Series: Lecture Notes in Mathematics , Vol. 1968
2009, Approx. 380 p., Softcover
ISBN: 978-3-540-89305-9
Due: January 26, 2009
The geometry of modular curves and the structure of their cohomology groups have been a rich source for various number-theoretical applications over the last decades. Similar applications may be expected from the arithmetic of higher dimensional modular varieties. For Siegel modular threefolds some basic results on their cohomology groups are derived in this book from considering topological trace formulas.
1 An Application of the Hard Lefschetz Theorem.- 2 CAP-Localization.- 3 The Ramanujan Conjecture for Genus two Siegel modular Forms.- 4 Character Identities and Galois Representations related to the group GSp(4).- 5 Endoscopy for GSp(4).- 6 A special Case of the Fundamental Lemma I.- 7 A special Case of the Fundamental Lemma II.- 8 The Langlands-Shelstad transfer factor.- 9 Fundamental lemma (twisted case).- 10 Reduction to unit elements.- 11 Appendix on Galois cohomology.- 12 Appendix on double cosets
Series: Springer Monographs in Mathematics
2009, Approx. 690 p., Hardcover
ISBN: 978-0-387-09780-0
Due: February 2009
Discoveries in finite semigroups have influenced several mathematical fields, including theoretical computer science, tropical algebra via matrix theory with coefficients in semirings, and other areas of modern algebra. This comprehensive, encyclopedic text will provide the reader - from the graduate student to the researcher/practitioner ? with a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research.
-Preface.- List of Tables.-List of Figures.-Introduction.-Part I. The q-operator and Pseudovarieties of Relational Morphisms.-1. Foundations for Finite Semigroup Theory.-2. The q-operator - 3.The Equational Theory -Part II. Complexity in Finite Semigroup Theory. -4. The Complexity of Finite Semigroups. -5. Two-Sided Complexity and the Complexity of Operators.-Part III. The Algebraic Lattice of Semigroup Pseudovarieties.-6. Algebraic Lattices, Continuous Lattices and Closure Operators.-7. The Abstract Spectral Theory of PV.-Part IV. Quantales, Indempotent Semirings, Matrix Algebras and the Triangular Product-8. Quantales.-9. The Triangular Product and Decomposition Results for Semirings.-A. The Green-Rees Local Structure Theory.-B. Tables on Preservation of Sups and Infs.- List of Problems.- References.- Table of Pseudovarieties.-Table of Operators and Products.-Index of Notation.-Author Index.-Index.
Series: Applied Mathematical Sciences , Vol. 90
2009, Approx. 415 p. 67 illus., Hardcover
ISBN: 978-0-387-09723-7
Due: February 2009
This text grew out of graduate level courses in mathematics, engineering and physics given at several universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. Topics covered include a detailed discussion of linear Hamiltonian systems, an introduction to variational calculus and the Maslov index, the basics of the symplectic group, an introduction to reduction, applications of Poincare's continuation to periodic solutions, the use of normal forms, applications of fixed point theorems and KAM theory. There is a special chapter devoted to finding symmetric periodic solutions by calculus of variations methods.
The main examples treated in this text are the N-body problem and various specialized problems like the restricted three-body problem. The theory of the N-body problem is used to illustrate the general theory. Some of the topics covered are the classical integrals and reduction, central configurations, the existence of periodic solutions by continuation and variational methods, stability and instability of the Lagrange triangular point.
Hamiltonian Differential Equations and the N-Body Problem.- Exterior Algebra and Differential Forms.- Symplectic transformations and coordinates.- Introduction to the Geometric Theory of Hamiltonian Dynamical Systems.- Continuation of Periodic Solutions.- Perturbation Theory and Normal Forms.- Bifurcations of Periodic Orbits.- Stability and KAM Theory.- Twist Maps and Invariant Curves.
Series: Undergraduate Topics in Computer Science
2009, Approx. 170 p. 91 illus., Softcover
ISBN: 978-1-84882-031-9
Due: March 2009
The development of programming languages has profoundly impacted our relationship with language, complexity and machines. By introducing the principles of programming languages, using the Java language as a support, Gilles Dowek provides the necessary fundamentals of this language as a first objective.
It is important to realise that knowledge of a single programming language is not really enough. To be a good programmer, you should be familiar with several languages and be able to learn new ones. In order to do this, youfll need to understand universal concepts, such as functions or cells, which exist in one form or another in all programming languages. The most effective way to understand these universal concepts is to compare two or more languages. In this book, the author has chosen Caml and C.
To understand the principles of programming languages, it is also important to learn how to precisely define the meaning of a program, and tools for doing so are discussed. Finally, there is coverage of basic algorithms for lists and trees.
Intended for students with some small experience of computer programming, learned empirically in a single programming language other than Java, students in both computer science and engineering will find this book a very welcome introduction to the principles of programming languages.
Imperative Core.- Functions.- Recursion.- Records.- Dynamic Data Types.- Programming with Lists.- Exceptions.- Objects.- Programming with Trees.- Index.
Series: Operator Theory: Advances and Applications , Preliminary entry 510
Set: Modern Analysis and Applications
2009, Approx. 500 p., Hardcover
ISBN: 978-3-7643-9918-4
Due: April 2009
This is the first of two volumes containing peer-reviewed research and survey papers based on invited talks at the International Conference on Modern Analysis and Applications. The conference, which was dedicated to the 100th anniversary of the birth of Mark Krein, one of the greatest mathematicians of the 20th century, was held in Odessa, Ukraine, on April 9-14, 2007. The papers describe the contemporary development of subjects influenced by Krein, such as the theory of operators in Hilbert and Krein spaces, differential operators, applications of functional analysis in function theory, theory of networks and systems, mathematical physics and mechanics.