Book Reports

An Intemational Joumal Available online at www.sciencedirect.com computers & .c,-.o. @o,..oT. mathematics with applications ELSEVIER Computers and Mathematics with Applications 49 (2005) 1585-1622 www.elsevier.com/locate/camwa

BOOK REPORTS

The Book Reports section is a regular feature of Computers ~ Mathematics with Applications. It is an unconventional section. The Editors decided to break with the longstanding custom of publishing either lengthy and discursive reviews of a few books, or just a brief listing of titles. Instead, we decided to publish every important material detail concerning those books submitted to us by publishers, which we judge to be of potential interest to our readers. Hence, breaking with custom, we also publish a complete table of contents for each such book, but no review of it as such. We welcome our readers' comments concerning this enterprise. Publishers should submit books intended for review to the Editor-in-Chief,

Professor Ervin Y. Rodin Campus Box 1040 Washington University in St. Louis One Brookings Drive St Louis, MO 63130, U.S.A.

Relevant Linquistics, An Introduction to the Structure and Use of Enqlish for Teachers. 2nd Edition, revised and expanded. Paul W. Justice. The University of Chicago Press. Chicago, IL, 2004. 311 pages. $22.00. Contents: To the Student. To the Instructor. Acknowledgements. 1. What is Linguistics? 1.1. What Do Linguists Do? 1.2. What is the Nature of Language? 1.3. Focus on Expressions: The Nature of Words. 1.4. The Nature of Grammar Rules: Prescriptivism vs. Descriptivism. 1.4.1. Prescriptivism. 1.4.2. Descriptivism. 1.4,3. Prescriptivism vs. Descriptivism over Time. 1.4.4. Descriptivism and the Language Arts Curriculum. 1.5. Narrowing the Focus: English and other Languages. 1.6. Tying It All Together: The Relevance of Linguistics. 1.7. Summary. 2. Phonetics: The Sounds of English. 2.1. Phonetics: Its Relevance to Classroom Teachers. 2.2. Spelling and Sounds in English. 2.3. The Smallest Units of Language: Phonemes, 2.4. The Consonants of English. 2.4.1. Describing the Features of Consonants: Place of Articulation. 2.4.2. Describing the Features of Consonants: Manner of Articulation. 2.4.3. Describing the Features of Consonants: Voicing. 2.5. The Vowels of English. 2.5.1. Describing English Vowels: Tongue Height. 2.5.2. Describing English Vowels: Frontness. 2.5.3. Describing English Vowels: Tenseness. 2.5.4. A Final Feature of Vowels: Roundedness. 2.5.5. Difficult to Describe Vowels: Diphthongs. 2.6. Some Important Points about Vowels. 2.6.1. Vowels as Approximations. 2.6.2. The Importance of Schwa in English. 2.7. Second Language Issues: Phonemic Inventories. 2.8. Summary. Exercises. E2.1. Phonetics Practice: Description of Phonemes. E2.2, Phonetics Practice: Phoneme Analogies. E2.3. - E2.5. Transcription Exercises. E2.6. -E2,8. Transcription Jokes. E2.9. Strange but True Transcriptions. E2.10. More Transcription Jokes. E2.11. The Connection between English Spelling and Sounds. 3. Phonology: The Sound System of English. 3.1. Levels of Representation. 3.2. Phonemes and Allophones. 3.3. The Systematicity of Phonology. 3.4. Determining the Relationship Between Sounds. 3.4.1. Contrastive Sounds. 3.4.2. Non-Contrastive Sounds. 3.5. Environment and Contrast. 3.6. Phonological Rules. 3.6.1. Determining the Basic Form of a Phoneme. 3.6.2. Rule Types. 3.7. Modeling Phonological Analysis with Four Rules of English. 3,7.1. Vowel Nasalization in English. 3.7.2. Vowel Lenghening in English. 3.7.3. Aspiration in English. 3.7.4. Flapping in American English. 3.8. Phonological Analysis Resource. 3.8.1. Goals of the Analysis. 3.8.2. Steps of the Analysis. 3.9. English Spelling Revisited. 3.10. English Phonotactics, 3.10.1. The Syllable. 3.10.2. Phonotactic Constraints on Syllable Structure. 3.11. Syllable Stress in English. 3.12. Summary. Exercises. E3.1. Minimal Pair Practice. E3.2. Contrastive and Non-Contrastive Sounds. E3.3. Practice with Natural Classes. E3.4. Determining Distribution. E3.5. English Phonology Practice. E3.6. - E3.8, English Phonology Problems. E3.9. - E3.10. Spanish Phonology Problems. E3.11. - E3.14. Additional Phonology Problems, E3.15. Practice with Phonotactics. 4. Morphology: English Word Structure and Formation. 4.1. Word Classes. 4.1.1. Classification Criteria. 4.2. Major Classes, 4.2.1. Nouns. 4.2.2. Verbs. 4,2.3. Adjectives. 4.2.4, Adverbs. 4.3. Minor Classes. 4.3.1. Pronouns. 4.4. The Structure of Words. 4.4.1. The Morpheme. 4.5. Classification of Morphemes. 4.5.1. Free Morphemes vs. Bound Morphemes. 4.5.2. Lexical Morphemes vs. Grammatical Morphemes. 4.5.3. Root Morphemes vs. Affix Morphemes. 4.5.4. Inflectional Affixes vs. Derivational Affixes. 4.6. Challenges in Identifying Morphemes: Form vs. Meaning. 4.7. The Hierarchical Structure of Words. 4.8. Word Creation in English. 4.8.1. Affixing. 4.8.2. Functional Shift. 4.8.3. Semantic Shift, 4.8.4. Compounding. 4.8.5. Blending. 4.8.6. Borrowing. 4.8.7. Acronyming. 4.8.8. Root Creation. 4.9. Summary. Exercises. E4.1. Word Class Exercise. E4.2. Morpheme Practice. E4.3. Creative Affixing. E4.4. Morphology Trees Exercise. E4.5. Derivational Morpheme Exercise (three pages). E4.6. Bound Roots in English. E4.7. English Word Creation Practice. 5. Morphophonology: Where Morphology Meets Phonology. 5.1, Key Concepts and Terms of Morphophonology. 5.2. Morphophonology Analysis. 5.2.1. Root Allomorphy. 5.2.2. Allomorphic Variation with Affixes. 5.2.3. Morphophonological Analysis Resource. 5.3. Some Rules of English Morphophonology. 5.3.1. The Past Tense in English. 5.3.2. The Plural in English. 5.3.3. Relevance at Three Levels, 5.4. Spelling and Morphophonology in English. 5.5. Summary. Exercises. Eh.1. English Morphophonology Practice. E5.2. - E5.4. English Morphophonology Problems. E5.5. Additional English Morphophonology Problem. E5.6. - E5.9. Foreign Language Morphophonology Problems. 6. Syntax: English Phrase and Sentence Structure. 6.1. More Word Classes. 6.2. Minor Classes. 6.2.1. Determiners, 6.2.2. Prepositions. 6.2.3. Auxiliaries. 6.2,4. Conjunctions. 6.3. Major Classes. 6.3.1. Nouns. 6.3.2. Verbs. 6.3.3. Adjectives. 6.3.4. Adverbs. 6.3.5. Pronouns. 6.4. Sentence Types. 6,4.1. Simple Sentences. 6.4.2. Coordinate Sentences. 6.4.3. Complex Sentences, 6,4.4. Complex-Coordinate Sentences. 6.4.5. Coordination vs. Subordination. 6,4.6. Different Kinds of Subordination. 6.5. The Purpose of Studying Syntax. 6.6. Constituents. 6,6.1. Basic Constituents. 6.6.2. The Importance of Hierarchical Constituent Structure. 6.6.3. Determining and Representing Hierarchical Structure. 6.6.4 Grammatical Relations. 6.6.5 Constituent Structure of Complex and Coorinate Sentences, 6.6.6. Diagramming Ambiguous Sentences. 6.6.7. Constituent Tests. 6.7. Phrase Structure. 6.8. Subcategorization. 6.9. Subcategories of English Verbs. 6.9.1. Transitive Verbs. 6.9.2. Intransitive Verbs. 6.9.3. Complex Transitive Verbs. 6.9.4. Linking Verbs. 6.9.5. Linking Verbs Revisited. 6.9.6. A Final Note about Subcategorization. 6.10. Transformations. 6.10.1. Deep and Surface Structures. 6.11. Transformational Rules. 6.11.1. Sub-Aux Inversion. 6.11.2. "Wh-" Movement. 6.11.3. "Wh-" Movement of Relative Pronouns. 6.11.4. A Final Note Regarding Transformations. 6.12. Tying It All Together. 6.13. Summary. Exercises. E6.1. Word Class Exercise. E6.2. Sentence Type Exercise. E6.3, Word Class/Sentence Type Exercise. E6.4. Passivization. E6.5. Beginning Syntax Trees. E6.6. Advanced Syntax Trees. E6.7. Grammatical Relation Practice. E6.8. BOOK REPORTS 1587

Phrase Structure Practice. E6.9. Even More Syntax Tree Practice. E6.10. Subcategorization Exercise. E6.11. Explaining Ungrammaticality. E6.12. Transformation Exercise. E6.13. That Word. 7. Language Variation: English Dialects. 7.1. The Language vs. Dialect Distinction. 7.2. Dimensions of Language Variation. 7.3. Absolutes vs. Relatives. 7.4. More Relatives: Correctness vs. Appropriateness. 7.5. Levels of Language Variation. 7.6. The Case of African-American English. 7.6.1. Phonological Features of AAE. 7.6.2. Morphological Features of AAE. 7.6.3. Syntactic Features of AAE. 7.6.4. An Additional Feature of AAE. 7.7. Implications of Dialect Study. 7.8. Expert Voices on Dialect Issues. 7.9. Summary. Exercises. E7.1 Classifying Variation. E7.2. Researching Language Variation. E7.3. Practice with AAE. E7.4. Discussion Exercise. Appendix 1: Introductory Matters. 1.1. Language Challenges: Ambiguity. 1.2. The History of English. 1.3. Illustrating Language History: Cognates. 1.4. The Language Tree for English. Appendix 2: Phonetics. 2.1. Distinctive Features. 2.2. More on Variation: Phonetic Alphabets. Appendix 3: Phonology. 3.1. Phonological Analysis Chart. 3.2. Ordering of Phonological Rules. Appendix 4: Morphology. 4.1. Words and Meaning: Semantics. 4.2. Internet Resources: Word-a-Day Mailing Lists. 4.3. The English Tense/Aspect System. 4.4. Verb Tense Exercise. Appendix 5: Morphophonology. 5.1 More on Spelling. Appendix 6: Syntax. 6.1. More Word Classes. 6.2. More about Phrase Structure. Appendix 7: Language Variation. 7.1. The History of English Inflections. Appendix 8: Analysis Questions. Phonology. Phonology/Morphology. Morphology. Morphophonology. Morphol- ogy/Syntax. Syntax. Glossary. References. Index.

Mathematics and Computer Science III, Alqorithms, Trees, Combinatorics and Probabilities. Michael Drmota, Philippe Flajolet, Dani~le Gardy, Bernhard Gittenberger, Editors. Spinger-Verlag, Birkh~user. Basel, Switzerland. 2004. 555 pages. $139.00. Contents: Part I. Combinatorics and Random Structures. Common Intervals of Permutations. Sylvie Corteel, Guy Louchard, and Robin Pemantle. Overpartitions and Generating Functions for Generalized Frobenius Partitions. Sylvie Corteel, Jeremy Lovejoy, and Ae Ja Yee. Enumerative Results on Integer Partitions Using the ECO Method. Luca Ferrari, Renzo Pinzani, and Simone Rinaldi. 321-Avoiding Permutations and Chebyshev Polynomials. Toufik Mansour. Iterated Logarithm Laws and the Cycle Lengths of a Random Permutation. Eugenijus Manstavius. Transcendence of Generating Functions of Walks on the Slit Plane. Martin Rubey. Some Curious Extensions of the Classical Beta Intergral Evaluation. Michael Schlosser. Divisor Functions and Pentagonal Numbers. Klaus Simon. Part II. Graph Theory. On Combinatorial Hoeffding Decomposition and Asymptotic Normality of Subgraph Count Statistics. Mindaugas Bloznelis. Avalanche Polynomials of Some Families of Graphs. Robert Cori, Arnaud Dartois, and Dominique Rossin. Perfect Matchings in Random Graphs with Prescribed Minimal Degree. Alan Frieze and Boris Pittel. Estimating the Growth Constant of Labelled Planar Graphs. Omer Gim~nez and Marc Noy. The Number of Spanning Trees in P4-Reducible Graphs. Stavros D. Nikolopoulos and Charis Papadopoulos. Part III. Analysis of Algorithms. On the Stationary Search Cost for the Move-to-Root Rule with Random Weights. Javiera Barrera and Christian Paroissin. Average-Case Analysis for the Probabilistic Bin Packing Problem. Monia Bellalouna~ Salma Souissi, and Bernard Ycart. Distribution of WriT Recurrences. Pawel Hitczenko, Jeremy R. Johnson, and Hung-Jen Huang. Probabilistic Analysis for Randomized Game Tree Evaluation. T~mur All Khan and Ralph Neininger. Polynomial Time Perfect Sampling Algorithm for Two-Rowed Contingency Tables. Shuji Kijima and Tomomi Matsui. An Efficient Generic Algorithm for the Generation of Unlabelled Cycles. Conrado Martfnez and Xaivier Molinero. Using Tries for Universal Data Compression. Yuriy A. Reznik and Anatoly V. Anisimov. Part IV. Trees. New Strahler Numbers for Rooting Plane Trees. David Auber, Jean-Philippe Domenger, Maylis Delest, Philippe Duchon, and Jean-Marc Fg

New Optimization Alqorithms in Physics. Edited by A.K. Hartmann and H. Rieger. Wiley. Hoboken, NJ. 2004. 300 pages. $155.00. Contents. List of Contributors. 1. Introduction. (A.K. Hartmann and H. Rieger). Part 1 Applications in Physics. 2. Cluster Monte Carlo Algorithms. (W. Krauth). 2.1. Detailed Balance and a priori Probabilities. 2.2. The Wolff Cluster Algorithm for the Ising Model. 2.3. Cluster Algorithm for Hard Spheres and Related Systems. 2.4. Applications. 2.4.1. Phase Separation in Binary Mixtures. 2.4.2. Polydisperse Mixtures. 2.4.3. Monomer-Dimer Problem. 2.5. Limitations and Extensions. References. 3. Probing Spin Glasses with Heuristic Optimization Algorithms. (O,C. Martin). 3.1. Spin Glasses. 3.1.1. Motivations. 3.1.2. The Ising Model. 3.1.3. Models of Spin Glasses, 3.1.4. Some Challenges. 3.2. Some Heuristic Algorithms. 3.2.1. General Issues. 3.2.2. Variable Depth Search. 3.2.3. Genetic Renormalization Algorithm. 3.3. A Survey of Physics Results. 3.3.1. Convergence of the Ground-state Energy Density. 3.3.2. Domain Walls. 3.3.3. Clustering of Ground States. 3.3.4. Low-energy Excitations. 3.3.5. Phase Diagram. 3.4. Outlook. References. 4. Computing Exact Ground States of Hard Ising Spin Glass Problems by Branch-and-cut. (F. Liers. M. Jfinger, G. Reinelt, and G. Rinaldi). 4.1. Introduction. 4.2. Ground States and Maximum Cuts. 4.3. A General Scheme for Solving Hard Max-cut Problems. 4.4. Linear Programming Relaxations of Max-cut. 4.5. Branch-and-cut. 4.6. Results of Exact Ground-state Computations. 4.7. Advantages of Branch-and-cut. 4.8. Challenges for the Years to Come. References. 5. Counting States and Counting Operations. (A. Alan Middleton). 5,1. Introduction. 5.2. Physical Questions about Ground States. 5.2.1. Homogeneous Models. 5.2.2. Magnets with Frozen Disorder. 5.3. Finding Low- energy Configurations. 5.3.1 Physically Motivated Approaches. 5.3.2 Combinatorial Optimization. 5.3.3 Ground- state Algorithm for the RFIM. 5.4. The Energy Landscape: Degeneracy and Barriers. 5.5. Counting States. 5.5.1. Ground-state Configuration Degeneracy. 5.5.2. Thermodynamic State. 5.5.3. Numerical Studies of Zero- temperature States. 5.6. Running Times for Optimization Algorithms. 5.6.1. Running Times and Evolution of the Heights. 5.6.2. Heuristic Derivation of Running Times. 5.7. Further Directions. References. 6. Computing the Ports Free Energy and Submodular Functions. (J.-C. Angl~s d'Auriac). 6.1. Introduction. 6.2 The Potts Model. 6.2.1. Definition of the Potts Model. 6.2.2. Some Results for Non-random Model. 6.2.3. The Ferromagnetic Random Bond Potts Model. 6.2.4. High Temperature Development. 6.2.5. Limit of an Infinite Number of States. 6.3. Basics on the Minimization of Submodular Functions. 6.3.1 Definition of Submodular Functions. 6.3.2. A Simple Characterization. 6.3.3. Examples. 6.3.4. Minimization of Submodular Function. 6.4. Free Energy of the Potts Model in the Infinite q-Limit. 6.4.1. The Method. 6.4.2. The Auxiliary Problem. 6.4.3. The Max-flow Problem: the Goldberg and Tarjan Algorithm. 6.4.4. About the Structure of the Optimal Sets. 6.5. Implementation and Evaluation. 6.5.1. Implementation. 6.5.2. Example of Application. 6.5.3. Evaluation of the CPU Time. 6.5.4. Memory Requirements. 6.5.5. Various Possible Improvements. 6.6. Conclusion. References. Part II. Phase Transitions in Combinatorial Optimization Problems. 7. The Random 3-satisfiability Problem: From the Phase Transition to the Efficient Generation of Hard, but Satisfiable Problem Instances. (M. Weigt). 7.1. Introduction. 7.2. Random 3-SAT and the SAT/UNSAT Transition. 7.2.1. Numerical Results. 7.2.2. Using Statistical Mechanics. 7.3. Satisfiable Random 3-SAT Instances. 7.3.1. The Naive Generator. 7.3.2. Unbiased Generators. 7.4. Conclusion. References. 8. Analysis of Backtracking Procedures for Random Decision Problems. (S. Cocco, L. Ein-Dor, and R. Monaeson). 8.1. Introduction. 8.2. Phase Diagram, Search Trajectories and the Easy SAT Phase. 8.2.1. Overview of Concepts Useful to DPLL Analysis. 8.2.2. Clause Populations: Flows, Averages and Fluctuations. 8.2.3. Average-case Analysis in the Absence of Backtracking. 8.2.4. Occurrence of Contradictions and Polynomial SAT Phase. 8.3. Analysis of the Search Tree Growth in the UNSAT Phase. 8.3.1. Numerical Experiments. 8.3.2. Parallel Growth Process and Markovian Evolution Martrix. 8.3.3. Generating Function and Large-size Scaling. 8.3.4. Interpretation in Terms of Growth Process. 8.4. Hard SAT Phase: Average Case and Fluctuations. 8.4.1. Mixed Branch and Tree Trajectories. 8.4.2. Distribution of Running Times. 8.4.3. Large Deviation Analysis of the First Branch in the Tree. 8.5. The Random Graph coloring Problem. 8.5.1. Description of DPLL Algorithm for Coloring. 8.5.2. Coloring in the Absence of Backtracking. 8.5.3. Coloring in the Presence of Massive Backtracking. 8.6. Conclusions. References. BOOK REPORTS 1589

9. New Iterative Algorithms for Hard Combinatorial Problems. (R. Zecchina). 9.1. Introduction. 9.2. Combi- natorial Decision Problems, K-SAT and the Factor Graph Representation. 9.2.1. Random K-SAT. 9.3. Growth Process Algorithm: Probabilities, Messages and Their Statistics. 9.4. Traditional Message-passing Algorithm: Belief Propagation as Simple Cavity Equations. 9.5. Survey Propagation Equations, 9.6. Decimating Variables According to Their Statistical Bias. 9.7. Conclusions and Perspectives. References. Part III. New Heuristics and Interdisciplinary Applications. 10. Hysteretic Opetimization. (K.F. P£1). 10.1. Hysteretic Optimization for Ising Spin Glasses. 10.2. General- ization to Other Optimization Problems. 10.3. Application to the Traveling Salesman Problem. 10.4. Outlook. References. 11. Extremal Optimization. (S. Boettcher). 11.1. Emerging Optimality. 11.2. Extremal Optimization. 11.2.1. Basic Notions. 11.2.2. EO Algorithm. 11.2.3. Extremal Selection. 11.2.4. Rank Ordering. 11.2.5. Defining Fitness. 11.2.6. Distinguishing EO from other Heuristics. 11.2.7. Implementing EO. 11,3. Numerical Results for EO. 11.3.1. Early Results. 11.3.2. Applications of EO by Others. 11.3.3. Large-scale Simulations of Spin Glasses. 11.4. Theoretical Investigations. References. 12. Sequence Alignments. (A.K. Hartmann). 12.1. Molecular Biology. 12.2. Alignments and Alignment Algo- rithms. 12.3. Low-probability Tail of Alignment Scores. References. 13 Protein Folding in Silico - the Quest for Better Algorithms. (U.H.E. Hansmann). 13.1. Introduction. 13.2. Energy Landscape Paving. 13.3. Beyond Global Optimization. 13.3.1. Parallel Tempering. 13.3.2. Multicanonieal Sampling and Other Generalized-ensemble Techniques. 13.4. Results. 13.4.1. Helix Formation and Folding. 13.4.2. Structure Predictions of Small Proteins. 13.5. Conclusion. References. Index.

Loqic in Computer Sciencej Modellinq and Reasoninq about Systems. Second Edition. Michael Huth and Mark Ryan. Cambridge University Press. New York, NY. 2004. 427 pages. $55.00. Contents. Foreword to the first edition. Preface to the second edition. Acknowledgements. 1. Propositional logic. 1.1 Declarative sentences. 1.2 Natural deduction. 1.2.1 Rules for natural deduction. 1.2.2 Derived rules. 1.2.3 Natural deduction in summary. 1.2.4 Provable equivalence. 1.2.5 An aside: proof by contradiction. 1.3 Propositional logic as a formal language. 1.4 Semantics of propositional logic. 1.4.1 The meaning of logical connectives. 1.4.2 Mathematical induction. 1.4.3 Soundness of propositional logic. 1.4.4 Completeness of propositional logic. 1.5 Normal forms. 1.5.1 Semantic equivalence, satisfiability and validity. 1.5.2 Conjunctive normal forms and validity. 1.5.3 Horn clauses and satisfiability. 1.6 SAT solvers. 1.6.1 A linear solver. 1.6.2 A cubic solver. 1.7 Exercises. 1.8 Bibliographic notes. 2. Predicate logic. 2.1 The need for a richer language. 2.2 Predicate logic as a formal language. 2.2.1 Terms. 2.2.2 Formulas. 2.2.3 Free and bound variables. 2.2.4 Substitution. 2.3 Proof theory of predicate logic. 2.3.1 Natural deduction rules. 2.3.2 Quantifier equivalences. 2.4 Semantics of predicate logic. 2.4.1 Models. 2.4.2 Semantic entailment. 2.4.3 The semantics of equality. 2.5 Undecidability of predicate logic. 2.6 Expressiveness of predicate logic. 2.6.1 Existential second-order logic. 2.6.2 Universal second-order logic. 2.7 Micromodels of software. 2.7.1 State machines. 2.7.2 Alma - re-visited. 2.7.3 A software micromodel. 2.8 Exercises. 2.9 Bibliographic notes. 3. Verification by model checking. 3.1 Motivation for verification. 3.2 Linear- time temporal logic. 3.2.1 Syntax of LTL. 3.2.2 Semantics of LTL. 3.2.3 Practical patterns of specifications. 3.2.4 Important equivalences between LTL formulas. 3.2.5 Adequate sets of connectives for LTL. 3.3 Model checking: systems, tools, properties. 3.3.1 Example: mutual exclusion. 3.3.2 The NuSMV model checker. 3.3.3 Running NuSMV. 3.3.4 Mutual exclusion revisited. 3.3.5 The ferryman. 3.3.6 The alternating bit protocol. 3.4 Branching- time logic. 3.4.1 Syntax of CTL. 3.4.2 Semantics of CTL. 3.4.3 Practical patterns of specifications. 3.4.4 Important equivalences between CTL formulas. 3.4.5 Adequate sets of CTL connectives. 3.5 CTL* and the expressive powers of LTL and CTL. 3.5.1 Boolean combinations of temporal formulas in CTL. 3.5.2 Past operators in LTL. 3.6 Model- checking algorithms. 3.6.1 The CTL model-checking algorithm. 3.6.2 CTL model checking with fairness. 3.6.3 The LTL model-checking algorithm. 3.7 The fixed-point characterization of CTL. 3.7.1 Monotone functions. 3.7.2 The correctness of SATEG. 3.7.3 The correctness of SAT EU. 3.8 Exercises. 3.9 Bibliographic notes. 4. Program verification. 4.1 Why should we specify and verify code? 4.2 A framework for software verification. 4.2.1 A core programming language. 4.2.2 Hoare triples. 4.2.3 Partial and total correctness. 4.2.4 Program variables and logical variables. 4.3 Proof calculus for partial correctness. 4.3.1 Proof rules. 4.3.2 Proof tableaux. 4.3.3 A case study: minimal-sum section. 4.4 Proof calculus for total correctness. 4.5 Programming by contract. 4.6 Exercises. 4.7 Bibliographic notes. 5. Modal logics and agents. 5.1 Modes of truth. 5.2 Basic modal logic. 5.2.1 Syntax. 5.2.2 Semantics. 5.3 Logic engineering. 5.3.1 The stock of valid formulas. 5.3.2 Important properties of the accessibility relation. 5.3.3 Correspondence theory. 5.3.4 Some modal logics. 5.4 Natural deduction. 5.5 Reasoning about knowledge in a multi-agent system. 5.5.1 Some examples. 5.5.2 The modal logic KT45n. 5.5.3 Natural deduction for KT45n. 5.5.4 Formalising the examples. 5.6 Exercises. 5.7 Bibliographic notes. 6. Binary decision diagrams. 6.1 Representing boolean functions. 6.1.1 Propositional formulas and truth tables. 6.1.2 Binary decision diagrams. 6.1,3 Ordered BDDs. 6.2 Algorithms for reduced OBDDs. 6.2.1 The algorithm reduce. 6.2.2 The algorithm apply. 6.2.3 The algorithm restrict. 6.2.4 The algorithm exists. 6.2.5 Assessment of OBDDs. 6.3 Symbolic model checking. 6.3.1 Representing subsets of the set of states. 6.3.2 Representing the transition relation. 6.3.3 Implementing the functions pre-exists and pre-forall. 6.3.4 Synthesising OBDDs. 6.4 A relational mu-calculus. 6.4.1 Syntax and semantics. 6.4.2 Coding CTL models and specifications. 6.5 Exercises. 6.6 Bibliographic notes. Bibliography. Index. 1590 BOOK REPORTS

Modelinq Reality, How Computers Mirror Life. Iwo Bialynicki-Birula and Iwona Bialynicka-Birula. Oxford Uni- versity Press. New York, NY. 2005. 180 pages. $44.50. Contents. 1. From building blocks to computers: Models and modeling. 2. The game of life: A legendary cellular automaton. 3. Heads or tails: Probability of an event. 4. Calton's board: Probability and statistics. 5. Twenty questions: Probability and information. 6. Snowflakes: The evolution of dynamical systems. 7. The Lorenz butterfly: Deterministic chaos. 8. From Cantor to Mandelbrot: Self-similarity and fractals. 9. Typing monkeys: Statistical linguistics. 10. The bridges of KSnigsberg: Graph theory. 11. Prinsoner's dilemma: Game theory. 12. Let the best man win: Genetic algorithms. 13. Computers can learn: Neural networks. 14. Unpredictable individuals: Modeling society. 15. Universal computer: The Turing machine. 16. Hal, R2D2, and Number 5: Artificial intelligence. Epilog. Programs. Further reading. Index.

Computational Methods for PDE in Mechanics. Berardino D'Acunto. World Scientific. Hackensak, NJ. 2004. 278 pages. $52.00. Contents. About the CD. 1. Finite differences. 1.1 Function discretization. 1.2 Finite~difference approximation of derivatives. 1.3 Approximation for higher-order derivatives. 1.4 Finite-difference operators. 2. Fourier model of heat conduction. 2.1 Fourier model of heat conduction. 2.2 Heat equation. 2.3 Initial and boundary conditions. 2.4 Phase-change problems. 2.5 Heat conduction in a moving medium. 2.6 Fick's law and diffusion. 3. An explicit method for the heat equation. 3.1 Non-dimensional form of the heat equation. 3.2 The classical explicit method. 3.3 Matrix form. 3.4 Stability. 3.5 Consistency. 3.6 Convergence. 3.7 Neumann boundary conditions. 3.8 Bound- ary conditions of the third kind. 4. A Windows program. 4.1 Introduction. 4.2 Creating a new project. 4.3 Equation data. 4.4 Initial data. 4.5 Boundary data. 4.6 Numerical results. 4.7 Analysis of data. 4.8 Graphical results. Examples. 4.9 Icons. 5. The Heat2 project. 5.1 Introduction. 5.2 The project. 5.3 Document class. 5.4 Equation class. 5.5 Initial and boundary data. 5.6 View class. 5.7 Examples. 6. Parabolic equations. 6.1 A simple implicit method. 6.2 Crank-Nicolson method. 6.3 Von Neumann stability. 6.4 Combined scheme. 6.5 An example of unstable method. 6.6 DuF0rt-Frankel method. 6.7 Matrix stability. 6.8 Stability analysis by the energy method. 6.9 Variable diffusivity coefficient. 6.10 Heat equation in two and three space dimensions. 6.11 Diffusion-convection equation. 6.12 Nonlinear equation. 6.13 A free boundary problem. 7. The Heat3 project. 7.1 Introduction. 7.2 Main menu. 7.3 Implementing the document class. 7.4 Dialog resources. 7.5 Implementing the view class. 7.6 Using the program. 8. Wave motions. 8.1 One-dimensional continuum. 8.2 Flexible strings. 8.3 Wave equation. 8.4 Waves in elastic solids. 8.5 Motion of fluids. 8.6 Free piston problem. 9. Finite-difference methods for the wave equation. 9.1 Courant-Friederichs-Lewy method. 9.2 Implicit methods. 9.3 Perturbed wave equation. 10. Hyperbolic equations. 10.1 First-order equations. Explicit methods. 10.2 Implicit methods. 10.3 Systems of first-order equations. 10.4 Nonlinear systems. 11. Elliptic equations. 11.1 Historic model. 11.2 Porous media. 11.3 Dirichlet problem. 11.4 Curved boundary. 11.5 Three-dimensional applications. 11.6 Green's identities. Consequences. 11.7 Neumann problem. 11.8 Third boundary value problem. Appendix A. Classificstion of PDE's. A.1 Second-order partial differential equations. A.2 Systems of first-order PDEs. Appendix B Elements of linear algebra. B.1 Eigenvalues and eigenvectors. B.2 Vector and matrix norms. Bibliography. Index.

Structural Dynamics Theory and Computation, Fifth Edition. Mario Pas and William Leigh. Kluwer Academic Publishers, Norwell, MA. 2004. 812 pages. $128.00. Contents: Preface to the Fifth Edition. Preface to the First Edition. Part I Structures Modeled as a Single-Degree-of-FreedomSystem. 1. Undamped Single-Degree-of-Freedom System. 1.1 Degrees of Freedom. 1.2 Undamped System. 1.3 Springs in Parallel or in Series. 1.4 Newton's Law of Motion. 1.5 Free Body Diagram. 1.6 D'Alembert's Principle. 1.7 Solution of the Differential Equation of Motion. 1.8 Frequency and Period. 1.9 Amplitude of Motion. 1.10 Summary. 1.11 Problems. 2. Damped Single-Degree-of- Freedom System. 2.1 Viscous Damping. 2.2 Equation of Motion. 2.3 Critically Damped System. 2.4 Overdamped System. 2.5 Underdamped System. 2.6 Logarithmic Decrement. 2.7 Summary. 2.8 Problems. 3. Response of One-Degree-of-Freedom System to Harmonic Loading. 3.1 Harmonic Excitation: Undamped System. 3.2 Harmonic Excitation: Damped System. 3.3 Evaluation of Damping at Resonance. 3.4 Bandwidth Method (Half-Power) to Evaluate Damping. 3.5 Energy Dissipated by Viscous Damping. 3.6 Equivalent Viscous Damping. 3.7 Response to Support Motion. 3.8 Force Transmitted to the Foundation. 3.9 Seismic Instruments. 3.10 Response of One-Degree- of-Freedom System to Harmonic Loading Using SAP2000. 3.11 Summary. 3.12 Analytical Problems. 3.13 Problems. 4. Response to General Dynamic Loading. 4.1 Duhamel's Integral-Undamped System. 4.2 Duhamel's Integral- Damped System. 4.3 Response by Direct Integration. 4.4 Solution of the Equation of Motion. 4.5 Program 2- Response by Direct Integration. 4.6 Program 3-Response to Impulsive Excitation. 4.7 Response to General Dynamic Loading Using SAP2000. 4.8 Summary. 4.9 Analytical Problems. 4.10 Problems. 5. Response Spectra. 5.1 Construction of Response Spectrum. 5.2 Response Spectrum for Support Excitation. 5.3 Tripartite Response Spectra. 5.4 Response Spectra for Elastic Design. 5.5 Influence of Local Soil Conditions. BOOK REPORTS 1591

5.6 Response Spectra for Inelastic Systems. 5.7 Response Spectra for Inelastic Design. 5.8 Program 6-Seismic Response Spectra. 5.9 Summary. 5.10 Problems. 6. Nonlinear Structural Response. 6.1 Nonlinear Single Degree-of-Freedom Model. 6.2 Integration of the Nonlin- ear Equation of Motion. 6.3 Constant Acceleration Method. 6.4 Linear Acceleration Step-by-Step Method. 6.5 The Newmark Beta Method. 6.6 Elastoplastic Behavior. 6.7 Algorithm for the Step-by-Step Solution for Elasto- plastic Single-Degree-of Freedom System. 6.8 Program 5-Response for Elastoplastic Behavior. 6.9 Summary, 6.10 Problems. Part II Structures Modeled as Shear Buildings. 7. Free Vibration of a Shear Building. 7.1 Stiffness Equations for the Shear Building. 7.2 Natural Frequencies and Normal Modes. 7.3 Orthogonality Property of the Normal Modes. 7.4 Rayleigh's Quotient. 7.5 Program 8-Natural Frequencies and Normal Modes. 7.6 Free Vibration of a Shear Building Using SAP2000. 7.7 Summary. 7.8 Problems. 8. Forced Motion of Shear Building. 8.1 Modal Superposition Method. 8.2 Response of a Shear Building to Base Motion. 8.3 Program 9oResponse by Modal Superposition. 8.4 Harmonic Forced Excitation. 8.5 Program 10-Harmonic Response. 8.6 Forced Motion Using SAP2000. 8.7 Combining Maximum Values of Modal Response. 8.8 Summary. 8.9 Problems. 9. Reduction of Dynamic Matrices. 9.1 Static Condensation. 9.2 Static Condensation Applied to Dynamic Problems. 9.3 Dynamic Condensation. 9.4 Modified Dynamic Condensation. 9.5 Program 12-Reduction of the Dynamic Problem. 9.6 Summary. 9.7 Problems. Part III Framed Structures Modeled as Discrete Multi-Degree- of-Freedom Systems. 10. Dynamic Analysis of Beams. 10.1 Shape Functions for a Beam Segment. 10.2 System Stiffness Matrix. 10.3 Inertial Properties-Lumped Mass. 10.4 Inertial Properties-Consistent Mass. 10.5 Damping Properties. 10.6 External Loads. 10.7 Geometric Stiffness. 10.8 Equations of Motion. 10.9 Element Forces at Nodal Coordinates. 10.10 Program 13-Modeling Structures as Beams. 10.11 Dynamic Analysis of Beams Using SAP2000, 10.12 Summary. 10.13 Problems. 11. Dynamic Analysis of Plane Frames. 11.1 Element Stiffness Matrix for Axial Effects. 11.2 Element Mass Matrix for Axial Effects. 11.3 Coordinate Transformation. 11.4 Program 14-Modeling Structures as Plane Frames. 11.5 Dynamic Analysis of Frames Using SAP2000. 11.6 Summary. 11.7 Problems. 12. Dynamic Analysis of Grid Frames. 12.1 Local and Global Coordinate Systems. 12.2 Torsional Effects. 12.3 Stiffness Matrix for a Grid Element. 12.4 Consistent Mass Matrix for a Grid Element. 12.5 Lumped Mass Matrix for a Grid Element. 12.6 Transformation of Coordinates. 12.7 Program 15-Modeling Structures as Grid frames. 12.8 Dynamic Analysis of Grid Frames Using SAP2000. 12.9 Summary. 12.10 Problems. 13. Dynamic Analysis of Three-Dimensional Frames. 13.1 Element Stiffness Matrix. 13.2 Element Mass Matrix. 13.3 Element Damping Matrix. 13.4 Transformation of Coordinates. 13.5 Differential Equation of Motion. 13.6 Dynamic Response. 13.7 Program 16-Modeling Structures as Space Frames. 13.8 Dynamic Response of Three- Dimensional Frames Using SAP2000. 13.9 Summary. 13.10 Problems. 14. Dynamic Analysis of Trusses. 14.1 Stiffness and Mass Matrices for the Plane Truss. 14.2 Transformation of Coordinates. 14.3 Program 17-Modeling Structures as Plane Trusses. 14.4 Stiffness and Mass Matrices for Space Trusses. 14.5 Equation of Motion for Space Trusses. 14.6 Program 18-Modeling Structures as Space Trusses. 14.7 Dynamic Analysis of Trusses Using SAP2000. 14.8 Summary. 14.9 Problems. 15. Dynamic Analysis of Structures Using the Finite Element Method. 15.1 Plane Elasticity Problems, 15.1.1 Triangular Plate Element for Plane Elasticity problems. 15.1.2 SAP2000 for Plane Elasticity Problem. 15.2 Plate Bending. 15.2.1 Rectangular Element for Plate Bending. 15.2.2 SAP2000 for Plate Bending and Shell Problems. 15.3 Summary. 15.4 Problems. 16. Time History Response of Multidegree~of-Freedom Systems. 16.1 Incremental Equations of Motion. 16.2 The Wilson-v~ Method. 16.3 Algorithm for Step-by-Step Solution of a Linear System Using the Wiison-v~ Method. 16.3.1 Initialization. 16.3.2 For Each Time Step. 16.4 Program 19-Response by Step Integration. 16.5 The Newmark Beta Method. 16.6 Elastoplastic Behavior of Framed Structures. 16.7 Member Stiffness Matrix. 16.8 Member Mass Matrix. 16.9 Rotation of Plastic Hinges. 16.10 Calculation of Member Ductility Ratio. 16.11 Time~ History Response of Multidegree-of-Freedom Systems Using SAP2000. 16.12 Summary. 16.13 Problems. Part IV Structures Modeled with Distributed Properties. 17. Dynamic Analysis of Systems with Distributed Properties. 17.1 Flexural Vibration of Uniform Beams. 17.2 Solution of the Equation of Motion in Free Vibration. 17.3 Natural Frequencies and Mode Shapes for Uniform Beams. 17.3.1 Both Ends Simply Supported. 17.3.2 Both Ends Free (Free Beam). 17.3.3 Both Ends Fixed. 17.3.4 One End Fixed and the other End Free (Cantilever Beam). 17.3.5 One End Fixed and the other End Simply Supported. 17.4 Orthogonality Condition Between Normal Modes. 17.5 Forced Vibration of Beams. 17.6 Dynamic Stresses in Beams. 17.7 Summary. 17.8 Problems. 18. Discretization of Continuous Systems. 18.1 Dynamic Matrix for Flexural Effects. 18.2 Dynamic Matrix for Axial Effects. 18,3 Dynamic Matrix for Torsional Effects. 18.4 Beam Flexure Including Axial-Force Effect. ]8.5 Power Series Expansion of the Dynamic Matrix for Flexural Effects. 18.6 Power Series Expansion of the Dynamic Matrix for Axial and for Torsional Effects. 18.7 Power Series Expansion of the Dynamic Matrix Including the Effects of Axial Forces. 18.8 Summary. Part V SpeciM Topics: Fourier Analysis, Evaluation of Absolute Damping, Generalized Coordinates. 19. Fourier Analysis and Response in the Frequency Domain. 19.1 Fourier Analysis. 19.2 Response to a Loading Represented by Fourier Series. 19.3 Fourier Coefficients for Piecewise Linear Functions. 19.4 Exponential Form 1592 BOOK REPORTS of Fourier Series.19.5 Discrete Fourier Analysis. 19.6 Fast Fourier Transform. 19.7 Program 4-Response in the Frequency Domain. 19.8 Summary. 19.9 Problems. 20. Evaluation of Absolute Damping from Modal Damping Ratios. 20.1 Equations for Damped Shear Build- ing. 20.2 Uncoupled Damped Equations. 20.3 Conditions for Damping Uncoupling. 20.4 Program 11- Absolute Damping From Modal Damping Ratios. 20.5 Summary. 20.6 Problems. 21. Generalized Coordinates and Rayleigh's Method. 21.1 Principle of Virtual Work. 21.2 Generalized Single- Degree-of-Freedom System-Rigid Body. 21.3 Generalized Single- Degree-of-Freedom System-Distributed Elasticity. 21.4 Shear Forces and Bending Moments. 21.5 Generalized Equation of Motion for a Multistory Building. 21.6 Shape Function. 21.7 Rayleigh's Method. 21.8 Improved Rayleigh's Method. 21.9 Shear Walls. 21.10 Summary. 21.11 Problems. Part VI Random Vibration. 22. Random Vibration. 22.1 Statistical Description of Random Functions. 22.2 Probability Density Function. 22.3 The Normal Distribution. 22.4 The Rayleigh Distribution. 22.5 Correlation. 22.6 The Fourier Transform. 22.7 Spectral Analysis. 22.8 Spectral Density Function. 22.9 Narrow-Band and Wide-Band Random processes. 22.10 Response to Random Excitation: Single-Degree-of-Freedom System. 22.11 Response to Random Excita- tion: Multiple- Degree-of-Freedom System. 22.11.1 Relationship Between Complex Frequency Response and Unit Impulse Response. 22.11.2 Response to Random Excitation: Two- degree-of-freedom System. 22.11.3 Response of Random Excitation: N Degree of Freedom System. 22.12 Summary. 22.13 Problems. Part VII Earthquake Engineering. 23. Uniform Building Code 1997: Equivalent Lateral Force Method. 23.1 Earthquake Ground Motion. 23.2 Equivalent Lateral Force Method. 23.3 Earthquake-Resistant Design Methods. 23.4 Seismic Zone Factor. 23.5 Base Shear Force. 23.6 Distribution of Lateral Seismic Forces. 23.7 Story Shear Force. 23.8 Horizontal Torsional Moment. 23.9 Overturning Moment. 23.10 P-Delta Effect (P - A). 23.11 Redundancy/Reliability Factor p. 23.12 Story Drift Limitation. 23.13 Diaphragm Design Forces. 23.14 Earthquake Load Effect. 23.15 Irregular Structures. 23.16 Summary. 23.17 Problems. 24. Uniform Building Code 1997: Dynamic Method. 24.1 Modal Seismic Response of Buildings. 24.1.1 Modal Equation and Participation Factor. 24.1.2 Modal Shear Force. 24.1.3 Effective Modal Weight. 24.1.4 Modal Lateral Forces. 24.1.5 Modal Displacements. 24.1.6 Modal Drift. 24.1.7 Modal Overturning Moment. 24.1.8 Modal Torsional Moment. 24.2 Total Design Values. 24.3 Provisions of UBC-97: Dynamic Method. 24.4 Scaling of Results. 24.5 Program 24-UBC 1997 Dynamic Lateral Force Method. 24.6 Summary. 24.7 Problems. 25.International Building Code IBC-2000. 25.1 Response Spectral Acceleration: Ss, S1. 25.2 Soil Modification Response Spectrual Acceleration: SMS, SM1. 25.3 Design Response Spectral Acceleration: SDS, SD1. 25.4 Site Class Definition: A, B,. .... F. 25.5 Seismic Use Group (SUG) and Occupancy Importance Factor (IE). 25.6 Seismic Design Category (A, B, C, D, E and F). 25.7 Design Response Spectral Curve: Sa v.s.T. 25.8 Determination of the Fundamental Period. 25.9 Minimum lateral Force Procedure [IBC-2000: Section 1616.4.1]. 25.10 Simplified Analysis Procedure [IBC-2000: Section 1617.5]. 25.10.1 Seismic Base Shear. 25.10.2 Response Modification Factor R. 25.10.3 Vertical Distribution of Lateral Forces. 25.11 Equivalent Seismic Lateral Force Method: [IBC-2000: Section 1617.4. 25.11.1 Distribution of Lateral Forces. 25.11.2 Overturning Moments. 25.11.3 Horizontal Torsional Moment. 25.11.4 P - Delta Effect (P - A). 25.11.5 Story Drift. 25.12 Redundancy/Reliability Factor. 25.13 Earthquake Load Effect. 25.14 Building Irregularities. 25.15 Summary. Appendices. Appendix I: Answers to Problems in Selected Chapters. Appendix II: Computer Programs. Appendix III: Glossary. Selected Bibliography. Index.

Molecular Modelinq and Simulation, An Interdisciplinary. Guide. Tamar Schlick. Springer. Heidelberg, Germany. 2002. 634 pages. $79.95. Contents. About the Cover. Book URLs. Preface. Prelude. List of Figures. List of Tables. Acronyms, Abbreviations, and Units. 1. Biomolecular Structure and Modeling: Historical Perspective. 1.1 A Multidisciplinary Enterprise. 1.1.1 Con- silience. 1.1.2 What is Molecular Modeling? 1.1.3 Need For Critical Assessment. 1.1.4 Text Overview. 1.2 Molecular Mechanics. 1.2.1 Pioneers. 1.2.2 Simulation Perspective. 1.3 Experimental Progress. 1.3.1. Protein Crystallography. 1.3.2 DNA Structure. 1.3.3 Crystallography. 1.3.4 NMR Spectroscopy. 1.4 Modern Era. 1.4.1 Biotechnology. 1.4.2 PCR and Beyond. 1.5 Genome Sequencing. 1.5.1 Sequencing Overview. 1.5.2 Human Genome. 2. Biomolecular Structure and Modeling: Problem and Application Perspective. 2.1 Computational Challenges. 2.1.1 Bioinformatics. 2.1.2 Structure From Sequence. 2.2 Protein Folding. 2.2.1 Folding Views. 2.2.2 Folding Challenges. 2.2.3 Folding Simulations. 2.2.4 Chaperones. 2.2.5 Unstructured Proteins. 2.3 Protein Misfolding. 2.3.1 Prions. 2.3.2 Infectious Proteins? 2.3.3 Hypotheses. 2.3.4 Other Midfolding Processes. 2.3.5 Function From Structure. 2.4 Practical Applications. 2.4.1 Drug Design. 2.4.2 AIDS Drugs. 2.4.3 Other Drugs. 2.4.4 A Long Way To Go. 2.4.5 Better Genes. 2.4.6 Designer Foods. 2.4.7 Designer Materials. 2.4.8 Cosmeceuticals. 3. Protein Structure Introduction. 3.1 Machinery of Life. 3.1.1 From Tissues to Hormones. 3.1.2 Size and Function Variability. 3.1.3 Chapter Overview. 3.2 Amino Acid Building Blocks. 3.2.1 Basic Cc~ Unit. 3.2.2 Essential and Nonessential Amino Acids. 3.2.3 Linking Amino Acids. 3.2.4 The Amino Acid Repertoire. 3.3 Sequence Variations in Proteins. 3.3.1 Globular Proteins. 3.3.2 Membrane and Fibrous Proteins. 3.3.3 Emerging BOOK REPORTS : 1593

Patterns from Genome Databases. 3.3.4 Sequence Similarity. 3.4 Protein Conformation Framework. 3.4.1 The Flexible ¢ and ¢ and Rigid w Dihedral Angles. 3.4.2 Rotameric Structures. 3.4.3 Ramachandran Plots. 3.4.4 Conformational Hierarchy. 4. Protein Structure Hierarchy. 4.1 Structure Hierarchy. 4,2 Helices. 4.2.1 Classic (x-Helix. 4.2.2 310 and ~r Helices. 4.2.3 Left Handed c~-Helix. 4.2.4 Collagen Helix. 4.3 ~-Sheets: A Common Secondary Structural Element. 4.4 Turns and Loops. 4.5 Supersecondary and Tertiary Structure. 4.5.1 Complex 3D Networks. 4.5.2 Classes in Protein Architecture. 4.5.3 Classes are Further Divided into Folds. 4.6 (~-Class Folds. 4.6.1 Bundles. 4.6.2 Folded Leafs. 4.6.3 Hairpin Arrays. 4.7 fl-Class Folds. 4.7.1 Anti-Parallel ]~ Domains. 4.7.2 Parallel and Antiparallel Combinations. 4.8 ~/~ and a -{- fl- Class Folds. 4.8.1 c~/fl Barrels. 4.8.2 Open Twisted a/f~ Folds. 4.8,3 Leucine-Rich c~//~ Folds. 4.8.4 a -t- ~ Folds. 4.9 Number of Folds. 4.9.1 Finite Number? 4.9.2 Concerted Target Selection: Structural Genomics. 4.10 Quaternary Structure. 4.10.1 Viruses. 4.10.2 From Ribosomes to Dynamic Networks. 4.11 Structure Classification. 5. Nucleic Acids Structure Minitutorial. 5.1 DNA, Life's Blueprint. 5.1.1 The Kindled Field of Molecular Biology. 5.1.2 DNA Processes. 5.1.3 Challenges in Nucleic Acid Structure. 5.1.4 Chapter Overview. 5.2 Basic Building Blocks. 5.2.1 Nitrogenous Bases. 5.2.2 Hydrogen Bonds. 5.2.3 Nucleotides. 5.2.4 Polynucleotides. 5.2.5 Stabilizing Polynucleotide Interactions. 5.2.6 Chain Notation. 5.2.7 Atomic Labeling. 5.2.8 Torsion Angle Labeling. 5.3 Conformational Flexibility. 5.3.1 The Furanose Ring, 5.3.2 Backbone Torsional Flexibility. 5.3.3 The Glycosyl Rotation. 5.3.4 Sugar/Glycosyl Combinations. 5.3.5 Basic Helical Descriptors. 5.3.6 Base-Pair Parameters. 5.4 Canonical DNA Forms. 5.4.1 B-DNA, 5.4.2 A-DNA. 5.4.3 Z-DNA. 5.4.4 Comparative Features. 6. Topics in Nucleic Acids Structure. 6.1 Introduction. 6.2 DNA Sequence Effects. 6.2.1 Local Deformations. 6.2.2 Orientation Preferences in Dinucleotide Steps. 6.2.3 Iutrinsic DNA Bending in A-Tracts. 6.2.4 Sequence Deformability Analysis Continues. 6.3 DNA Hydration and Ion Interactions. 6.3.1 Resolution Difficulties. 6.3.2 Basic Patterns. 6.4 DNA/Protein Interactions. 6.5 Variations on a Theme. 6.5.1 Hydrogen Bonding Patterns in Polynucleotides. 6.5.2 Hybrid Helical/Nonhelical Forms. 6.5.3 Overstretched and Understretched DNA. 6.6 RNA Structure. 6.6.1 RNA Chains Fold Upon Themselves. 6.6.2 RNA's Diversity. 6.6.3 RNA at Atomic Resolution. 6.6.4 Emerging Themes in RNA Structure and Folding. 6.7 Cellular Organization of DNA. 6.7.1 Compaction of Genomic DNA. 6,7.2 Coiling of the DNA Helix Itself. 6.7.3 Chromosomal Packaging of Coiled DNA. 6.8 Mathematical Characterization of DNA Supercoiling. 6.8.1 DNA Topology and Geometry. 6.9 Computational Treatments of DNA Supercoiling. 6.9.1 DNA as a Flecible Polymer. 6.9.2 Elasticity Theory Framework. 6.9.3 Simulations of DNA Supercoiling. 7. Theoretical and Computational Approaches to Biomolecular Structure. 7.1 Merging of Theory and Experiment. 7.1.1 Exciting Times of Computationalists! 7.1.2 The Future of Biocomputations. 7.1.3 Chapter Overview. 7.2 QM Foundations. 7.2.1 The Schrhdinger Wave Equation. 7.2.2 The Born-Oppenheimer Approximation. 7.2,3 Ab Initio. 7.2,4 Semi-Empirical QM. 7.2.5 Recent Advances in Quantum Mechanics. 7.2.6 From Quantum to Molecular Mechanics. 7.3 Molecular Mechanics Principles. 7.3.1 The Thermodynamic Hypothesis. 7.3.2 Additivity. 7.3.3 Transferability. 7.4 Molecular Mechanics Formulation. 7.4.1 Configuration Space. 7.4.2 Functional Form. 7.4.3 Some Current Limitations. 8. Force Fields. 8.1 Formulation of the Model and Energy. 8.2 Normal Modes. 8.2.1 Characteristics Motions. 8.2.2 Spectra of Biomolecules. 8.2.3 Spectra As Force Constant Sources. 8.2.4 In-Plane and Out-of-Plane Bending. 8.3 Bond Length Potentials. 8.3.1 Harmonic Term. 8.3.2 Morse Term. 8.3.3 Cubic and Quartic Terms. 8.4 Bond Angle Potentials. 8.4.1 Harmonic and Trigonometric Terms. 8.4.2 Cross Bond Stretch / Angle Bend Terms. 8.5 Torsional Potentials. 8,5,1 Origin of Rotational Barriers. 8.5.2 Fourier Terms. 8.5,3 Torsional Parameter Assignment. 8.5.4 Improper Torsion. 8.5.5 Cross Dihedral/Bond Angle and Improper/Improper Dihedral Terms. 8,6 van der Waals Potential. 8.6.1 Rapidly Decaying Potential. 8.6.2 Parameter Fitting From Experiment. 8,6.3 Two Parameter Calculation Protocols. 8.7 Coulomb Potential. 8.7.1 Coulomb's Law: Slowly Decaying Potential. 8.7.2 Dielectric Function. 8.7.3 Partial Charges. 8.8 Parameterization. 8.8.1 A PafAmge Deal. 8.8.2 Force Field Performance. 9. Nonbonded Computations. 9.1 Computational Bottleneck. 9.2 Reducing Computational Cost. 9.2.1 Simple Cutoff Schemes. 9.2.2 Ewald and Multipole Schemes. 9.3 Spherical Cutoff Techniques. 9.3.1 Technique Categories. 9.3,2 Guidelines for Cutoff Functions. 9.3.3 General Cutoff Formulations. 9.3.4 Potential Switch. 9.3.5 Force Switch. 9.3.6 Shift Functions. 9.4 Ewald Method. 9.4.1 Periodic Boundary Conditions. 9.4.2 Ewald Sum and Crystallography. 9.4.3 Morphing A Conditionally Convergent Sum. 9.4.4 Finite- Dielectric Corection. 9.4.5 Ewald Sum Complexity. 9.4.6 Resulting Ewald Summation. 9.4.7 Practical Implementation. 9.5 Multipole Method. 9.5.1 Basic Hierarchical Strategy. 9.5.2 Historical Perspective. 9.5.3 Expansion in Spherical Coordinates. 9.5.4 Biomolecular Implementations. 9.5.5 Other Variants. 9.6 Continuum Solvation. 9.6.1 Need for Simplification! 9.6.2 Potential of Mean Force. 9.6.3 Stochastic Dynamics 9.6.4 Continuum Electrostatics. 10. Multivariate Minimization in Computational Chemistry. 10.1 Optimization Applications. 10.1.1 Algorithmic Understanding Needed. 10.1.2 Chapter Overview. 10.2 Fundamentals. 10.2.1 Problem Formulation. 10.2.2 Independent Variables. 10.2.3 Function Characteristics. 10.2.4 Local and Global Minima. 10.2.5 Derivatives. 10.2.6 Hessian Matrix. 10.3 Basic Algorithms. 10.3.1 Greedy Descent. 10.3.2 Line Searches. 10.3.3 Trust Region Methods. 10.3.4 Convergence Criteria. 10.4 Newton's Method, 10,4.1 Newton in One Dimension. 10.4,2 Newton's Method for Minimization. 10.4.3 Multivariate Newton. 10.5 Large-Scale methods. 10.5.1 Quasi- Newton (QN). 10.5.2 Conjugate Gradient (CG). 10.5.3 Truncated-Newton (TN). 10.5.4 Simple Example. 10.6 Software. 10.6.1 Popular Newton and CG. 10.6.2 CHARMM's ABNR. 10.6.3 CHARMM's TN. 10.6.4 Comparative Performances on Molecular Systems. 10.7 Recommendations. 10.8 Future Outlook. 11. Monte Carlo Techniques. 11,1 Monte Carlo Popularity. 11.1.1 A Winning Combination, 11.1.2 From Nee- 1594 Book REPORTS dles to Bombs. 11.1.3 Chapter Overview. 11,1.4 Importance of Error Bars.11.2 Random Number Generators. 11.2.1 What is Random? 11.2.2 Properties of Generators? 11.2.3 Linear Congruential Generators. 11.2.4 Other Generators. 11.2.5 Artifacts. 11.2.6 Recommendations. 11.3 Gaussian Random Variates. 11.3.1 Manipulation of Uniform Random Variables. 11.3.2 Normal Variates in Molecular Simulations. 11.3.3 Odeh/Evans. 11.3.4 Box/Muller/Marsaglia. 11.4 Monte Carlo Means. 11.4.1 Expected Values. 11.4.2 Error Bars. 11.4.3 Batch Means. 11.5 Monte Carlo Sampling. 11.5.1 Probability Density Function. 11.5.2 Equilibria or Dynamics. 11.5.3 Ensembles. 11.5.4 Importance Sampling. 11.6 Hybrid MC. 11.6.1 MC and MD. 11.6.2 Basic Idea. 11.6.3 Variants and Other Hybrid Approaches. 12. Molecular Dynamics: Basics. 12.1 Introduction. 12.I.1 Why Molecular Dynamics? 12.1.2 Background. 12.1.3 Outline of MD Chapters. 12.2 Laplace's Vision. 12.2.1 The Dream 12.2.2 Deterministic Mechanics. 12.2.3 Neglect of Electronic Motion. 12.2.4 Critical Frequencies. 12.2.5 Electron/Nuclear Treatment. 12.3 Basics. 12.3.1 Following Motion. 12.3.2 Trajectory Quality. 12.3.3 Initial System Settings. 12.3.4 Trajectory Sensitivity. 12.3.5 Simulation Protocol. 12.3.6 High-Speed Implementations. 12.3.7 Analysis and Visualization. 12.3.8 Reliable Numerical Integration. 12.3.9 Computational Complexity. 12.4 Verlet Algorithm. 12.4.1 Position and Velocity Propagation. 12.4.2 Leapfrog, Velocity Verlet, and Position Verlet. 12.5 Constrained Dynamics. 12.6 Various MD Ensembles. 12.6.1 Ensemble Types. 12.6.2 Simple Algorithms. 12.6.3 Extended System Methods. 13. Molecular Dynamics: Further Topics. 13.1 Introduction. 13.2 Symplectic Integrators. 13.2.1 Sympleco tic Transformation. 13.2.2 Harmonic Oscillator Example. 13.2.3 Linear Stability. 13.2.4 Timestep-Dependent Rotation in Phase Space. 13.2.5 Resonance Condition for Periodic Motion. 13.2.6 Resonance Artifacts. 13.3 Multiple-Timestep (MTS) Methods. 13.3.1 Basic Idea. 13.3.2 Extrapolation. 13.3.3 Impulses. 13.3.4 Resonances in Impulse Splitting. 13.3.5 Resonance Artifacts in MTS. 13.3.6 Resonance Consequences. 13.4 Langevin Dynam- ics. 13.4.1 Uses. 13.4.2 Heat Bath. 13.4,3 Effect of ~. 13.4.4 Generalized Verlet for Langevin Dynamics. 13.4.5 LN Method. 13.5 Brownian Dynamics (BD). 13.5.1 Brownian Motion. 13.5.2 Brownian Framework. 13.5.3 Gen- eral Propagation Framework. 13.5.4 Hydrodynamics. 13.5.5 BD Propagation. 13.6 Implicit Integration. 13.6.1 Implicit vs. Explicit Euler. 13.6.2 Intrinsic Damping. 13.6.3 Computational Time. 13.6.4 Resonance Artifacts. 13.7 Future Outlook. 13.7.1 Integration Ingenuity. 13.7.2 Current Challenges. 14. Similarity and Diversity in Chemical Design. 14.1 Introduction to Drug Design. 14.1.1 Chemical Libraries. 14.1.2 Early Days. 14.1.3 Rational Drug Design. 14.1.4 Automated Technology. 14.1.5 Chapter Overview. 14.2 Database Problems. 14.2.1 Database Analysis. 14.2.2 Similarity and Diversity Sampling. 14.2.3 Bioactivity. 14.3 General Problem Definitions. 14.3.1 The Dataset. 14.3.2 The Compound Descriptors. 14.3.3 Biological Activity. 14.3.4 The Target Function. 14,3.5 Scaling Descriptors. 14.3.6 The Similarity and Diversity Problems. 14.4 Data Compression and Cluster Analysis. 14.4.1 PCA compression. 14.4.2 SVD compression. 14.4.3 PCA and SVD. 14.4.4 Projection Application. 14.4.5 Example. 14.5 Future Perspectives. Epilogue. Appendix A. Molecular Modeling Sample Syllabus. Appendix B. Article Reading List. Appendix C. Supplementary Course Texts. Appendix D. Homework Assignments. Index.

Applied Partial Differential Equations with Fourier Series and Boundary. Value Problems. Fourth Edition. Ri- chard Haberman. Pearson/Prentice Hall. Upper Saddle River, NJ. 2004. 769 pages. $100.00. Contents: Preface. 1. Heat Equation. 1.1. Introduction. 1.2 Derivation of the Conduction of Heat in a One-Dimensional Rod. 1.3 Boundary Conditions. 1.4 Equilibrium Temperature Distribution. 1.4.1 Prescribed Temperature. 1.4.2 Insulated Boundaries. 1.5 Derivation of the Heat Equation in Two or Three Dimensions. 2. Method of Separation of Variables. 2.1 Introduction. 2.2 Linearity. 2.3 Heat Equation with Zero Temperatures at Finite Ends. 2.3.1 Introduction. 2.3.2 Separation of Variables. 2.3.3 Time-Dependent Equation. 2.3.4 Boundary Value Problem. 2.3.5 Product Solutions and the Principle of Superposition. 2.3.6 Orthogonality of Sines. 2.3.7 Formulation, Solution, and Interpretation of an Example. 2.3.8 Summary. 2.4 Worked Examples with the Heat Equation: Other Boundary Value Problems. 2.4.1 Heat Conduction in a Rod with Insulated Ends. 2.4.2 Heat Conduction in a Thin Circular Ring. 2.4.3 Summary of Boundary Value Problems. 2.5 Laplace's Equation: Solutions and Qualitative Properties. 2.5.1 Laplace's Equation Inside a Rectangle. 2.5.2 Laplace's Equation for a Circular Disk. 2,5.3 Fluid Flow Past a Circular Cylinder (Lift). 2.5.4 Qualitative Properties of Laplace's Equation. 3. Fourier Series. 3.1 Introduction. 3.2 Statement of Convergence Theorem. 3.3. Fourier Cosine and Sine Series. 3.3.1 Fourier Sine Series. 3.3.2 Fourier Cosine Series. 3.3.3 Representing f (x) by Both a Sine and Cosine Series. 3.3.4 Even and Odd Parts. 3.3.5 Continuous Fourier Series. 3.4 Term-by-Term Differentiation of Fourier Series. 3.5 Term-by-Term Integration of Fourier Series. 3.6 Complex Form of Fourier Series. 4. Wave Equation: Vibrating String and Membranes. 4.1 Introduction. 4.2 Derivation of a Vertically Vibrating String. 4.3 Boundary Conditions. 4.4 Vibrating String with Fixed Ends. 4.5 Vibrating Membrane. 4.6 Reflection and Refraction of Electromagnectic (Light) and Acoustic (Sound) Waves. 4.6.1 Shell's Law of Refraction. 4.6.2 Intensity (Amplitude) of Reflected and Refracted Waves. 4.6.3 Total Internal Reflection. 5. Sturm-Liouville Eigenvalue Problems. 5.1 Introduction. 5.2 Examples. 5.2.1 Heat Flow in a Nonuniform Rod. 5.2.2 Circularly Symmetric Heat Flow. 5.3 Sturm-Liouville Eigenvalue Problems. 5.3.1 General Classification. 5.3.2 Regular Sturm-Liouville Eigenvalue Problem. 5.3.3 Example and Illustration of Theorems. 5.4 Worked Example: Heat Flow in a Nonuniform Rod without Sources. 5.5 Self-Adjoint Operators and Sturm-Liouville Eigenvalue Problems. 5.6 Rayleigh Quotient. 5.7 Worked Example: Vibrations of a Nonuniform String. 5.8 Boundary Conditions of the Third Kind. 5.9 Large Eigenvalues (Asymptotic Behavior). 5.10 Approximation Properties. BOOK REPORTS 1595

6. Finite Difference Numerical Methods for Partial Differential Equations. 6.1 Introduction, 6.2 Finite Differences and Truncated Taylor Series. 6.3 Heat Equation. 6.3.1 Introduction. 6.3.2 A Partial Difference Equation. 6.3,3 Computations. 6.3.4 Fourier-von Neumann Stability Analysis. 6.3.5 Separation of Variables for Partial Difference Equations and Analytic Solutions of Ordinary Difference Equations. 6.3.6 Matrix Notation. 6.3.7 Nonhomogeneous Problems. 6.3.8 Other Numerical Schemes, 6.3.9 Other Types of Boundary Conditions. 6.4 Two- Dimensional Heat Equation. 6.5 Wave Equation. 6.6 Laplace's Equation. 6.7 Finite Element Method, 6.7.1 Approximation with Nonorthogonal Functions (Weak Form of the Partial Differential Equation). 6.7.2 The Simplest Triangular Finite Elements. 7. Higher Dimensional Partial Differential Equations. 7.1 Introduction. 7.2 Separation of the Time Variable. 7.2.1 Vibrating Membrane: Any Shape. 7.2.2 Heat Conduction: Any Region. 7.2.3 Summary. 7.3 Vibrating Rectangular Membrane. 7.4 Statements and Illustrations of Theorems for the Eigenvalue Problem V2¢ + A¢ ----0. 7,5 Green's Formula, Self-Adjoint Operators and Multidimensional Eigenvalue Problems. 7.6 Rayleigh Quotient and Laplace's Equation. 7,6.1 Rayleigh Quotient. 7.6.2 Time- Dependent Heat Equation and Laplace's Equation. 7.7 Vibrating Circular Membrane and Bessel Functions. 7.7.1 Introduction. 7,7.2 Separation of Variables. 7.7.3 Eigenvalue Problems (One Dimensional). 7.7.4 Bessel's Differential Equation. 7.7.5 Singular Points and Bessel's Differential Equation. 7.7.6 Bessel Functions and Their Asymptotic Properties (near z -~ 0). 7.7.7 Eigenvalue Problem Involving Bessel Functions. 7.7.8 Initial Value Problem for a Vibrating Circular Membrane. 7.7.9 Circularly Symmetric Case. 7.8 More on Bessel Functions. 7.8.1 Qualitative Properties of Bessel Functions. 7.8.2 Asymptotic Formulas for the Eigenvalues, 7.8.3 Zeros of Bessel Fhnctions and Nodal Curves. 7.8.4 Series Representation of Bessel Functions. 7.9 Laplace's Equation in a Circular Cylinder. 7.9.1 Introduction. 7.9.2 Separation of Variables. 7.9.3 Zero Temperature on the Lateral Sides and on the Bottom or Top. 7.9.4 Zero Temperature on the Top and Bottom. 7.9.5 Modified Bessel Functions. 7.10 Spherical Problems and Legendre Polynomials. 7.10.1 Introduction. 7.10.2 Separation of Variables and One- Dimensional Eigenvalue Problems. 7.10.3 Associated Legendre Functions and Legendre Polynomials. 7.10.4 Radial Eigenvalue Problems. 7.10.5 Product Solutions, Modes of Vibration, and the Initial Value Problem. 7.10.6 Laplace's Equation Inside a Spherical Cavity. 8. Nonhomogeneous Problems. 8.1 Introduction. 8.2 Heat Flow with Sources and Nonhomogeneous Boundary Conditions. 8.3 Method of Eigenfunction Expansion with Homogeneous Boundary Conditions (Differentiating Series of Eigenfunctions). 8.4 Method of Eigenfunction Expansion Using Green's Formula (With or Without Homogeneous Boundary Conditions). 8.5 Forced Vibrating Membranes and Resonance. 8.6 Poisson's Equation. 9. Green's Functions for Time-Independent Problems. 9.1 Introduction. 9.2 One-Dimensional Heat Equation. 9.3 Green's Functions for Boundary Value Problems for Ordinary Differential Equations, 9.3.1 One-Dimensional Steady- State Heat Equation. 9.3.2 The Method of Variation of Parameters. 9.3.3 The Method of Eigenfunction Expansion for Green's Functions. 9.3.4 The Dirac Delta Function and Its Relationship to Green's Functions. 9.3.5 Nonhomogeneous Boundary Conditions. 9.3.6 Summary. 9.4 Fredholm Alternatives and Generalized Green's Functions. 9.4.1 Introduction. 9.4,2 Fredholm Alternatives. 9.4.3 Generalized Green's Functions. 9.5 Green's Functions for Poisson's Equation. 9.5.1 Introduction. 9.5.2 Multidimensional Dirac Delta Function and Green's Functions. 9.5.3 Green's Functions by the Method of Eigenfunction Expansion and the Fredholm Alternative. 9.5.4 Direct Solution of Green's Fucntions (One-Dimensional Eigenfunctions). 9.5.5 Using Green's Functions for Problems with Nonhomogeneous Boundary Conditions. 9.5.6 Infinite Space Green's Functions, 9.5,7 Green's Functions for Bounded Domains Using Infinite Space Green's Functions, 9.5.8 Green's Functions for a Semi- Infinite Plane (y ~ 0) Using Infinite Space Green's Functions: The Method of Images. 9.5.9 Green's Functions for a Circle: The Method of Images. 9.6 Perturbed Eigenvalue Problems. 9.6.1 Introduction. 9.6.2 Mathematical Example. 9.6.3 Vibrating Nearly Circular Membrane. 9.7 Summary. 10. Infinite Domain Problems: Fourier Transform Solutions of Partial Differential Equations. 10.1 Introduction. 10.2 Heat Equation on an Infinite Domain. 10.3 Fourier Transform Pair. 10.3.1 Motivation from Fourier Series Identity. 10.3.2 Fourier Transform. 10.3.3 Inverse Fourier Transform of a Gaussian. 10.4 Fourier Transform and the Heat Equation. 10.4.1 Heat Equation. 10,4.2 Fourier Transforming the Heat Equation: Transforms of Derivatives. 10.4.3 Convolution Theorem, 10.4.4 Summary of Properties of the Fourier Transform. 10.5 Fourier Sine and Cosine Transforms: The Heat Equation on Simi-Infinite Intervals. 10.5.1 Introduction. 10.5.2 Heat Equation on a Semi-Infinite Interval I. 10.5.3 Fourier Sine and Cosine Transforms. 10.5.4 Transforms of Derivatives. 10.5.5 Heat Equation on a Semi-Infinite Interval II. 10.5.6 Tables of Fourier Sine and Cosine Transforms. 10.6 Worked Examples Using Transforms. 10.6.1 One-Dimensional Wave Equation on an Infinite Interval. 10.6.2 Laplace's Equation in a Semi-Infinite Strip. 10.6.3 Laplace's Equation in a Half-Plane. 10.6.4 Laplace's Equation in a Quarter-Plane. 10.6.5 Heat Equation in a Plane (Two-Dimensional Fourier Transforms), 10.6.6 Table of Double- Fourier Transforms. 10.7 Scattering and Inverse Scattering. 11. Green's Functions for Wave and Heat Equations. 11.1 Introduction. 11.2 Green's Functions for the Wave Equation. 11.2.1 Introduction. 11.2.2 Green's Formula. 11.2.3 Reciprocity. 11.2.4 Using the Green's Function. 11.2.5 Green's Function for the Wave Equation. 11.2,6 Alternate Differential Equation for the Green's Function. 11.2.7 Infinite Space Green's Function for the One-Dimensional Wave Equation and d'Alembert's Solution. 11.2.8 Infinite Space Green's Function for the Three-Dimensional Wave Equation (Huygens' Principle). 11.2.9 Two- Dimensional Infinite Space Green's Function. 11.2.10 Summary. 11.3 Green's Functions for the Heat Equation. 11.3.1 Introduction. 11.3.2 Non-Self-Adjoint Nature of the Heat Equation. 11.3.3 Green's Formula. 11.3.4 Adjoint Green's Function. 11.3.5 Reciprocity. 11.3.6 Representation of the Solution Using Green's Functions. 11.3.7 Alternate Differential Equation for the Green's Function. 11.3.8 Infinite Space Green's Function for the Diffusion Equation. 11.3.9 Green's Function for the Heat Equation (Semi-Infinite Domain). 11.3.10 Green's Function for the Heat Equation (on a Finite Region). 1596 BOOK REPORTS

12. The Method of Characteristics for Linear and Quasilinear Wave Equations. 12.1 Introduction. 12.2 Charac- teristics for First-Order Wave Equations. 12.2.1 Introduction. 12.2.2 Method of Characteristics for First-Order Partial Differential Equations. 12.3 Method of Characteristics for the One-Dimensional Wave Equation. 12.3.1 General Solution. 12.3.2 Initial Value Problem (Infinite Domain). 12.3.3 D'alembert's Solution. 12.4 Semi-Infinite Strings and Reflections. 12.5 Method of Characteristics for a Vibrating String of Fixed Length. 12.6 The Method of Characteristics for Quasilinear Partial Differential Equations. 12.6.1 Method of Characteristics. 12.6.2 Traf- fic Flow. 12.6.3 Method of Characteristics (Q = 0). 12.6.4 Shock Waves. 12.6.5 Quasilinear Example. 12.7 First-Order Nonlinear Partial Differential Equations. 12.7.1 Eikonal Equation Derived from the Wave Equation. 12.7.2 Solving the Eikonal Equation in Uniform Media and Reflected Waves. 12.7.3 First-Order Nonlinear Partial Differential Equations. 13. Laplace Transform Solution of Partial Differential Equations. 13.1 Introduction. 13.2 Properties of the Laplace Transform. 13.2.1 Introduction. 13.2.2 Singularities of the Laplace Transform. 13.2.3 Transforms of Derivatives. 13.2.4 Convolution Theorem. 13.3 Green's Functions for Initial Value Problems for Ordinary Differential Equa- tions. 13.4 A Signal Problem for the Wave Equation. 13.5 A Signal Problem for a Vibrating String of Finite Length. 13.6 The Wave Equation of its Green's Function. 13.7 Inversion of Laplace Transforms Using Con- tour Integrals in the Complex Plane. 13.8 Solving the Wave Equation Using Laplace Transforms (with Complex Variables). 14. Dispersive Waves: Slow Variations, Stability, Nonlinearity, and Perturbation Methods. 14.1 Introduction. 14.2 Dispersive Waves and Group Velocity. 14.2.1 Traveling Waves and the Dispersion Relation. 14.2.2 Group Velocity I. 14.3 Wave Guides. 14.3.1 Response to Concentrated Periodic Sources with Frequency wf. 14.3.2 Green's Function If Mode Propagates. 14.3.3 Green's Function If Mode Does Not Propagate. 14.3.4 Design Considerations. 14.4 Fiber Optics. 14.5 Group Velocity II and the Method of Stationary Phase. 14.5.1 Method of Stationary Phase. 14.5.2 Application to Linear Dispersive Waves. 14.6 Slowly Varying Dispersive Waves (Group Velocity and Caustics). 14.6.1 Approximate Solutions of Dispersive Partial Differential Equations. 14.6.2 Formation of a Caustic. 14.7 Wave Envelope Equations (Concentrated Wave Number). 14.7.1 SchrSdinger Equation. 14.7.2 Linearized Korteweg-de Vries Equation. 14.7.3 Nonlinear Dispersive Waves: Korteweg-de Vries Equation. 14.7.4 Solitons and Inverse Scattering. 14.7.5 Nonlinear SchrSdinger Equation. 14.8 Stability and Instability. 14.8.1 Brief Ordinary Differential Equations and Bifurcation Theory. 14.8.2 Elementary Example of a Stable Equilibrium for a Partial Differential Equation. 14.8.3 Typical Unstable Equilibrium for a Partial Differential Equation and Pattern Formation. 14.8.4 Ill posed Problems. 14.8.5 Slightly Unstable Dispersive Waves and the Linearized Complex Ginzburg-Landau Equation. 14.8.6 Nonlinear Complex Ginzburg-Landau Equation. 14.8.7 Long Wave Instabilities. 14.8.8 Pattern Formation for Reaction-Diffusion Equations and the Turing Instability. 14.9 Singular Perturbation Methods: Multiple Scales. 14.9.1 Ordinary Differential Equation: Weakly Nonlinearly Damped Oscillator. 14.9.2 Ordinary Differential Equation: Slowly Varying Oscillator. 14.9.3 Slightly Unstable Partial Differential Equation on Fixed Spatial Domain. 14.9.4 Slowly Varying Medium for the Wave Equation. 14.9.5 Slowly Varying Linear Dispersive Waves (Including Weak Nonlinear Effects). 14.10 Singular Perturbation Methods: Boundary Layers Method of Matched Asymptotic Expansions. 14.10.1 Boundary Layer in an Ordinary Differential Equation. 14.10.2 Diffusion of a Pollutant Dominated by Convection. Bibliography. Answers to Starred Exercises. Index.

Cambridqe Series in Statistical and Probabilistic Mathematics, Exercise in Probability, A Guided Tour from Measure Theory to Random Processes, via Conditioninq. Lo'fc Chaumont and Marc Yor. Cambridge University Press. New York, NY. 2003. 236 pages. $50.00. Contents: Preface. Some frequently used notations. 1. Measure theory and probability. 1.1 Sets which do not belong in a strong sense, to a a-field. 1.2 Some criteria for uniform integrability. 1.3 When does weak convergence imply the convergence of expectations? 1.4 Conditional expectation and the Monotone Class Theorem. 1.5 Lp-convergence of conditional expectations. 1.6 Measure preserving transformations. 1.7 Erodic transformations. 1.8 Invariant a-fields. 1.9 Extremal solutions of (general) moments problems. 1.10 The log normal distribution is moments indeterminate. 1.11 Conditional expectations and equality in law. 1.12 Simplifiable random variables. 1.13 Mellin transform and simplification. Solutions for Chapter 1. 2. Independence and conditioning. 2.1 Independence does not imply measurability with respect to an independent complement. 2.2 Complement to Exercise 2.1: further statements of independence versus measurability. 2.3 Inde- pendence and mutual absolute continuity. 2.4 Size-biased sampling and conditional laws. 2.5 Think twice before exchanging the order of taking the supremum and intersection of a-fields! 2.6 Exchangeability and conditional independence: de Finetti's theorem. 2.7 Too much independence implies constancy. 2.8 A double paradoxical inequality. 2.9 Euler's formula for primes and probability. 2.10 The probability, for integers, of being relatively prime. 2.11 Bernoulli random walks considered at some stopping time. 2.12 cosh, sinh, the Fourier transform and conditional independence. 2.13 cosh, sinh, and the Laplace transform. 2.14 Conditioning and changes of probabilities. 2.15 Radon-Nikodym density and the Acceptance-Rejection Method of yon Neumann. 2.16 Negligible sets and conditioning. 2.17 Gamma laws and conditioning. 2.18 Random variables with independent fractional and integer parts. Solutions for Chapter 2. 3. Caussian variables. 3.1 Constructing Gaussian variables from, but not belonging to, a Gaussian space. 3.2 A complement to Exercise 3.1. 3.3 On the negative moments of norms of Gaussian vectors. 3.4 Quadratic functionals of Gaussian vectors and continued fractions. 3.5 Orthogonal but non-independent Caussian variables. BOOK REPORTS 1597

3.6 Isotropy property of multidimensional Gaussian laws. 3.7 The Gaussian distribution and matrix transposition. 3.8 A law whose n-samples are preserved by every orthogonal transformation is Gaussian. 3.9 Non-canonical representation of Gaussian random walks. 3.10 Concentration inequality for Gaussian vectors. 3.11 Determining a jointly Gaussian distribution from its conditional marginals. Solutions for Chapter 3. 4. Distributional computations. 4.1 Hermite polynomials and Gaussian variables. 4.2 The beta-gamma algebra and Poincar~'s Lemma. 4.3 An identity in law between reciprocals of gamma variables. 4.4 The Gamma process and its associated Dirichlet processes. 4.5 Gamma Variables and Gauss multiplication formulae. 4.6 The beta- gamma algrebra and convergence in law. 4.7 Beta-gamma variables and changes of probability measures. 4.8 Exponential variables and powers of Gaussian variables. 4.9 Mixtures of exponential distributions. 4.10 Some computations related to the lack of memory property of the exponential law. 4.11 Some identities in law between Gaussian and exponential variables. 4.12 Some functions which preserve the Cauchy law. 4.13 Uniform laws on the circle. 4.14 Trigonometric formulae and probability. 4.15 A multidimensional version of the Cauchy distribution. 4.16 Some properties of the Gauss transform. 4.17 Unilateral stable distributions (1). 4.18 Unilateral stable distributions (2). 4.19 Unilateral stable distributions (3). 4.20 A probabilistic translation of Selberg's integral formulae. 4.21 Mellin and Stieltjes transforms of stable variables. 4.22 Solving certain moment problems via simplification. Solutions for Chapter 4. 5. Convergence of random variables. 5.1 Convergence of sum of squares of independent Gaussian variables. 5.2 Convergence for moments and convergence in law. 5.3 Borel test functions and convergence in law. 5.4 Convergence in law of the normalized maximum of Cauchy variables. 5.5 Large deviations for the maximum of Caussian vectors. 5.6 A logarithmic normalization. 5.7 A ~ normalization. 5.8 The Central Limit Theorem involves convergence in law, not in probability. 5.9 Changes of probabilities and the Central Limit Theorem. 5.10 Convergence in law of stable (p) variables, as /z -%--* 0. 5.11 Finite dimensional convergence in law towards Brownian motion. 5.12 The empirical process and the Brownian bridge. 5.13 The Poisson process and Brownian motion. 5.14 Brownian bridges converging in law to Brewnian motions. 5.15 An almost sure convergence result for sums of stable random variables. Solutions for Chapter 5. 6. Random processes. 6.1 Solving a particular SDE. 6.2 The range process of Brownian motion. 6.3 Symmetric Levy processes reflected at their minimum and maximum; E. Cs£ki's formulae for the ratio of Brownian extremes. 6.4 A toy example for Westwater's renormalization. 6.5 Some asymptotic laws of planar Brownian motion. 6.6 Windings of the three- dimensional Brownian motion around a line. 6.7 Cyclic exchangeability property and uniform law related to the Brownian bridge. 6.8 Local time and hitting time distributions for the Brownian bridge. 6.9 Partial absolute continuity of the Brownian bridge distribution with respect to the Brownian distribution. 6.10 A Brownian interpretation of the duplication formula for the gamma function. 6.11 Some deterministic time- changes of Brownian motion. 6.12 Random scaling of the Brownian bridge. 6.13 Time-inversion and quadratic functionals of Brownian motion; L@vy's stochastic area formula. 6.14 Quadratic variation and local time of semimartingales. 6.15 Geometric Brownian motion. 6.16 0-self similar processes and conditional expectation. 6.17 A Taylor formula for semimartingales; Markov martingales and iterated infinitesimal generators. 6.18 A remark of D.Williams: the optional stopping theorem may hold for certain "non-stopping times". 6.19 Stochastic affine processes, also known as "Harnesses". 6.20 A martingale "in the mean over time" is a martingale. 6.21 A reinforcement of Exercise 6.20. Solutions for Chapter 6. Where is the notion N discussed? Final suggestions: how to go further? References. Index.

Chaos and Fractals, New Frontiers of Science, Second Edition. Heinz-Otto Peitgen, Hartmut Jiirgens and Diet- mar Saupe. Springer-Verlag. New York, NY. 2004. 864 pages. $69.95. Contents: Forward. Introduction: Causality Principle, Deterministic Laws and Chaos. 1. The Backbone of Practals: Feedback and the Iterator. 1,1 The Principle of Feedback. 1.2 The Multiple Reduction Copy Machine. 1.3 Basic Types of Feedback Processes. 1.4 The Parable of the Parabola - Or: Don't Trust Your Computer. 1.5 Chaos Wipes Out Every Computer. 2. Classical Fractals and Self-Similarity. 2.1 The Cantor Set 2.2 The Sierpinski Gasket and Carpet. 2.3 The Pascal Triangle. 2.4 The Koch Curve. 2.5 Space- Filling Curves. 2.6 Fractals and the Problem of Dimension. 2.7 The Universality of the Sierpinski Carpet. 2.8 Julia Sets. 2.9 Pythagorean Trees. 3. Limits and Self-Similarity. 3.1 Similarity and Scaling. 3.2 Geometric Series and the Koch Curve. 3.3 Corner the New from Several Sides: Pi and the Square Root of Two. 3.4 Fractals as Solutions of Equations. 4. Length, Area and Dimension: Measuring Complexity and Scaling Properties. 4.1 Finite and Infinite Length of Spirals. 4.2 Measuring Fractal Curves and Power Laws. 4.3 Fractal Dimension. 4.4 The Box-Counting Dimension. 4.5 Borderline Fractals: Devil's Staircase and Peano Curve. 5. Encoding Images by Simple Transformations. 5.1 The Multiple Reduction Copy Machine Metaphor. 5.2 Composing Simple Transformations. 5.3 Relatives of the Sierpinski Gasket. 5.4 Classical Fractals by IFSs. 5.5 Image Encoding by IFSs. 5.6 Foundation of IFS: The Contraction Mapping Principle. 5.7 Choosing the Right Metric. 5.8 Composing Self-Similar Images. 5.9 Breaking Self-Similarity and Self-Affinity: Networking with MRCMs. 6. The Chaos Game: How Randomness Creates Deterministic Shapes. 6.1 The Fortune Wheel Reduction Copy Machine. 6.2 Addresses: Analysis of the Chaos Game. 6.3 Tuning the Fortune Wheel. 6.4 Random Number Generator Pitfall. 6.5 Adaptive Cut Methods. 1598 BOOK REPORTS

7. Recursive Structures: Growing Fractals and Plants. 7.1 L-Systems: A Language for Modeling Growth. 7.2 Growing Classical Fractals with MRCMs. 7.3 Turtle Graphics: Graphical interpretation of L-Systems. 7.4 Growing Classical Fractals with L-systems. 7.5 Growing Fractals with Networked MRCMs. 7.6 L-System Trees and Bushes. 8. Pascal's Triangle: Cellular Automata and Attractors. 8.1 Cellular Automata. 8.2 Binomial Coefficients and Divisibility. 8.3 IFS: From Local Divisibility to Global Geometry. 8.4 HIFS and Divisibility by Prim Powers. 8.5 Catalytic Converters, or How Many Cells Are Black? 9. Irregular Shapes: Randomness in Fractal Constructions. 9.1 Randomizing Deterministic Fractals. 9.2 Percola- tion: Fractals and Fires in Random Forests. 9.3 Random Fractals in a Laboratory Experiment. 9.4 Simulation of Brownian Motion. 9.5 Scaling Laws and Fractional Brownian Motion. 9.6 Fractal Landscapes. 10. Deterministic Chaos: Sensitivity, Mixing, and Periodic Points. 10.1 The Signs of Chaos: Sensitivity. 10.2 The Signs of Chaos: Mixing and Periodic Points. 10.3 Ergodic Orbits and Histograms. 10.4 Metaphor of Chaos: The Kneading of Dough. 10.5 Analysis of Chaos: Sensitivity, Mixing, and Periodic Points. 10.6 Chaos for the Quadratic Iterator. 10.7 Mixing and Dense Periodic Points Imply Sensitivity. 10.8 Numerics of Chaos: Worth the Trouble or Not? 11. Order and Chaos: Periodic-Doubling and Its Chaotic Mirror. 11.1 The First Step from Order to Chaos: Stable Fixed Points. 11.2 The Next Step from Order to Chaos: The Period-Doubling Scenario. 11.3 The Feigenbaum Point: Entrance to Chaos. 11.4 From Chaos to Order: A Mirror Image. 11.5 Intermittency and Crises: The Backdoors to Chaos. 12. Strange Attractors: The Locus of Chaos. 12.1 A Discrete Dynamical System in Two Dimensions: H6non's Attractor, 12.2 Continuous Dynamical Systems: Differential Equations. 12.3 The RSssler Attractor. 12.4 The Lorenz Attractor. 12.5 Quantitative Characterization of Strange Chaotic Attractors: Ljapunov Exponents. 12.6 Quantitative Characterization of Strange Chaotic Attractors: Dimensions. 12.7 The Reconstruction of Strange Attractors. 12.8 Fractal Basin Boundaries. 13. Julia Sets: Fractal Basin Boundaries. 13.1 Julia Sets as Basin Boundaries. 13.2 Complex Numbers - A Short Introduction. 13.3 Complex Square Roots and Quadratic Equations. 13.4 Prisoners versus Escapees. 13.5 Equipotentials and Field Lines for Julia Sets. 13.6 Binary Decomposition, Field Lines and Dynamics. 13.7 Chaos Game and Self-Similarity for Julia Sets. 13.8 The Critical Point and Julia Sets as Cantor Sets. 13.9 Quaternion Julia Sets. 14. The Mandelbrot Set: Ordering the Julia Sets. 14.1 From the Structural Dichotomy to the Binary Decompo- sition. 14.2 The Mandelbrot Set - A Road Map for Julia Sets. 14.3 The Mandelbrot Set as a Table of Content. Bibliography. Index.

Fundamentals of Ocean Climate Models. Stephen M. Griffies. Princeton University Press. Princeton, N J, 2004. 518 pages. $65.00. Contents: Forward. Preface. Acknowledgments. About the Cover. List of Symbols. Chapter 1. Ocean Climate Models. 1.1 Ocean models as tools for ocean science. 1.2 Ocean climate models. 1.3 Challenges of climate change. Part 1. Fundamental Ocean Equations. Chapter 2. Basics of Ocean Fluid Mechanics. 2.1 Some fundamental ocean processes. 2.2 The continuum hypothesis. 2.3 Kinematics of fluid motion. 2.4 Kinematical and dynamical approximations. 2.5 Averaging over scales and realizations. 2.6 Numerical discretization. 2.7 Chapter summary. Chapter 3. Kinematics. 3.1 Introduction. 3.2 Mathematical preliminaries. 3.3 The divergence theorem and budget analysis. 3.4 Volume and mass conserving kinematics. 3.5 Chapter summary. Chapter 4. Dynamics. 4.1 Introduction. 4.2 Motion on a rotating sphere. 4.3 Principles of continuum dynamics. 4.4 Dynamics of fluid parcels. 4.5 Hydrostatic pressure. 4.6 Dynamics of hydrostatic fluid columns. 4.7 Fluid motion in a rapidly rotating system. 4.8 Vertical stratification. 4.9 Vorticity and potential vorticity. 4.10 Particle dynamics on a rotating sphere. 4.11 Symmetry and conservation laws. 4.12 Chapter summary. Chapter 5. Thermo-Hydrodynamics. 5.1 General types of ocean tracers. 5.2 Basic equilibrium thermodynamics. 5.3 Energy of a fluid parcel. 5.4 Global mechanical energy balance. 5.5 Basic non-equilibrium thermodynamics. 5.6 Thermodynamical tracers. 5.7 Ocean density. 5.8 Chapter summary. Chapter 6. Generalized Vertical Coordinates. 6.1 Introduction. 6.2 Concerning the choice of vertical coordinate. 6.3 Generalized surfaces. 6.4 Local orthonormal coordinates. 6.5 Mathematics of generalized vertical coordinates. 6.6 Metric tensors. 6.7 The din-surface velocity component. 6.8 Conservation of mass and volume for parcels. 6.9 Kinematic boundary conditions. 6.10 Primitive equations. 6.11 Transformation of SGS tracer flux components. 6.12 Chapter summary. Part 2. Averaged Descriptions. Chapter 7. Concerning Unresolved Physics. 7.1 Represented dynamics and parameterized physics. 7.2 Lateral (neutral) and vertical processes. 7.3 Basic mechanisms for dianeutral transport. 7.4 Dianeutral transport in models. 7.5 Numerically induced spurious dianeutral transport. 7.6 Chapter summary. Chapter 8. Eulerian Averaged Equations. 8.1 Introducton. 8.2 The nonhydrostatic shallow ocean equations. 8.3 Averaged kinematics. 8.4 Averaged kinematics over finite domains. 8.5 Averaged tracer. 8.6 Averaged momentum budget. 8.7 Summary of the Eulerian averaged equations. 8.8 Mapping to ocean model variables. 8.9 Chapter summary. BOOK REPORTS 1599

Chapter 9. Kinematics of an Isentropic Ensemble. 9.1 Parameterizing mesoscale eddies. 9.2 Advection and skewsion. 9.3 Volume conservation. 9.4 Ensemble mean tracer equation. 9.5 Quasi-Stokes transport in z-models. 9.6 Chapter summary. Part 3. Semi-discrete Equations and Algorithms. Chapter 10. Discretization Basics. 10.1 Discretization methods. 10.2 An introduction to Arakawa grids. 10.3 Time stepping. 10.4 Chapter summary. Chapter 11. Mass and Tracer Budgets. 11.1 Summary of the continuous model equations. 11.2 Tracer and mass/volume compatibility. 11.3 Mass budget for a grid cell. 11.4 Mass budget for a discrete fluid column. 11.5 Tracer budget for a grid cell. 11.6 Fluxes for turbulence mixed layer schemes. 11.7 Flux plus restore boundary conditions. 11.8 Z-like vertical coordinate models. 11.9 Chapter summary. Chapter 12. Algorithms for Hydrostatic Ocean Models. 12.1 Summary of the continuous model equations. 12.2 Budget of linear momentum for a grid cell. 12.3 Strategies for time stepping momentum. 12.4 A leap-frog algorithm. 12.5 Discretization of time tendencies. 12.6 A time staggered algorithm. 12.7 Barotropic updates with a predictor-corrector. 12.8 Stability considerations. 12.9 Smoothing the surface height in B-grid models. 12.]0 Rigid lid streamfunction method. 12.11 Chapter summary. Part 4. Neutral Physics. Chapter 13. Basics of Neutral Physics. 13.1 Concerning the utility of neutral physics. 13.2 Notation and summary of scalar budgets. 13.3 Compatibility in the mean field budgets. 13.4 The SGS tracer transport tensor. 13.5 Advection and skewsion. 13.6 Neutral tracer fluxes. 13.7 Chapter summary and a caveat on the conjecture. Chapter 14. Neutral Transport Operations. 14.1 Neutral diffusion. 14.2 Gent-McWilliams stirring. 14.3 Sum- marizing the neutral physics fluxes. 14.4 Flow-dependent diffusivities. 14.5 Biharmonic operators. 14.6 Chapter summary and some challenges. Chapter 15. Neutral Physics Near the Surface Boundary. 15.1 Linear stability for neutral diffusion. 15.2 Linear stability for GM stirring. 15.3 Neutral physics near boundaries. 15.4 Chapter summary and caveats. Chapter 16. Functional Discretization of Neutral Physics. 16.1 Foundations for discrete neutral physics. 16.2 Introduction to the discretization. 16.3 A one-dimensional warm-up. 16.4 Elements of the discrete dissipation functional. 16.5 Triad stencils and some more notation. 16.6 The discrete diffusion operator. 16.7 Diffusive flux components. 16.8 Further issues of numerical implementation. 16.9 Chapter summary. Part 5. Horizontal Friction. Chapter 17. Horizontal Friction in Models. 17.1 Boussinesq and non-Boussinesq friction. 17.2 Introduction and general framework. 17.3 Properties of the stress tensor. 17.4 Properties of the viscosity tensor. 17.5 Transverse isotropy. 17.6 Transverse anisotropy. 17.7 Generalized orthogonal coordinates. 17.8 Dissipation functional. 17.9 Biharmonic friction. 17.10 Some mathematical details. 17.11 Chapter summary. Chapter 18. Choosing the Horizontal Viscosity. 18.1 Stability and resolution considerations. 18.2 Comparing Laplacian and biharmonic mixing. 18.3 Smagorinsky viscosity. 18.4 Background viscosity. 18.5 Viscosities for anisotropic friction. 18.6 Chapter summary. Chapter 19. Functional Discretization of Friction. 19.1 Comments on notation. 19.2 Summary of the various formulations. 19.3 Horizontal friction discretization. 19.4 Laplacian plus metric form of isotropic friction. 19.5 Chapter summary. Part 6. Tensor Analysis. Chapter 20. Elementary Tensor Analysis. 20.1 Introduction 20.2 Some practical motivation. 20.3 Coordinates and vectors. 20.4 The metric and coordinate transformations. 20.5 Transformations of a vector. 20.6 One-forms. 20.7 Mapping between vectors and one-forms. 20.8 Transformation of a one-form. 20.9 Arbitrary tensors and their transformations. 20.10 Tensorial properties of the gradient operator. 20.11 The invariant volume element. 20.12 Determinants and the Levi-Civita symbol. 20.13 Surfaces embedded in Euclidean space. 20.14 Chapter summary. Chapter 21. Calculus on Curved Manifolds. 21.1 Fundamental character of tensor equations. 21.2 Covariant differentiation. 21.3 Covariant derivative of a second order tensor. 21.4 Christoffel symbols in terms of the metric. 21.5 Covariant divergence of a vector. 21.6 Covariant divergence of a second order tensor. 21.7 Covariant Laplacian of a scalar. 21.8 Covariant curl of a vector. 21.9 Covariant Laplacian of a vector. 21.10 Integral theorems. 21.11 Orthogonal curvilinear coordinates. 21.12 Summary of curvilinear tensor analysis. Part 7. Epilogue. Chapter 22. Some Closing Comments and Challenges. Bibliography. Index.

Semantic Coqnition, A Parallel Distributed Processinq Approach. Timothy T. Rogers and James L. McClelland. The MIT Press. Cambridge, MA. 2004. 425 pages. $50.00. Contents: Preface. 1. Categories, Hierarchies, and Theories. Categorization-Based Models. The Theory-Theory. Toward a Mecha- nistic Model of Semantic Knowledge. Summary. 2. A PDP Theory of Semantic Cognition. The Rumelhart Feed-Forward Network. Interpretation and Storage of New Information. Inferences Based on New Semantic Information. Discussion of the Rumelhart Network. 3. Latent Hierarchies in Distributed Representations. Simulation 3.1: Progressive Differentiation of Concept Representations. Simulation 3.2: Simulating Loss of Differentiation in Dementia. Summary of Basic Simulations. Extended Training Corpus for Use in Subsequent Simulations. 4. Emergence of Category Structure in Infancy. A Brief Overview of the Literature. Simulating Preverbal Conceptual Development in the Rumelhart Model. Simulation 4.1: Capturing Conceptual Differentiation in Infancy. Discussion. 1600 BOOK REPORTS

5. Naming Things: Privileged Categories, Familiarity, Typicality, and Expertise. A PDP Account of Basic- Level Effects. Simulation 5.1: Learning with Basic Names Most Frequent. Simulation 5.2: Learning with All Names Equally Frequent. Simulation 5.3: Naming Behavior Effects of the Attribute Structure of the Training Corpus. Conclusions form Simulations 5.1-5.3. Influences of Differential Experience with Objects and Their Properties: Familiarity and Expertise Effects. Simulation 5.4: Effects of Familiarity on Naming in Development and Dementia. Simulation 5.5: Domain-Specific Expertise. Simulation 5.6: Different Kinds of Expertise in the Same Domain. Generality of the Observed Simulation Results. 6. Category Coherence. Category Coherence. Simulation 6.1: Category Coherence. Simulation 6.2: Illusory Correlations. Simulation 6.3: Category-Dependent Attribute Weighting. Summary of Findings. 7. Inductive Projection and Conceptual Reorganization. Inductive Projection. Simulation 7.1: Inductive Pro- jection and Its Differentiation in Development. Simulation 7.2: Differential Projection of Different Kinds of Properties. Reorganization and Coalescence. Simulation 7.3 Coalescence. Discussion. 8. The Role of Causal Knowledge in Semantic Task Performance. The Role of Causal Properties of Objects in Se- mantic Cognition. Toward a PDP Account of Causal Knowledge and Causal Inference. The Basis of Explanations. Comparison of the PDP Approach with Theory-Based Approaches. 9. Core Principles, General issues, and Future Directions. Core Principles. Perspectives on General Issues in the Study of Cognition. Semantic Cognition in the Brain. Conclusion. Appendix A: Simulation Details. Appendix B: Training Patterns. Appendix C: Individuating Specific Items in the Input. Notes. References. Index.

Ant Colony Optimization. Marco Doriqo and Thomas Stiitzle. The MIT Press. Cambridge, MA. 2004. 305 pages. $40.00. Contents: Preface. Acknowledgements. 1, From Real to Artificial Ants. 1.1 Ants' Foraging Behavior and Optimization. 1.2 Toward Artificial Ants. 1.3 Artificial Ants and Minimum Cost Paths. 1.4 Bibliographical Remarks. 1.5 Things to Remember. 1.6 Thought and Computer Exercises. 2. The Ant Colony Optimization Metaheuristic. 2.1 Combinatorial Optimization. 2.2 The ACO Metaheuristic. 2.3 How Do I Apply ACO? 2.4 Other Metaheuristics. 2.5 Bibliographical Remarks. 2.6 Things to Remember. 2.7 Thought and Computer Exercises. 3. Ant Colony Optimization Algorithms for the Traveling Salesman Problem. 3.1 The Traveling Salesman Problem. 3.2 ACO Algorithms for the TSP. 3.3 Ant System and Its Direct Successors. 3.4 Extensions of Ant System. 3.5 Parallel Implementations. 3.6 Experimental Evaluation. 3.7 ACO Plus Local Search. 3.8 Implementing ACO Algorithms. 3.9 Bibliographical Remarks. 3.10 Things to Remember. 3.11 Computer Exercises. 4. Ant Colony Optimization Theory. 4.1 Theoretical Considerations on ACO. 4.2 The Problem and the Algo- rithm. 4.3 Convergence Proofs. 4.4 ACO and Model-Based Search. 4.5 Bibliographical Remarks. 4.6 Things to Remember. 4.7 Thought and Computer Exercises. 5. Ant Colony Optimization for NP- Hard Problems. 5.1 Routing Problems. 5.2 Assignment Problems. 5.3 Scheduling Problems. 5.4 Subset Problems. 5.5 Application of ACO to Other NP-Hard Problems. 5.6 Machine Learning Problems. 5.7 Application Principles of ACO. 5.8 Bibliographical Remarks. 5.9 Things to Remember. 5.10 Computer Exercises. 6. AntNet: An ACO Algorithm for Data Network Routing. 6.1 The Routing Problem. 6.2 The AntNet Algorithm. 6.3 The Experimental Settings. 6.4 Results. 6.5 AntNet and Stigmergy. 6.6 AntNet, Monte Carlo Simulation, and Reinforcement Learning. 6.7 Bibliographical Remarks. 6.8 Things to Remember. 6.9 Computer Exercises. 7. Conclusions and Prospects for the Future. 7.1 What Do We Know about ACO? 7.2 Current Trends in ACO. 7.3 Ant Algorithms. Appendix: Sources of Information about the ACO Field. References. Index.

Handbook of Mathematics, I.N. Bronshtein, K.A. Semendyayev, G.Musiol, H.Meuhlig, Springer, Berlin, (2004) 1153 pages. $59.95. Contents 1. Arithmetic 1.1. Elementary Rules for Calculations 1.1.1. Numbers 1.1.1.1. Natural, Integer, and Rational Numbers 1.1.1.2. Irrational and Transcendental Numbers 1.1.1.3. Real Numbers 1.1.1.4. Continued Fraction 1.1.1.5. Commensurability 1.1.2. Methods for Proof 1.1.2.1. Direct Proof 1.1.2.2. Indirect Proof or Proof by Contradiction 1.1.2.3. Mathematical Induction 1.1.2.4. Constructive Proof 1.1.3. Sums and Products 1.1.3.1. Sums 1.1.3.2. Products 1.1.4. Powers, Roots, and Logarithms 1.1.4.1. Powers 1.1.4.2. Roots 1.1.4.3. Logarithms 1.1.4.4. Special Logarithms 1.1.5. Algebraic Expressions 1.1.5.1. Definitions 1.1.5.2. Algebriac Espressions in Detail 1.1.6. Integral Rational Expressions 1.1.6.1. Representaion in Polynomial Form 1.1.6.2. Factorizing a Polynomial 1.1.6.3. Special Formulas 1.1.6.4. Binomial Theorum 1.1.6.5. Determination of the Greatest Common Divisor of Two Polynomials 1.1.7. Rational Expressions 1.1.7.1. Reducing to the Simplest Form 1.1.7.2. Deter- mination of the Integral Rational Part 1.1.7.3. Decomposition into Partial Fractions 1.1.7.4. Transformations of Proportions 1.1.8. Irrational Expressions 1.2. Finite Series 1.2.1. Definition of a Finite Series 1.2.2. Arithmetic Series 1.2.3. Geometric Series 1.2.4. Special Finite Series 1.2.5. Mean Values 1.2.5.1. Arithmetic Mean or Arith- metic Average 1.2.5.2. Geometric Mean or Geometric Average 1.2.5.3. Harmonic Mean 1.2.5.4. Quadratic Mean BOOK REPORTS 1601

1.2.5.5. Realtions Between the Means of Two Positive Values 1.3. Business Mathematics 1.3.1. Calculation fo Interest or Percentage 1.3.2. Calculation of Compound Interest 1.3.2.1. Interest 1.3.2.2. Compound Interest 1.3.3. Amortization Calculus 1.3.3.1. Amortization 1.3.3.2. Equal Principal Repayments 1.3.3.3. Equal Annuities 1.3.4. Annuity Calculations 1.3.4.1. Annuities 1.3.4.2. Future Amount of an Ordinary Annuities 1.3.4.3. Balance after n Annuity Payments 1.3.5. Depriciation 1.4. Inequalities 1.4.1. Pure Inequalities 1.4.1.1. Definitions 1.4.1.2. Properties of Inequalities of Type I and II 1.4.2. Special Inequalities 1.4.2.1. Triangle Inequality for Real Numbers 1.4.2.2. Triangle Inequality for Complex Numbers 1.4.2.3. Inequalities for Absolute Values of Differences of Real and Complex Numbers 1.4.2.4. Inequality for Arithmetic and Geometric Means 1.4.2.5. Inequality for Arithmetic and Quadratic Means 1.4.2.6. Inequalities for Different Means of Real Numbers 1.4.2.7. Bernoulli~s Inequality 1.4.2.8. Binomial Inequality 1.4.2.9. Cauchy-Schwarz Inequality 1.4.2.10. Chebyshev Inequality 1.4.2.11. Gener- alized Chebyshev Inequality 1.4.2.12. Holder Inequality 1.4.2.13. Minkowski Inequality 1.4.3. Solution of Linear and Quadratic Inequalities 1.4.3.1. General Remarks 1.4.3.2. Linear Inequalities 1.4.3.3. Quadratic Inequalities 1.4.3.4. General Case for Inequalities of Second Degree 1.5. Complex Numbers 1.5.1. Imaginary and Complex Numbers 1.5.1.1. Imaginary Unit 1.5.1.2. Complex Numbers 1.5.2. Geometric Representation 1.5.2.1. Vector Representation 1.5.2.2. Equality of Complex Numbers 1.5.2.3. Trigonometric Form of Complex Numbers 1.5.2.4. Exponential Form of a Complex Number 1.5.2.5. Conjucate Complex Numbers 1.5.3. Calculation with Complex Numbers 1.5.3.1. Addition and Subtraction 1.5.3.2. Multiplication 1.5.3.3. Division 1.5.3.4. General Rules for the Basic Operations 1.5.3.5. Taking Powers of Complex Numbers 1.5.3.6. Taking of the n-th Root of a Complex Number 1.6. Algebraic and Transcendental Equations 1.6.1. Transforming Algebraic Equations to Normal Form 1.6.1.1. Definition 1.6.1.2. Systems of n Algebraic Equations 1.6,1.3. Superfious Roots 1.6.2. Equations of Degree at Most Four 1.6.2.1. Equations of Degree One (Linear Equations) 1.6.2.2. Equations of Degree Two (Quadratic Equations) 1.6.2.3. Equations of Degree Three (Cubic Equations) 1.6.2.4. Equations of Degree Four 1.6.2.5. Equa- tions of Higher Degree 1.6.3. Equations of Degree n 1.6.3.1. General Properties of Algebraic Equations 1.6.3.2. Equations with Real Coefficients 1.6.4, Reducing Transcendental Equations to Algebraic Equations 1.6.4.1. Def- inition 1.6.4.2. Exponential Equations 1.6.4.3. Logarithmic Equations 1.6.4.4. Trigonometric Equations t.6.4.5. Equations with Hyperbolic Functions 2. Fuctions 2.1. Notion of Functions 2.1.1. Defintion of a Function 2.1.1.1. Function 2.1.1.2. Real Fuctions 2.1.1.3. Functions of Several Variables 2.1.1.4. Complex Functions 2.1.1.5. Further Functions 2.1.1.6. Functionals 2.1.1.7. Functions and Mappings 2.1.2. Methods for Defining a Real Function 2.1.2.1. Defining a Function 2.1.2.2. Analytic Representation of a Function 2.1.3. Certain Types of Functions 2.1.3.1. Monotone Functions 2.1.3.2. Bounded Functions 2.1.3.3. Even Functions 2.1.3.4. Odd Functions 2.1.3.5. Representation with Even and Odd Functions 2.1.3.6. Periodic Functions 2.1.3.7. Inverse Functions 2.1.4. Limits of Functions 2.1.4.1. Definition of the Limit of Function 2.1.4.2. Definition by Limit of Sequences 2.1.4.3. Cauchy Condition for Convergence 2.1.4.4. Infinity as a Limit of a Functions 2.1.4.5. Left-Hand and Right-Hand Limit of a Equation 2.1.4.6. Limit of a Function as x Tends to Infinity 2.1.4.7. Theorems About Limits of Functions 2.1.4.8. Calculations of Limits 2.1.4.9. Order of Magnitude of Functions and Landau Order Symbols 2.1.5. Continuity of a Function 2.1.5.1. Notion of Continuity and Discontinuity 2.1.5.2. Defintion of Continuity 2.1.5.3. Most Frequent Types of Discontinuities 2.1.5.4. Continuity and Discontinuity of Elementary Functions 2.1.5.5. Properties of Continuous Functions 2.2. Elementary Functions 2.2.1. Algebraic Functions 2.2.1.1. Polynomials 2.2.1.2. Rational Functions 2.2.1.3. Irrational Functions 2.2.2. Transcendental Functions 2.2.2.1. Exponential Functions 2.2.2.2. Logarithmic Functions 2.2.2.3. Trigonometric Functions 2.2.2.4. Inverse Trigonometric Functions 2.2.2.5. Hyperbolic Functions 2.2.2.6. Inverse Hyperbolic Functions 2.2.3. Composite Functions 2.3. Polynomials 2.3.1. Linear Function 2.3.2. Quadratic Polynomial 2.3.3. Cubic Polynomial 2.3.4. Polynomials of n-th Degree 2.3.5. Parabola of n-th Degree 2.4. Rational Functions 2.4.1. Special Fractional Linear Function (Inverse Proportionality) 2.4.2. Linear Fractional Function 2.4.3. Curves of Third Degree, Type 1 2.4.4. Curves of Third Degree, Type 2 2.4.5. Curves of Third Degree, Type 3 2.4.6. Reciprocal Powers 2.5. Irrational Functions 2.5.1. Square Root of a Linear Binomial 2.5.2. Square Root of a Quadratic Binomial 2.5.3. Power Function 2.6. Exponetial Functions and Logarithmic Functions 2.6.1. Exponential Functions 2.6.2. Logarithmic Functions 2.6.3. Error Curve 2.6.4. Exponential Sum 2.6.5. Generalized Error Function 2.6.6. Product of Power and Exponential Fucntiens 2.7. Trigonometric Functions (Functions of Angles) 2.7.1. Basic Notion 2.7.1.1. Definition and Representation 2.7.1.2. Range and Behavior of the Functions 2.7.2. Important Formulas for Trigonometric Functions 2.7.2.1. Realtions Between the Trigonometric Functions of the Same Angle (Addition Theorems) 2.7.2.2. Trigonometric Functions of the Sum and Difference of Two Angles 2.7.2.3. Trigonometric Functions of an Integer Multiple of an Angle 2.7.2.4. Trigonometric Functions of Half-Angles 2.7.2.5. Sum and Difference of Two Trigonometric Functions 2.7.2.6. Products of Trigonometric Functions 2.7.2.7. Powers of Trigonometric Functions 2.7.3. Description of Oscillations 2.7.3.1. Formulation of the Problem 2.7.3.2. Superpostion of Oscillations 2.7.3.3. Vector Diagram for Oscillations 2.7.3.4. Damping of Oscillations 2.8. Inverse Trigonometric Functions 2.8.1. Defintion of the Inverse Trigonometric Functions 2.8.2. Reduction to the Principal Value 2.8.3. Realtions Between the Principal Values 2.8.4. Formulas for Negative Arguments 2.8.5. Sum and Difference of arcsin x and arcsiny 2.8.6. Sum and Difference of arccos x and arccosy 2.8.7. Sum and Difference of arctan x and arctony 2.8.8. Special Relations for arcsin ~, arccosx, arctan x 2.9. Hyperbolic Function 2.9.1. Defintion of Hyperbolic Functions 2.9.2. Graphical Representation of the Hyperbolic Functions 2.9.2.1. Hyperbolic Sine 2.9.2.2. Hyperbolic Cosine 2.9.2.3. Hyperbolic Tangent 2.9.2.4. Hyperbolic Contangent 2.9.3. Important Formulas for the Hyperbolic Functions 2.9.3. I. Hyperbolic Functions of One Variable 2.9.3.2. Expressing a Hyperbolic Function by Another One with the Same Argument 2.9.3.3. Formulas for Negative Arguments 2.9.3.4. Hyperbolic Functions of the Sum and Difference of Two Arguments (Additional Theorems) 2.9.3.5. Hyperbolic Fuctions of Double Arguments 2.9.3.6. De moivre Formula for Hyperbolic Functions 1602 BOOK REPORTS

2.9.3.7. Hyperbolic Functions of Half-Arguments 2.9.3.8. Sum and Difference of Hyperbolic Functions 2.9.3.9. Relation Between Hyperbolic and Trigonometric Functions with Complex Arguments z 2.10. Area Functions 2.10.1. Defiutions 2.10.1.1. Area Sine 2.10.1.2. Area Cosine 2.10.1.3. Area Tangent 2.10.1.4. Area Cotangent 2.10.2. Determination of Area Functions Using Natural Logarithm 2.10.3. Relations Between Different Area Functions 2.10.4. Sum and Difference of Area Functions 2.10.5. Formulas for Negative Arguments 2.11. Curves of Order Three (Cubic Curves) 2.11.1. Semicubic Parabola 2.11.2. Witch of Agnesi 2.11.3. Cartesian Folium (Folium of Descartes) 2.11.4. Cissoid 2.11.5. Strophoide 2.12. Curves of Order Four (Quartics) 2.12.1. Conchoid of Nocomedes 2.12.2. General Conchoid 2.12.3. Pascals Limacon 2.12.4. Cardioid 2.12.5. Cassinian Curve 2.12.6. lemniscate 2.13. Cycloids 2.13.1. Common (Standard) Cycloid 2.13.2. Prolate and Curtate Cycloids or Trochoids 2.13.3. Epicycloid 2.13.4. Hypocycloid and Astroid 2.13.5. Prolate and Curtate Epicycloid and Hypocycloid 2.14. Spirals 2.14.1. Archimedean Spiral 2.14.2. Hyperbolic Spiral 2.14.3. Logarithmic Spiral 2.14.4. Evolvent of the Circle 2.14.5. Clothoid 2.15. Various Other Curves 2.15.1. Catenary Curve 2.15.2. Tt'actrix 2.16. Determination of Empirical Curves 2.16.1. Procedure 2.16.1.1. Curve-Shape Comparison 2.16.1.2. Rectification 2.16.1.3. Determination of Parameters 2.16.2. Useful Epirical Curves 2.16.2.1. Power Functions 2.16.2.2. Exponential Functions 2.16.2.3. Quadratic Polynomial 2.16.2.4. Rational Linear Function 2.16.2.5. Square Root of a Quadratic Polynomial 2.16.2.6. General Error Curve 2.16.2.7. Curve of Order Three, Type 2 2.16.2.8. Curve of Order Three, Type 3 2.16.2.9. Curve of Order Thre% Type 1 2.16.2.10. Product of Power and Exponential Functions 2.16.2.11. Exponential Sum 2.16.2.12. Numerical Example 2.17. Scales and Graph Paper 2.17.1. Scales 2.17.2. Graph Paper 2.17.2.1. Semilogarithmic Paper 2.17.2.2. Double logarithmic Paper 2.17.2.3. Graph Paper with a Reciprocal Scale 2.17.2.4. Remark 2.18. Functions of Several Variables 2.18.1. Definition and Representation 2.18.1.1. Representation of Functions of Several Variables 2.18.1.2. Geometric Representation of Functions of Several Variables 2.18.2. Different Domains in the Plane 2.18.2.1. Domain of a Function 2.18.2.2. Two-Dimensional Domains 2.18.2.3. Three or Multidimensional Domains 2.18.2.4. Methods to Determine a Functions 2.18.2.5. Various Ways to Define a Function 2.18.2.6. Dependence of Functions 2.18.3. Limits 2.18.3.1. Definition 2.18.3.2. Exact Definition 2.18.3.3. Generalization for Several Variables 2.18.3.4. Iterated Limit 2.18.4. Continutiy 2.18.5. Properties of Continuous Functions 2.18.5.1. Theorem on Zeros of Bolanzo 2.18.5.2. Intermediate Value Theorem 2.18.5.3. Theorem About the Boundedness of a Function 2.18.5.4. Weierstrass Theorem (About the Existence of Maximum and Minimum) 2.19. Nomography 2.19.1. Nomograms 2.19.2. Net Charts 2.19.3. Alignment Charts 2.19.3.1. Alignment charts with Three Straight-Line Scales Through a Point 2.19.3.2. Alignment Charts with Two Parallel and One Inclined Straight-Line Scales 2,19.3.3. Alignment Charts with two Parallel Straight Lines and a Curved Scale 2.19.4. Net Charts for More Than Three Variables 3. Geometry 3.1. Plane Geometry 3.1.1. Basic Notation 3.1.1.1. Point, Line, Ray, Segment 3.1.1.2. Angle 3.1.1.3. Angle Between Two Intersecting Lines 3.1.1.4. Pairs of Angles with Intersecting Parallels 3.1.1.5. Angles Measured in Degrees and in Radians 3.1.2. Geometrical Definition of Circular and Hyperbolic Functions 3.1.2.1. Definition of Circular or Trigonometric Functions 3.1.2.2. Definitions of the Hyperbolic Functions 3.1.3. Plane Triangles 3.1.3.1. Statements about Plane Triangles 3.1.3.2. Symmetry 3.1.4. Plane Quadrangles 3.1.4.1. Parallelogram 3.1.4.2. Rectangle and Square 3.1.4.3. Rhombus 3.1.4.4. Trapezoid 3.1.4.5. General Quadrangle 3.1.4.6. Inscribed Quadrangle 3.1.4.7. Circumscribing Quadrangle 3.1.5. Polygons in the Plane 3.1.5.1. General Polygons 3.1.5.2. Regular Convex Polygons 3.1.5.3. Some Regular Convex Polygons 3.1.6. The Circle and Related Shapes 3.1.6.1. Circle 3.1.6.2. Circular Segment and Circular Sector 3.1.6.3. Annulus 3.2. Plane Trigonometry 3.2.1. Triangles 3.2.1.1. Calculations in Right-Angled Triangles in the Plane 3.2.1.2. Calculations in General Triangles in the Plane 3.2.2. Geodesic Applications 3.2.2.1. Geodetic Coordinates 3.2.2.2. Angles in Geodesy 3.2.2.3. Applications in Surveying 3.3. Stereometry 3.3.1. Lines and Planes in Space 3.3.2. Edge, Corner, Solid Angle 3.3.3. Polyeder or Polyhedron 3.3.4. Solids Bounded by Curved Serfaces 3.4. Spherical Trigonometry 3.4.1. Basic Concepts of Geometry on the Sphere 3.4.1.1. Curve, Arc, and Angle on the Sphere 3.4.1.2. Special Coordinate Systems 3.4.1.3. Spherical Lune or Biangle 3.4.1.4. Spherical Triangle 3.4.1.5. Polar Triangle 3.4.1.6. Euler Triangles and Non-Euler Triangles 3.4.1.7. Trihedral Angles 3.4.2 Basic Properties of Spherical Triangles 3.4.2.1. General Statements 3.4,2.2. Fundamental Formulas and Applications 3.4.2.3. Further Formulas 3.4.3. Calculation of Spherical Triangles 3.4.3.1. Basic Problems, Accuracy, Observations 3.4.3.2. Right-Angled Spherical Triangles 3.4.3.3. Spherical Triangles with Oblique Angles 3.4.3.4. Spherical Curves 3.5. Vector Algebra and Analytical Geometry 3.5.1. Vector Algebra 3.5.1.1. Definition of Vectors 3.5.1.2. Calculation Rules for Vectors 3.5.1.3. Coordinates of a Vector 3.5.1.4. Directional Coefficient 3.5.1.5. Scalar Product and Vector Product 3.5.1.6. Combination of Vector Products 3.5.1.7. Vector Equations 3.5.1.8. Covariant and Contravariant Coordinates of a Vector 3.5.1.9. Geometric Applications of Vector Algebra 3.5.2. Analytical Geometry of the Plane 3.5.2.1. Basic Concepts, Coordinate Systems in the Plane 3.5.2.2. Coordinate Transformations 3.5.2.3. Special Notation in the Plane 3.5.2.4. Line 3.5.2.5. Circle 3.5.2.6. Eclipse 3.5.2.7. Hyperbola 3.5.2.8. Parabola 3.5.2.9. Quadratic Curves(Curves of Second Order or Conic Sections) 3.5.3. Analytical Geometry of Space 3.5.3.1. Basic Concepts, Spatial Coordinate Systems 3.5,3.2. Transformation of Orthogonal Coordinates 3.5.3.3. Special Quantities in Space 3.5.3.4. Line and Plane in Space 3.5.3.5. Surfaces of Second Order, Equations in Normal Form 3.5.3.6. Surfaces of Second Order or Quadratic Surfaces, General Theory 3.6. Defferential Geometry 3.6.1. Plane Curves 3.6.1.1. Ways to Define a Plane Curve 3.6.1.2. Local Elements of a Curve 3.6.1.3. Special Points of a Curve 3.6.1.4. Asymptotes of Curves 3.6.1.5. General Discussion of a Curve Given by an Equation 3.6.1.6. Evolutes and Evolents 3.6.1.7. Envelope of a Family of Curves 3.6.2. Space Curves 3.6.2.1. Ways to Define a Space Curve 3.6.2.2. Moving Trihedral 3.6.2.3. Curvature and Torsion 3.6.3. Surfaces 3.6.3.1. Ways to Define a Surface 3.6.3.2. Tangent Plane and Surface Normal 3.6.3.3. Line Elements of a Surface 3.6.3.4. Curvature of a Surface 3.6.3.5. Ruled Surfaces and Developable Surfaces 3.6.3.6. Geodesic Liens on a Surface BOOK REPORTS 1603

4. Linear Algebra 4.1. Matrices 4.1.1. Notion of Matrix 4.1.2. Square Matrices 4.1.3. Vectors 4.1.4. Arithmeti- cal Operations with Matrices 4.1.5. Rules of Calculation for Matrices 4.1.6. Vector and Matrix Norms 4.1.6.1. Vector Norms 4.1.6.2. Matrix Norms 4.2. Determinants 4.2.1. Definitions 4.2.2. Subdetermants 4.2.3. Rules of Calculation for Determinants 4.2.4. Evaluation of Dterminants 4.3. Tensors 4.3.1. Transformation of Coordinate Systems 4.3.2. Tensors in Cartesian Coordinates 4.3.3. Tensors with Special Properties 4.3.3.1. Tensors of Rank 2 4.3.3.2. Invariant Tensors 4.3.4. Tensors in Curvilinear Coordinate Systems 4.3.4.1. Covariant and Contravari- ant Basis Vectors 4.3.4.2. Covariant and Contravariant Coordinates of Tensors of Rank 1 4.3.4.3. Covariant, Contravariant and Mixed Coordinates of Tensors of Rank 2 4.3.4.4. Rules of Calcualtion 4.3.5. Psuedotensors 4.3.5.1. Symmetry with Respect to the Origin 4.3.5.2. Introduction to the Notion of Psuedotensors 4.4. Systems of Linear Equations 4.4.1. Linear Systems, Pivoting 4.4.1.1. Linear Systems 4.4.1.2. Pivoting 4.4.1.3. Linear Dependence 4.4.1.4. Calculation of the Inverse of a Matrix 4.4.2. Solution of Systems of Linear Equations 4.4.2.1. Definition and Solvability 4.4.2.2. Application of Pivoting 4.4.2.3. Cramer's Rule 4.4.2.4. Gauss's Algorithm 4.4.3. Overdetermined Linear Equation Sytems 4.4.3.1. Overdetermined Linear Systems of Equations and Linear Mean Square Value Problems 4.4.3.2. Suggestions for Numerical Solutions of Mean Square Value Problems 4.5. Eigenvalue Problems for Matrices 4.5.1. General Eigenvalue Problem 4.5.2. Special Eigenvalue Problem 4.5.2.1, Characteristic Polynomial 4.5.2.2. Real Symmetric Matrices, Similarity Transformations 4.5.2.3. Transformation of Principal Axes of Quadratic Forms 4.5.2.4. Suggestions for the Numerical Calculations of Eigenvalues 4.5.3. Singular Value Decomposition 5. Algebra and Discrete Mathematics 5.1. Logic 5.1.1. Propositional Calculus 5.1.2. Formulas in Predicate Calculus 5.2. Set Theory 5.2.1. Concept of Set, Special Sets 5.2.2. Operations with Sets 5.2.3. Relations and Mappings 5.2.4. Equivalence and Order Relations 5.2.5. Cardinality of Sets 5.3. Classical Algebraic Structures 5.3.1. Operations 5.3.2. Semigroups 5.3.3. Groups 5.3.3.1. Definition and Basic Properties 5.3.3.2. Subgroups and Direct Products 5.3.3.3. Mappings Betweem Groups 5.3.4. Group Representations 5.3.4.1. Defintions 5.3.4.2. Par- ticular Representation 5.3.4.3. Direct Sum of Representations 5.3.4.4. Direct Product of Representations 5.3.4.5. Reducible and Irreducible Representations 5.3.4.6. Schur's Lemma 1 5.3.4.7. Clebsch-Gordan Series 5.3.4.8. Irre- ducible Representations of the Symmetric Group SM 5.3.5. Applications of Groups 5.3.5.1. Symmetry Operations, Symmetry Elements 5.3.5.2. Symmetry Groups or Point Groups 5.3.5.3. Symmetry Operations with Molecules 5.3.5.4. Symmetry Groups in Crystallography 5.3.5.5. Symmetry Groups in Quantam Mechanics 5.3.5.6. Further Applications of Group Theory in Physics 5.3.6. Rings and Fields 5.3.6.1. Definitions 5.3.6.2. Subrings, Ideals 5.3.6.3. Homomorphism, Isomorphism, Homomorphism Theorem 5.3.7. Vector Spaces 5.3.7.1. Defintion 5.3.7.2. Linear Dependence 5.3.7.3. Linear Mappings 5.3.7.4. Subspaces, Dimension Formula 5.3.7.5. Euclidean Vec- tor Spaces, Euclidean Norm 5.3.7.6. Linear Operators in Vector Spaces 5.4. Elementary Number Theory 5.4.1. Divisibility 5.4.1.1. Divisibility and Elementary Divisibility Rules 5.4.1.2. Prime Numbers 5.4.1.3. Criteria for Divisibility 5.4.1.4. Greatest Common Divisor and Least Common Multiple 5.4.1.5. Fibonacci Numbers 5.4.2. Linear Diophantine Equations 5.4.3. Congruences and Residue Classes 5.4.4. Theorems of Fermat, Euler, and Wilson 5.4.5. Codes 5.5. Cryptology 5.5.1. Problem of Cryptology 5.5.2. Cryptosystems 5.5.3. Mathematical Foundation 5.5.4. Security of Cryptosystems 5.5.4.1. Methods of Conventional Cryptography 5.5.4.2. Linear Substitution Ciphers 5.5.4.3. Vigenere Cipher 5.5.4.4. Matrix Substitution 5.5.5. Methods of Classical Cryptanal- ysis 5.5.5.1. Statistical Analysis 5.5.5.2. Kasiski-Friedman Test 5.5.6. One-Time Pad 5.5.7. Public Key Nethods 5.5.7.1. Diffie-Hellman Key Exchange 5.5.7.2. One-Way Function 5.5.7.3. RSA Method 5.5.8. DES Algorithm (Data Encryption Standard) 5.5.9. IDEA Algorithm (International Data Encryptions Algorithm) 5.6. Universal Algebra 5.6.1. Defintion 5.6.2. Congrience Relations, Factor Algebra 5.6.3. Homomorphism 5.6.4. Homomor- phism Theorem 5.6.5. Varieties 5.6.6. Term Algebras, Free Algebras 5.7. Boolean Algebras and Switch Algebra 5.7.1. Definition 5.7.2. Duality Principle 5.7.3. Finite Boolean Algebras 5.7.4. Boolean Algebras as Orderings 5.7.5. Boolean Functions, Boolean Expressions 5.7.6. Normal Forms 5.7.7. Switch Algebra 5.8. Algorithms of Graph Theory 5.8.1. Basic Notions and Notation 5.8.2. Traverse of Undirected Graphs 5.8.2.1. Edge Sequences or Paths 5.8.2.2. Euler Trails 5.8.2.3. Hamiltonian Cycles 5.8.3. Trees and Spanning Trees 5.8.3.1. Trees 5.8.3.2. Spanning Trees 5.8.4. Matchings 5.8.5. Planar Graphs 5.8.6. Paths in Directed Graphs 5.8.7. Transport Networks 5.9. Fuzzy Logic 5.9.1. Basic Notions of Fuzzy Logic 5.9.1.1. Interpretation of Fuzzy Sets 5.9.1.2. Membership Functions on the Real Line 5.9.1.3. Fuzzy Sets 5.9.2. Aggregation of Fuzzy Sets 5.9.2.1. Concepts for Aggre- gation of Fuzzy Sets 5.9.2.2. Practical Aggregator Operations of Fuzzy Sets 5.9.2.3. Compensatory Operators 5.9.2.4. Extension Principle 5.9.2.5. Fuzzy Complement 5.9.3. Fuzzy Valued Relations 5.9.3.1. Fuzzy Relations 5.9.3.2. Fuzzy Product Relation R o S 5.9.4. Fuzzy inference(Approximate Reasoning) 5.9.5. Defuzzification Methods 5.9.6. Knowledge-Based Fuzzy Systems 5.9.6.1. Method of Mamdani 5.9.6.2. Method of Sugeno 5.9.6.3. Cognitive Systems 5.9.6.4. Knowledge-Based Interpolation Systems 6. Differentiation 6.1. Differentiation of Functions of One Variable 6.1.1. Differential quotient 6.1.2. Rules of Differentiation for Functions of One Variable 6.1.2.1. Derivatives of the Elementary Functions 6.1.2.2. Basic Rules of Differentiation 6.1.3. Derivatives of the Elementary Functions 6.1.3.1. Defintion of Derivatives of Higher Order 6.1.3.2. Derivatives of Higher Order of some Elementary Functions 6.1.3.3. Leibniz's Formula 6.1.3.4. Higher Derivatives of Functions Given in Parametric Form 6.1.3.5. Derivatives of Higher Order of the inverse Function 6.1.4. Fundamental Theorems of Differential Calculus 6.1.4.1. Monotonicity 6.1.4.2. Fermat's Theorem 6.1.4.3. Rolle's Theorem 6.1.4.4. Mean Value Theorem of Differential Calculus 6.1.4.5. Taylor's Theorem of Functions of One Variable 6.1.4.6. Generalized Mean Value Theorem of Differential Calculus (Cauchy's Theorem) 6.1.5. Determination of the Extreme Values and Inflection Points 6.1.5.1. Maxima and Minima 6.1.5.2. Necessary Conditions for the Existence of a Relative Extreme Value 6.1.5.3. Relative Extreme Values of a Differentiable, Explicit Function 6.1.5.4. Determination of Absolute Extrema 6.1.5.5. Determination of the Extrema of Implicit 1604 BOOK REPORTS

Functions 6.2. Differentiation of Functions of Several Variables 6.2.1. Partial Derivatives 6.2.1.1. Partial Derivative of a Function 6.2.1.2. Geometrical Meaning for Functions of two Variables 6.2.1.3. Differentials of x and $(x) 6.2.1.4. Basic Properties of the Differential 6.2.1.5. Partial Differential 6.2.2. Total Differential and Differentials of Higher Order 6.2.2.1. Notion of Total Differential of a Function of Several Variables (Complete Differential) 6.2.2.2. Derivatives and Differentials of Higher Order 6.2.2.3. Taylor's Theorem for Functions of Several Variables 6.2.3. Rules of Differentiation for Functions of Several Variables 6.2.3.1. Differentiation of Composite Functions 6.2.3.2. Differentiation of Implicit Functions 6.2.4. Substitution of Variables in Differential Expressions and Coordinate Transformations 6.2.4.1. Function of One Variable 6.2.4.2. Function of Two Variables 6.2.5. Extreme Values of Functions of Several Variables 6.2.5.1. Definition 6.2.5.2. Geometric Representation 6.2.5.3. Determination of Extreme Values of Functions of Two Variables 6.2.5.4. Determination of the Extreme Values of a Function of n Variables 6.2.5.5. Solution of Approximation Problems 6.2.5.6. Extreme Value Problem with Side Conditions 7. Infinite Series 7.1. Sequence of Numbers 7.1.1. Properties of Sequences of Numbers 7.1.1.1. Definiton of Sequence of Numbers 7.1.1.2. Monotone Sequences of Numbers 7.1.1.3. Bounded Sequences 7.1.2. Limits of Sequences of Numbers 7.2. Numbers Series 7.2.1. General Convergence Theorems 7.2.1.1. Convergence and Divergence of Infinite Series 7.2.1.2. General Theorems anout the Convergence of Series 7.2.2. Convergence Criteria for Series with Positive Terms 7.2.2.1. Comparison Criterion 7.2.2.2. D'Alembert's Ratio Test 7.2.2.3. Root Test of Cauchy 7.2.2.4. Integral Test of Cauchy 7.2.3, Absolute and Conditional Convergence 7.2.3.1. Definiton 7.2.3.2. Properties of Absolutely Convergent Series 7.2.3.3. Alternation Series 7.2.4. Some Special Series 7.2.4.1. The Values of Some Important Number Series 7.2.4.2. Bernoulli and Euler Numbers 7.2.5. Estimation of the Remainder 7.2.5.1. Estimation with Majorant 7.2.5.2. Alternating Convergent Series 7.2.5.3. Special Series 7.3. Function Series 7.3.1. Definitons 7.3.2. Uniform Convergence 7.3.2.1. Defintion, Weierstrass Theorem 7.3.2.2. Properties of Uniformly Convergent Series 7.3.3. Power Series 7.3.3.1. Definiton, Convergence 7.3.3.2. Calculations with Power Series 7.3.3.3. Taylor Series Expansion, maclautin Series 7,3.4. Approximation Formulas 7.3.5. Asymptotic Power Series 7.3.5.1. Asymptotic Behavior 7.3.5.2. Asymptotic Power Series 7.4. Fourier Series 7.4.1. Trigonometric Sum and Fourier Series 7.4.1.1, Basic Notions 7.4.1.2. Most important Properties of the Fourier Series 7.4.2. Determination of Coefficients for the Symmetric Functions 7.4.2.1. Different Kinds of Symmetries 7A.2,2. Forms of the Expansion ito a Fourier Series 7.4.3. Determination of the Fourier Coefficients with Numerical Methods 7.4.4. Fourier series and Fourier Integrals 7.4.5. Remarks on the Table of Some Fourier Expansions 8. Integral Calculus 8.1. Indefinite Integrals 8.1.1. Primitive Function or Antiderivative 8.1.1.1. Indefinite Integrals 8.1,1.2. Integrals of Elementary Functions 8.1.2. Rules of Integration 8.1.3. integration of Rational Functions 8.1.3.1. Integrals of Integer Rational Functions (Polynomials) 8.1.3.2. Integrals of Fractional Rational Functions 8.1.3.3, Four Cases of Partial Fraction Decomposition 8.1.4. Integration of Irrational Functions 8.1.4.1. Substitution to Reduce to Integration of Rational Functions 8.1.4,2. Integration of Binomial Integrands 8.1.4.3. Elliptic Integrals 8.1.5. Integration of Trigonometric Functions 8.1.5.1. Substitution 8.1.5.2. Simplified Methods 8.1.6. Integration of Further Transcendental Functions 8.1.6.1. Integrals with Exponential Functions 8.1.6.2. Integrals with Hyperbolic Functions 8.1,6.3. Application of Integration by Parts 8.1.6.4. Integrals of Transcenental Functions 8,2. Definite Integrals 8.2.1. Basic Notions, Rules and Theorems 8.2.1.1. Defintion and existence of the Definite Integral 8.2.1.2. properties of Definite Integrals 8.2.1.3. Further Theorems about the Limits of Integration 8.2.1,4. Evaluation of the Definite Integral 8.2.2. Application of Definite Integrals 8.2.2.1. General Principles for Application of the Definite Integral 8.2.2.2. Applications in Geometry 8.2.2.3. Applications in Mechanics and Physics 8.2.3. improper Integrals, Stieltjes and Lebesgue Integrals 8,2.3.1. Generalization of the Notion of the Integeral 8.2.3.2. Integrals with Infintie Integration Limits 8.2.3.3. Integrals with Unbouonded Integrand 8.2.4. Parametric Integrals 8.2.4.1. Defintion of Parametric Integrals 8.2.4.2. Differentiation Under the Symbol of Integration 8.2.4.3. Integration Under the Symbol of Integrations 8.2.5. Integration by Series Expansion, Special Non-Elementary Functions 8.3. line Integrals 8.3.1. Line integrals of the First Type 8.3.1.1. Defintions 8.3.1.2. Existence Theorem 8.3.1.3. Evalutation of the Line Integral of the First Type 8.3.1.4. Application of the Line Integral of the First Type 8.3.2. Line Integrals of the Second Type 8.3.2.1. Definitions 8.3.2.2. Existence Theorem 8.3.2.3. Calculation of the line Integral of the Second Type 8.3.3. Line Integrals of General Type 8.3.3.1. Defintion 8.3.3.2. Properties of the line Integral of General Type 8.3.3.3. Integral Along a Closed Curve 8.3.4. Independence of the Line Integral of the Path of Integration 8.3.4.1, Two-Dimenional Case 8.3.4.2. Existence of a Primitive Function 8.3.4.3. Three-Dimensional Case 8.3.4.4. Determination of the Primitive Function 8.3.4.5. Zero-Valued Integral Along a Closed Curve 8.4. multiple Integrals 8.4.1. Double integrals 8.4.1.1. Notion of the Double Integral 8.4.1.2. Evaluation of the Triple integral 8.4.1.3. Applications of the Double Integral 8.4.2. Triple integrals 8.4.2.1. Notion of the Triple integral 8.4.2.2. Evalulation of the Triple integral 8.4.2.3. Applications of the Triple integral 8.5. Surface Integrals 8.5.1. Surface Integral of the First Type 8.5.1.1. Notion of the Surface Integral of the First Type 8.5.1.2. Evaluation of the Surface Integral of the First Type 8.5.1.3. Applications of the Surface Integral of the First Type 8.5.2. Surface Integral of the Second Type 8.5.2.1. Notion of the Surface Integral of the Second Type 8.5.2.2. Evaluation of Surface Integrals of the Second Type 8.5.2.3. An Application of the Surface Integrals 9. Differential Equations 9.1. Ordinary Differential Equations 9.1.1. First-Order Differential Equations 9,1.1.1, Existence Theorems, Directions Field 9.1.1.2. Important Solution Mehods 9.1.1.3. Implicit Differential Equations 9.1.1.4. Singular Integrals and Singular Points 9.1.1.5. Approximation Methods for Solution of First-Order Dif- ferential Equations 9.1.2. Differential Equations of Higher Order and Sustems of Differential Equations 9.1.2.1. Basic Results 9.1.2.2. Lowering the Order 9.1.2.3. Linear n-th Order Defferential Equations 9.1.2.4. Solution of Linear Differential Equations with Constant Coefficients 9.1.2.5. Systems of Linear Differential Equations with Constant Coefficients 9.1.2.6. Liner Second-Order Differential Equations 9.1.3. Boundary Value Problems 9.1.3.1. BOOK REPORTS 1605

Problem Formulation 9.1.3.2. Fhndamental Properties of Eigenfunctions and Eigenvalues 9.1.3.3. Expansion in Eigenfunctions 9.1.3.4. Singular Cases 9.2. Partial Difference Equations 9.2.1. First-Order Partial Differential Equations 9.2.1.1. Linear First-Order Partial Differential Equations 9.2.1.2. Non-Linear First-Order Partial Differ- ential Equations 9.2.2. Linear Second-Order Partial Differnetial Equations 9.2.2.1. Classification and Properties of Second-Order Differential Equations with Two Independent Variables 9.2.2.2. Classification and Properties of Lin- ear Second-Order Differential Equations with more than two Independent Variables 9.2.2.3. Integration Methods for Linear Second-Order Partial Differential Equations 9.2.3. Some Furhter Partial Differential Equations From NaturM Sciences and Engineering 9.2.3.1. Formulation of the Problem and the Boundary Conditions 9.2.3.2. Wave Equation 9.2.3.3. Heat Conduction and Diffusion Equation for Homogeneous Media 9.2.3.4. Potential Equation 9.2.3.5. Schrodinger's Equation 9.2.4. Non-Linear Partial Differential Equations: Solitions, Periodic Patterns and Chaos 9.2.4.1. Formulation of the Physical-Mathematical Problem 9.2.4.2. Korteweg de Vries Equation (KdV) 9.2.4.3. Non-Linear Schrodinger Equation (NLS) 9.2.4.4. Sine:Gordon Equation (SG) 9.2.4.5. Further Non-Linear Evolution Equations with Soliton Solutions 10. Calculus of Variations 10.1. Defining the Problem 10.2. Historical Problems 10.2.1. Isoperimetric Problem 10.2.2. Brachistochrone Problem 10.3. Variational Problems of One-Variable 10.3.1. Simple Variational Problems and Extremal Curves 10.3.2. Euler Differential Equation of the Variational Calculus 10.3.3. Variational Problems with Side Conditions 10.3.4, Variational Problems with Higher-Order Derivatives 10.3.5. Variational Problem with Several Unknown Functions 10.3.6. Variational Problems using Parametric Representation 10.4. Variational Problems with Functions of Several Variables 10.4.1. Simple Variational Problems 10.4.2. More General Varia- tional Problems 10.5. Numerical Solution of Variational Problems 10.6. Supplementary Problems 10.6.1. First and Second Variation 10.6.2. Application in physics 11. Linear Integral Equations 11.1. Indroduction and Classification 11.2. Fredholm Integral Equations of the Sec- ond Kind 11.2.1. Integral Equations with Degenerate Kernel 11.2.2. Successive Approximation Method Neumann Series 11.2.3. Fredholm Solution Methodm, Fredholm Theorems 11.2.3.1. Fredholm Solution Method 11.2.3.2. Fredholm Theorems 11.2.4. Numerical Methods for Fredholm Integral Equations of the Second Kind 11.2.4.1. Approximation of the Integral 11.2.4.2. Kernel Approximation 11.2.4.3. Colloction Method 11.3. Fredholm In- tegral Equations of the First Kind 11.3.1. Integral Equations with Degenerate Kernels 11.3.2. Analytic Basis 11.3.3. Reduction of an Integral Equation into a Linear System of Equations 11.3.4. Solution of the Homogeneous Integral Equation of the first kind 11.3.5. Construction of Two-Special Orthonormal Sustems for a Given Kernel 11.3.6. Iteration Method 11.4. Volterra Integral Equations 11.4.1. Theoretical Foundations 11.4.2. Solution by Differentiation 11.4.3. Solution of the Volterra Integral Equations of the second kind by Neumann Series 11.4.4. Convolution Type Volterra Integral Equations 11.4.5. Numerical Methods for Volterra Integral Equations of the Second Kind 11.5. Singular integral Equations 11.5.1. Abel Integral Equations 11.5.2. Singular integral Equation with Cauchy Kernel 11.5.2.1. Formulation of the Problem 11.5.2.2. Existence of a Solution 11.5.2.3. Properties of Cauchy Type Integrals 11.5.2.4. The Hilbert Boundary Value Problem 11.5.2.5. Solution of the Hilbert Boundary Value Problem (in short:Hilbert Problem) 11.5.2.6. Solution of the Characteristic Integral Equation 12. Functional Analaysis 12.1. Vector Spaces 12.1.1. Notion of a Vector Space 12.1.2. Linear and Affine Linear Subsets 12.1.3. Linearly Independent Elements 12.1.4. Convex Subsets and the Convex Hull 12.1.4.1. Convex Sets 12.1.4.2. Cones 12.1.5. Linear Operators and Functionals 12.1.5.1. Mappings 12.1.5.2. Homomorphism and Endomorphism 12.1.5.3. Isomorphic Vector Spaces 12.1.6. Complexification of Real Vector Spaces 12.1.7. Ordered Vector Spaces 12.1.7.1. Cone and Partial Ordering 12.1.7.2. Order Bouded Sets 12.1.7.3. Positive Operators 12.1.7.4. Vector Lattices 12.2. Metric Spaces 12.2.1. Notion of a Metric Space 12.2.1.1. Balls, Neighborhoods and Open Sets 12.2.1.2. Convergence of Sequences in Metric Spaces 12.2.1.3. Closed Sets and Closure 12.2.1.4. Dense Subsets and Separable Metric Spaces 12.2.2. Complete Metric Spaces 12.2.2.1. Cauchy Sequences 12.2.2,2. Complete Metric Spaces 12.2.2.3. Some Fundamental Theorems in Complete Metric Spaces 12.2.2.4. Some Applications of the Contraction Mapping Principle 12.2.2.5. Completion of a Metric Space 12.2.3. Continuous Operators 12.3. Normed Spaces 12.3.1. Notion of a Normed Space 12.3.1.1. Axioms os a Normed Space 12.3.1.2. Some properties of a Normed Space 12.3.2. Banach Spaces 12.3.2.1. Series in Normed Spaces 12.3.2.2. Examples of Banach Spaces 12.3.2.3. Sobolev Spaces 12.3.3. Ordered Normed Spaces 12.3.4. Normed Algebras 12.4. Hilbert Spaces 12.4.1. Notion of a Hilbert Space 12.4.1.1. Scalar Product 12.4.1.2. Unitary Spaces and Some of their Properties 12.4.1.3. Hilbert Space 12.4.2. Orthogonality 12.4.2.1. Properties of Orthogonality 12.4.2.2. Orthogonal Systems 12.4.3. Fourier Series in Hilbert Spaces 12.4.3.1. Best Approximation 12.4.3.2. Parseval Equation, Riesz Fischer Theorem 12.4.4. Existence of a Basis, Isomorphic Hilbert Spaces 12.5. Continuous Linear Operators and Functionals 12.5.1. Boundedness, Norm and Continuity of Linear Operators 12.5.1.1. Boundedness and the Norm of Linear Operators 12.5.1.2. The Space of Linear Continuous Operators 12.5.1.3. Convergence of Operator Sequences 12.5.2. Linear Continuous Operators in Banach Spaces 12.5.3. Elements of the SpectrM Theory of Linear Operators 12.5.3.1. Resolvent Set and the Resolvent of an Operator 12.5.3.2. Spectrum of an Operator 12.5.4. Continuous Linear Functionals 12.5.4.1. Definition 12.5.4.2. Continuous linear Functionals in Hilbert Spaces Riesz Representation Theorem 12.5.4.3. Continuous Linear Functionals in L p 12.5.5. Extension of a Linear Functional 12.5.6. Seperation of Convex Sets 12.5.7. Second Adjoint Space and Reflexive Spaces 12.6. Adjoint Operators in Normed Spaces 12.6.1. Adjoint of a Bounded Operator 12.6.2. Adjoint Operator of and Unbounded Operators 12.6.3. Self-Adjoint Operators 12.6.3.1. Positive Definite Operators 12.6.3.2. Projectors in a Hilbert Space 12.7. Compact Sets and Compact Operators 12.7.1. Compact Subsets of a Normed Space 12.7.2. Compact Operators 12.7.2.1. Defintion of a Compact Operator 12.7.2.2. Properties of Linear Compact Operators 12.7.2.3. Weak Convergence of Elements 12.7.3. Fredholm Alternative 12.7.4. Compact Operators in Hilbert Space 12.7.5. Compact Self-Adjoint Operators 12.8. Non-Linear Operators 12.8.1. Examples of Non-Linear 1606 BOOK REPORTS

Operators 12.8.2. Differentiability of Non-Linear Operators 12.8.3. Newton's Method 12.8.4. Schauder's Fixed- Point Theorem 12.8.5. Leray-Schauder Theory 12.8.6. Positive Non-Linear Operators 12.8.7. Monotone Operators in Banach Spaces 12.9. Measure and Lebesgue Integral 12.9.1. Sigma Algebra and Measures 12.9,2. Measurable Functions 12.9.2.1. Properties of the Class of Measurable Functions 12.9.2.2. Measurable Functions 12.9.3. Integration 12.9.3,1. Definiton of the Integral 12.9.3.2. Some Properties of the Integral 12.9.3.3. Convergence Theorems 12,9.4. L p Spaces 12.9.5. Distributions 12.9.5.1. Formula of Partial Intergration 12.9.5.2. Generalized Derivative 12.9.5.3. Distribution 12.9.5.4. Derivative of a Distrubution 13. Vector Analysis and Vector Fields 13.1. Basic Notions of the Theory of Vector Fields 13.1.1. Vector Functions of a Scalar Variable 13.1.1.1. Definitions 13.1.1.2. Derivative of a Vector Functions 13.1,1.3. Rules of Differentiation for Vectors 13.1.1.4. Taylor Expansion for Vector Functions 13.1.2. Scalar Fields 13.1.2.1. Scalar Fields or Scalar Point Functions 13.1.2.2. Important Special Cases of Scalar Fields 13.1.2.3. Coordinate Definition of a Fie;d 13.1.2.4. level Surfaces and Level Lines of a Field 13.1.3. Vector Fields 13.1.3.1. Vector Field or Vector Point Functions 13.1.3.2. Important Cases of Vector Fields 13.1.3.3. Coordinate Representation of Vector Fields 13.1.3.4. Transformation of Coordinate Systems 13.1.3.5. Vector Lines 13.2. Differential Operators of Space 13.2.1. Directional and Space Derivatives 13.2.1.1. Directional Derivative of a Scalar Field 13.2.1.2. Directional Derivative os a Vector Field 13.2.1.3. Volume Derivative 13.2.2. Gradient of a Scalar Field 13.2.2.1. Defintion of the Gradient 13.2.2.2. Gradient and Volume Derivative 13.2.2,3. Gradient and Directional Derivative 13.2.2.4. Further Properties of the Gradient 13.2.2.5. Gradiant of the Scalar Field in Different Coordinates 13.2.2.6. Rules of Calculations 13.2.3. Vector Gradient 13.2.4. Divergence of Vector Fields 13.2.4.1. Definition of Divergence 13.2.4.2. Divergence in Different Coordinates 13.2.4.3. Rules for Evaluation of the Divergence 13.2.4.4. Divergence of a Central Field 13.2.5. Rotation of Vector Fields 13.2.5.1. Definitions of the Rotation 13.2.5.2, Rotation in Differemt Coordinates 13.2.5.3. Rules for Evaluating the Rotation 13.2.5.4. Rotation of a Potential Field 13.2.6. Nabla Operator, Laplace Operator 13.2.6.1. Nabla Operator 13.2.6.2. Rules for Calculations with the Nabla Operator 13.2.6.3. Vector Gradient 13.2.6.4. Nabla Operator Applied Twice 13.2.6.5. Laplace Operator 13.2.7. Review of Spatial Differential Operations 13.2.7.1. Fundamental Relations and Results(see table 13.2) 13.2.7.2. Rules of Calculation for Spatial Differential Operators 13.2.7.3, Expressions of Vector Analysis in Cartesian, Cylindrical, and Spherical Coordinates 13.3. Integration in Vector Fields 13.3.1. Line Integral and Potential in Vector Fields 13.3.1.1. Line Integral in Vector Fields 13.3.1.2. Interpretation of the Line Integral in Mechanics 13.3.1.3. Properties of the Line Integral 13.3.1.4. line Integral in Cartesian Coordinates 13.3.1.5. Integral Along a closed Curve in a Vector Field 13.3.1.6. Conservative or Potential Field 13.3.2. Surface Integrals 13.3.2.1. Vector of a Plane Sheet 13.3.2.2. Evaluation of the Surface Integral 13.3.2.3. Surface Integrals and Flow of Fields 13.3.2.4. Surface Integrals in Cartesian Coordinates as Surface Integral of Second Type 13.3.3. Integral Theorems 13.3.3.1. Integral Theorem and Integral Formula of Gauss 13.3.3.2. Integral Theorem of Stokes 13.3.3.3. Integral Theirems of Green 13,4. Evaluation of Fields 13.4.1. Pure Source Fields 13.4.2. Pure Rotation Field or Zero-Divergence Field 13.4.3. Vector Fields with Point-Like Sources 13.4.3.1. Coulomb Field of a Point-Like Charge 13.4.3.2. Gravitational Field of a Point Mass 13.4.4. Superposition of Fields 13.4.4.1. Discrete Source Distribution 13.4.4.2. Continuous Source Distribution 13.4.4.3. Conclusion 13.5. Differential Equations of Vector Field Theory 13.5.1. Laplace Differential Equation 13.5.2. Poisson Differential Equation 14. Function Theory 14.1. Functions of Complex Variables 14.1.1. Continuity, Differentiability 14.1.1.1. Definition of a Complex Function 14.1.1.2. Limit of a Complex Function 14.1.1.3. Continuous Complex Functions 14.1.1.4. Differentiability of a Complex Function 14.1.2. Analytic Functions 14.1.2.1. Definition of Analytic Functions 14.1.2.2. Examples of Analytic Functions 14.1.2.3. Properties of Analytic Functions 14.1.2.4. Singular Points 14.1.3. Confromal Mapping 14.1.3.1. Notion and Properties of Conformal Mappings 14,1.3.2. Simplest Conformal Mappings 14.1.3.3. The Schwarz Reflection Principle 14.1.3.4. Complex Potential 14.1.3.5. Superposition Principle 14.1.3.6. Arbitrary Mappings of the Complex Plane 14.2. Intergration in the Complex Plane 14.2.1. Definite and Indefinite Integral 14.2.1.1. Definition of the Integral in the Complex Plane 14.2.1.2. Properties and Evaluation of Complex Integrals 14.2.2. Canchy Integral Theorem 14.2.2,1. Cauchy Integral Theorem for Simply Connected Domains 14.2.2.2. Cauchy Integral Theorem for Multiply Connected Domains 14.2,3, Cauchy Integral Formulas 14.2.3.1. Analytic Function on the Interior of a Domain 14.2.3.2. Analytic Function on the Exterior of a Domain 14.3. Power Series Expansion of Analytic Functions 14.3.1. Convergence of Series with Complex Terms 14.3.1.1. Convergence of a Number Sequence with Complex Terms 14.3.1.2. Convergence of an Infinite Series with Complex Terms 14.3.1.3. Power Series with Complex Terms 14.3.2. Taylor Series 14.3.3. Principle of Analytic Continuation 14.3.4. Laurent Expansion 14.3.5. Isolated Singular Points and the Residue Theorem 14.3.5.1. Isolated Singular Points 14.3.5.2. Meromorphic Functions 14.3.5.3. Elliptic Functions 14.3.5.4. Residue 14.3.5.5. Residue Theorem 14.4. Evaluation of Real Integrals by Complex Integrals 14.4.1. Application of Cauchy Integral Formulas 14.4.2. Application of the Residue Theorem 14.4.3. Application of the Jordan Lemma 14.4.3.1. Jordan lemma 14.4.3.2. Examples of the Jordan Lemma 14.5. Algebraic and Elementary Transcendental Functions 14.5.1. Algebraic Functions 14.5.2. Elementary Transcendental Functions 14.5.3. Description of Curves in Complex Form 14.6. Elliptic Functions 14.6.1. Relation to Elliptic Integrals 14.6.2. Jacobian Functions 14.6.3. Theta Function 14.6.4, Weierstrass Functions 15. Integral Transformation 15.1. Notion of Integral Transformation 15.1.1. General Defintion of Integral Trans- formations 15.1.2. Special Integral Transformations 15.1.3. Inverse Transformations 15.1.4. Linearity of Integral Transformations 15.1.5. Integral Transformations for Functions of Several Variables 15.1.6. Applications of In- tegral Transformations 15.2. Laplace Transformation 15.2.1. Properties of the Laplace Transformation 15.2.1.1. Laplace Transformation, Original and Image Space 15.2.1.2. Rules for the Evaluation of the Laplace Transfor- mation 15.2.1.3. Transforms of Special Functions 15.2.1.4. Dirac 5 Function and Distributions 15.2.2. Inverse BOOK REPORTS 1607

Transformation into the Original Space 15.2.2.1. Inverse Transformation with the help of Tables 15.2.2.2. Partial Fraction Decomposition 15.2.2.3. Series Expansion 15.2.2.4. Inverse Integral 15.2.3. Solution of Differential Equa- tions using Laplace Transformation 15.2.3.1. Ordinary Linear Defferential Equations with Constant Coefficients 15.2.3.2. Ordinary Linear Defferential Equations with Coefficients Depending on the Variable 15.2.3.3 Partial Dif- ferential Equations 15.3. Fourier Transformation 15.3.1. Properties of the Fourier Transformation 15.3.1.1. Fourier Integrals 15.3.1.2. Fourier Transformation and Inverse Transformations 15.3.1.3. Rules of Calculation with the Fourier Transformation 15.3.1.4. Transforms of Special Functions 15.3.2. Solution of Differential Equations using the Fourier Transformation 15.3.2.1. Ordinary Linear Differential Equations 15.3.2.2. Partial Differential Equa- tions 15.4. Z-Transformation 15.4.1. Properties of the Z-Transformation 15.4.1.1. Discrete Functions 15.4.1.2. Definition of the Z-Transformation 15.4.1.3. Rules of Calculations 15.4.1.4. Relation to the Laplace Transfor- mation 15.4.1.5. Inverse of the Z-Transformation 15.4.2. Applications of the Z-Transformation 15.4.2.1. General Solution of Linear Difference Equations 15.4.2.2. Second-Order Difference Equations (Initial Value Problem) 15.4.2.3. Second-Order Difference Equations (Boundary Value Problem) 15.5. Wavelet Transformation 15.5.1. Signals 15.5.2. Wavelets 15.5.3. Wavelet Transformation 15.5.4. Discrete Wavelet Transformation 15.5.4.1. Fast Wavelet Transformation 15.5.4.2. Discrete Haar Wavelet Transformation 15.5.5. Gabor Transformation 15.6. Walsh Functions 15.6.1. Step Functions 15.6.2. Walsh Systems 16. Probability Theory and Mathematical Statistics 16.1. Combinatorics 16.1.1. Permutations 16.1.2. Combi- nations 16.1.3. Arrangments 16.1.4. Collection of the Formulas of Combinatories (see table 16.1) 16.2. Proba- bility Theory 16.2.1. Event, Frequency and Probability 16.2.1.1. Events 16.2,1.2. Frequencies and Probabilities 16.2.1.3. Conditional Probability, Bayes Theorem 16.2.2. Random Variables, Distribution Functions 16.2.2.1. Random Variable 16.2.2.2. Distribution Function 16.2.2.3. Expected Value and Variance, Chebyshev Inequal- ity 16.2.2.4. Multidimensional Random Variable 16.2.3. Discrete Distributions 16.2.3.1. Binomial Distribution 16.2.3.2. Hypergeometric Distribution 16.2.3.3. Poisson Distribution 16.2.4. Continuous Distributions 16.2.4.1. Normal Distribution 16.2.4.2. Standard Normal Distribution, Gaussin Error Function 16.2.4.3. Logarithmic Nor- mal Distribution 16.2.4.4. Exponential Distribution 16.2.4.5. Weibull Distribution 16.2.4.6. X2 (Chi-Square) Distribution 16.2.4.7. Fisher F Distribution 16.2.4.8. Student t Distribution 16.2.5. Law of Large Numbers, Limit Theorems 16.2.6. Stochastic Processes and Stochastic Chains 16.2.6.1. Basic Notions, Markov Chains 16.2.6.2. Poisson Process 16.3. Mathematical Statistics 16.3.1. Statistic Function or Sample Function 16.3.1.1. Population, Sample, Random Vector 16.3.1.2. Statistic Function or Sample Function 16.3.2. Descriptive Statistics 16.3.2.1. Statistical Summarization and Analysis of Given Data 16.3.2.2. Statistical Parameters 16.3.3. Important Tests 16.3.3.1. Goodness of Fit Test for a Normal Distribution 16.3.3.2. Distribution of the Sample Mean 16.3.3.3. Confidence 16.3.3.4. Confidence 16.3.3.5. Structure of Hyposthesis Test 16.3.4. Correlation and Regression 16.3.4.1. Linear Correlation of two Measurable Characters 16.3.4.2. Linear Regression for two Measurable Char- acters 16.3.4.3. Multidimensional Regression 16.3.5. Monte Carlo Methods 16.3.5.1. Simulation 16.3.5.2. Random Numbers 16.3.5.3. Example of a Monte Carlo Simulation 16.3.5.4. Application of the Monte Carlo Method in Numerical Mathematics 16.3.5.5. Further Applications of the Monte Carlo Method 16.4. Calculus of Errors 16.4.1. Measurement Error and its Distribution 16.4.1.1. Qualitative Characterization of Measurement Error 16.4.1.2. Density Function of the Measurement Error 16.4.1.3. Quantitative Characterization of the Measurement Error 16.4.1.4. Determining the Result of a Measurement with Bounds on the Error 16.4.1.5. Error Estimation for Direct Measurements with the Same Accuracy 16.4.1.6. Error Estimation for Direct Measurements with Different Accuracy 16.4.2. Error Propagation and Error Analysis 16.4.2.1. Gauss Error Propagation Law 16.4.2.2. Error Analysis 17. Dynamical Systems and Chaos 17.1. Ordinary Differential Equations and Mappings 17.1.1. Dynamical Systems 17.1.1.1. Basic Notions 17.1.1.2. Invariant Sets 17.1.2. Qualitative Theory of Ordinary Differential Equations 17.1.2.1. Existence of Flows, Phase Space Structure 17.1.2.2. Linear Differential Equations 17.1.2.3. Stability Theory 17.1.2.4. Invariant Manifolds 17.1.2.5. Poincare Mapping 17.1.2.6. Topological Equivalence of Differential Equations 17.1.3. Discrete Dynamical Systems 17.1.3.1. Steady States, Periodic Orbits and Limit Sets 17.1.3.2. Invariant Manifolds 17.1.3.3. Topological Conjugacy of Discrete Systems 17.1.4. Structural Sta- bility (Robustness) 17.1.4.1. Structurally Stable Differential Equations 17.1.4.2. Structurally Stable Discrete Systems 17.1.4.3. Generic Properties 17.2. Quantitative Description of Attractors 17.2.1. Probability Measures on Attractors 17.2.1.1. Invartiant Measure 17.2.1.2. Elements of Ergodic Theory 17.2.2. Entropies 17.2.2.1. Topological Entropy 17.2.2.2. Metric Entropy 17.2.3. Lyapunov Exponents 17.2.4. Dimensions 17.2.4.1. Metric Dimensions 17.2.4.2. Dimensions Defined by Invariant Measures 17.2.4.3. Local Hausdorff Dimension According to Douady and Oesterle 17.2.4.4. Examples of Attractors 17.2.5. Strange Attractors and Chaos 17.2.6. Chaos in One-Dimensional Mappings 17.3. Bifurcation Theory and Routes to Chaos 17.3.1. Bifurcations in Morse-Smale Systems 17.3.1.1. Local Bifurcations in Neighborhoods of Steady States 17.3.1.2. Local Bifurcations in a Neigh- borhood of a Periodic Orbit 17.3.1.3. Global Bifurcation 17.3.2. Transitions to Chaos 17.3.2.1. Cascade of Period Doublings 17.3.2.2. Intermittency 17.3.2.3. Global Homoclinic Bifurcations 17.3.2.4. Destruction of a Torus 18. Optimization 18.1. Linear Programming 18.1.1. Formulation of the Problem and Geometrical Representation 18.1.1.1. The Form of a Linear Programming Problem 18.1.1.2. Examples and Graphical Solutions 18.1.2. Basic Notions of Linear Programming, Normal Form 18.1.2.1. Extreme Points and Basis 18.1.2.2. Normal Form of the Linear Programming Problem 18.1.3. Simplex Method 18.1.3.1. Simplex Tableau 18.1.3.2. Transition to the New Simplex Tableau 18.1.3.3. Determination of an Initial simplex Tableau 18.1.3.4. Revised Simplex Tableau 18.1.3.5. Duality in Linear Programming 18.1.4. Special Linear Programming Problems 18.1.4.1. Transportation Problem 18.1.4.2. Assignment Problem 18.1.4.3. Distribution Problem 18.1.4.4. Travelling Salesman 18.1.4.5. Scheduling Problem 18.2. Non-Linear Optimization 18.2.1. Formulation of the problem, Theoretical Basis 18.2.1.1. Formula- 1608 BOOK REPORTS tion of the Problem 18.2.1.2. Optimality Conditions 18.2.1.3. Duality in Optimization 18.2.2. Special Non-Linear Optimazation Problems 18.2.2.1. Convex Optimization 18.2.2.2. Quadratic Optimization 18.2.3. Solution Meth- ods for Quadratic Optimization Problems 18.2.3.1. Wolfe's Method 18.2.3.2. Hildreth-d'Esopo Method 18.2.4. Numerical Search Procedures 18.2.4.1. One-Dimensional Search 18.2.4.2. Minimum Search in n-Dimensional Eu- clidean Vector Space 18.2.5. Methods ofr Unconstrained Problems 18.2.5.1. Method of Steepest Descent 18.2.5.2. Application of the Newton Method 18.2.5.3. Cnjugate Gradient Methods 18.2.5.4. Method of Davidon, Fletcher and Powell (DFP) 18.2.6. Gradient Methods for Problems with Inequality Type constraint(s) 18.2.6.1. Method of Feasible Directions 18.2.6.2. Gradient Projection Methods 18.2.7. Penalty Function Method 18.2.7.1. Penalty Function Method 18.2.7.2. Barrier Method 18.2.8. Cutting Plane Methods 18.3. Discrete Dynamic Programming 18.3.1. Discrete Dynamic Decision Models 18.3.1.1. n-Stage Decision Process 18.3.1.2. Dynamic Programming Problem 18.3.2. Examples of Discrete Decision Models 18.3.2.1. Purchasing Problem 18.3.2.2. Knapsack Prob- lem 18.3.3. Bellman Functional Equations 18.3.3.1. Properties of the Cost Function 18.3.3.2. Formulation of the Functional Equations 18.3.4. Bellman Optimality Principle 18.3.5. Bellman Functional Equation Method 18.3.5.1. Determination of Minimal Costs 18.3.5.2. Determination of the Optimal Policy 18.3.6. Examples of Applications of the Functional Equation Method 18.3.6.1. Optimal Purchasing Policy 18.3.6.2. Knapsack Problem 19. Numerical Analysis 19.1. Numerical Solution of Non-Linear Equations in a Single Unknown 19.1.1. Iter- ation Method 19.1.1.1. Ordinary Iteration Method 19.1.1.2. Newton's Methods 19.1.1.3. Regula Falsi 19.1.2. Solution of Polynomial Equations 19.1.2.1. Homer's Scheme 19.1.2.2. Positions of the Roots 19.1.2.3. Numerical Methods 19.2. Numerical Solution of Equation Systems 19.2.1. Systems of Linear Equations 19.2.1.1. Triangular Decompositon of a Matrix 19.2.1.2. Cholesky's Methods for a Symmetric Coefficient Matrix 19.2.1.3. Orthogo- nalization Method 19.2.1.4. Iteration Methods 19.3. Numerical Integration 19.3.1. General Quadrature Formulas 19.3.2. Interpolation Quadratures 19.3.2.1. Rectangular Formula 19.3.2.2. Trapezoidal Formula 19.3.2.3. Simp- son's Formula 19.3.2.4. Hermite's Trapezoidal Formula 19.3.3. Quadrature Formulas of Gauss 19.3.3.1. Gauss Quadrature Formulas 19.3.3.2. Lobatto's Quadrature Formulas 19.3.4. Method of Romberg 19.3.4.1. Algorithm of the Romberg Method 19.3.4.2. Extrapolation Priciple 19.4. Approximate Integration of Ordinary Differen- tial Equations 19.4.1. Initial Value Problems 19.4.1.1. Euler Polygonal Method 19.4.1.2. Runge-Kutta Methods 19.4.1.3. Multi-Step Methods 19.4.1.4. Predictor Corrector Method 19.4.1.5. Convergence, Consistency, Stability 19.4.2. Boundary Value Problems 19.4.2.1. Difference Method 19.4.2.2. Approximation by Using Given Functions 19.4.2.3. Shooting Method 19.5. Approximate integration of Partial Differential Equations 19.5.1. Difference Method 19.5.2. Approximation by Given Functions 19.5.3. Finite Element Method (FEM) 19.6. Approximation, Computation of Adjustment, Harmonic Analysis 19.6.1. Polynomial Interpolation 19.6.1.1. Newton's Interpola- tion Formula 19.6.1.2. Lagrange's Interpolation Formula 19.6.1.3. Aitken-Necille Interpolation 19.6.2. Approxi- mation in Mean 19.6.2.1. Continuous Problems, Normal Equation 19.6.2.2. Discrete Problems, Normal Equations, householder's Method 19.6.2.3. Multidimensional Problems 19.6.2.4. Non-Linear Least Squares Problems 19.6.3. Chebyshev Approximation 19.6.3.1. Problem Definition and the Alternating Point Theorem 19.6.3.2. Properties of the Chebyshev Polynomials 19.6.3.3. Remes Algorithm 19.6.3.4. Discrete Chebyshev Approximation and Op- timization 19.6.4. Harmonic Analysis 19.6.4.1. Formulas for Trigonometric Interpolation 19.6.4.2. Fast Fourier Transformation (FFT) 19.7. Representation of Curves and Surfaces with Splines 19.7.1. Cubic Splines 19.7.1.1. Interpolation Splines 19.7.1.2. Smoothing Splines 19.7.2. Bicubic Splines 19.7.2.1. Use of Bicubic splines 19.7.2.2. Bicubic Interpolation Splines 19.7.2.3. Bicubic Smoothing Splines 19.7.3. Bernstein-Bezier Representation of Curves and Surfaces 19.7.3.1. Principle of the B-B Curve Representation 19.7.3.2. B-B Surface Representation 19.8. Using the Computer 19.8.1. Internal Symbol Representation 19.8.1.1. Number Systems 19.8.1.2. Internal Number Representation 19.8.2. Numerical Problems in Calculations with Computers 19.8.2.1. Introduction, Er- ror Types 19.8.2.2. Normalized Decimal Numbers and Round-Off 19.8.2.3. Accuracy in Numerical Calculations 19.8.3. Libraries of Numerical Methods 19.8.3.1. NAG Library 19.8.3.2. IMSL Library 19.8.3.3. Aachen Library 19.8.4. Application of Computer Algebra Systems 19.8.4.1. Mathematics 19.8.4.2. Maple 20. Computer Algebra System 20.1. Introduction 20.1.1. Brief Characterization of Computer Algebra Systems 20.1.2. Examples of Basic Application Fields 20.1.2.1. Manipulation of Formulas 20.1.2.2. Graphical Repre- sentaion 20.1.2.3. Programming in Computer Algebra Systems 20.1.3. Structure of Computer Algebra Systems 20.1.3.1. Basic Structure Elements 20.2. Mathematica 20.2.1. Basic Structure Elements 20.2.2. Types of Numbers in Mathematica 20.2.2.1. Basic Types of Numbers in Mathematica 20.2.2.2. Special Numbers 20.2.2.3. Represen- tation and Conversion of Numbers 20.2.3. Important Operators 20.2.4. Lists 20.2.4.1. Notions 20.2.4.2. Nested Lists, Arrays or Tabels 20.2.4.3. Operations with Lists 20.2.4.4. Special Lists 20.2.5. Vectors and Matrices as Lists 20.2.5.1. Creating Appropriate Lists 20.2.5.2. Operations with Matrices and Vectors 20.2.6. Functions 20.2.6.1. Standard Functions 20.2.6.2. Special Functions 20.2.6.3. Pure Functions 20.2.7. Patterns 20.2.8. Functional Operations 20.2.9. Programming 20.2.10. Supplement about Synatx, Information, Messages 20.2.10.1. Contexts, Attributes 20.2.10.2. Information 20.2.10.3. Messages 20.3. Maple 20.3.1. Basic Structure Elements 20.3.1.1. Types and Objects 20.3.1.2. Input and Output 20.3.2. Types of Numbers in Maple 20.3.2.1. Basic Types of Numbers in Maple 20.3.2.2. Special Numbers 20.3.2.3. Representation and Conversion of Numbers 20.3.3. Im- portant Operators in Maple 20.3.4. Algebraic Expressions 20.3.5. Sequences and Lists 20.3.6. Tables, Arrays, Vectors and Matrices 20.3.6.1. Tables and Arrays 20.3.6.2. One-Dimensional Arrays 20.3.6.3. Two-Dimensional Arrays 20.3.6.4. Special Commands for Vectors and Matrices 20.3.7. Functions and Operators 20.3.7.1. Functions 20.3.7.2. Operators 20.3.7.3. Differential Operators 20.3.7.4. The Functional Operator map 20.3.8. Programming in Maple 20.3.9. Supplement about Syntax, Information and Help 20.3.9.1. Using the Maple Library 20.3.9.2. Environment Variable 20.3.9.3. Information and Help 20.4. Applications of Computer Algebra Systems 20.4.1. Manipulation of Algebraic Expressions 20.4.1.1. Mathematica 20.4.1.2. Maple 20.4.2. Solution of Equations and BOOK REPORTS 1609

Systems of Equations 20.4.2.1. Mathematica 20.4.2.2. Maple 20.4.3. Elements of Linear Algebra 20.4.3.1. Math- ematica 20.4.3.2. Maple 20.4.4. Differential and Integral Calculus 20.4.4.1. Mathematica 20.4.4.2. Maple 20.5. Graphics in Computer Algebra Systems 20.5.1. Graphics with Mathematica 20.5.1.1. Basic Elements of Graphics 20.5.1.2. Graphics Primitives 20.5.1.3. Syntax of Graphical Representation 20.5.1.4. Graphical Options 20.5.1.5. Two-Dimensional Curves 20.5.1.6. Parametric Representation of Curves 20.5.1.7. Representation of Surfaces and Spare Curves 20.5.2. Graphics with Maple 20.5.2.1. Two-Dimensional Graphics 20.5.2.2. Three-Dimensional Graphics 21. Tables 21.1. Frequently Used Constants 21.2. Natural Constants 21.3. Important Series Expansions 21.4. Fourier Series 21.5. Indefinite Integrals 21.5.1. Integral Rational Functions 21.5.1.1. Integrals with X = ax + b 21.5.1.2. Integrals with X = ax 2 q- bx -b c 21.5.1.3. Integrals with X = a 2 =[=2:2 21.5.1.4. Integrals with X = a 3 -4-x 3 21.5.1.5. Integrals with X ----a 4 q-x4 21.5.1.6. Integrals with X --- a 4 -x 4 21.5.1.7. Some Cases of Partial Fraction Decomposition 21.5.2. Integrals of Irrational Functions 21.5.2.1. Integrals with xf~ and a 2 4- b2x 21.5.2.2. Other Integrals with v~ 21.5.2.3. Integrals with ~ b 21.5.2.4. Integrals with ~ b and v/~ + g 21.5.2.5. Integrals with ~ 21.5.2.6. Integrals with ~ 21.5.2.7. Integrals with ~ 21.5.2.8. Integrals with ~/ax 2 + bx + c 21.5.2.9. Intergrals with other Irrational Expressions 21.5.2.10. Recursion Formulas for an Integral with Binomial Differential 21.5.3. Integrals of Trigonometric Functions 21.5.3.1. Integrals with Sine Function 21.5.3.2. Integrals with Cosine Function 21.5.3.3. Integrals with Sine and Cosine Function 21.5.3.4. Integrals with Tangent Function 21.5.3.5. Integrals with Cotangent Function 21.5.4. Integrals of other Transcendental Functions 21.5.4.1. Integrals with Hyperbolic Functions 21.5.4.2. Integrals with Exponential Functions 21.5.4.3. Integrals with Logarithmic Functions 21.5.4.4. Integrals with Inverse Trigonometric Functions 21.5.4.5. Integrals with Inverse Hyperbolic Functions 21.6. Definite Integrals 21.6.1. Definite Integrals of Trigonometric Functions 21.6.2. Definite Integrals of Exponential Functions 21.6.3. Definite Integrals of Logarithmic Functions 21.6.4. Definite Integrals of Algebraic Functions 21.7. Elliptic Integrals 21.7.1. Elliptic Integral of the First Kind F(¢, k), k = sina 21.7.2. Elliptic Integral of the Second Kind E(¢, k), k = sin a 21.7.3. Complete Elliptic Integral, k = sin a 21.8. Gamma Function 21.9. Bessel Functions (Cylindrical Functions) 21.10. Legendre Polynomials of the First Kind 21.11. Laplace Transformation 21.12. Fourier Transformation 21.12.1. Fourier Cosine Transformation 21.12.2. Fourier Sine Transformation 21.12.3. Fourier Transformation 21.12.4. Exponential Fourier Transformation 21.13. Z Transformation 21.14. Poisson Distribution 21.15. Standard Normal Distribution 21.15.1. Standard Normal Distribution for 0.00 < x < 1.99 21.15.2. Standard Normal Distribution for 2.00 < x < 3.90 21.16. X2 Distribution 21.17. Fisher F Distribution 21.18. Student t Distribution 21.19. Random Numbers 22. Bibliography Index Mathematic Symbols

The Economics of Knowledqe Dominique Foray, The MIT Press, Cambridge, MA (2004) 275 Pages. $35.00. Contents Ackknowledgments vii Introduction ix 1. An Original Discipline 2. Macro- and Microeconomic References: Continuity and Breaks 3. Production and Knowledge 4. Reproduction of Knowledge 5. Knowledge Spillovers 6. Knowledge as a Public God 7. Intellectual Property Rights in the Knowledge Economy 8. Knowledge Openness and Economic Incentives 9. On the Uneven Development of Knowledge across Sectors 10. A New Organizational Capability:Knowledge Managment 11. The Public Dimension of the Knowledge Economy Conclusion Postscript Notes References Index vskip0.5cm underbar Combinatorial Enumeration Ian P. Goulden, David M Jackson, Dover Publications, INC. Mineola, New York, (1983) 569 pages, $34.95. Contents Notation 1. Mathematical Preliminaries 1.1. The Ring of Formal Power Series 1.1.1. Formal Power Series 1.1.2. The Coefficient Operator 1.1.3. Infinite Sums and Products 1.1.4. Compostitonal and Multiplicative Inverses 1.1.5. The Former Derivative and the Integral 1.1.6. The Logarithmic, Exponential, and Binomial Power Series 1.1.7. Circular and Hyperbolic Power Series 1.1.8. Formal Differential Equations 1.1.9. Roots of a Power Series 1.1.10. Matrices Over the Ring of Formal Power Series 1.1.11. Formal Laurent Series Notes and References 1610 BOOK REPORTS

Exercises 1.2. The Lagrange Theorem for Implicit Functions 1.2.1. Proposition 1.2.2. Theorem (Residue Composition) 1.2.3. An Identity (by Residue Composition) 1.2.4. Theorem (Lagrange) 1.2.5. A Functional Equation 1.2.6. The Central Trinomial Numbers 1.2.7. Abel's Extension of the Binomial Theorem 1.2.8. Theorem (Multivariate Residue Composition) 1.2.9. Theorem (Multivaruate Lagrange) 1.2.10. A Functional Equation in Two-Variables 1.2.11. Theorem (MacMahon Master Theorem) 1.2.12. Dixon's Indentity 1.2.13. Corollary (Lagrange Theorem for Monomials) Notes and References Exercises 2. The Combinatorics of the Ordinary Generating Function 2.1. Introduction 2.1.1. The Elementary Counting Lemmas 2.1.2. Decompositions and Weight Functions 2.1.3. Direct and Indirect Decompositions, Combinatorial Marking, and Multivariate Generating Functions 2.1.4. A Classical Application of Enumerative Arguments 2.1.5. Recursive and "At-Least" Decompositions 2.2. The Elementary Counting Lemmas 2.2.1. Definition (Distinguisha- bility) 2.2.2. Definition (Weight Function, Weight) 2.2.3. Remark (The General Enumerative Problem) 2.2.4. Example (Enumerative Problems) 2.2.5. Definition (Ordinary Generating Function) 2.2.6. Remark (s-Objects) 2.2.7. Example (a Generating Function) 2.2.8. Proposition 2.2.9. Definition (Decomposition, w-Preserving) 2.2.10. Proposition 2.2.11. Example (Terquem Problem:Decompositiom) 2.2.12. Lemma (Sum) 2.2.13. Example (Sum) 2.2.14. Lemma (Product) 2.2.15. Example (Terquem Problem: Generating Function) 2.2.16. Definition (Ad- ditively V/eight-Preserving Decomposition) 2.2.17. Remark (Direct, Indirect, Recursive Decompositions) 2.2.18. Example (An Indirect Decomposition) 2.2.19. Example (a Recursive Decomposition) 2.2.20. Definition (Com- position) 2.2.21. Example (Composition) 2.2.22. Lemma (Composition) 2.2.23. Example (Composition) 2.2.24. Definition (s-Derivative) 2.2.25. Example (s-Derivative of a Set of Permutations) 2.2.26. Lemma (Differentiation) 2.2.27. Example (s-Derivative) 2.2.28. Definition ("Exact, " "At Least" Generating Functions) 2.2.29. Lemma (The Principle of Inclusion and Exclusion) 2.2.30. Example (Derangements) Notes and References 2.3. Preliminary Examples 2.3.1. Decomposition (Subsets) 2.3.2. Subsets 2.3.3. Recurrence Equation for BinomiM Coefficients 2.3.4. Decomposition (Multisets) 2.3.5. Multisets 2.3.6. Definiton (Com- position of an Integer) 2.3.7. Decomposition (Compositions of an Integer) 2.3.8. Compositions of an Integer 2.3.9. Correspondence (Multisets-Compositions) 2.3.10. Compositions and Parts 2.3.11. Recurrence Equation for Compositions and Parts 2.3.12. An Identity from Compositions 2.3.13. Defintion (Succession in a Set) 2.3.14. Decomposition (Subsets) 2.3.15. Subsets with Successions 2.3.16. Definition (Skolem Subsets) 2.3.17. Decomposi- tion (Skolem Subsets) 2.3.18. The Skolem Problem 2.3.19. Defintion (Circular Succession) 2.3.20. Decomposition (Subsets) 2.3.21. Example (Circular Successions) 2.3.22. Subsets and Circular Successions Notes and References Exercises 2.4. Sequences 2.4.1. Definition (Substring, Subsequence, Block) 2.4.2. Definition (Maximal Block) 2.4.3. Decomposition (0, 1-Sequences) 2.4.4. 0, 1-Sequences and Maximal Blocks of l's 2.4.5. Decomposition (0, 1-Sequences) 2.4.6. 0, 1-Sequences and Maximal Blocks of O's and l's 2.4.7. Definiton (q~pe of a Sequence) 2.4.8. Sequences and Type 2.4.9. Sequences and Type Restrictions 2.4.10. Compositions and Part Restrictions 2.4.11. Remark (Sequences and Compositions) 2.4.12. Ordered Factorizations) 2.4.13. Definition (Rise, Level, Fall) 2.4.14. Definition (Smirnov Sequence) 2.4.15. Decomposition (Smirnov Sequences) 2.4.16. The Smirnov Problem 2.4.17. Sequences and Levels 2.4.18. Sequences and Maximal Blocks 2.4.19. Decomposition (Sequences and Fall) 2.4.20. The Simon Newcomb Problem 2.4.21. Permutations and Falls 2.4.22. Definition (Sequences with Strictly Increasing Support) 2.4.23. Decomposition (Sequences with Strictly Increasing Support) 2.4.24. Sequences of Type (2, ..., 2) With Strictly Increasing Support 2.4.25. Definition (Dirichlet Generating Function) 2.4.26. Lemma (Product) 2.4.27. Definition (Multiplicatively Weight-Preserving Decomposition) 2.4.28. Ordered Factorizations and Dirichlet Generating Functions 2.4.29. Remark (Sequences and Ordered Factorizations) Notes and References Exercises 2.5. Partitions of an Integer 2.5.1. Definition (Partition) 2.5.2. Decomposition (Partitions) 2.5.3. The Number of Partitions 2.5.4. Example (Calculation of p(6) 2.5.5. Distinct Parts 2.5.6. Largest Part Exactly ra 2.5.7. Definition (Conjugate) 2.5.8. Decomposition (Partitions with Given Largest Part) 2.5.9. All Partitions-Euler's Theorem 2.5.10. Defintion (Ferrers Graph, Durfee Square) 2.5.11. Defintion (Abutment) 2.5.12. Decomposition (All Partitions) 2.5.13. All Partitions-q-Analogue of Kummer's Theorem 2.5.14. All Partitions-Euler's Theorem 2.5.15. Definiton-MaximM Triangle 2.5.16. Decomposition (Partitions with Distinct Parts) 2.5.17. Partition with Distinct Parts-An Identity 2.5.18. Partition with Distinct Parts-Euler's Theorem 2.5.19. Decomposition (Self-Conjugate Partitions) 2.5.20. Decomposition (Self-Conjugate Partitions) 2.5.21. Self-conjugate Partitions- An Identity 2.5.22. Self-conjugate Partitions-Euler's Theorem 2.5.23. Decomposition (Sylvester: All Partitions) 2.5.24. The Jacobi Triple Product Identity 2.5.25. Euler's Theorem for Pentagonal Numbers Notes and References Exercises 2.6. Inversions in Permutations and q-Identities 2.6.1. Definiton (Inversion) 2.6.2. Algorithm (Inversion) 2.6.3. Proposition 2.6.4. Lemma (Inversions) 2.6.5. Example (Between-Set and Within-Set Generating Functions) 2.6.6. Lemma (Between Set and Within-Set Inversions) 2.6.7. Recurrence Equation for q-Binomial Coefficients 2.6.8. Definition (Increasing, Decreasing, Cup-, Cap-permutations) 2.6.9. Lemma (Cup- and Cap-permutations) 2.6.10. Theorem Bimodal Permutation) 2.6.11. Corollary (q-Analogue of the Binomial Theorem) 2.6.12. Three Finite Product Identities 2.6.13. Proposition 2.6.14. Four Infinite Product Identities Notes and References Exercises 2.7. Planted Plane Trees 2.7.1. Definition (Branch, Branch List) 2.7.2. Decomposition (Planted Plane Cubic Trees) 2.7.3. Planted Plane Cubic Trees and Nonroot Monovalent Vertices 2.7.4. Decomposition (Branch) BOOK REPORTS 1611

2.7.5. Planted Plane Trees and Nonroot Monovalent Vertices 2.7.6. Definition (Degree Sequence) 2.7.7. Planted Plane Trees and Degree Sequence 2.7.8, Planted Plane Trees and Bivalent Vertices 2.7.9. Decomposition (Planted Plane Trees 2.7.10. Planted Plane Trees and Bivalent Vertices, by Composition 2.7.11. Planted Plane Trees with No Isolated Bivalent Vertices 2.7.12. Defintion (2-Chromatic Tree) 2.7.13. Decomposition (Planted Plane 2- Chromatic Trees) 2.7.14. Planted Plane 2-Chromatic Trees 2.7.15. Defintion (Height of Vertex) 2.7.16. Vertices of Given Degree and Height in Planted Plane Trees (First Method) 2.7.17. Decomposition (Planted Plane Trees with a Single Dustinguished Vertex of Degree d and Height h) 2.7.18. Vertices of Given Degree and Height in Planted Plane Trees (Second Method) 2.7.19. Remark (Finding Decompositions) 2.7.20. Definition (Left-most Path) 2.7,21. Decomposition (Left-most Path) 2.7.22. Planted Plane Trees, Left-Most Paths, and Degree Sequence, Notes and References Exercises 2.8. Sequences with Distinguished Substring 2.8.1. Definition (A-Type of a Sequence) 2.8.2. Definition (k-Cluster) 2.8.3. Definition (Cluster Generating Function) 2.8.4. Definition 2.8.5. Proposition 2.8.6. Theorem (Distinguished Substring) 2.8.7. Sequences with no pth powers of Strings of Length k 2.8.8. Sequences and Stricly Increasing Substrings 2.8.9. Definition (Connector Matrix) 2.8.10. Lemma (Cluster Generating Function for an Arbitrary Set) 2.8.11. Example Notes and References Exercises 2.9. Rooted Planar Maps and the Quadratic Method 2.9.1. The Quadratic Method 2.9.2. Defini- tion (Planar Map) 2.9.3. Proposition (Euler's Polyhedral Formula) 2.9.4. Defintion (Rooted Planar Map, Root Edge, Root Face, Root Vertex) 2.9.5. Decomposition (Rooted Near-triangulation;Root Edge) 2.9.6. Rooted Near-triangulations and Inner Faces 2.9.7. Rooted Near-triangulations, Inner Faces, and Degree of Outer Face, 2.9.8. Decomposition (Rooted Planar Map;Root Edge) 2.9.9, Rooted Planar Maps 2.9.10. Decomposition (2- Edge-Connected Rooted Planar Map) 2.9.11. 2-Edge-Connected Rooted Planar Maps 2.9.12. Deeompostion (Nonseparable Rooted Planar Map) 2.9.13. Nonseparable Rooted Planar Maps Notes and References Exercises 3. The Combinatorics of the Exponential Generating Function 3.1. Introduction 3.1.1. The Elementary Counting Lemmas 3.1.2. The *-Product and *-Composition 3.1.3. The *-Derivative 3.1.4. The F-Series 3.2. The Elemen- tary Counting Lemmas 3.2.1. Definition (s-Tagged Confiuration, Tag Set, Tag Weight) 3.2.2. Example (s-Tagged Confiurations) 3.2.3. Definition (Exponential Generating Function) 3.2.4. Proposition 3.2.5. Proposition 3.2.6. Lemma (Sum) 3.2.7. Example (Exponential Generating Function) 3.2.8. Example (Derangements) 3.2.9. Def- inition (*-Product) 3.2.10. Example (*-Product) 3.2.11. Lemma (*-Product) 3.2.12. Example (A Permutation Problem) 3.2.13. Example (A Sequence Problem) 3.2.14. Definition (*-Composition with Respect to s Objects) 3.2.15. Example (,-Composition) 3.2.16. Lemma (*-Composition) 3.2.17. Partitions of a Set 3.2.18. Definition (*-Differentiation) 3.2.19. Lemma (*-Differentiation) 3.2.20. Remark (a Construction for the *-Derivative) 3.2.21. Definition (Alternating Permutation) 3.2.22. Andre's Problem Notes and References 3.3. Trees and Cycles in Permutations and Functions 3.3.1. Decomposition (Derangements) 3.3.2. Derangements (Indirect Decomposition) 3.3.3. A Recurrence Equation for the Derangement Number 3.3.4. Defintion (Circular Permutation) 3.3.5. Decomposition (Cycle; for Permutations) 3.3.6. Derangements (Direct Decomposition) 3.3.7. Involutions 3.3.8. Defintion (Labeled Tree) 3.3.9. Decomposition (Labeled Branch) 3.3.10. Rooted Label Trees 3.3.11. Proposition 3.3.12. Decomposition (Cycle;for Functions) 3.3.13. Functions and Cycle Type 3.3.14. Expectation of the number of Cycles of Given Length in Functions 3.3.15. Idempotent Func- tions 3.3.16. Decomposition (Recursive Cycle;for Permutations) 3.3.17. Derangments and Involutions (Recursive Composition) 3.3.18. Remark (Distinguished Tagged s-Objects) 3.3.19. Correspondence (Functions for Nn to Nn-Rooted Labeled Trees) 3.3.20. Rooted Labeled Trees (Direct Decomposition) 3.3.21. Definition (Spanning Tree) 3.3.22. Lemma (Edge-Weighted Tree) 3.3.23. Theorem (Matrix-Tree) 3.3.24. In-Directed and Out-Directed Spanning Arborescences 3.3.25. Matrix-Tree Theorem for Undirected Graphs 3.3.26. Labeled Trees Notes and References Exercises 3.4. 2-Covers of a Set and Homeomorphieally Irreducible Labeled Graphs 3.4.1. Decomposition (0, 1- Matrices) 3.4.2. Example 3.4.3. 0, 1-Matrices with No Rows or Columns of O's 3.4.4. Recurrence Equation 3.4.5. A Differential Decomposition for Matrices with No 0 Rows or Columns 3.4.6. Definition (Proper k-Cover, Restricted Proper k-Cover) 3.4.7. Decomposition (Proper 2-Covers) 3.4.8. Proper 2-Covers 3.4.9. Restricted Proper 2-Covers 3.4.10. A Differential Equation for Restricted Proper 2-Covers 3.4.11. A Differential Decomposition for Restricted Proper 2-Covers 3.4.12. Decomposition (Simple Labeled h-Graphs 3.4.13. Proposition 3.4.14. Simple Labeled h-Graphs 3.4.15. A Recurrence Equations for Simple Labeled h-Graphs Notes and References Exercises 3.5. Coefficient Extraction for Symmetric Functions 3.5.1. Definition (p-Regular Graph) 3.5.2. The Ordinary Generating Function for Simple Labeled Graph 3.5.3. Definition (Monomial Symmetric Function) 3.5.4. Proposition 3.5.5. A Differential Equation for Simple Labeled Graphs in terms of Power Sum Symmetric Functions 3.5.6. Proposition 3.5.7. Theorem (F-Series) 3.5.8. The F-Series for Simple 3-Regular Labeled Graphs 3.5.9. A Recurrence Equations for Simple 3-Regular Labeled Graphs 3.5.10. Non-negative Integer Matrices with Line Sum equal to 2, 3.5.11. Differential Decomposition for Simple 3-Regular Labeled Graphs Notes and References Exercises 4. The Combinatorics of Sequences 4.1. Introduction 4.2. The Maximal String Decomposition Theorem 4.2.1. Definition (Trl-String, Maximal 7rl-String Type) 4.2.2. Definition (~l-Enumerator, Maximal ~r1-String Length Enu- merator) 4.2.3. Theorem (Maximal String Decomposition) 4.2.4. Definition (Rises, Successions, c-Successions) 1612 BOOK REPORTS

4.2.5. Lemma (i-Transformation, +-Transformation) 4.2.6. Definition (~vl-Alternating Sequence) 4.2.7. Corollary (~rl-Alternating Sequences of Even Length 4.2.8. i-Alternating Permutations of Even Length 4.2.9. +-Alternating Permutations of Even Length 4.2.10. @-Alternating Permutations of Even Length 4.2.11. i-Alternating Permu- tations of Even Length, Inversions 4.2.12. Corollary (Sequences, Type, Occurences of ~rl) 4.2.13. Sequences and Rises (Simon Newcomb Problem) 4.2.14. Sequences and Levels (Smirnov Problem) 4.2.15. Corollary (Sequences, ~rl-Strings of Length p) 4.2.16. Sequences wtih ~rl Strings of Length 3 4.2.17. Permutations with i-Strings of Length 3, Inversions 4.2.18. Permutations with Prescribed Product of Maximal i-String Length 4.2.19. Theorem (Maximal String Decomposition;Distinguished Final String) 4.2.20. Corollary (Trl-Alternating Sequences of Odd Length) 4.2.21. i-Alternating Permutations of Odd Length, with Inversions 4.2.22. i-Alternating Permutations of Odd Length Notes and References Exercises 4.3. The Pattern Algebra 4.3.1. Definition (Pattern) 4.3.2. Definition (Incidence Matrix, Set of Encod- ings) 4.3.3. Definition (Fundamental Generating Functions) 4.3.4. Proposition (Incidence Matrices for Union and Product) 4.3.5. Lemma (Sum, Product for the Fundamental Generating Functions) 4.3.6. Proposition (~rl-String Enumerator) 4.3.7. ~l-Alternating Sequences of Odd Length 4.3.8. Theorem (Elimination) 4.3.9. Definition (Left-, Right-Expansion) 4.3.10. Algorithm (Factores Expansion) 4.3.11. Remark (General Strategy) 4.3.12. Proof of the Maximal String Decomposition Theorem 4.3.13. Definition (Sequence with Repeated Pattern) 4.3.14. Sequences with Repeated Pattern ~rl~r2 2 4.3.15. Permutations with Repeated Pattern ~r~ 2, for Rises 4.3.16. Sequences with Fixed Pattern 4.3.17. Permutations with Fixed Pattern and Inversion 4.3.18. A Tripartite Problem 4.3.19. A q-Identity for the Tangent Function 4.3.20. A q-Identity from Permutations with Repeated Pattern Notes and References Exercises 4.4. The Logarithmic Connection for Circular Permutations 4.4.1. Definition (Circular Sequence) 4.4.2. Theorem (Logarithmic Connection) 4.4.3. Theorem (Maximal String Decomposition for Circular Permutations) 4.4.4. Circular Premutations and Maxima 4.4.5. Directed Hamiltonian Cycles of the Complete Directed Graph with Distinguished Hamiltonian Cycles 4.4.6. Hamiltonian Cycles of the Complete Graph with a Distinguished Hamiltonian Cycle 4.4.7. The Menage Problem Notes and References Exercises 4.5. Permanents and Absolute Problems 4.5.1. Proposition (Permanent) 4.5.2. Definition (Absolute Partition for Permuatations) 4.5.3. Lemma (Absolute Patrition) 4.5.4. Derangements 4.5.5. The Menage Problem (Absolute) 4.5.6. Definition (k-Discordant Premutation) 4.5.7. 3-Discordant Permutations 4.5.8. Definition (Latin Rectangle) 4.5.9. Decomposition ((3 x n)-Latin Rectangles) 4.5.10. (3 x n)-Latin Rectangles 4.5.11. A Correspondence for Sequences and Absolute Sequences 4.5.12. Permutations Whose Cycles Have Repeated Pattern 7rlTr2 2 Notes and References Exercises 5. The Combinatorics of Paths 5.1. Introduction 5.1.1. Continued Fractions 5.1.2. Arbitrary Steps and Noninter- secting Paths 5.1.3. A q-Analogue of the Lagrange Theorem 5.2. Weighted Paths 5.2.1. Definition (J-Fraction, S-Fraction) 5.2.2. Proposition (Contraction) 5.2.3. Defintion (Height of a Planted Plane Tree) 5.2.4. Proposi- tion (Stieltjes-Rogers Polynomials) 5.2.5. Definition (Altitude, Path, Height) 5.2.6. Decomposition (path) 5.2.7. Lemma (Path) 5.2.8. Definition (Addition Formula) 5.2.9. Decomposition (path) 5.2.10. The Stieltjes-Rogers J-Fraction Theorem 5.2.11. A Continued Fraction Associated with Factorials 5.2.12. Lemma (Weighted Path) 5.2.13. Definition (Double Rise, Double Fall, Modified Maximum, Modified Minimum 5.2.14. Algorithm (Associ- ated Tree) 5.2.15. Decomposition (Francon-Viennot) 5.2.16. All Premutations 5.2.17. /.-Alternating Permutations of Odd Length 5.2.18. Corollary (Right-most Element in a Permutation) 5.2.19. L-Alternating Permutations of Even Length 5.2.20. L-Alternating Permutations of Even Length with Even-Valued minima-The Jacobi Ellip- tic Function cn(x,a) 5.2.21. Proposition (Recurrence Equation, Determinant Identity) 5.2.22. Theorem (Path Enumeration) 5.2.23. k-Alternating Permutations of Even Length with Respect to Height-Meixner Polynomial Notes and References Exercises 5.3. Lattice Paths 5.3.1. Definition (Altitude, Path, Step) 5.3.2. Definition (Minus-, Zero-, Plus-path) 5.3.3. Decomposition (Lattice Path) 5.3.4. Theorem (Lattice Path) 5.3.5. Example 5.3.6. Paths with an Oblique Barrier Notes and References Exercises 5.4. ordered Sets of Paths 5.4.1. Decomposition (intersecting n-Path) 5.4.2. Theorem (Nonintersecting n-Path) 5.4.3. Definition (Column-Strict Plane Partition, Shape, Size) 5.4.4. Decomposition (n-Path:for Column- Strict Plane Partitions) 5.4.5. Theorem (Column-Strict Plane Parition:Shape, Size, Type) 5.4.6. Kreweras' Theorem for Dominance Systems 5.4.7. Columns-Strict Plane Partitions:Fixed Shape 5.4.8. Young Tableaux:Fixed Shape Notes and References Exercises 5.5. A q-Analogue of the Lagrange Theorem 5.5.1. Decomposition (Additive (for Sequences)) 5.5.2. A Proof of the Lagrange Theorem 5.5.3. Proposition 5.5.4. Theorem (q-Lagrange) 5.5.5. Corollary 5.5.6. Lead Codes Notes and References Exercises Solutions. Chapter 1. Chapter 2. Chapter 3. Chapter 4. Chapter 5. References Index Book REPORTS 1613

Eztremal Grpah Theory Bela Bollobas, Dover Publications Inc., Mineola, NY, (1978) 492 pages, $29.95. Contents Preface Basic Definitions Chapter 1: Connectivity 1. Elementary Properties 2. Menger's Theorem and its Consequences 3. The Structure of 2- and 3-Connected Graphs 4. Minimally k-Connected Graphs 5. Graphs with Given Maximal Local Connectivity 6. Exercises, Problems~ and Conjectures Chapter 2: Matching 1. Fundamental Matching Theorems 2. The Number of 1-Factors 3. f-Factors 4. Matching in Graphs with Restrictions on the Degrees 5. Coverings 6. Exercises, Problems and Conjectures Chapter 3: Cycles 1. Graphs with Large Minimal Degree and Large Girth 2. Vertex Disjoint Cycles 3. Edge Disjoint Cycles 4. The Circumference 5. Graphs with Cycles of Given Lengths 6. Exercises, Problems and Conjectures Chapter 4: The Diameter 1. Diameter, Maximal Degree and Size 2. Diameter and Connectivity 3. Graphs with Large Subgraphs of Small Diameter 4. Factors of Small Diameter 5. Exercises, Problems and Cdonjectures Chapter 5: Colourings 1. General Colouring Theorems 2. Critical k-Chromatic Graphs 3. Colouring Graphs on Surfaces 4. Sparse Graphs of Large Chromatic Numbers 5. Perfect Graphs 6. Ramsey Type Theorems 7. Exercises, Problems and Conjectures Chapter 6: Complete Subgraphs 1. The Number of Complete Subgraphs 2. Complete Subgraphs of r-Partite Graphs 3. The Structure of Graphs 4. The Structure of Extremal Graphs without Forbidden Subgraphs 5. Independendt Complete Subgraphs 6. Exercises, Problems and Conjectures Chapter 7: Topological Subgraphs 1. Contractions 2. Topological Complete Subgraphs 3. Semi-Topological Subgraphs 4. Exercises, Problems and Conjectures Chapter 8: Complexity and Packing 1. The Complexity of Graph Properties 2. Monotone Properties 3. The Main Packing Theorem 4. Packing Graphs of Small Size 5. Applications of Packing Results to Complexity 6. Exercises, Problems and Conjecture References Index of Symbols Index of Definitions

Fermi Remembered James W. Cronin, University of Chicago Press, Chicago, IL (2004) 287 pages, $45.00. Contents Preface Chapter 1. Biographical Introduction Editor's Comment Emilio Segre Boigraphical Introduction Chapter 2. Fermi and the Elucidation of Matter Editor's Comment Frank Wilczek Fermi and the Elucidation of Matter Chapter 3. Letter and Documents Relating to the Development of Nuclear Energy. Editor's Introductory comments. To Harry M. Durning, January 16, 1939. From George B. Pegram to S.C. Hooper, March 18, 1939. From Leo Szilard, July 3, 1939. From Leo Szilard, July 5~ 1939. From Leo Szilard, July 8, 1939. To Leo Szilard, July 9.1939. From Leo Szilard, July 11, 1939. From Vannevar Bush, August 19, 1941. From Harry S. Truman, August 11, 1950. Outline for the speech "The Genesis of the Nuclear Energy. Project" January 30, 1954. Text of the speech "The Genesis of the Nuclear Energy Project". November 1955. Chapter 4. Correspondence between Fermi and Colleagues: Scientific, Political, Personal. Editor's Comments on letters. To James F. Byrnes, October 16, 1945. From C.N. Yang, January 5, 1950. To C.N. Yang, January 12, 1950. From Erwin Schrodinger, February 10, 1951. To Erwin Schrodinger, February 27~ 1951. From Fred Reines and Clyde Cowan, October 4, 1952. To Fred Reines, October 8, 1952. To Dean G. Acheson, May 22, 1952. From Linus Pauling, June 16, 1952. From George Gamow, March 13, 1953. To George Gamow, March 24, 1953. From Samuel Goudsmith, March 11, 1953. To Samuel Goudsmith, March 24, 1953. From George Kistiakowsky, September 29, 1953. To George Kistiakowsky, September 30, 1953. From Arthur Compton~ December 2, 1953. To Arthur Compton, December 14, 1953. From Owen Chamberlain, February 2, 1954. Chapter 5 Research and Teaching:Selections from the Archives: International House Application, June 10, 1940 To Walter Bartky, December 3, 1945. Participants at the inauguration of the research institutes, at the University of Chicago, August 1945. Staff of the Institute for Nuclear Studies, 1950. Genesis of theory of cosmic ray acceleration, 1948-1949. To Hannes Alfven, December 24, 1948. Abstract for Fermi's paper on cosmic radiation, January 3, 1949. Comments by Herbert Anderson and Edward Teller on Fermi's. Paper on cosmic rays, Summary page from data book on meson-nucleon scattering, February 1952. Program for calculation of cyclotron orbits on the Maniac computer, 1951. Equations for a charged particle in a cylindrically symmetric magnetic field. The instruction set for the maniac computer. Fermi~s flowchart for a program to calculate the orbits emanating from a target. Notes for setting up the calculation of the orbits. Program for calculating initial direction cosines. Quantum mechanics exam, Spring quarter, 1954. Outline for the Speech "The Future of Nuclear Physics" Rochester, January 10, 1952. Chapter 6. Reminiscences of Fermi's Faculty and Research Colleagues 1945-1954. Richard L. Garwin Working with Fermi at Chicago and postwar Los Alamos. Murray Gell-Mann No Shortage of Memories. Marvin L. Goldberger Enrico Fermi (1901-1954). The Complete Physicist. Roger Hildebrand Fermi's Classrooms. Darragh Nagle With Fermi at Columbia, Chicago, and Los Alamos. Valentine Telegdi Reminiscences of Enrico Fermi. AI Wattenberg Fermi as My Chauffuer (Fermi at Argonne National Laboratory and Chicago 1946-1948). Courtenay Wright Fermi in Action. 1614 BOOK REPORTS

Chapter 7. Reminiscences of Fermi's Students, 1945-1954. Harold Agnew A Snapshot of my interaction with Fermi. Owen Chamberlain A Brief Remininscence of Enrico Fermi. G.F. Chew Personal Recollections from 1944- 1948. George W. Farwell Reminiscences of Fermi. Uri Haber-Schaim Fermi in Varenna, Summer 1954. T.D. Lee Reminiscences of Chicago Days. Jay Orear My First Meetings with Fermi. Arthur Rosenfeld Reminiscences of Fermi. Robert Schluter Three Reminiscences of Enrico Fermi. Jack Steinberger Fermi and My Graduate Years at Chicago: Happy Reminiscences. Chapter 8. Reminiscences of Students of the Fermi Period, 1945-1954. Nina Byers Fermi and Szilard. Jerome I. Friedman A Student's View of Fermi. Maurice Glicksman Enrico Fermi: Teacher, Colleague, Mentor. Marshall N. Rosenbluth A Young Man Encounters Enrico Fermi. Lincoln Wolfenstein Fermi Interactions. Chen Ning Yang Reminiscences of Enrico Fermi. Guarang Yodh This Account is Not According to the Mahabharata! Chapter 9. What Can We Learn with High Energy Accelerators? James W. Cronin Fermi's Look into His Crystal Ball. Further Reading List of Contributors Index

The Nature of Scientific Evidence. Statistical, Philosophical, and Empirical Considerations Mark L. Taper and Subhash R. Lele, University of Chicago Press, Chicago. (2004) 567pages $30.00. Contents Foreword by C. R. Rao Preface Part 1. Scientific Process Overview, Mark L. Taper and Subhash R. Lele 1. A Brief Tour of Statistical Con- cepts, Nicholas Lewin-Koh, Mark L. Taper and Subhash R. Lele 2. Models of Scientific Inquiry and Statistical Practice: Implications for the Structure of Scientific Knowledge, Brian A. Maurer 2.1. Commentary, Prasanta S. Bandyipadhyay and John G. Bennett 2.2. Commentary, Mark L. Wilson 2.3. Rejoinder, Brian A. Maurer 3. Experiments, Observations, and Other Kinds of Evidence, Samuel M. Scheiner 3.1. Commentary, Marie~Josee Fortin 3.2. Commentary, Manuel C. Molles, Jr. 3.3. Rejoinder, Samuel M. Sheiner Part 2. Logics of Evidence Overview, V.P. Godambe 4. An Error-Statistical philosophy of Evidence, Deborah G. Mayo 4.1. Commentary, Earl D. McCoy 4.2. Commentary, George Casella 4.3. Rejoinder, Deborah G. Mayo 5. The Likelihood Paradigm for Statistical Evidence, Richard Royall 5.1. Commentary, D.R. Cox 5.2. Commentary, Martin Curd 5.3. Rejoinder, Richard Royatl 6. Why Likelihood? Malcolm Forster and Elliot Sober 6.1. Commentary, Micheal Kruse 6.2. Commentary, Robert J Boik 6.3. Rejoinder, Malcolm Forster and Elliot Sober 7. Evidence Functions and the Optimality of the Law of Likelihood~ Subhash R. Lele 7.1. Commentary, Christopher C. Heyde 7.2. Commentary, Paul I. Nelson 7.3. Rejoinder, Subhash R. Lele Part 3. Realities of Nature Overview, Mark S. Boyce 8. Whole-Ecosystem Experiments: Replication and Arguing from Error, Jean A. Miller and Thomas M. Frost 8.1. Commentary, William A. Link 8.2. Commentary, Charles E. McCulloch 8.3. Rejoinder, Jean A. Miller 9. Dynamical Models as Paths to Evidence in Ecology, Mark L. Taper and Subhash R. Lele 9.1. Commentary, Steven Hecht Orzack 9.2. Commentary, Philip M. Dixon 9.3. Rejoinder, Mark L. Taper and Subhash R. Lele 10. Constraints on Negative Relationships: Mathematical Causes and Ecological Consequences, James H. Brown, Edward J. Bedrick, S. K. Morgan Ernest, Jean-Luc E. Cartron, and Jeffery F. Kelly 10.1. Commentary, Robert D. Holt and Norman A. Slade 10.2. Commentary, Steve Cherry 10.3. Rejoinder, James H. Brown, Edward J. Bedrick, S. K. Morgan Ernest, Jean-Luc E. Cartron, and Jeffery F. Kelly Part 4. Science, Opinion, and Evidence Overview, Mark L. Taper and Subhash R. Lele 11. Statistics and the Scientific Method in Ecology, Brian Dennis 11.1. Commentary, Charles E McCulloch 11.2. Commentary, Aaron M. Ellison 11.3. Rejoinder, Brian Dennis 12. Taking the Prior Seriously: Bayesian Analysis without Subjective Probability, Daniel Goodman 12.1. Commentary, Nozer D. Singpurwalla 12.2. Rejoinder, Daniel Goodman 13. Elicit Data, Not Prior: On Using Expert Opinion in Ecological Studies, Subhash R. Lele 13.1. Commentary, R. Cary Tuckfield 13.2. Commentary, Lance A. Waller 13.3. Rejoinder, Subhash R. Lele Part 5. Models, Realities, and Evidence Overview, Mark L. Taper and Subhash R. Lele 14. Statistical Distances as Loss Functions in Assessing Model Adequacy, Bruce G. Lindsay 14.1. Commentary, D.R. Cox 14.2. Commentary, Stephen P. Ellner 14.3. Rejoinder, Bruce G. Lindsay 15. Model Indentification from Many Candidates, Mark L. Taper 15.1. Commentary, Isabella Verdinelli and Larry Wasserman 15.2. Commentary, Hamparsum Bozdogan 15.3. Rejoinder, Mark L. Taper Part 6. Conclusion 16. The Nature of Scientific Evidence: A Forward-Looking Synthesis, Mark L. Taper and Subhash R. Lele List of Contributors Index

Handbook of Numerical Analysis, Volume XII, Computational Models for the Human Body P.G. Ciarlet, Elsevi- er North Holland, Amsterdam, (2004) 670 pages $215.00. Contents Chapter I. 1. Introduction 2. A brief description of the human vascular system 3. The main variables for the mathematical description of blood flow 4. Some relevant issues BOOK REPORTS 1615

Chapter II. 5. The derivation of the equations for the flow field 6. Some nomenclature 7. The motion of continuous media 8. The derivation of the basic equations of fluid mechanics 9. The Navier-Stokes equations Chapter III. 10. The incompressible Navier-Stokes equations and the approximation 11. Weak form of Navier- Stokes equation 12. An energy inequality for the Navier-Stokes equation 13. The Stokes equations 14. Numerical approximation of Navier-Stokes equations Chapter IV. 15. Mathematical modelling of the vessel wall 16. Derivation fo ID Models of vessel wall mechanics 17. Analysis of vessel wall models Chapter V. 18. The coupled fluid structure problem 19. An iterative algorithm to solve the coupled fluid-structure problem Chapter VI. 20. One-dimensional models of blood flow in arteries Chapter VII. 21. Some numerical results 22. Conclusions Acknowledgements References

Calculus of Variations, Mechanics, Control, and Other Applications Charles R. MacCluer, Pearson Prentice Hall, N J, (2005) 254 pages, $84.00. Contents Preface Acknowledgments 1. Preliminaries 1.1. Directional Derivatives and Gradients 1.2. Calculus Rules 1.3. Contour Surfaces and Sublevel Sets 1.4. Lagrange Multipliers 1.5. Convexity Exercises 2. Optimization 2.1. Mathematical Programming 2.2. Linear Programming 2.3. Statistical Problems 2.4. Varia- tional Problems Exercises 3. Formulating Variational Problems 3.1. Shortest Distance between Two Points (CVP 1) 3.2. Craph with Least Surface of Revolution (CVP 2) 3.3. The Catenary (CVP 3) 3.4. The Brachistochrone (CVP 4) 3.5. Cruise-Climb (CVP 5) 3.6. Shapes of Minimum Resistance (CVP 6) 3.7. Hamilton's Principle 3.8. Isoperimetric problems Exercises 4. The Euler-Lagrange Equation 4.1. One Degree of Freedom 4.2. Two special Cases:No y, No x 4.3. Multiple Degrees of Freedom 4.4. The Hamiltonian 4.5. A Closer Look Exercises 5. Constrained Problems 5.1. Dido's Problem 5.2. Statement of the Problem 5.3. The Inverse Function Theorem 5.4. The Euler-Lagrange Equation for Constrained Problem 5.5. Example Applications 5.6. Multiple Degrees of Freedom 5.7. Nonintegral Constraints 5.8. Hamilton's Principle with Contraints Exercises 6. Extremal Surfaces 6.1. A Soap Film (CVP 15) 6.2. Stable Flows (CVP 16) 6.3. Schrodinger's Equation (CVP 18) 6.4. Eigenvalue Problems 6.5. Rayleigh-Ritz Numerics Exercises 7. Optimal Control 7.1. A Rolling cart (OCP 1) 7.2. General Formulation 7.3. Reinvestments (OCP 2) 7.4. Average Voltage (OCP 3) 7.5. A Time-Optimal Problem (OCP 4) 7.6. The Bang-Bang Principle 7.7. The Maximum Principle 7.8. Example Applications Exercises 8. The LQ Problem 8.1. Problem Statement 8.2. State Feedback 8.3. Stability 8.4. The LQR Problem 8.5. A Tracking Servo Exercises 9. Weak Sufficiency 9.1. Weak versus Strong Extrema 9.2. First and Second Variations 9.3. In Application 9.4. The Integrand p~12 _{_ q~?2 9.5. Weak Local Sufficiency Exercises 10. Strong Sufficiency 10.1. The Goal 10.2. Flows 10.3. Flows of the Euler-Lagrange Equation 10.4. The E Function and Strong Sufficiency 10.5. The Existence of Flows Exercises 11. Corner Points 11.1. Corners and Extremals 11.2. First Erdmann Corner Condition 11.3. The Figurative 11.4. Second Erdmann Corner Condition Exercises Appendix A. The Inverse Function Theorem Appendix B. Picard's Theorem Appnedix C. The Divergence Theorem Appendix D. A MATLAB Cookbook References Index

JPEG2000 Standard for Imaqe Compression Tinku Acharya &: Ping-Sing Tsai, John Wiley ~ Sons, Inc., N J, (2005) 274 pages. $64.95. Contents Preface 1. Introduction to Data Compression 1.1. Introduction 1.2. Why Compression? 1.2.1. Advantages of Data Com- pression 1.2.2. Disadvantages of Data Compression 1.3. Information Theory Concepts 1.3.1. Discrete Memoryless Model and Entropy 1.3.2. Noiseless Source Coding Theorem 1.3.3. Unique Decipherability 1.4. Classification of Compression algorithms 1.5. A Data Compession Model 1.6. Compression Performance 1.6.1. Compression Ratio and Bits per Sample 1.6.2. Quality Metrics 1.6.3. Coding Delay 1.6.4. Coding Complexity 1.7. Overview of Image Compression 1.8. multimedia Data Compression Standards 1.8.1. Still Image Coding Standard 1.8.2. Video Coding Standards 1.8.3. Audio Coding Standards 1.8.4. Text Compression 1.9. Summary References 2. Source Coding Algorithms 2.1. Run-Length Coding 2.2. Huffman Coding 2.2.1. Limitations of Huffman Coding 2.2.2. Modified Huffman Coding 2.3. Arithmetic Coding 2.3.1. Encoding Algorithm 2.3.2. Decoding Algorithm 2.4. Binary Arithmetic Coding 2.4.1. Implementation with Integer Mathematics 2.4.2. The QM-Coder 1616 BOOK REPORTS

2.5. Ziv-Lempel Coding 2.5.1. The LZ77 Algorithm 2.5.2. The LZ78 Algorithm 2.5.3. THe LZW Algorithm 2.6. Summary References 3. JPEG: Still Image Compression Standard 3.1. Introduction 3.2. The JPEG Lossless Coding Algorithm 3.3. Baseline JPEG Compression 3.3.1. Color Space Conversion 3.3.2. Source Image Data arrangement 3.3.3. The Baseline Compression Algorithm 3.3.4. Discrete Cosine Transform 3.3.5. Coding the DCT Coefficients 3.3.6. Decompression Process in Baseline JPEG 3.4. Progressive DCT-Based Mode 3.5. Hierarchical Mode 3.6. Summary References 4. Introduction to Discrete Wavelet Transform 4.1. Introudction 4.2. Wavelet Transforms 4.2.1. Discrete Wavelet Transforms 4.2.2. Concept of Multiresolution Analysis 4.2.3. Implementation by Filters and the Pyramid Algo- rithm 4.3. Extension to Two-Dimensional Signals 4.4. Lifting Implementation of the Discrete Wavelet Transform 4.4.1. Finite Impulse Response Filter and Z-Transformation 4.4.2. Euclidean Algorithm for Laurent Polynomials 4.4.3. Perfect Reconstruction and Polyphase Representation of Filters 4.4.4. Lifting 4.4.5. Data Dependancy Diagram for Lifting Computation 4.5. Why Do We Care About Lifting? 4.6. Summary References 5. VSLI Architectures for Discrete Wavelet Transforms 5.1. Introduction 5.2. A VLSI Architecture for the Convolution Approach 5.2.1. Mapping the DWT in a Semi-Systolic Architecture 5.2.2. Mapping the Inverse DWT in a Semi-Systolic Architecture 5.2.3. United Architecture for DWT and Inverse DWT 5.3. VLSI Architectures for Lifting-based DWT 5.3.1. Mapping the Data Dependency Diagram in Pipeline Architectures 5.3.2. Enhanced Pipeline Architecture by Folding 5.3.3. Flipping Architecture 5.3.4. A Register Allocation Scheme for Lifting 5.3.5. A Recursive Architecture for Lifting 5.3.6. A DSP-Type Architecture for Lifting 5.3.7. A Generalized and Highly Programmable Architecture For Lifting 5.3.8. A Generalized Two-Dimensional Architecture 5.4. Summary References 6. JPEG2000 Standard 6.1. Introduction 6.2. Why JPEG2000 6.3. Parts of the JPEG2000 Standard 6.4. Overview of the JPEG2000 Part 1 Encoding System 6.5. Image Preprocessing 6.5.1. Tiling 6.5.2. DC Level Shifting 6.5,3. Multicomponent Transformations 6.6. Compression 6.6. i. Descrete Wavelet Transformation 6.6.2. Quantization 6.6.3. Region of Interest Coding 6.6.4. Rate Control 6.6.5. Entropy Encoding 6.7. Tier-2 Coding and Bitstream Formation 6.8. Summary References 7. Coding algorithms in JPEG2000 7.1. Introduction 7.2. Partitioning Data for Coding 7.3. Tier-1 Coding in JPEG2000 7.3.1. Fractional Bit-Plane Coding 7.3.2. Examples of BPC Encoder 7.3,3. Binary Arithmetic Coding-MQ-Coder 7,4. Tier-2 Coding in JPEG2000 7.4.1. Basic Tag Tree Coding 7.4.2. Bitstream Formation 7.4.3. Packet Header Information Coding 7.5. Summary References 8. Code-Stream Organization and File Format 8.1. Introduction 8.2. Syntax and Code-Stream Rules 8.2.1. Basic Rules 8,2.2. Markers and Marker Segments Definitions 8.2.3. Headers Definition 8.3. File Format for JPEG2000 Part I:JP2 Format 8.3.1. File Format Organization 8.3.2. JP2 Required Boxes 8.4. Example 8.5. Summary References 9. VSLI Architectures for JPEG2000 9.1. Introduction 9.2. A JPEG2000 Architecture for VLSI Implementation 9.3. VLSI Architectures for EBCOT 9.3.1. Combinational Logic Blocks 9.3.2. Functionality of the Registers 9.3.3. Control Mechanism for the EBCOT architecture 9.4. VLSI Architecture for Binary Arithmetic Coding:MQ- Coder 9.5. Decoder Architecture for JPEG2000 9.6. Summary of Other Architectures for JPEG2000 9.6.1. Pass-Parallel Architectures for EBCOT 9.6.2. Memory Saving architecture for EBCOT 9.6.3, ComputationaUy Efficient EBCOT architecture by Skipping 9.7. Summary References 10. Beyond Part 1 of JPEG2000 Standard 10.1. Introduction 10.2. Part 2: Extensions 10.2.1. Variable DC Offset 10.2.2. Variable Scalsar Quantization Offsets 10.2.3. Trellis-Coded Quantization 10.2.4. Visual Masking 10.2.5. Arbitrary Wavelet Decomposition 10.2.6. Arbitrary Wavelet Transformation 10.2.7. Single Sample Overlap Descrete Wavelet Transformation 10.2.8. Multiple Component Transforms 10.2.9. Nonlinear Transformations 10.2.10. Region of Interest Extension 10.2.11. File Format Extension and Metadata Definitions 10,3. Part 3: Motion JPEG2000 10.4. Part 4: Conformance Testing 10.5. Part 5: Reference Software 10.6. Part 6: Compound hnage File Format 10.7. Other Parts (7w12) 10.8. Summary References Index About the Authors

Circuit Desiqn with VHDL Volnei A. Pedroni, MIT Press Cambridge, MA,~363 pages (2004) $40.00. Contents Preface I. Circuit Design 1. Introduction 1.1. About VDHL 1.2. Design Flow 1.3. EDA Tools 1.4. Translation of VHDL Code into a Ciruit 1.5. Design Examples 2. Code Structure 2.1. Fundamental VHDL Units 2.2. Library Declarations 2.3. Entity 2.4. Architecture 2.5. Introductory Examples 2.6. Problems 3. Data Types 3.1. Pre-Defined Data Types 3.2. User-Defined Data Types 3.3. Subtypes 3.4. Arrays 3.5. Port Array 3.6. Records 3.7. Signed and Unsigned Data Types 3.8. Data Conversion 3.9, Summary 3.10. Additional Examples 3.11. Problems 4. Operators and Attributes 4.1. Operators 4.2. Attributes 4.3. User-Defined Attributes 4.4. Operator Overload- ing 4.5. Generic 4.6. Examples 4.7. Summary 4.8. Problem 5. Concurrent Code 5.1. Concurrent versus Sequential 5.2. Using Operators 5.3. WHEN (Simple and Selected) 5.4. GENERATE 5.5. BLOCK 5.6. Problems BOOK REPORTS 1617

6. Sequential Code 6.1. PROCESS 6.2. Signals and Variables 6.3. If 6.4. Wait 6.5. Case 6.6. Loop 6.7. Case versus If 6.8. Case versus When 6.9. Bad Clocking 6.10. Using Sequential Code to Design combinational Circuits 6.11. Problems 7. Signals and Variables 7.1. Constant 7.2. Signal 7.3. Variable 7.4. Signal versus Variable 7.5. Number of Registers 7.6. Problems 8. State Machines 8.1. Introduction 8.2. Design Style ~1 8.3. Design style ~2 (stored output) 8.4. Encoding Style: From Binary to OneHot 8.5. Problems 9. Additional Circuit Designs 9.1. Barrel Shifter 9.2. Signed and Unsigned Comparators 9.3. Carry Ripple and Carry Look Ahead Adders 9.4. Fixed-Point Division 9.5. Vending-Machine Controllers 9.6. Serial Data Receiver 9.7. Parallel-to-Serial Convereter 9.8. Playing with a Seven-Segment Display 9.9. Signal Generators 9.10. Memory Design 9.11. Problems II. SYSTEM DESIGN 10. Packages and Components 10.1. Introduction 10.2. Package 10.3. Component 10.4. Port Map 10.5. Generic Map 10.6. Problems 11. Functions and Procedures 11.1. Function 11.2. Function Location 11.3. Procedure 11.4. Procedure Location 11.5. b-hlnctionversus Procedure Summary 11.6. Assert 11.7. Problems 12. Additional System Designs 12.1. Serial-Parallel Multiplier 12.2. Parallel Multiplier 12.3. Multiply-Accumulate Circuits 12.4. Digital Filters 12.5. Neural Networks 12.6. Problems Appendix A: Programmable Logic Devices Appendix B: Xilinx ISE + ModelSim Tutorial Appendix C: Altera MaxPlus II q- Adavanced Synthesis Software Tutorial Appendix D: Altera Quartus II Tutorial Appendix E: VHDL Reserved Words Bibliography Index

Discoverinq Knowledqe in Data, An Introduction to Data Mininq Daniel T. Larose, John Wiley and Sons Inc., Hoboken, NJ (2005) 222 pages. $69.95. Contents Preface 1. Introduction to Data Mining What is Data Mining? Why Data Mining7 Need for human Direction of Data Min- ing. Cross-Industry Standard Process:CRISP-DM. Case Study 1: Analyzing Automobile Waranty Claims:Example of the CRISP-DM Industry Standard Process in Action. Fallacies of Data Mining. What Tasks Can Data Mining Accomplish. Description. Estimation. Prediction. Classification. Clustering, Association. Case Study 2: Pre- dicting Abnormal Stock Market Returns Using Neutral Networks. Case Study 3: Mining Association Rules from Legal Databases. Case Study 4: Predicting Corporate Bankruptcies using Decision Trees. Case Study 5: Profiling the Tourism Market Using k Means Clustering Analysis. 1%eferences. Exercises. 2. Data Preprocesssing Why Do We need to Preprocess the Data? Data Cleaning. Handling Missing Data. Identifying Misclassifications Graphical Mehtods for Identifying Outliers. Data Transformation. Min-Max Nor- malization. Z-Score Standardization. Numerical Methods for Indentifying Outlier. References. Exercises. 3. Exploratory Data Analysis. Hypothesis Testing versus Exploratory Data Analysis. Getting to Know the Data Set. Dealing with Correlated Variables. Exploring Categorical Variables. Using EDA to Uncover Anomalous Fields. Exploring Numerical Variables, Exploring multivariate Relationships. Selecting interesting Subsets of the Data for Further Investigation. Binning. Summary. References. Exercises. 4. Statistical Approaches to Estimation and Prediction. Data Mining Tasks in Discovering Knoledge in Data. Statistical Approaches to Estimation and Prediciton. Univariate Methods:Measures of Center and Spread. Sta- tistical Inteference. How Confident are we in Our Estimates? Confidence Interval Estimation. Bivariate Methods: Simple Linear Regression. Dangers of Extrapolation. Confidence Intervals for the Mean Value of y Given x. Pre- diction Intervals for a Randomly Chosen Value of y Given x. Multiple Regression. Verifying Model Assumptions. References. Exercises. 5. k-Nearest Neighbor Algorithm. Supervised versus Unsupervised Methods. Methodoligy for Supervises Mod- eling. Bias-Variance Trade-Off. Classification Task, k-Nearest Neighbor Algorithm. Distance Function. Com- bination Function. Simple Unweighted Voting. Weighted Voting. Quantifying Attribute Relevance: Stretching the Axes. Database Considerations. k-Nearest Neighbor Algorithm for Estimation and Prediction. Choosing k. References. Exercises. 6. Decision Trees, Classification and Regression Trees. C4.5 Algorithm. Decision Rules. Comparison of the C5.0 and CART Algorithms Applied to Real Data. References. Exercises. 7. Neural Networks. Input and Output Encoding. Neural Networks for Estimation and Prediction. Simple Exam- ple of a Neural Network. Sigmoid Activation Function. Back-Propagation Rules. Example of Back-Propagation. Termination Criteria. Learning Rate. Momentum Term, Sensitivity Analysis. Application of Neural Network Modeling. References. Exercises. 8. Heirarchial and k-Means Clustering. Clustering Task. Hierarchical Clustering Methods. Single-Linkage Clus- tering. Complete-Linkage Clustering. k-Means Clustering. Example of k-Means Clustering at Work. Application of k-Means Clustering using SAS Enerprise Miner. Using Cluster Membership to predict Churn. References. Exercises. 1618 BOOK REPORTS

9. Kohonen Networks. Self-Organizing Maps. Kohonen Networks. Example of a Kohonen Network Study. Cluster Validity. Application of Clustering Using Kohonen Networks. Interpreting the Cluster. Cluster Profiles. Using Cluster Membership as Input to Downstream Data Mining Models. References. Exercises. 10. Association Rules. Affinity Analysis and Market Based AnMysis. Data Representation for Market Based Analysis. Support, Confidence, Frequent Itemsets, and the A Priori Property. How Does the A Priori Algorithm Work (Part 1)? Generating Frequent Itemsets. How Does the A Priori Algorithm Work (Part 2)? Generating Association Rules. Extension from Flag Data to General Categorical Data. Information~Theoretic Approach: Generalized Rule Induction Method. J-Measure. Application of Generalized Rule Induction. When Not To Use Association Rules. Do Association Rules Represent Supervised or Unsupervised Learning? Local Patterns versus Global Models. References. Exercises. 11. Model Evaluation Techniques. Model Evaluation Techniques for the Description Task. Model Evaluation Techniques for the Estimation and Prediction. Model Evaluation Techniques for the Classification Task. Error Rate, False Positive, and False Negatives. Misclassification cost Adjnstment Reflect Real-World Concerns. Deci- sion cost/Benefits Analysis. Lift Charts and Gains Charts. Interweaving Model Evaluation with Model Building. Confluence of Results: Applying a Suite of Models. References. Exercises. Epilogue: "We've Only Just Begun". Index.

An Introduction to Bioinformatics Alqorithms Nell C. Jones and Pavel A. Pevzner, MIT Press, Cambridge, MA, 435 pages (2004) $55.00. Contents Preface 1. Introduction 2. Algorithms and Complexity 2.1. What is an Algorithm? 2.2. Biological Algorithms versus Computer Algo- rithms 2.3. The Change Problem 2.4. Correct versus Incorrect Algorithms 2.5. Recursive Algorithms 2.6. Iterative versus Recursive Algorithms 2.7. Fast versus Slow Algorithms 2,8. Big-O Notation 2.9. Algorithm Design Tech- niques 2.9.1. Exhaustive Search 2.9.2. Branch-and-Bound Algorithms 2.9.3. Greedy Algorithms 2.9.4. Dynamic Programming 2.9.5. Divide-and-Conquer Algorithms 2.9.6. Machine Learning 2.9.7. Randomized Algorithms 2.10. Tractable versus Intractable Problems 2.11. Notes. Biobox: Richard Karp 2.12. Problems 3. Molecular Biology Primer 3.1. What is Life Made of? 3.2. What is the Genetic Material? 3.3. What Do Genes Do? 3.4. What Molecule Codes For Genes? 3.5. What Is the Structure of DNA? 3.6. What Carries Information between DNA and Proteins? 3.7. How are Proteins Made? 3.8. How Can We Analyze DNA? 3.8.1. Copying DNA 3.8.2. Cutting and Pasting DNA 3.8.3. Measuring DNA Length 3.8.4. Probing DNA 3.9. How Do Idividuals of a Species Differ? 3.10, How Do Different Species Differ? 3.11. Why Bioinformatics? Biobox:Russell Doolittle 4. Exhaustive Search 4.1. Restriction Mapping 4.2. Impractical Restriction Mapping Algorithms 4.3. A Practical Restriction Mapping Algorithms 4.4. Regulatory Motifs in DNA Sequences 4.5. Profiles 4.6. The Motif Finding Problem 4.7. Search Trees 4.8. Finding Motifs 4.9. Finding a Median String 4.10. Notes. Biobox: Gary Stormo 4.11. Problems 5. Greedy Algorithms 5.1. Geonome Rearrangements 5.2. Sorting by Reversals 5.3. Approximation Algorithms 5.4. Breakpoints: A Different Face of Greed 5.5. A Greedy Approach to Motif Finding 5.6. Notes Biobox: Davud Sankhoff 5.7. Problems 6. Dynamic Programming Algorithms 6.1. The Power of DNA Sequence Comparison 6.2. The Change Problem Revisited 6.3. The Manhattan Tourist Problem 6.4. Edit Distance and Alignments 6.5. Longest Common Subsequences 6.6. Global Sequence Alignment 6.7. Scoring Alignments 6.8. Local Sequence Alignment 6.9. Alignment with Gap Penalties 6.10. Multiple Alignment 6,11. Gene Prediction 6.12. Statistical Approaches to Gene Prediction 6.13. Similarity-Based Approaches to Gene Prediction 6.14. Spliced Alignment 6.15. Notes. Biobox: Michael Waterman 6.16. Problems 7. Divide-and-Conquer Algorithms 7.1. Divide-and-Conquer Approach to Sorting 7.2. Space-Efficient Sequence Alignment 7.3. Block Alignment and the Four-Russians Speedup 7.4. Constructing Alignments in Subquadratic Time 7.5. Notes. Biobox: Webb Miller 7.6, Problems 8. Graph Algorithms 8.1. Graphs 8.2. Graphs and Genetics 8.3. DNA Sequencing 8.4. Shortest Superstring Problem 8.5. DNA Arrays as an Alternative Sequencing Technique 8.6. Sequencing by Hybridization 8.7. SBH as a Hamiltonian Path Problem 8.8. SBH as an Eulerian Path Problem 8.9. Fragment Assembly in DNA Sequencing 8.10. Protein Sequencing and Identification 8.11. The Peptide Sequenceing Problem 8.12. Spectrum Graphs 8.13. Protein Indentification via Database Search 8.14. Spectral Convolution 8.15. Spectral Alignment 8.16. Notes 8.17. Problems 9. Combinatorial Pattern Matching 9.1. Repeat Finding 9.2. Hash Tables 9.3. Exact Pattern Matching 9.4. Keyword Trees 9.5. Suffix Trees 9.6. Heuristic Similarity Search Algorithms 9.7. Approximate Pattern Matching 9.8. BLAST'Comparing a Sequence against a Database 9.9. Notes Biobox: Gene Myers 9.10. Problems 10. Clustering and Trees 10.1. Cene Expression Analysis 10.2. hierarchical Clustering 10.3. k-Means Clustering 10.4. Clustering and Corrupted Cliques 10.5. Evolutionary Trees 10.6. Distance-Based Tree Reconstruction 10.7. Reconstructing Trees from Additive Matrices 10.8. Evolutionary Trees and Hierarchical Clustering 10.9. Character-Based Tree Reconstruction 10.10. Small Pasimony Problem 10.11. Large Pasimony Problem 10.12. Notes. Biobox: Ron Shamir 10.13. Problems BOOK REPORTS 1619

11. Hidden Markov Models 11.1. CG-Islands and the "Fair Bet Casino" 11.2. The Fair Bet Casino and Hidden Markov Models 11.3. Decoding Algorithm 11.4. HMM-Parameter Estimation 11.5. Profile HMM Alignment 11.6. Notes. Biobox: David Haussler 11.7. Problems 12. Randomized Algoritms 12.1. The Sorting Problem Revisited 12.2. Gibbs Sampling 12.3. Random Projections 12.4. Notes 12.5. Problems Using Bioinformatics Tools Bibliography Index

Infinitesimal Methods for Mathematical Analysis J. Sousa Pinto, Horwood Publishing, Chichester, West Sussex, 256 pages (2004) $64.00. Contents 1. Calculus and Infinitesimals 1.1. The Origins of the Calculus 1.1.1. Determination of tangents 1.1.2. The Calculation of plane areas 1.2. Infinitesimals in Historical Perspective 1.2.1. In Archimedes~ time 1.2.2. The 17th, 18th, and 19th centuries 1.2.3. The rigour of mathematical analysis 1.2.4. End of the 20th century: nonstandard analysis 2. "Standard" Infinitesimal Methods 2.1. Introduction 2.2. Rings of L numbers 2.2.1. t-Numbers of the first order 2.2.2. e-numbers of the higher order 2.2.3. L-numbers of infinite order 2.3. Fields of ~-numbers 2.3.1. The field of the superreal numbers 2.3.2. The fields of Levi-Civita 3. Introduction to Nonstandard Analysis 3.1. NSA:an Elementary Model 3.1.1. Preliminary aspects 3.1.2. The hyperreal numbers 3.2. The Elementary Leibniz Principle 3.2.1. Canonical extensions of sets and functions 3.2.2. The Leibniz Principle relative to IR 4. Applications to Elementary Real Analysis 4.1. Convergence 4.1.1. Sequences of real numbers 4.1.2. Series of real numbers 4.2. Topology and Continuity 4.2.1. The ususal topology of the real line 4.2.2. Continuous functions 4.3. Infinitesimal Calculus 4.3.1. Differentiation 4.3.2. Integration of continuous functions 5. Further Developments 5.1. Internal and External Sets and Functions 5.1.1. Internal sets 5.1.2. Internal functions 5.1.3. The Dirac delts "function" 5.1.4. Nonstandard representations 6. Foundations of Nonstandard Analysis 6.1. Standard and Nonstandard Models 6.1.1. Formal Languages and models 6.1.2. First order arithmetic 6.2. Proper Extensions of IR 6.3. The (second) Leibniz Principle 6.3.1. Superstructures 6.3.2. Internal and external entities 6.3.3. Complementary results 7. Hyperfinite Analysis 7.1. Introduction 7.1.1. SH-continuous functions 7.1.2. H-derivatives and II-integrals 7.2. The Loeb Counting Measure 7.2.1. The Loeb construction 7.2.2. Hyperfinite representation of Lebesgue measure 7.3. Integration 7.3.1. Generalities 7.3.2. Integration and H-integration 8. Hyperfinite Representation of Distributions 8.1. Sketch of the Theory of Distributions 8.1.1. Test fucntion spaces 8.1.2. Duality and Schwartz distributions 8.1.3. Axiomatic definition of finite order distributions 8.2. *Finite Representation of Distributions 8.2.1. Introduction 8.2.2. The module Doo (over *¢2b) 8.2.3. The module Dri (over *Cb) 9. Hyperfinite Fourier Analysis 9.1. Standard Fourier Transformation 9.1.1. Tempered Distributions 9.1.2. Fourier Transforms in S t 9.2. The H-Fourier Transforms 9.2.1. Preliminary definations 9.2.2. Hyperfinite representation of tempered distributions 9.2.3. The H-Fourier Transforms on Tn 9.3. Study of H-Band-limited Functions 9.3.1. Preliminary definition 9.3.2. H-periodic functions 9.3.3. The H-cardinal series Appendices A. Evolution of the concept of function B. The Theorem of Los

I.n..troduction to Numerical Ordinary and Partial Dif[erential Equations usinq MATLAB Alexander Stanoyevitch, Wiley-Interscience Publication, (2005) 813 pages, $110.00. Contents Preface Part 1: Introduction to MATLAB and Numerical Preliminaries Chapter 1: MATLAB Basics Section 1.1. What is MATLAB? Section 1.2. Starting and Ending a MATLAB Sessions Section 1.3. A First MATLAB Tutorial Section 1.4. Vectors and an Introduction to MATLAB Graphics Section 1.5. A Tutorial Introduction to Recursion on MATLAB Chapter 2: Basic Concepts of Numerical Analysis with Taylor's Theorem Section 2.1. What is Numerical Analysis? Section 2.2. Taylor Polynomials Section 2.3. Taylor's Theorem Chapter 3: Introduction to M-Files Section 3.1. What are M-Files? Section 3.2. Creating an M-file for a Mathematical Function Chapter 4: Programming in MATLAB Section 4.1. Some Basic Logic Section 4.2. Logical Control Flow in MATLAB Section 4.3. Writing Good Programs Chapter 5: Floating Point Arithmetic and Error Analysis Section 5.1. Floating Point Numbers Section 5.2. Floating Point Arithmetic: The Basics *Section 5.3. Floating Point Arithmetic: Further Examples and Details Chapter 6: Rootfinding Section 6.1. A Brief Account of the History of Rootfinding Section 6.2. The Bisection Method Section 6.3. Newton's Methods *Section 6.4. The Secant Method *Section 6.5. Error Analysis and Comparison of Rootfinding Methods 1620 BOOK REPORTS

Chapter 7: Matricess and Linear Systems Section 7.1. Matrix Operations and Manipulations with MATLAB *Section 7.2. Introduction to Computer Graphics and Animation Section 7.3. Notations and Concepts of Linear Systems Section 7.4. Solving General Linear Systems with MATLAB Section 7.5. Gaussuan Elimination, Pivoting, and LU Factorization *Section 7.6. Vector and Matrix Norms, Error Analysis, and Eigendata Section 7.7. Iterative Methods Part 2: Ordinary Differential Equations Chapter 8: Introduction to Differential Equations Section 8.1. What Are Differential Equations? Section 8.2. Some Basic Differential Equation Models and Euler's Method Section 8.3. More Accurate Methods for Initial Value Problems *Section 8.4. Theory and Error Analysis for Initial Value Problems *Section 8.5. Adaptive, Multistep, and Other Nuemrical Methods for Initial Value Problems Chapter 9: System of First-Order Differential Equations and Higher-Order Differential Equations Section 9.1. Notation and Relations Section 9.2. Two-Dimensional First-Order Systems Section 9.3. Phase-Plane Analysis for Autonomous First-Order Systems Section 9.4. General First-Order Systems and Higher-Order Differential Equations Chapter 10: Boundary Value Problems for Ordinary Differential Equations Section 10.1. What Are Boundary Value Problems and How Can They Be Numerically Solved? Section 10.2. The Linear Shooting Method Section 10.3. The Nonlinear Shooting Method Section 10.4. The Finite Difference Method for Linear BVPs *Section 10.5. Rayleigh-Ritz Methods Part 3: Partial Differential Equations Chapter 11: Introduction to Partial Differential Equations Section 11.1. Three-Dimensional Graphics with MATLAB Section 11.2. Examples and Concepts of Partial Differential Equations Section 11.3. Finite Diffrence Methods for Elliptic Equations Section 11.4. General Boundary Conditions for Elliptic problems and Block Matrix Formulations Chapter 12: Hyperbolic and Parabolic Partial Differential Equations Section 12.1. Examples and Concepts of Hyperbolic PDEs Section 12.2. Finite Difference Methods for Hyperbolic PDEs Section 12.3. Finite Difference Methods for Parabolic PDEs Chapter 13: The Finite Element Method Section 13.1. A Nontechnical Overview of the Finite Element Methods Section 13.2. Two-Dimensional Mesh Generation and Basis Functions Section 13.3. The Finite Element Method for Elliptic PDEs Appendix A. Introduction to MATLAB'S Symbolic Toolbox Appendix B. Solutions to All Exercises for the Reader References MATLAB Command Index General Index

Control and Optimal Control Theories with Applications David Burghes and Alexander Graham, Horwood Pub- lishing Limited, Chichester, West Sussex (2004) 400 pages, $46.00. Table of Contents Preface Part 1-Control Chapter 1. System Dynamics and Differential Equations 1.1. Introduction 1.2. Some System Equations 1.3. System Control 1.4. Mathematical Models and Differential Equations 1.5. The Classical and Modern Control Theory Chapter 2. Transfer Functions and Block Diagrams 2.1. Introduction 2.2. State-Space Forms 2.3. Applications to Differential Equations 2.4. Transfer Functions 2.5. Block Diagrams Chapter 3. State-Space Formulation 3.1. Introduction 3.2. State-Space Forms 3.3. Using the Transfer Function to Define State Variables 3.4. Direct Solutions of the State Equation 3.5. Solution of the State Equation by Laplace Transforms 3.6. The Transformation from the Companion to the Diagonal State Form 3.7. The Transfer Function from the State Equation Chapter 4. Transient and Steady State Response Analysis 4.1. Introduction 4.2. Response of First Order Systems 4.3. Response of Second Order Systems 4.4. Response of Higher Order Systems 4.5. Steady State Error 4.6. Feedback Control Chapter 5. Stability 5.1. Introduction 5.2. The concept of Stability 5.3. Routh Stability Criterion 5.4. In- troduction to Liapunov's Method 5.5. Quadratic Forms 5.6. Determination of Liapunov's 5.7. The Nyquist Stability Criterion 5.8. The Frequency Response 5.9. An Introduction to Conformal Mappings 5.10. Application of Conformal Mapping to the Frequency Response Chapter 6. Contollability and Observability 6.1. Introduction 6.2. Controllability 6.3. Observability 6.4. Decom- position of the System State 6.5. A Transformation into the Companion Form Chapter 7. Multivariable Feedback and Pole Location 7.1. Introduction 7.2. State Feedback of a SISO System 7.3. Multivariable Systems 7.4. Observers Part ll-Optimal Control Chapter 8. Introduction to Optimal Control 8.1. Control and Optimal Control 8.2. Examples 8.2.1. Economic Growth 8.2.2. Resource Depletion 8.2.3. Exploited Populations 8.2.4. Advertising Policies 8.2.5. Rocket Trajec- tories 8.2.6. Servo Problems 8.3. Funcitonals 8.4. The Basic Optimal Control Problem Chpater 9. Variational Calculus 9.1. The Brachistochrone Problem 9.2. Euler Equation 9.3. Free End Conditions 9.4. Constraints BOOK REPORTS 1621

Chapter 10. Optimal Control with Unbounded Continuous Controls 10.1. Introduction 10.2. The Hamiltonian 10.3. Extension to Higher Order Systems 10.4. Ceneral Problem Chapter 11. Bang-Bang Control 11.1. Introduction 11.2. Pontryagin's Principle 11.3. Switching Curves 11.4. Transversality Conditions 11.5. Extension to the Boltza Problem Chapter 12. Applicatons of Optimal Control 12.1. Introduction 12.2. Economic Growth 12.3. Resource Depletion 12.4. Exploited Populations 12.5. Advertising Policies 12.6. Rocket Trajectories 12.7. Servo Problem Chapter 13. Dynamic Programming 13.1. Introduction 13.2. Routing Problems 13.3, D.P. Notation 13.4. Examples 13.4.1. Resources Allocation 13.4.2. Production Planning 13.5. Bellman's Equation 13.6. The Maximum principle Appendix 1. Partial Fractions Appendix 2. Notes on Determinants and Matrices A2.1. Determinants A2.2. Partitioned Matrices A2.3. Eigen- vectors and Eigenvalues A2.4. The Companion Matrix A2.5. The Cayley-Hamilten Theorem A2.6. Linear Dependence and the Rank of a Matrix Solutions to Problems Bibliography Index

Orqanizational Principle for Multi-Aqent Architectures Chris van Aart Birkauser Verlag, Basel (2000) 203 pages, $36.38. Contents 1. Introduction 1,1, Backround 1.2. Research Questions 1.3. Approach 1.4. Outline 2. Agent Organization Framework 2.1. Introduction 2.2. Building Blocks of Agent Organizational models 2.2.1. Concepts 2.2.2. Organizational Relations 2.2.3. Coordination Mechanisms 2.3. Organizational Structures 2.3.1. Machine Bureaucracy 2.3.2. Professional Bureaucracy 2.3.3. Adhocracy 2.4. Agent Organizational Design Activ- ities 2.4.1. Task Analysis 2.4.2. Operator Collaboration Design 2.4.3. Organizational Design 2.5. Agent-Based Supply Chain Managment 2.5.1. Task Analysis 2.5.2. Operator Collaboration Design 2.5.3. Organizational Design 2.5.4. Implementation 2.5.5. Results 2.6. Discussion 3. Coordination Strategies for Multi-Agent Systems 3.1. Introduction 3.2. Coordination as problem-Solving 3.2.1. Coordination Task 3.2.2. Task-Method Ontology 3.3. Coordination Strategy Methods 3.3.1. Coordination by Direct Supervision 3.3.2. Coordination by Standardization of Work 3.3.3. Mutual Adustment 3.4. Implication for External Agent Design 3.4.1. Operator Agent Behavior 3.4.2. Manager Agent Behavior 3.5. Mini experiments 3.5.1. Direct Supervision 3.5.2. Standardization of Work 3.5.3. Mutual Adjustment 3.5.4. Evaluation 3.6. Discussion 4. Five Capabilities Model 4.1. Introduction 4.2. The Five Dimensions 4.2.1. Competence Model 4.2.2. Com- munication Model 4.2.3. Self Model 4.2.4. Planner Model 4.2.5. Environment Model 4.3. The 5C Architecture 4.4. International insurance Traffic 4.4.1. Approach 4.4.2. Green Card Traffic 4.4.3. Agent Collaboration 4.4.4. Interface To The Back-Office System 4.4.5. The Kir System 4.4.6. Operationalization 4.4.7. Extension 4.4.8. Evaluation 4.5. Discussion 5. Interoperation within a Complex Multi-Agent Architecture 5.1. Introduction 5.2. IBROW approach 5.3. Agent Architecture 5.3.1. User Space 5.3.2. Broker Space 5.3.3. Execution Space 5.4. Levels of Interoperability 5.4.1. Technical Interoperability 5.4.2. Syntactic Interoperability 5.4.3. Semantic Interoperability 5.4.4. Coordination Interoperability 5.5. Implementation 5.5.1. Technology Set 5.5,2. Agent Implementation 5.5.3. Agent Log 5.5.4. Inspection Tools 5.6. Classification of Conference Submissions 5.6.1. Brokering 5.6.2. Execution 5.7. Discussion 6. Message Content Ontologies 6.1. Introduction 6.2. Ontologies in a Nutshell 6.3. Message Content Ontology Framework 6.3.1. Agent communication Meta Ontology 6.3.2. Reference Model 6.3.3. Message Content Ontology 6.3.4. Message Content Ontology Creation 6.3.5. Message Content Ontology Application 6.3.6. Agent Design 6.4. Operationalization of Ontology based Communication 6.4.1. Message Content Ontology Implementation 6.4.2. Message Content Ontology Application 6.4.3. Application of Bean Generator 6.5. Legal Advisor 6.5.1. Architecture 6.5.2. Message Content Ontology Design 6.5.3. Simple Scenario 6.5.4. Evaluation 6.6. Discussion 7. Conclusions 7.1. Application of Organizational Decomposition Principles and Coord- ination in Multi-Agent Systems 7.2. Coordination Mechanisms for Multi-Agent Systems 7.3. Agent Design Principles 7.4. Discussion and Future Research Summary Bibliography

Geometry. and Meaninq Dominic Widdows. CSLI Publications, Stanford, CA. (2004) 319 pages. $25.00. Contents Foreword Introudction 1. Geometry~ Numbers and Sets 2. The Graph Model: Networks of Concepts 3. The Vertical Direction:Concept Hierarchies 4. Measuring Similarity and Distance 5. Word-Vectors and Search Engines 6. Exploring Vector Spaces in One and More Languages 1622 BOOK REPORTS

7. Logic with Vectors: Ambiguous Words and Quantam States 8. Concept Lattices: Binding Everything Loosely Together Conclusions and Curtain Call References Index

Data Mininq, Next Generation Challenges and Future Directions, Hillol Kargupta, Anupam Joshi, Krishnamoor- thy Sivakumar & Yelena Yesha. AAAi Press/The MIT Press, Menlo Park, CA (2004) 558 pages, $40.00. Contents Foreword Preface Pervasive, Distributed, and Stream Data Mining 1. Existential Pleasures of Distributed Data Mining, Hillol Kargupta and Krishamoorthy Sivakumar 2. Research Issues in Mining and Monitoring of Intelligence Data, Alan Demers, Jahannes Gehrke, and Mirek Riedewald 3. A Consensus Framework for integrating Distributed Clusterings Under Limited Knowledge Sharing, Joydeep Ghosh, Alexander Strehl, and Srujana Merugu 4. Design of Distributed Data Mining Applications on the Knowledge Grid, Mario Cannataro, Domenico Talia, and Paolo Trunfio 5. Photonic Data Services:Integrating Data, Network and Path Services to Support Next Generation Data Mining Applications, Robert L. Grossman, Yunhong Gu, Dave Hanley, Xinwei Hong, Jorge Leveera, Marco Mazzucco, David Lillethun, Joe Mambretti, and Jeremy Weinberger 6. Mining Frequent Patterns in Data Streams at Multiple Time Granularities, Chris Giannella, Jiawei Han, Jian Pei, Xifeng Yan, and Phillip S. Yu 7. Efficient Data-Reduction Methods for On-Line association Rules Discovery, Herve Bronnomann, Bin Chen, Manoranjan Dash, Peter Haas, and Peter Scheuermann 8. Discovering Recurrent Events in Multichannel Data Streams Using Unsupervised Methods, Milind R. Naphade, Chung-Sheng Li, and Thomas S. Huang Counterterrorism, Privacy, and Data Mining 9. Data Mining for Counterterrorism, Bhavani Thuraisingham 10. Biosurveillance and Outbreak Detection, Paola Sebastiani and Kenneth D. Mandl 11. MINDS-Minnesota Intrusion Detection System, Levent Ertoz, Eric Eilertson, Aleksandar Lazarevic, Paug-Ning Tan, Vipin Kumar, Jaideep Srivastava, and Paul Dokas 12. Marshalling Evidence Through data Mining in Support of Counter Terrorism, Daniel Barbard, James J. Nolan, David Schum, and Arun Sood 13. Relational Data Mining with Indective Logic Programming for Link Discovery, Raymond J. Mooney, Prem Melville, Lappoon Rupert Tang, Jude Shavlik, ines de Castro Dutra, David Page, and Vitor Santos Costa 14. Defining Privacy for Data Mining, Chris Clifton, Murat Kantarcioglu, and Jaideep Vaidya Scientific Data Mining 15. Mining Temporally-Varying Phenomena in Scientific Datasets, Raghu Machiraju, Srinicasan Parthasarathy, John Wilkins, David S. Thompson, Boyd Gatlin, David Richie, Tat-Sang S. Choy, Ming Jiang, Sameep Mehta, Matthew Coatney, Stephen A. Barr, and Kaden Hazzard 16. Methods for Mining Protein Contact Maps, Mohammed J. Zaki, Jingjing Hu, and Chris Bystroff 17. Mining Scientific Data Sets using Graphs, Michihiro kuramochi, Mukund Deshpande, and George Karypis 18. Challenges in Environmental Data Warehousing and Mining, Nabil R. Adam, Vijayalakshmi Atluri, Dihua Guo, and Songmei Yu 19. Trends in Spatial Data Mining, Shashi Shekhar, Pusheng Xhang, Yan Huang, and Ranga Raju Vatsavai 20. Challenges in Scientific Data Mining:Heterogeneous, Biased, and Large Samples, Zoran Obradovic and Slobo- dan Vucetic Web, Semantics.and Data Mining 21. Web Mining-Concepts, Applications, and Research Directions, Jaideep srivastava, Prasanna Desikan, and Vipin Kumar 22. Advancements in Text Mining Algorithms and Software, Svetlana Y. Mironova, Michael W. Berry, Scott Atchley, and Micah Beck 23. On Data Mining, Semantics, and intrusion Detection:What to Dig for and Where to Find it, Anupam Joshi and Jeffery L. Undercoffer 24. Usage Mining for on and on the Semantic Web, Bettina Berendt, Gerd Stumme, and Andreas Hotho Bibliography Index