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1.

図書

図書
Sukumar Das Adhikari
出版情報: New Delhi : Narosa, c1999  xiii, 153 p. ; 24 cm
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2.

図書

図書
A. Ehrenfeucht, T. Harju, G. Rozenberg
出版情報: Singapore : World Scientific, c1999  xvi, 290 p. ; 23 cm
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目次情報: 続きを見る
Preface
Preliminaries / Chapter 1:
Notations / 1.1:
Sets and functions / 1.1.1:
Closure operators / 1.1.2:
Relations / 1.1.3:
Equivalence relations / 1.1.4:
Partial orders / 1.2:
Downsets / 1.2.1:
Order embeddings / 1.2.2:
Linear orders / 1.2.3:
Semigroups and groups / 1.3:
Notations for semigroups and monoids / 1.3.1:
Free monoids (with involution) / 1.3.2:
Preliminaries on groups / 1.3.3:
Group actions / 1.3.4:
Free groups, commutators and verbal identities / 1.3.5:
Graph Theoretical Preliminaries / Chapter 2:
Directed and Undirected Graphs / 2.1:
Basic notions / 2.1.1:
Connectivity of graphs / 2.1.2:
Some special graphs / 2.1.3:
Comparability graphs / 2.2:
Transitively oriented graphs / 2.2.1:
Permutation graphs and cographs / 2.2.2:
Construction trees of cographs / 2.2.3:
2-Structures and Their Clans / Chapter 3:
Introduction and representations / 3.1:
Definition of a 2-structure / 3.1.1:
Isomorphic 2-structures / 3.1.2:
Reversibility / 3.1.3:
Substructures and clans / 3.2:
Substructures, clans and factors / 3.2.1:
Refinements and similarity / 3.2.2:
Reversible version / 3.2.3:
Graphs and packed components / 3.2.4:
Some special 2-structures / 3.2.5:
Closure properties of clans / 3.3:
Basic closures / 3.3.1:
Sibas: set theoretic closure properties / 3.3.2:
Clans of factors / 3.3.3:
Prime clans / 3.4:
Prime members in sibas / 3.4.1:
Minimal overlapping clans / 3.4.2:
Quotients and Homomorphisms / Chapter 4:
Quotients / 4.1:
Factorizations and quotients / 4.1.1:
Homomorphisms / 4.1.2:
Natural epimorphisms and decompositions / 4.1.3:
Clans and epimorphisms / 4.2:
Homomorphism theorem / 4.2.1:
Prime clans in quotients / 4.2.2:
Primitive quotients / 4.2.3:
Other operations / 4.3:
Premorphisms / 4.3.1:
Extensions / 4.3.2:
Clan Decomposition / Chapter 5:
The clan decomposition theorem / 5.1:
Maximal prime clans / 5.1.1:
Special sibas and 2-structures / 5.1.2:
The relationship of sibas to 2-structures / 5.1.3:
The shape of a 2-structure / 5.2:
The shape and its representation as a tree / 5.2.1:
Same shapes / 5.2.2:
A construction of prime clans / 5.3:
A construction of clans / 5.3.1:
Primitive 2-Structures / 5.3.2:
Small primitive substructures / 6.1:
Uniformly imprimitive 2-structures / 6.1.1:
Primitive substructures of 3 or 4 nodes / 6.1.2:
Hereditary properties / 6.2:
Local and global nodes / 6.2.1:
Critically primitive 2-structures / 6.2.2:
The parity theorem / 6.3.1:
The list of critically primitive 2-structures / 6.3.2:
Angular 2-Structures / Chapter 7:
Angularity / 7.1:
All-connectivity / 7.1.1:
All-connected skew angular 2-structures / 7.1.2:
T-structures / 7.2:
T-structures and partial orders / 7.2.1:
T[subscript 2]-structures / 7.2.2:
Linear orders and Schroder numbers / 7.3:
Bi-orders and linear orders / 7.3.1:
Uniformly imprimitive linear orders / 7.3.2:
Parenthesis words and Schroder numbers / 7.3.3:
Labelled 2-Structures / Chapter 8:
Introduction to l2-structures / 8.1:
Definitions / 8.1.1:
Substructures, clans and quotients / 8.1.2:
Clan decomposition of l2-structures / 8.2:
Uniqueness of decompositions / 8.2.1:
The shape of an l2-structure / 8.2.2:
Graphs and their representations / 8.2.3:
Graphs as l2-structures / 8.3.1:
On comparability graphs / 8.3.2:
Unstable Labelled 2-Structures / Chapter 9:
Triangle free and unstable l2-structures / 9.1:
Removable edges / 9.1.1:
Internal and external nodes / 9.1.2:
Triangle-free l2-structures / 9.1.3:
Heredity in unstable l2-structures / 9.2:
The partition of nodes / 9.2.1:
Alternating structures / 9.2.2:
Degrees of nodes / 9.2.3:
A composition of unstable l2-structures / 9.3:
A constructive reduction of primitive l2-structures / 9.3.1:
Pendant components / 9.3.2:
Automorphisms of Labelled 2-Structures / Chapter 10:
Label preserving automorphisms / 10.1:
The l-automorphism groups / 10.1.1:
Transitivity / 10.1.2:
Automorphic actions on factors / 10.1.3:
Universality of l-automorphism groups / 10.1.4:
Nonpreserving automorphisms / 10.2:
Connections to l-automorphisms / 10.2.1:
Transitivity and associated permutations / 10.2.2:
Representing labels by automorphisms / 10.2.3:
Switching of Graphs / Chapter 11:
Introduction to switching / 11.1:
The group of graphs / 11.1.1:
Switching classes / 11.1.3:
Structural properties of switching classes / 11.2:
A local characterization / 11.2.1:
Automorphisms / 11.2.2:
Special problems on undirected graphs / 11.3:
Two-graphs / 11.3.1:
Eulerian graphs / 11.3.2:
Pancyclic graphs / 11.3.3:
Trees / 11.3.4:
Labelled Structures over Groups / Chapter 12:
Introduction / 12.1:
Groups and involutions / 12.1.1:
Selectors and switching classes / 12.1.2:
An interpretation in networks / 12.2:
Concurrent behaviour in networks / 12.2.1:
Reducing the actions to groups / 12.2.2:
Introducing reversibility / 12.2.3:
Examples for some special groups / 12.3:
The cyclic groups Z[subscript 3] and Z[subscript 4] / 12.3.1:
The symmetric group S[subscript 3] / 12.3.2:
Clans of Switching Classes / Chapter 13:
Associated groups / 13.1:
The group of selectors / 13.1.1:
The group of abelian switching classes / 13.1.2:
Clans and horizons / 13.2:
Spanning trees / 13.2.1:
Horizons and constant selectors / 13.2.2:
Clans / 13.2.3:
Cardinalities of switching classes / 13.3:
Some special cases / 13.3.1:
Centralizers / 13.3.2:
Some improvements / 13.3.3:
Quotients and Plane Trees / Chapter 14:
Quotients of switching classes / 14.1:
Planes and plane trees / 14.1.1:
Planes / 14.2.1:
Plane trees / 14.2.2:
Bijective correspondence of plane trees / 14.2.3:
Forms / 14.2.4:
Invariants / Chapter 15:
Free invariants / 15.1:
General invariants / 15.1.1:
Edge monoids / 15.1.2:
Variable functions and free invariants / 15.1.3:
Group properties of free invariants / 15.2:
Abelian property / 15.2.1:
Graphs of words / 15.2.2:
Verbal identities / 15.2.3:
Invariants on abelian groups / 15.3:
Independency of free invariants / 15.3.1:
Complete sets of invariants / 15.3.2:
Invariants on nonabelian groups / 15.4:
General observations / 15.4.1:
Central characters / 15.4.2:
A characterization theorem / 15.4.3:
Bibliography
Index
Preface
Preliminaries / Chapter 1:
Notations / 1.1:
3.

図書

図書
Nikolai G. Ushakov
出版情報: Utrecht : VSP, 1999  ix, 355 p. ; 26 cm
シリーズ名: Modern probability and statistics
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4.

図書

図書
Huzihiro Araki ; translated by Ursula Carow-Watamura
出版情報: Oxford : Oxford University Press, 1999  xii, 236 p. ; 24 cm
シリーズ名: The international series of monographs on physics ; v. 101
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States and observables / 1:
Probabilistic description / 1.1:
Functions of observables / 1.2:
The expectation value of an observable / 1.4:
Mixture and pure states / 1.5:
The physical topology of the states / 1.6:
Equivalent theories / 1.7:
Symmetries / 1.8:
Quantum theory / 2:
The quantum mechanical descrption / 2.1:
Algebraic viewpoint / 2.2:
The representation associated with a state: GNS construction / 2.3:
The symmetries of quantum mechanics / 2.4:
Symmetries from the algebraic point of view / 2.5:
The relativistic symmetry / 3:
Minkowski space / 3.1:
The inhomogeneous Lorentz group / 3.2:
The relativistic symmetry in quantum mechanics / 3.3:
Irreducible representations and one-particle states / 3.4:
Free particle system and Fock space / 3.5:
Energy momentum / 3.6:
Local observables / 4:
General properties of local observables / 4.1:
The vacuum state / 4.2:
Irreducibility / 4.3:
Mass gap and exponential clustering property / 4.4:
The JLD representation / 4.5:
Truncated expectation values and multiple clustering property / 4.6:
Additivity assumption and Reeh-Schlieder theorem / 4.7:
Quantum field theory / 4.8:
From quantum fields to local observables / 4.9:
Scattering theory / 5:
The concept of scattering states and the S-matrix / 5.1:
Description of asymptotic states / 5.2:
Construction of asymptotic states / 5.3:
The counter interpretation of asymptotic states--verification of an appropriate asymptotic behaviour / 5.4:
Asymptotic conditions and reduction formula for the S-matrix / 5.5:
Analyticity and TCP symmetry / 5.6:
Sector theory / 6:
Superselection rules and localized excitations / 6.1:
Localized endomorphisms and sectors / 6.2:
Permutation of excitations and statistics of a sector / 6.3:
Charge conjugate sector / 6.4:
Operator algebra system of fields and gauge groups / 6.5:
Theory of local charges / 6.6:
Hilbert space and operators / Appendix A:
Hilbert space / A.1:
Pre-Hilbert space and completion / A.2:
Orthonormal basis / A.3:
Unitary and antiunitary maps / A.4:
Subspaces and projection operators / A.5:
Direct sum and direct integral / A.6:
Spectral decomposition / A.7:
Trace / A.8:
Unbounded operators / A.9:
One-parameter group of unitary operators / A.10:
Tensor product / A.11:
Operator algebras / Appendix B:
C* algebras / B.1:
Von Neumann algebras / B.2:
Free fields / Appendix C:
Charged scalar field / C.1:
One particle system with positive mass and arbitrary spin / C.2:
Examples of free fields with positive mass and integer spin / C.3:
Examples of free fields with positive mass and half odd integer spin / C.4:
General literature and references
References for Chapter 1
References for Chapter 2
References for Chapter 3
References for Chapter 4
References for Chapter 5
References for Chapter 6
Literature for appendices
Index
States and observables / 1:
Probabilistic description / 1.1:
Functions of observables / 1.2:
5.

図書

図書
edited by Christopher C. Bernido ... [et al.]
出版情報: Amsterdam : Gordon and Breach Science, c1999  xviii, 343 p. ; 24 cm
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6.

図書

図書
Wayne Raskind, Charles Weibel, editors
出版情報: Providence, RI : American Mathematical Society, 1999  xi, 315 p. ; 26 cm
シリーズ名: Proceedings of symposia in pure mathematics ; v. 67
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Conjectures de type local-global sur l'image des groupes de Chow dans la cohomologie etale / J.-L. Colliot-Thelene
Algebraic theory of characteristic classes of bundles with connection / H. Esnault
Polylogarithmic identities in cubical higher Chow groups / H. Gangl ; S. Muller-Stach
Topological cyclic homology of schemes / T. Geisser ; L. Hesselholt
Filtrations on higher algebraic $K$-theory / H. Gillet ; C. Soule
Motivic cohomology of smooth geometrically cellular varieties / B. Kahn
Integral homology of $PGL_2$ over elliptic curves / K. P. Knudson
Application of motivic complexes to negligible classes / E. Peyre
Two-primary algebraic $K$-theory of spaces and related spaces of symmetries of manifolds / J. Rognes
A mini-course on recent progress in algebraic $K$-theory and its relationship with topology and analysis / J. Rosenberg
The Chow ring of a classifying space / B. Totaro
Voevodsky's Seattle lectures: $K$-theory and motivic cohomology / V. Voevodsky
Products in higher Chow groups and motivic cohomology / C. Weibel
Conjectures de type local-global sur l'image des groupes de Chow dans la cohomologie etale / J.-L. Colliot-Thelene
Algebraic theory of characteristic classes of bundles with connection / H. Esnault
Polylogarithmic identities in cubical higher Chow groups / H. Gangl ; S. Muller-Stach
7.

図書

図書
edited by Louis J. Billera ... [et al.]
出版情報: Cambridge : Cambridge University Press, 1999  ix, 345 p. ; 25 cm
シリーズ名: Mathematical Sciences Research Institute publications ; 38
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8.

図書

図書
edited by Massimo Picardello, Wolfgang Woess
出版情報: Cambridge : Cambridge University Press, 1999  viii, 361 p. ; 24 cm
シリーズ名: Symposia mathematica ; v. 39
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9.

図書

図書
G. Meurant
出版情報: Amsterdam ; Tokyo : Elsevier Science, 1999  xxii, 753 p. ; 24 cm
シリーズ名: Studies in mathematics and its applications ; v. 28
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Introductory Material
Vector and matrices norms
Eigenvalues
Irreducibility and diagonal dominance
M--Matrices and generalizations
Splittings
Positive definite matrices
The graph of a matrix
Chebyshev polynomials
Discretization methods for partial diffential equations
Eigenvalues and Fourier analysis
Floating point arithmetic
Vector and parallel computers
BLAS and LAPACK
Bibliographical comments
Gaussian elimination for general linear systems
Introduction to Gaussian elimination
Gaussian elimination without permutations
Gaussian elimination with permutations (partial piv-oting)
Gaussian elimination with other pivoting strategies
Operation counts
Gaussian elimination for symmetric systems
The outer product algorithm
The bordering algorithm
The inner product algorithm
Coding the three factorization algorithms
Positive definite systems
Indefinite systems
Gaussian elimination for H-matrices
Block methods
Tridiagonal and block tridiagonal systems
Roundoff error analysis
Perturbation analysis
Scaling
Iterative refinement
Parallel solution of general linear systems
Gaussian elimination for sparse linear systems
Introduction
The fill--in phenomenon
Graphs and fill--in for symmetric matrices
Characterization of the fill--in
Band and envelope numbering schemes for symmetric matrices
The Cuthill--McKee and reverse Cuthill--McKee orderings
Sloan's algorithm
Spectral schemes
The basic idea
The multilevel spectral algorithm
The Kumfert and Pothen hybrid algorithm
The Boman--Hendrickson multilevel algorithm
The minimum degree ordering
The nested dissection ordering
Generalization of dissection algorithms
General dissection algorithms
Graph bisection improvement techniques
The multisection algorithm
The multifrontal method
Non--symmetric sparse matrices
Numerical stability for sparse matrices
Parallel algorithms for sparse matrices
Fast solvers for separable PDEs
Fast Fourier Transform
The basics of the FFT
The complex FFT
The real transforms
FFT on vector and parallel computers
Stability of the FFT
Other algorithms
Double Fourier analysis
The Fourier tridiagonal Method
The cyclic reduction method
The FACR(l) method
The capacitance matrix method
Classical iterative methods
The Jacobi method
The Gauss-Seidel method
The SOR Method
The SSOR method
Alternating direction methods
Richardson methods
Acceleration techniques
Stability of classical iterative methods
The conjugate gradient and related methods
Introductory Material
Vector and matrices norms
Eigenvalues
10.

図書

図書
John N. McDonald, Neil A. Weiss ; biographies by Carol A. Weiss
出版情報: San Diego : Academic Press, c1999  xvii, 745 p. ; 24 cm
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Set Theory
The Real Numbers and Calculus Lebesque
Theory on the Real Line Measure
Theory Elements of Probability Differentiation
Elements of Topological and Metric
Spaces Completeness, Compactness, and Approximation
Hilbert Spaces
Classical Banach Spaces
Basic Theory of Normed and Locally
Convex Spaces
Elements of Harmonic
Analysis Measurable Dynamical Systems
Index
Set Theory
The Real Numbers and Calculus Lebesque
Theory on the Real Line Measure
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