Series: Lecture Notes in Mathematics, Vol. 1979
Subseries: Seminaire de Probabilites ,
2009, Approx. 450 p., Softcover
ISBN: 978-3-642-01762-9
Due: June 18, 2009
The tradition of specialized courses in the Seminaires de Probabilites is continued with A. Lejay's Another introduction to rough paths. Other topics from this 42nd volume range from the interface between analysis and probability to special processes, Levy processes and Levy systems, branching, penalization, representation of Gaussian processes, filtrations and quantum probability.
Antoine Lejay Yet another introduction to rough paths.- Laurent Miclo Monotonicity of the extremal functionsfor one-dimensional inequalities of log-Sobolev type.- Walter Schachermayer, Uwe Schmock, Josef Teichmann Non-monotone convergence in the quadratic Wasserstein distance.- Fangjun Xu On the equation $\mu=S_t\mu\ast \mu_t$.- Philippe Biane Shabat polynomials and harmonic measure.- Nizar Demni Radial Dunkl processes associated with dihedral systems.- Philippe Biane Matrix valued Brownian motion and a paper by P\'olya.- Kouji Yano, Yuko Yano, Marc Yor On the laws of first hitting times of points for one-dimensional symmetric stable Levy processes.-Patrick J. Fitzsimmons, Ronald K. Getoor Levy systems and time changes.- Nathalie Krell Self-similar branching Markov chains.- Robert Hardy, Simon C. Harris A spine approach to branching diffusions with applications to $L^p$-convergence of martingales.- Pierre Debs Penalisation of the standard random walk by a function of the one-sided maximum, of the local time, or of the duration of the excursions.- M. Erraoui, E.H. Essaky Canonical representation for Gaussian processes.- Michel Emery Recognising whether a filtration is Brownian: a case study.- Ameur Dhahri Markovian properties of the spin-boson model.- Stephane Attal and Nadine Guillotin-Plantard Statistical properties of Pauli matrices going through noisy channels.- Miklos Rasonyi Erratum to: "New methods in the arbitrage theory of financial markets with transaction costs'', in Seminaire XLI
2009, Approx. 700 p., Hardcover
ISBN: 978-0-387-98127-7
Due: July 2009
Fractional differentiation inequalities are by themselves an important area of research. They have many applications in pure and applied mathematics and many other applied sciences. One of the most important applications is in establishing the uniqueness of a solution in fractional differential equations and systems and in fractional partial differential equations. They also provide upper bounds to the solutions of the above equations.
In this book the author presents the Opial, Poincare, Sobolev, Hilbert, and Ostrowski fractional differentiation inequalities. Results for the above are derived using three different types of fractional derivatives, namely by Canavati, Riemann-Liouville and Caputo. The univariate and multivariate cases are both examined. Each chapter is self-contained. The theory is presented systematically along with the applications. The application to information theory is also examined.
This monograph is suitable for researchers and graduate students in pure mathematics. Applied mathematicians, engineers, and other applied scientists will also find this book useful.
Introduction.- Opial Type Inequalities for Functions and Their Ordinary and Canavati Fractional Derivatives.- Canavati Fractional Opial Type Inequalities and Fractional Differential Equations.- Riemann-Liouville Opial Type Inequalities for Fractional Derivatives.- Opial Type L^p-Inequalities for Riemann-Liouville Fractional Derivatives.- Opial Type Inequalities Involving Canavati Fractional Derivatives of Two Functions and Applications.- Opial Type Inequalities for Riemann-Liouville Fractional Derivatives of Two Functions with Applications.- Canavati Fractional Opial Type Inequalities for Several Functions and Applications.- Riemann-Liouville Fractional Opial Type Inequalities for Several Functions and Applications.- Converse Canavati Fractional Opial Type Inequalities for Several Functions.- Converse Riemann-Liouville Fractional Opial Type Inequalities for Several Functions.- Multivariate Canavati Fractional Taylor Formula.- Multivariate Caputo Fractional Taylor Formula.- Canavati Fractional Multivariate Opial Type Inequalities on Spherical Shells.- Riemann-Liouville Fractional Multivariate Opial Type Inequalities Over a Spherical Shell.- Caputo Fractional Multivariate Opial Type Inequalities Over a Spherical Shell.- Poincare Type Fractional Inequalities.- Various Sobolev Type Fractional Inequalities.- General Hilbert-Pachpatte Type Inequalities.- General Multivariate Hilbert-Pachpatte Type Integral Inequalties.- Other Hilbert-Pachpatte Type Fractional Interal Inequalities.- Canavati Fractional and Other Approximation of Csiszar's f-Divergence.- Caputo and Riemann-Liouville Fractional Approximation of Csiszar's f-Divergence.- Canavati Fractional Ostrowski Type Inequalities.- Multivariate Canavati Fractional Ostrowski Type Inequalities.- Caputo Fractional Ostrowski Type Inequalities.- Appendix.- References.- List of Symbols.- Index
Series: Progress in Mathematical Physics , Vol. 58
2010, Approx. 230 p., Hardcover
ISBN: 978-3-0346-0077-4
Due: October 2009
Available in English for the first time, for more than 20 years only available in Russian
Volkenstein presents highly complex issues in a readable style
Covers a topic that is still of interest and researched today: how entropy as a physical concept can be found also in other domains, such as biology, information theory, and even arts
Provides a timely introduction to entropy from a thermodynamic perspective
The book "Entropy and Information" deals with the thermodynamical concept of entropy and its relationship to information theory. It is successful in explaining the universality of the term "Entropy" not only as a physical phenomenon, but reveals its existence also in other domains. E.g., Volkenstein discusses the "meaning" of entropy in a biological context and shows how entropy is related to artistic activities.
Written by the renowned Russian bio-physicist Mikhail V. Volkenstein, this book on "Entropy and Information" surely serves as a timely introduction to understand entropy from a thermodynamic perspective and is definitely an inspiring and thought-provoking book that should be read by every physicist, information-theorist, biologist, and even artist.
1. "Reflections on the motive power of fire ...".- 2. The laws of thermodynamics.- 3. Entropy and free energy.- 4. Entropy and probability.- 5. Statistics and mechanics.- 6. Open systems.- 7. Information.- 8. Entropy, information, life.
Series: Graduate Texts in Mathematics , Vol. 255
2009, XX, 716 p. 10 illus., Hardcover
ISBN: 978-0-387-79851-6
Due: June 2009
Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highly-acclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications.
The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the complete arguments now given in the general case.
Preface.- Organization and Notation.- Lie Groups and Algebraic Groups.- Structure of Classical Groups.- Highest-Weight Theory.- Algebras and Representations.- Classical Invariant Theory.- Spinors.- Character Formulas.- Branching Laws.- Tensor Representations of GL(n).- Tensor Representations of O(V) and Sp(V).- Algebraic Groups and Homogeneous Spaces.- Representations on Function Spaces.- Algebraic Geometry.- Linear and Multilinear Algebra.- Associative Algebras and Lie Algebras.- Manifolds and Lie Groups.- References.- Index of Symbols.- Subject Index.
2009, Approx. 250 p., Softcover
ISBN: 978-3-0346-0049-1
Due: August 2009
Develops the basic theory of inequalities
Gradually increases the level of difficulty
Introduces a wide range of techniques used in Mathematical Olympiads
Quest for an equilibrium between algebraic and geometric inequalities
This book presents classical inequalities and specific inequalities which are particularly useful for attacking and solving optimization problems. Most of the examples, exercises and problems that appear in the book originate from Mathematical Olympiad contests around the world. The material is divided into four chapters. In Chapter 1 algebraic inequalities are presented, starting with the basic ones and ending with more sophisticated techniques; Chapter 2 deals with geometric inequalities and Chapter 3 comprises a comprehensive list of recent problems that appeared in those contests during the last 14 years. Finally, hints and solutions to all exercises and problems are given in Chapter 4.
Introduction.- 1 Numerical Inequalities.- 1.1 Order in the real numbers.- 1.2 The quadratic function ax2 + 2bx + c.- 1.3 A fundamental inequality, arithmetic mean-geometric mean.- 1.4. A wonderful inequality: the rearrangement inequality.- 1.5 Convex functions.- 1.6 A helpful inequality.- 1.7 The substitutions strategy.- 1.8 Muirhead's theorem.- 2 Geometric Inequalities.- 2.1 Two basic inequalities.- 2.2 Inequalities between the sides of a triangle.- 2.3 The use of inequalities in the geometry of the triangle.- 2.4 Euler's inequality and some applications.- 2.5 Symmetric functions of a, b and c.- 2.6 Inequalities with areas and perimeters. 2.7 Erdos-Mordell theorem.- 2.8 Optimization problems.- 3 Recent Inequality Problems.- 4 Solutions to Exercises and Problems.- Bibliography.- Index.