close
1.

図書

図書
Robert M. Mazo
出版情報: Oxford : Clarendon Press, 2002  xii, 289 p. ; 24 cm
シリーズ名: The international series of monographs on physics ; 112
Oxford science publications
所蔵情報: loading…
目次情報: 続きを見る
Historical Background / 1:
Robert Brown / 1.1:
Between Brown and Einstein / 1.2:
Albert Einstein / 1.3:
Marian von Smoluchowski / 1.4:
Molecular Reality / 1.5:
The Scope of this Book / 1.6:
Probability Theory / 2:
Probability / 2.1:
Conditional Probability and Independence / 2.2:
Random Variables and Probability Distributions / 2.3:
Expectations and Particular Distributions / 2.4:
Characteristic Function; Sums of Random Variables / 2.5:
Conclusion / 2.6:
Stochastic Processes / 3:
Distribution Functions / 3.1:
Classification of Stochastic Processes / 3.3:
The Fokker-Planck Equation / 3.4:
Some Special Processes / 3.5:
Calculus of Stochastic Processes / 3.6:
Fourier Analysis of Random Processes / 3.7:
White Noise / 3.8:
Einstein-Smoluchowski Theory / 3.9:
What is Brownian Motion? / 4.1:
Smoluchowski's Theory / 4.2:
Smoluchowski Theory Continued / 4.3:
Einstein's Theory / 4.4:
Diffusion Coefficient and Friction Constant / 4.5:
The Langevin Theory / 4.6:
Stochastic Differential Equations and Integrals / 5:
The Langevin Equation Revisited / 5.1:
Stochastic Differential Equations / 5.2:
Which Rule Should Be Used? / 5.3:
Some Examples / 5.4:
Functional Integrals / 6:
The Wiener Integral / 6.1:
Wiener Measure / 6.3:
The Feynman-Kac Formula / 6.4:
Feynman Path Integrals / 6.5:
Evaluation of Wiener Integrals / 6.6:
Applications of Functional Integrals / 6.7:
Some Important Special Cases / 7:
Several Cases of Interest / 7.1:
The Free Particle / 7.2:
The Distribution of Displacements / 7.3:
The Harmonically Bound Particle / 7.4:
A Particle in a Constant Force Field / 7.5:
The Uniaxial Rotor / 7.6:
An Equation for the Distribution of Displacements / 7.7:
Discussion / 7.8:
The Smoluchowski Equation / 8:
The Kramers-Klein Equation / 8.1:
Elimination of Fast Variables / 8.2:
The Smoluchowski Equation Continued / 8.4:
Passage over Potential Barriers / 8.5:
Concluding Remarks / 8.6:
Random Walk / 9:
The Random Walk / 9.1:
The One-Dimensional Pearson Walk / 9.2:
The Biased Random Walk / 9.3:
The Persistent Walk / 9.4:
Boundaries and First Passage Times / 9.5:
Random Remarks on Random Walks / 9.6:
Statistical Mechanics / 10:
Molecular Distribution Functions / 10.1:
The Liouville Equation / 10.2:
Projection Operators--The Zwanzig Equation / 10.3:
Projection Operators--The Mori Equation / 10.4:
Stochastic Equations from a Statistical Mechanical Viewpoint / 10.5:
The Langevin Equation A Heuristic View / 11.1:
The Fokker-Planck Equation--A Heuristic View / 11.2:
What is Wrong with these Derivations? / 11.3:
Eliminating Fast Processes / 11.4:
The Distribution Function / 11.5:
Two Exactly Treatable Models / 11.6:
Two Illustrative Examples / 12.1:
Brownian Motion in a Dilute Gas / 12.2:
The Particle Bound to a Lattice / 12.3:
The One-Dimensional Case / 12.5:
Brownian Motion and Noise / 12.6:
Limits on Measurement / 13.1:
Oscillations of a Fiber / 13.2:
A Pneumatic Example / 13.3:
Electrical Systems / 13.4:
Diffusion Phenomena / 13.5:
Brownian Motion in Configuration Space / 14.1:
Diffusion Controlled Reactions / 14.2:
The Effect of Forces / 14.3:
The Coagulation of Colloids / 14.4:
Taylor Diffusion / 14.5:
Rotational Diffusion / 15:
Fluorescence Depolarization / 15.1:
Non-Spherical Brownian Particles / 15.3:
Polymer Solutions / 15.4:
A Model for Dilute Solutions of Polymers / 16.1:
Hydrodynamic Interaction / 16.2:
The Equation of Motion / 16.3:
Diffusion and Intrinsic Viscosity / 16.4:
Historical Remarks and Additional Reading / 16.5:
Interacting Brownian Particles / 17:
Effects of Concentration / 17.1:
The Multiparticle Smoluchowski Equation / 17.2:
The Diffusion Coefficient / 17.4:
The Viscosity / 17.5:
Dynamics, Fractals, and Chaos / 17.6:
Brownian Dynamics / 18.1:
Brownian Paths as Fractals / 18.2:
Brownian Motion and Chaos / 18.3:
The Applicability of Stokes' Law / 18.4:
Functional Calculus / B:
An Operator Identity / C:
Euler Angles / D:
The Oseen Tensor / E:
Mutual Diffusion and Self-Diffusion / F:
Mutual Diffusion / F.1:
Self-Diffusion / F.2:
Relation between D[subscript m] and D[subscript s] / F.3:
References
Index
Historical Background / 1:
Robert Brown / 1.1:
Between Brown and Einstein / 1.2:
2.

図書

図書
edited by Makoto Maejima, Tokuzo Shiga
出版情報: New Jersey : World Scientific, c2002  xi, 430 p. ; 26 cm
所蔵情報: loading…
3.

図書

図書
Juan Arias de Reyna
出版情報: Berlin ; Tokyo : Springer, c2002  xviii, 175 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1785
所蔵情報: loading…
目次情報: 続きを見る
Preface
Introduction
About the notation
Fourier series and Hilbert Transform / Part I:
Hardy-Littlewood maximal function / 1:
Weak Inequality / 1.1:
Differentiability / 1.3:
Interpolation / 1.4:
A general inequality / 1.5:
Fourier Series / 2:
Dirichlet / 2.1:
Fourier Series of Continuous Functions / 2.3:
Banach continuity principle / 2.4:
Summability / 2.5:
The Conjugate Function / 2.6:
The Hilbert transform on R / 2.7:
The conjecture of Luzin / 2.8:
Hilbert Transform / 3:
The Hilbert Transform / 3.1:
Maximal Hilbert Transform / 3.6:
The Carleson-Hunt Theorem / Part II:
The Basic Step / 4:
Carleson maximal operator / 4.1:
Local norms / 4.3:
Dyadic Partition / 4.4:
Some definitions / 4.5:
Basic decomposition / 4.6:
The first term / 4.7:
Notation ?/? / 4.8:
The second term / 4.9:
The third term / 4.10:
First form of the basic step / 4.11:
Some comments about the proof / 4.12:
Choosing the partition ?? The norm || / 4.13:
Basic theorem, second form / 4.14:
Maximal inequalities / 5:
Maximal inequalities for ?(?, ×) / 5.1:
Maximal inequalities for Hf / 5.2:
Growth of Partial Sums / 6:
The seven trick / 6.1:
The exceptional set / 6.3:
Bound for the partial sums / 6.4:
Carleson Analysis of the Function / 7:
A musical interlude / 7.1:
The notes of f / 7.3:
The set X / 7.4:
The set S / 7.5:
Allowed pairs / 8:
The length of the notes / 8.1:
Well situated notes / 8.2:
The length of well situated notes / 8.3:
Pair Interchange Theorems / 8.4:
Choosing the shift m / 9.1:
A bound of || f|| ? / 9.3:
Selecting an allowed pair / 9.4:
All together / 10:
End of proof / 10.1:
Consequences / Part III:
Some spaces of functions / 11:
Decreasing rearrangement / 11.1:
The Lorentz spaces Lp,1(µ) and Lp,?(µ) / 11.3:
Marcinkiewicz interpolation theorem / 11.4:
Spaces near L1(µ) / 11.5:
The spaces Llog L(µ) and Lexp(µ) / 11.6:
The Maximal Operator of Fourier series / 12:
Maximal operator of Fourier series / 12.1:
The maximal space Q / 12.3:
The theorem of Antonov / 12.8:
Fourier transform on the line / 13:
Fourier transform / 13.1:
References
Comments
Subject Index
Preface
Introduction
About the notation
4.

図書

図書
Bruce A. Magurn
出版情報: Cambridge : Cambridge University Press, 2002  xiv, 676 p. ; 24 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 87
所蔵情報: loading…
目次情報: 続きを見る
Preface
Preliminaries / Chapter 0:
Groups of Modules: K[subscript 0] / Part I:
Free Modules / Chapter 1:
Bases / 1A:
Matrix Representations / 1B:
Absence of Dimension / 1C:
Projective Modules / Chapter 2:
Direct Summands / 2A:
Summands of Free Modules / 2B:
Grothendieck Groups / Chapter 3:
Semigroups of Isomorphism Classes / 3A:
Semigroups to Groups / 3B:
Resolutions / 3C:
Stability for Projective Modules / Chapter 4:
Adding Copies of R / 4A:
Stably Free Modules / 4B:
When Stably Free Modules Are Free / 4C:
Stable Rank / 4D:
Dimensions of a Ring / 4E:
Multiplying Modules / Chapter 5:
Semirings / 5A:
Burnside Rings / 5B:
Tensor Products of Modules / 5C:
Change of Rings / Chapter 6:
K[subscript 0] of Related Rings / 6A:
G[subscript 0] of Related Rings / 6B:
K[subscript 0] as a Functor / 6C:
The Jacobson Radical / 6D:
Localization / 6E:
Sources of K[subscript 0] / Part II:
Number Theory / Chapter 7:
Algebraic Integers / 7A:
Dedekind Domains / 7B:
Ideal Class Groups / 7C:
Extensions and Norms / 7D:
K[subscript 0] and G[subscript 0] of Dedekind Domains / 7E:
Group Representation Theory / Chapter 8:
Linear Representations / 8A:
Representing Finite Groups Over Fields / 8B:
Semisimple Rings / 8C:
Characters / 8D:
Groups of Matrices: K[subscript 1] / Part III:
Definition of K[subscript 1] / Chapter 9:
Elementary Matrices / 9A:
Commutators and K[subscript 1](R) / 9B:
Determinants / 9C:
The Bass K[subscript 1] of a Category / 9D:
Stability for K[subscript 1](R) / Chapter 10:
Surjective Stability / 10A:
Injective Stability / 10B:
Relative K[subscript 1] / Chapter 11:
Congruence Subgroups of GL[subscript n](R) / 11A:
Congruence Subgroups of SL[subscript n](R) / 11B:
Mennicke Symbols / 11C:
Relations Among Matrices: K[subscript 2] / Part IV:
K[subscript 2](R) and Steinberg Symbols / Chapter 12:
Definition and Properties of K[subscript 2](R) / 12A:
Elements of St(R) and K[subscript 2](R) / 12B:
Exact Sequences / Chapter 13:
The Relative Sequence / 13A:
Excision and the Mayer-Vietoris Sequence / 13B:
The Localization Sequence / 13C:
Universal Algebras / Chapter 14:
Presentation of Algebras / 14A:
Graded Rings / 14B:
The Tensor Algebra / 14C:
Symmetric and Exterior Algebras / 14D:
The Milnor Ring / 14E:
Tame Symbols / 14F:
Norms on Milnor K-Theory / 14G:
Matsumoto's Theorem / 14H:
Sources of K[subscript 2] / Part V:
Symbols in Arithmetic / Chapter 15:
Hilbert Symbols / 15A:
Metric Completion of Fields / 15B:
The p-Adic Numbers and Quadratic Reciprocity / 15C:
Local Fields and Norm Residue Symbols / 15D:
Brauer Groups / Chapter 16:
The Brauer Group of a Field / 16A:
Splitting Fields / 16B:
Twisted Group Rings / 16C:
The K[subscript 2] Connection / 16D:
Appendix
Sets, Classes, Functions / A:
Chain Conditions, Composition Series / B:
Special Symbols
References
Index
Preface
Preliminaries / Chapter 0:
Groups of Modules: K[subscript 0] / Part I:
5.

図書

図書
Klaus Bichteler
出版情報: Cambridge : Cambridge University Press, 2002  xiii, 501 p. ; 24 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 89
所蔵情報: loading…
目次情報: 続きを見る
Preface
Introduction / Chapter 1:
Motivation: Stochastic Differential Equations / 1.1:
Wiener Process / 1.2:
The General Model / 1.3:
Integrators and Martingales / Chapter 2:
The Elementary Stochastic Integral / 2.1:
The Semivariations / 2.2:
Path Regularity of Integrators / 2.3:
Processes of Finite Variation / 2.4:
Martingales / 2.5:
Extension of the Integral / Chapter 3:
The Daniell Mean / 3.1:
The Integration Theory of a Mean / 3.2:
Countable Additivity in p-Mean / 3.3:
Measurability / 3.4:
Predictable and Previsible Processes / 3.5:
Special Properties of Daniell's Mean / 3.6:
The Indefinite Integral / 3.7:
Functions of Integrators / 3.8:
Ito's Formula / 3.9:
Random Measures / 3.10:
Control of Integral and Integrator / Chapter 4:
Change of Measure--Factorization / 4.1:
Martingale Inequalities / 4.2:
The Doob-Meyer Decomposition / 4.3:
Semimartingales / 4.4:
Previsible Control of Integrators / 4.5:
Levy Processes / 4.6:
Stochastic Differential Equations / Chapter 5:
Existence and Uniqueness of the Solution / 5.1:
Stability: Differentiability in Parameters / 5.3:
Pathwise Computation of the Solution / 5.4:
Weak Solutions / 5.5:
Stochastic Flows / 5.6:
Semigroups, Markov Processes, and PDE / 5.7:
Complements to Topology and Measure Theory / Appendix A:
Notations and Conventions / A.1:
Topological Miscellanea / A.2:
Measure and Integration / A.3:
Weak Convergence of Measures / A.4:
Analytic Sets and Capacity / A.5:
Suslin Spaces and Tightness of Measures / A.6:
The Skorohod Topology / A.7:
The L[superscript p]-Spaces / A.8:
Semigroups of Operators / A.9:
Answers to Selected Problems / Appendix B:
References
Index of Notations
Index
Answers
Full Indexes
Errata
Preface
Introduction / Chapter 1:
Motivation: Stochastic Differential Equations / 1.1:
6.

図書

図書
Ernst Hairer, Christian Lubich, Gerhard Wanner
出版情報: Berlin ; Tokyo : Springer, c2002  xiii, 515 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; v. 31
所蔵情報: loading…
7.

図書

図書
edited by Roland Glowinski, Hideo Kawarada, Jacques Periaux
出版情報: Tokyo : Gakkōtosho, c2002  346 p. ; 27 cm
シリーズ名: GAKUTO international series ; . Mathematical sciences and applications ; vol. 16
所蔵情報: loading…
8.

図書

図書
K.P.S. Bhaskara Rao
出版情報: London : Taylor and Francis, c2002  xi, 167 p. ; 24 cm
シリーズ名: Algebra, logic and applications series ; 17
所蔵情報: loading…
目次情報: 続きを見る
Elementary Results on Rings
Foreword
Matrix Algebra Over Rings
Regular Elements in a Ring
Preface
Regularity - Principal Ideal Rings
Regularity - Basics / 1:
Regularity - Integral Domains
Elementary results on rings
Regularity - Commutative Rings
Special Topics / 2:
Matrix algebra over rings
Elementary notions / 2.1:
Determinants / 2.2:
The [partial differential]/[partial differential]a[subscript ij] notation / 2.3:
Rank of a matrix / 2.4:
Compound matrices / 2.5:
Regular elements in a ring / 3:
The Moore-Penrose equations / 3.1:
Regular elements and regular matrices / 3.2:
A Theorem of Von Neumann / 3.3:
Inverses of matrices / 3.4:
M-P inverses / 3.5:
Regularity - principal ideal rings / 4:
Some results on principal ideal rings / 4.1:
Smith Normal Form Theorem / 4.2:
Regular matrices over Principal Ideal Rings / 4.3:
An algorithm for Euclidean domains / 4.4:
Reflexive g-inverses of matrices / 4.5:
Some special integral domains / 4.6:
Examples / 4.7:
Regularity - basics / 5:
Regularity of rank one matrices / 5.1:
A basic result on regularity / 5.2:
A result of Prasad and Robinson / 5.3:
Regularity - integral domains / 6:
Regularity of matrices / 6.1:
All reflexive g-inverses / 6.2:
M-P inverses over integral domains / 6.3:
Generalized inverses of the form PCQ / 6.4:
{1,2,3}- and {1,2,4}-inverses / 6.5:
Group inverses over integral domains / 6.6:
Drazin inverses over integral domains / 6.7:
Regularity - commutative rings / 7:
Commutative rings with zero divisors / 7.1:
Rank one matrices / 7.2:
Rao-regular matrices / 7.3:
Regular matrices over commutative rings / 7.4:
All generalized inverses / 7.5:
M-P inverses over commutative rings / 7.6:
Group inverses over commutative rings / 7.7:
Drazin inverses over commutative rings / 7.8:
Special topics / 8:
Generalized Cramer Rule / 8.1:
A rank condition for consistency / 8.2:
Minors of reflexive g-inverses / 8.3:
Bordering of regular matrices / 8.4:
Regularity over Banach algebras / 8.5:
Group inverses in a ring / 8.6:
M-P inverses in a ring / 8.7:
Group inverse of the companion matrix / 8.8:
Bibliography
Index
Elementary Results on Rings
Foreword
Matrix Algebra Over Rings
9.

図書

図書
edited by Zoltán Daróczy, Zsolt Páles
出版情報: Dordrecht : Kluwer Academic, c2002  x, 360 p. ; 25 cm
シリーズ名: Advances in mathematics ; v. 3
所蔵情報: loading…
10.

図書

図書
Martin A. Moskowitz
出版情報: Singapore ; New Jersey : World Scientific, c2002  ix, 149 p. ; 23 cm
所蔵情報: loading…
目次情報: 続きを見る
Preface and Acknowledgments
First Concepts / 1:
Fundamentals of the complex field / 1.1:
Holomorphic functions / 1.2:
Some important examples / 1.3:
The Cauchy-Riemann equations / 1.4:
Some elementary differential equations / 1.5:
Conformality / 1.6:
Power series / 1.7:
Integration Along a Contour / 2:
Curves and their trajectories / 2.1:
Change of Parameter and a Fundamental Inequality / 2.2:
Some important examples of contour integration / 2.3:
The Cauchy theorem in simply connected domains / 2.4:
Some immediate consequences of Cauchy's theorem for a simply connected domain / 2.5:
The Main Consequences of Cauchy's theorem / 3:
The Cauchy theorem in multiply connected domains and the pre-residue theorem / 3.1:
The Cauchy integral formula and its consequences / 3.2:
Analyticity, Taylor's theorem and the identity theorem / 3.3:
The area formula and some consequences / 3.4:
Application to spaces of square integrable holomorphic functions / 3.5:
Spaces of holomorphic functions and Montel's theorem / 3.6:
The maximum modulus theorem and Schwarz' lemma / 3.7:
Singularities / 4:
Classification of isolated singularities, the theorems of Riemann and Casorati-Weierstrass / 4.1:
The principle of the argument / 4.2:
Rouche's theorem and its consequences / 4.3:
The study of a transcendental equation / 4.4:
Laurent expansion / 4.5:
The calculation of residues at an isolated singularity, the residue theorem / 4.6:
Application to the calculation of real integrals / 4.7:
A more general removable singularities theorem and the Schwarz reflection principle / 4.8:
Conformal Mappings / 5:
Linear fractional transformations, equivalence of the unit disk and the upper half plane / 5.1:
Automorphism groups of the disk, upper half plane and entire plane / 5.2:
Annuli / 5.3:
The Riemann mapping theorem for planar domains / 5.4:
Applications of Complex Analysis to Lie Theory / 6:
Applications of the identity theorem: Complete reducibility of representations according to Hermann Weyl and the functional equation for the exponential map of a real Lie group / 6.1:
Application of residues: The surjectivity of the exponential map for U(p,q) / 6.2:
Application of Liouville's theorem and the maximum modulus theorem: The Zariski density of cofinite volume subgroups of complex Lie groups / 6.3:
Applications of the identity theorem to differential topology and Lie groups / 6.4:
Bibliography
Index
Preface and Acknowledgments
First Concepts / 1:
Fundamentals of the complex field / 1.1:
文献の複写および貸借の依頼を行う
 文献複写・貸借依頼