure. But there is an enormous wealth of intellectual development available, and this permits considerable flexibility for the instructor in curricula and emphasis. The prime objective is to encourage the student to contact and utilize this rich heritage. Thus, the student's activity is critical, and it is also critical that this activity be precisely formulated and communicated.

Integration of Fuzzy Logic and Chaos Theory

Author: Zhong Li,Wolfgang A. Halang

Publisher: Springer Science & Business Media

ISBN: 3540268995

Category: Computers

Page: 625

View: 2423

The 1960s were perhaps a decade of confusion, when scientists faced d- culties in dealing with imprecise information and complex dynamics. A new set theory and then an in?nite-valued logic of Lot? A. Zadeh were so c- fusing that they were called fuzzy set theory and fuzzy logic; a deterministic system found by E. N. Lorenz to have random behaviours was so unusual that it was lately named a chaotic system. Just like irrational and imaginary numbers, negative energy, anti-matter, etc., fuzzy logic and chaos were gr- ually and eventually accepted by many, if not all, scientists and engineers as fundamental concepts, theories, as well as technologies. In particular, fuzzy systems technology has achieved its maturity with widespread applications in many industrial, commercial, and technical ?elds, ranging from control, automation, and arti?cial intelligence to image/signal processing,patternrecognition,andelectroniccommerce.Chaos,ontheother hand,wasconsideredoneofthethreemonumentaldiscoveriesofthetwentieth century together with the theory of relativity and quantum mechanics. As a very special nonlinear dynamical phenomenon, chaos has reached its current outstanding status from being merely a scienti?c curiosity in the mid-1960s to an applicable technology in the late 1990s. Finding the intrinsic relation between fuzzy logic and chaos theory is certainlyofsigni?cantinterestandofpotentialimportance.Thepast20years have indeed witnessed some serious explorations of the interactions between fuzzylogicandchaostheory,leadingtosuchresearchtopicsasfuzzymodeling of chaotic systems using Takagi–Sugeno models, linguistic descriptions of chaotic systems, fuzzy control of chaos, and a combination of fuzzy control technology and chaos theory for various engineering practices.

Formal Methods for Industrial Critical Systems

A Survey of Applications

Author: Stefania Gnesi,Tiziana Margaria

Publisher: John Wiley & Sons

ISBN: 1118459873

Category: Computers

Page: 292

View: 8017

Today, formal methods are widely recognized as an essential step inthe design process of industrial safety-critical systems. In itsmore general definition, the term formal methods encompasses allnotations having a precise mathematical semantics, together withtheir associated analysis methods, that allow description andreasoning about the behavior of a system in a formal manner. Growing out of more than a decade of award-winning collaborativework within the European Research Consortium for Informatics andMathematics, Formal Methods for Industrial Critical Systems: ASurvey of Applications presents a number of mainstream formalmethods currently used for designing industrial critical systems,with a focus on model checking. The purpose of the book isthreefold: to reduce the effort required to learn formalmethods, which has been a major drawback for theirindustrial dissemination; to help designers to adopt the formalmethods which are most appropriate for their systems; and to offera panel of state-of-the-art techniques and tools for analyzingcritical systems.

Introduction to the Numerical Modeling of Groundwater and Geothermal Systems

Fundamentals of Mass, Energy and Solute Transport in Poroelastic Rocks

Author: Jochen Bundschuh,Mario César Suárez A.

Publisher: CRC Press

ISBN: 0203848101

Category: Technology & Engineering

Page: 522

View: 3354

This book provides an introduction to the scientific fundamentals of groundwater and geothermal systems. In a simple and didactic manner the different water and energy problems existing in deformable porous rocks are explained as well as the corresponding theories and the mathematical and numerical tools that lead to modeling and solving them. This approach provides the reader with a thorough understanding of the basic physical laws of thermoporoelastic rocks, the partial differential equations representing these laws and the principal numerical methods, which allow finding approximate solutions of the corresponding mathematical models. The book also presents the form in which specific useful models can be generated and solved. The text is introductory in the sense that it explains basic themes of the systems mentioned in three areas: engineering, physics and mathematics. All the laws and equations introduced in this book are formulated carefully based on fundamental physical principles. This way, the reader will understand the key importance of mathematics applied to all the subjects. Simple models are emphasized and solved with numerous examples. For more sophisticated and advanced models the numerical techniques are described and developed carefully. This book will serve as a synoptic compendium of the fundamentals of fluid, solute and heat transport, applicable to all types of subsurface systems, ranging from shallow aquifers down to deep geothermal reservoirs. The book will prove to be a useful textbook to senior undergraduate and graduate students, postgraduates, professional geologists and geophysicists, engineers, mathematicians and others working in the vital areas of groundwater and geothermal resources.

Advances in Multimedia, Software Engineering and Computing Vol.1

Proceedings of the 2011 MESC International Conference on Multimedia, Software Engineering and Computing, November 26-27, Wuhan, China

Author: David Jin,Sally Lin

Publisher: Springer Science & Business Media

ISBN: 3642259898

Category: Computers

Page: 688

View: 2491

MSEC2011 is an integrated conference concentrating its focus upon Multimedia ,Software Engineering, Computing and Education. In the proceeding, you can learn much more knowledge about Multimedia, Software Engineering ,Computing and Education of researchers all around the world. The main role of the proceeding is to be used as an exchange pillar for researchers who are working in the mentioned field. In order to meet high standard of Springer, AISC series ,the organization committee has made their efforts to do the following things. Firstly, poor quality paper has been refused after reviewing course by anonymous referee experts. Secondly, periodically review meetings have been held around the reviewers about five times for exchanging reviewing suggestions. Finally, the conference organization had several preliminary sessions before the conference. Through efforts of different people and departments, the conference will be successful and fruitful.

Views on Fuzzy Sets and Systems from Different Perspectives

Philosophy and Logic, Criticisms and Applications

Author: Rudolf Seising

Publisher: Springer Science & Business Media

ISBN: 354093801X

Category: Computers

Page: 580

View: 1971

This book presents the complete philosophy of Fuzzy Set Theory. It offers a collection of views from scholars involved in various research projects concerning fuzziness in science, technology, economic systems, social sciences, logics and philosophy.

Statistics with Vague Data

Author: Rudolf Kruse,Klaus Dieter Meyer

Publisher: Springer Science & Business Media

ISBN: 9789027725622

Category: Mathematics

Page: 279

View: 2120

This monograph is an attempt to unify existing works in the field of random sets, random variables, and linguistic random variables with respect to statistical analysis. It is intended to be a tutorial research compendium. The material of the work is mainly based on the postdoctoral thesis (Ha­ bilitationsschrift) of the first author and on several papers recently published by both authors. The methods form the basis of a user-friendly software tool which supports the statistical inferenee in the presence of vague data. Parts of the manuscript have been used in courses for graduate level students of mathematics and eomputer scienees held by the first author at the Technical University of Braunschweig. The textbook is designed for readers with an advanced knowledge of mathematics. The idea of writing this book came from Professor Dr. H. Skala. Several of our students have significantly contributed to its preparation. We would like to express our gratitude to Reinhard Elsner for his support in typesetting the book, Jorg Gebhardt and Jorg Knop for preparing the drawings, Michael Eike and Jiirgen Freckmann for implementing the programming system and Giinter Lehmann and Winfried Boer for proofreading the manuscript. This work was partially supported by the Fraunhofer-Gesellschaft. We are indebted to D. Reidel Publishing Company for making the pub­ lication of this book possible and would especially like to acknowledge the support whieh we received from our families on this project.

A First Course in Fuzzy Logic, Third Edition

Author: Hung T. Nguyen,Elbert A. Walker

Publisher: CRC Press

ISBN: 1420057103

Category: Mathematics

Page: 440

View: 9419

A First Course in Fuzzy Logic, Third Edition continues to provide the ideal introduction to the theory and applications of fuzzy logic. This best-selling text provides a firm mathematical basis for the calculus of fuzzy concepts necessary for designing intelligent systems and a solid background for readers to pursue further studies and real-world applications. New in the Third Edition: A section on type-2 fuzzy sets - a topic that has received much attention in the past few years Additional material on copulas and t-norms More discussions on generalized modus ponens and the compositional rule of inference Complete revision to the chapter on possibility theory Significant expansion of the chapter on fuzzy integrals Many new exercises With its comprehensive updates, this new edition presents all the background necessary for students and professionals to begin using fuzzy logic in its many-and rapidly growing- applications in computer science, mathematics, statistics, and engineering.

Soft Computing and Fractal Theory for Intelligent Manufacturing

Author: Oscar Castillo,Patricia Melin

Publisher: Springer Science & Business Media

ISBN: 9783790815474

Category: Computers

Page: 283

View: 9797

The book describes the application of soft computing techniques and fractal theory to intelligent manufacturing. Hybrid intelligent systems, which integrate different soft computing techniques and fractal theory, are also presented. The text covers the basics of fuzzy logic, neural networks, genetic algorithms, simulated annealing, chaos and fractal theory. It also describes in detail different hybrid architectures for developing intelligent manufacturing systems for applications in automated quality control, process monitoring and diagnostics, adaptive control of non-linear plants, and time series prediction. Real-world applications covered in this book include: tuning of televisions, battery charging, sound speaker testing, fruit classification, and stepping motors.

Nonlinear and Mixed-Integer Optimization

Fundamentals and Applications

Author: Christodoulos A. Floudas

Publisher: Oxford University Press on Demand

ISBN: 9788426713339

Category: Science

Page: 462

View: 6620

Filling a void in chemical engineering and optimization literature, this book presents the theory and methods for nonlinear and mixed-integer optimization, and their applications in the important area of process synthesis. Other topics include modeling issues in process synthesis, and optimization-based approaches in the synthesis of heat recovery systems, distillation-based systems, and reactor-based systems. The basics of convex analysis and nonlinear optimization are also covered and the elementary concepts of mixed-integer linear optimization are introduced. All chapters have several illustrations and geometrical interpretations of the material as well as suggested problems. Nonlinear and Mixed-Integer Optimization will prove to be an invaluable source--either as a textbook or a reference--for researchers and graduate students interested in continuous and discrete nonlinear optimization issues in engineering design, process synthesis, process operations, applied mathematics, operations research, industrial management, and systems engineering.

Electrorheological Fluids: Modeling and Mathematical Theory

Author: Michael Ruzicka

Publisher: Springer Science & Business Media

ISBN: 9783540413851

Category: Mathematics

Page: 176

View: 3484

This is the first book to present a model, based on rational mechanics of electrorheological fluids, that takes into account the complex interactions between the electromagnetic fields and the moving liquid. Several constitutive relations for the Cauchy stress tensor are discussed. The main part of the book is devoted to a mathematical investigation of a model possessing shear-dependent viscosities, proving the existence and uniqueness of weak and strong solutions for the steady and the unsteady case. The PDS systems investigated possess so-called non-standard growth conditions. Existence results for elliptic systems with non-standard growth conditions and with a nontrivial nonlinear r.h.s. and the first ever results for parabolic systems with a non-standard growth conditions are given for the first time. Written for advanced graduate students, as well as for researchers in the field, the discussion of both the modeling and the mathematics is self-contained.

An Introduction to Fuzzy Logic Applications

Author: J. Harris

Publisher: Springer Science & Business Media

ISBN: 9781402003950

Category: Computers

Page: 219

View: 6421

Fuzzy logic provides a unique method of approximate reasoning in an imperfect world. This text is a bridge to the principles of fuzzy logic through an application-focused approach to selected topics in Engineering and Management. The many examples point to the richer solutions obtained through fuzzy logic and to the possibilities of much wider applications. There are relatively few texts available at present in fuzzy logic applications. The style and content of this text is complementary to those already available. New areas of application are presented in a graded approach in which the underlying concepts are first described. The text is broadly divided into two parts which treat Processes and Materials and also System Applications. The level enables a selection of the text to be made for the substance of a senior undergraduate level course. There is also sufficient volume and quality for the basis of a postgraduate course. A more restricted and judicious selection can provide the material for a professional short course.

Post-Cold War Conflict Deterrence

Author: National Research Council,Division on Engineering and Physical Sciences,Commission on Physical Sciences, Mathematics, and Applications,Naval Studies Board

Publisher: National Academies Press

ISBN: 030905639X

Category: Technology & Engineering

Page: 244

View: 6734

Deterrence as a strategic concept evolved during the Cold War. During that period, deterrence strategy was aimed mainly at preventing aggression against the United States and its close allies by the hostile Communist power centers--the Union of Soviet Socialist Republics (USSR) and its allies, Communist China and North Korea. In particular, the strategy was devised to prevent aggression involving nuclear attack by the USSR or China. Since the end of the Cold War, the risk of war among the major powers has subsided to the lowest point in modern history. Still, the changing nature of the threats to American and allied security interests has stimulated a considerable broadening of the deterrence concept. Post-Cold War Conflict Deterrence examines the meaning of deterrence in this new environment and identifies key elements of a post-Cold War deterrence strategy and the critical issues in devising such a strategy. It further examines the significance of these findings for the U.S. Navy and Marine Corps. Quantitative and qualitative measures to support judgments about the potential success or failure of deterrence are identified. Such measures will bear on the suitability of the naval forces to meet the deterrence objectives. The capabilities of U.S. naval forces that especially bear on the deterrence objectives also are examined. Finally, the book examines the utility of models, games, and simulations as decision aids in improving the naval forces' understanding of situations in which deterrence must be used and in improving the potential success of deterrence actions.

Geographic Information Systems in Water Resources Engineering

Author: Lynn E. Johnson

Publisher: CRC Press

ISBN: 9781420069143

Category: Technology & Engineering

Page: 316

View: 3327

State-of-the-art GIS spatial data management and analysis tools are revolutionizing the field of water resource engineering. Familiarity with these technologies is now a prerequisite for success in engineers’ and planners’ efforts to create a reliable infrastructure. GIS in Water Resource Engineering presents a review of the concepts and applications of GIS in the various sub-fields of water resource engineering. After a summary review of analyses and database functions, the book addresses concepts and applications in the following areas: Surface Water Hydrology Groundwater Hydrology Water Supply and Irrigation systems Wastewater and Stormwater Systems Floodplain Management Water Quality Water Resource Monitoring and Forecasting River Basin Planning and Management The book develops a general understanding of the nature of GIS and how it is used to create and analyze geographic data. The author first introduces primary field data collection methods and describes procedures for interpretation and analysis. The second portion of the book focuses on the linkage of GIS data with water resource analysis and management models. Applications are presented with descriptions of GIS database development, analysis background theory, and model integration with GIS. The profound impact of GIS systems on water resources engineering continues to grow. GIS in Water Resource Engineering arms engineers and planners with an arsenal of tools to assist in the creation of a reliable, environmentally sensitive, infrastructure.