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Book
1 online resource (xii, 162 pages 5 illustrations).
  • 1 Generalities.- 1.1 Basic definitions, examples.- 1.2 Structure constants.- 1.3 Relations with Lie groups.- 1.4 Elementary algebraic concepts.- 1.5 Representations-- the Killing form.- 1.6 Solvable and nilpotent.- 1.7 Engel's theorem.- 1.8 Lie's theorem.- 1.9 Cartan's first criterion.- 1.10 Cartan's second criterion.- 1.11 Representations of A1.- 1.12 Complete reduction for A1.- 2 Structure Theory.- 2.1 Cartan subalgebra.- 2.2 Roots.- 2.3 Roots for semisimple g.- 2.4 Strings.- 2.5 Cartan integers.- 2.6 Root systems, Weyl group.- 2.7 Root systems of rank two.- 2.8 Weyl-Chevalley normal form, first stage.- 2.9 Weyl-Chevalley normal form.- 2.10 Compact form.- 2.11 Properties of root systems.- 2.12 Fundamental systems.- 2.13 Classification of fundamental systems.- 2.14 The simple Lie algebras.- 2.15 Automorphisms.- 3 Representations.- 3.1 The Cartan-Stiefel diagram.- 3.2 Weights and weight vectors.- 3.3 Uniqueness and existence.- 3.4 Complete reduction.- 3.5 Cartan semigroup-- representation ring.- 3.6 The simple Lie algebras.- 3.7 The Weyl character formula.- 3.8 Some consequences of the character formula.- 3.9 Examples.- 3.10 The character ring.- 3.11 Orthogonal and symplectic representations.- References.- Symbol Index.
  • (source: Nielsen Book Data)9780387972640 20160614
(Cartan sub Lie algebra, roots, Weyl group, Dynkin diagram, ...) and the classification, as found by Killing and Cartan (the list of all semisimple Lie algebras consists of (1) the special- linear ones, i. e. all matrices (of any fixed dimension) with trace 0, (2) the orthogonal ones, i. e. all skewsymmetric ma- trices (of any fixed dimension), (3) the symplectic ones, i. e. all matrices M (of any fixed even dimension) that satisfy M J = - J MT with a certain non-degenerate skewsymmetric matrix J, and (4) five special Lie algebras G2, F , E , E , E , of dimensions 14,52,78,133,248, the "exceptional Lie 4 6 7 s algebras" , that just somehow appear in the process). There is also a discus- sion of the compact form and other real forms of a (complex) semisimple Lie algebra, and a section on automorphisms. The third chapter brings the theory of the finite dimensional representations of a semisimple Lie alge- bra, with the highest or extreme weight as central notion. The proof for the existence of representations is an ad hoc version of the present standard proof, but avoids explicit use of the Poincare-Birkhoff-Witt theorem. Complete reducibility is proved, as usual, with J. H. C. Whitehead's proof (the first proof, by H. Weyl, was analytical-topological and used the exis- tence of a compact form of the group in question). Then come H.
(source: Nielsen Book Data)9780387972640 20160614
Book
xii, 162 p. : ill. ; 24 cm.
SAL3 (off-campus storage)
Book
p. [29]-31 ; 26 cm.
SAL1&2 (on-campus shelving)
Book
139 l.
SAL3 (off-campus storage)
Book
125 p. diagrs. 29 cm.
SAL3 (off-campus storage)
Book
xi, 265 p. illus. 24 cm.
SAL3 (off-campus storage), Science Library (Li and Ma)
Book
vi, 165 p. illus. 21 cm.
SAL3 (off-campus storage)
Book
26 l. 27-79 p. 29 cm.
SAL3 (off-campus storage)
Book
1 online resource.
  • 1. Introduction
  • 2. Principles of Algol translation
  • 2.1. Basic linguistic definitions
  • 2.2. The Backus normal form
  • 2.3. The analyzing process
  • 2.4. The method of the 'Klammergebirge'
  • 2.5. Recursive sequential methods and push down lists
  • 2.6. Example for the use of two push down lists and of precedence rules
  • 2.7. The concept of recursive translation
  • 2.8. Organization of the translator
  • 3. Languages involved in the translation process
  • 3.1. Source language
  • 3.2. Target language
  • 3.3. Meta-language for describing the translator
  • 4. Correspondence between elements of source and target language
  • 4.1. Declarations in general
  • 4.2. Declaration of variables and arrays and data storage allocation in the main program
  • 4.3. Handling of types
  • 4.4. Assignment statements
  • 4.5. Boolean expressions
  • 4.6. Conditional statements and expressions
  • 4.7. For statements
  • 4.8. Go to statement and switch declaration
  • 4.9. Procedures and dynamic storage
  • 4.10. Procedure calls and declarations
  • 5. Recursive address calculation
  • 5.1. Introduction
  • 5.2. Assumptions necessary for the use of recursive address calculation
  • 5.3. Use of recursive address calculation for one loop
  • 5.4. Nested loops
  • 5.5. Loops with more than one list element
  • 5.6. Further optimization possibilities
  • 6. Run time organization
  • 6.1. The instruction storage allocation
  • 6.2. The instruction procedure call
  • 6.3. The instruction formal procedure call
  • 6.4. The instruction normal procedure exit
  • 6.5. The instruction jump to
  • 6.6. The instruction formal procedure exit
  • 6.7. The instructions name address and name call
  • 6.8. The instruction name procedure exit
  • 7. Model translator. Description
  • 7.1. Introduction
  • 7.2. Pass 1. The preparatory pass
  • 7.3. Pass 2. The implementation of recursive address calculation
  • 7.4. Pass 3. Decomposition and production of target program
  • 7.5. Editorial functions
  • 7.6. Run time system. The target language program interpreter
  • 8. Algol 60 model translator. Formal part
  • Pass 1: preparatory pass
  • Pass 2: recursive address calculation pass
  • Pass 3: decomposition and generation pass
  • Check routine: check procedure calls and substitutions of formal parameters by actuals
  • Check routine: check agreeability of actual parameter and specification
  • Run time system: target language program interpreter
  • START TRANSLATION
  • Appendix: Correspondence matrix for actual and formal parameters.
Problem oriented programming languages as they have developed over the last ten years essentially serve two purposes which somewhat crudely can be described by the terms man-man communication and man-machine communication, respectively. As a carrier of information between humans, the problem oriented programming language is designed to express the essence of an algorithm in a way which is un ambiguous and concise as well as independent of (and therefore meaning ful without any reference to) the changing details of computing machine ry. As a carrier of information from man to computer, the language permits the human programmer to express his computational needs in a compact way adapted to the general characteristics of computers, but freed from the burdening details of specific computer facilities. This presupposes the existence of algorithms, or programs, which permit the computer itself to transform efficiently programs written in the problem oriented language into machine programs. Thus the entire computing community profits from the work of the individual programmer. The primary purpose of the Handbook is to present a set of algorithms of broad utility from the domain of numerical mathematics written in the problem oriented language ALGOL 60. Therefore, volumes I a and I b are in a sense supplementary as they serve to introduce this language. Volume I a gives a description of the language proper and of its use for writing correct programs. Thus, volume I a primarily covers the aspect of man-man communication by means of ALGOL 60.
Book
1 online resource (vii, 200 p).
  • A report on the unitary group / Raoul Bott
  • <a href="http://www.ams.org/pspum/003">http://www.ams.org/pspum/003</a> <a href="https://doi.org/10.1090/pspum/003/0132553">https://doi.org/10.1090/pspum/003/0132553</a> Vector bundles and homogeneous spaces / M. F. Atiyah and F. Hirzebruch
  • <a href="http://www.ams.org/pspum/003">http://www.ams.org/pspum/003</a> <a href="https://doi.org/10.1090/pspum/003/0139181">https://doi.org/10.1090/pspum/003/0139181</a> A procedure for killing homotopy groups of differentiable manifolds. / John Milnor
  • <a href="http://www.ams.org/pspum/003">http://www.ams.org/pspum/003</a> <a href="https://doi.org/10.1090/pspum/003/0130696">https://doi.org/10.1090/pspum/003/0130696</a> Some remarks on homological analysis and structures / D. C. Spencer
  • <a href="http://www.ams.org/pspum/003">http://www.ams.org/pspum/003</a> <a href="https://doi.org/10.1090/pspum/003/0126289">https://doi.org/10.1090/pspum/003/0126289</a> Vector form methods and deformations of complex structures / Albert Nijenhuis
  • <a href="http://www.ams.org/pspum/003">http://www.ams.org/pspum/003</a> <a href="https://doi.org/10.1090/pspum/003/0126859">https://doi.org/10.1090/pspum/003/0126859</a> Almost-product structures / A. G. Walker
  • <a href="http://www.ams.org/pspum/003">http://www.ams.org/pspum/003</a> <a href="https://doi.org/10.1090/pspum/003/0123993">https://doi.org/10.1090/pspum/003/0123993</a> Homology of principal bundles / Eldon Dyer and R. K. Lashof
  • <a href="http://www.ams.org/pspum/003">http://www.ams.org/pspum/003</a> <a href="https://doi.org/10.1090/pspum/003/0124045">https://doi.org/10.1090/pspum/003/0124045</a> Alexander-Pontrjagin duality in function spaces / James Eells, Jr.
  • <a href="http://www.ams.org/pspum/003">http://www.ams.org/pspum/003</a> <a href="https://doi.org/10.1090/pspum/003/0125580">https://doi.org/10.1090/pspum/003/0125580</a> The cohomology of Lie rings / Richard S. Palais
  • <a href="http://www.ams.org/pspum/003">http://www.ams.org/pspum/003</a> <a href="https://doi.org/10.1090/pspum/003/0125867">https://doi.org/10.1090/pspum/003/0125867</a> On the theory of solvmanifolds and generalization with applications to differential geometry / Louis Auslander
  • <a href="http://www.ams.org/pspum/003">http://www.ams.org/pspum/003</a> <a href="https://doi.org/10.1090/pspum/003/0125178">https://doi.org/10.1090/pspum/003/0125178</a> Homogeneous complex contact manifolds / William M. Boothby
  • <a href="http://www.ams.org/pspum/003">http://www.ams.org/pspum/003</a> <a href="https://doi.org/10.1090/pspum/003/0124863">https://doi.org/10.1090/pspum/003/0124863</a> On compact, Riemannian manifolds with constant curvature. I / Eugenio Calabi
  • <a href="http://www.ams.org/pspum/003">http://www.ams.org/pspum/003</a> <a href="https://doi.org/10.1090/pspum/003/0133787">https://doi.org/10.1090/pspum/003/0133787</a> Elementary remarks on surfaces with curvature of fixed sign / L. Nirenberg
  • <a href="http://www.ams.org/pspum/003">http://www.ams.org/pspum/003</a> <a href="https://doi.org/10.1090/pspum/003/0125542">https://doi.org/10.1090/pspum/003/0125542</a> Canonical forms on frame bundles of higher order contact / Shoshichi Kobayashi
  • <a href="http://www.ams.org/pspum/003">http://www.ams.org/pspum/003</a> <a href="https://doi.org/10.1090/pspum/003/0126810">https://doi.org/10.1090/pspum/003/0126810</a> On immersion of manifolds / Hans Samelson
  • <a href="http://www.ams.org/pspum/003">http://www.ams.org/pspum/003</a> <a href="https://doi.org/10.1090/pspum/003/0126242">https://doi.org/10.1090/pspum/003/0126242</a>
Book
xii, 323 p. : ill ; 24 cm.
  • Preface-- 1. What is nonlinear Perron-Frobenius theory?-- 2. Non-expansiveness and nonlinear Perron-Frobenius theory-- 3. Dynamics of non-expansive maps-- 4. Sup-norm non-expansive maps-- 5. Eigenvectors and eigenvalues of nonlinear cone maps-- 6. Eigenvectors in the interior of the cone-- 7. Applications to matrix scaling problems-- 8. Dynamics of subhomogeneous maps-- 9. Dynamics of integral-preserving maps-- Appendix A. The Birkhoff-Hopf theorem-- Appendix B. Classical Perron-Frobenius theory-- Notes and comments-- References-- List of symbols-- Index.
  • (source: Nielsen Book Data)9780521898812 20160609
In the past several decades the classical Perron-Frobenius theory for nonnegative matrices has been extended to obtain remarkably precise and beautiful results for classes of nonlinear maps. This nonlinear Perron-Frobenius theory has found significant uses in computer science, mathematical biology, game theory and the study of dynamical systems. This is the first comprehensive and unified introduction to nonlinear Perron-Frobenius theory suitable for graduate students and researchers entering the field for the first time. It acquaints the reader with recent developments and provides a guide to challenging open problems. To enhance accessibility, the focus is on finite dimensional nonlinear Perron-Frobenius theory, but pointers are provided to infinite dimensional results. Prerequisites are little more than basic real analysis and topology.
(source: Nielsen Book Data)9780521898812 20160609
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