Sets, Sequences and Mappings


Book Description

This text bridges the gap between beginning and advanced calculus. It offers a systematic development of the real number system and careful treatment of mappings, sequences, limits, continuity, and metric spaces. 1963 edition.







High-Integrity Software


Book Description

4. 3 The Gypsy language 72 4. 4 The Gypsy Verification Environment 73 4. 5 A simple example 81 4. 6 Specification data types 91 4. 7 Future directions 95 100 4. 8 Conclusions 5 Reliable programming in standard languages 102 Bernard Carre, Program Validation Ltd. 5. 1 Introduction 102 5. 2 Language requirements for high-integrity programming 103 5. 3 The use of standard languages 108 5. 4 Programming in Pascal and Ada 110 1'19 5. 5 Practical experiences NewSpeak: a reliable programming language 6 122 I. F. Currie, Royal Signals and Radar Establishment 6. 1 Introduction 122 6. 2 Types and values 127 6. 3 Declarations and variables 132 6. 4 Guarded declarations 134 6. 5 Cases and conditionals 136 6. 6 Loops 138 6. 7 Procedures 140 6. 8 Assertions 145 6. 9 Timing 147 6. 10 Conclusion 149 6. 11 Appendix 1: summary of syntax 150 6. 12 Appendix 2: type lattice and widening 156 7 Program analysis and systematic testing 159 M. A. Hennell, University of Liverpool, and D. Hedley and I. J. Riddell, Liverpool Data Research Associates Ltd. 7. 1 Introduction 159 7. 2 The basic requirement 160 7. 3 The Liverpool experience 161 7. 4 The Liverpool experiments 162 7. 5 The LDRA Testbeds 163 Interpretation 169 7. 6 7. 7 Applicability and benefits 171 7. 8 Safety-critical systems 173 VI 8 Program analysis and verification 176 Bernard Carre, Program Validation Ltd. 8. 1 Introduction 176 8.




Fixed Point Theory


Book Description

Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then, is that they can't see the problem. one day, perhaps you will find the final G. K. Chesterton, The Scandal of Father question. Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.




Set-Valued Mappings and Enlargements of Monotone Operators


Book Description

This is the first comprehensive book treatment of the emerging subdiscipline of set-valued mapping and enlargements of maximal monotone operators. It features several important new results and applications in the field. Throughout the text, examples help readers make the bridge from theory to application. Numerous exercises are also offered to enable readers to apply and build their own skills and knowledge.




Set Valued Mappings with Applications in Nonlinear Analysis


Book Description

Interest in the mathematical analysis of multi-functions has increased rapidly over the past thirty years, partly because of its applications in fields such as biology, control theory and optimization, economics, game theory, and physics. Set Valued Mappings with Applications to Nonlinear Analysis contains 29 research articles from leading mathematicians in this area. The contributors were invited to submit papers on topics such as integral inclusion, ordinary and partial differential inclusions, fixed point theorems, boundary value problems, and optimal control. This collection will be of interest to researchers in analysis and will pave the way for the creation of new mathematics in the future.







Soft-Ware 2002: Computing in an Imperfect World


Book Description

This was the ?rst conference of a new series devoted to the e?ective handling of soft issues in the design, development, and operation of computing systems. The conference brought together contributors from a range of relevant disciplines, including arti?cial intelligence, information systems, software engineering, and systems engineering. The keynote speakers, Piero Bonissone, Ray Paul, Sir Tony Hoare, Michael Jackson, and Derek McAuley have interests and experience that collectively span all of these ?elds. Soft issues involve information or knowledge that is uncertain, incomplete, or contradictory. Examples of where such issues arise include: – requirements management and software quality control in software engine- ing, – con?ict or multiple sources information management in information systems, – decision making/prediction in business management systems, – quality control in networks and user services in telecommunications, – traditional human rationality modeling in arti?cial intelligence, – data analysis in machine learning and data mining, – control management in engineering. The concept of dealing with uncertainty became prominent in the arti?cial intel- gence community nearly 20 years ago, when researchers realized that addressing uncertainty was an essential part of representing and reasoning about human knowledge in intelligent systems. The main methodologies that have emerged in this area are soft computing and computational intelligence.




Hyperbolic Sets, Shadowing and Persistence for Noninvertible Mappings in Banach Spaces


Book Description

This text gives a self-contained and detailed treatment of presently known results, and new theorems on hyperbolicity, shadowing, complicated motion, and robustness. The book is intended to provide a dependable reference for researchers wishing to apply such results. This book will be of particular interest to researchers and students interested in dynamical systems, particularly in noninvertible maps and infinite dimensional semi-flows or maps and global analysis.




Data Integration in the Life Sciences


Book Description

This book constitutes the refereed proceedings of the Third International Workshop on Data Integration in the Life Sciences, DILS 2006, held in Hinxton, UK in July 2006. Presents 19 revised full papers and 4 revised short papers together with 2 keynote talks, addressing current issues in data integration from the life science point of view. The papers are organized in topical sections on data integration, text mining, systems, and workflow.