Included in series
Les Houches Summer School Proceedings,
Description
The proceedings of the 2005 les Houches summer school on
Mathematical Statistical Physics give and broad and clear
overview on this fast developing area of interest to both
physicists and mathematicians.
Audience
Libraries of mathematics and physics, Individual scientists
Contents
Chapter 1 - K. Johansson: Random Matrices and Determinantal
Processes
Chapter 2 - W. Werner: Some Recent Aspects of Random Conformally
Invariant Systems
Chapter 3 - B. Duplantier: Conformal Random Geometry
Chapter 4 - A.-S. Sznitman: Random Motions in Random Media
Chapter 5 - F. Guerra: An Introduction to Mean Field Spin Glas
Theory: Methods and Results
Chapter 6 - C.M. Newman and D.L. Stein: Short-Range Spin Glasses:
Selected Open Problems
Chapter 7 - G. Parisi: Computing the Number of Metastable States
in Infinite-Range Models
Chapter 8 - Gerard Ben Arous and Jiri Cerny: Dynamics of Trap
Models
Chapter 9 - N. Datta: Quantum Entropy and Quantum Information
Chapter 10 - A. Montanari: Two Lectures on Iterative Coding and
Statistical Mechanics
Chapter 11 - A. Etheridge: Evolution in Fluctuating Populations
Chapter 12 - A. Greven: Multi-Scale Analysis of Population Models
Chapter 13 - Christian Maes: Elements of Nonequilibrium
Statistical Mechanics
Chapter 14 - Frank Redig: Mathematical Aspects of the Abelian
Sandpile Model
Chapter 15 - R. Fernandez: Gibbsianness and Non-Gibbsianness in
Lattice Random Fields
Chapter 16 - A.D. Sokal: Simulation of Statistical Mechanics
Models
Bibliographic & ordering Information
Hardbound, ISBN: 0-444-52813-X, 850 pages, publication date: 2006
Included in series
North-Holland Mathematics Studies, 205
Description
The monograph is written with a view to provide basic tools for
researchers working in Mathematical Analysis and Applications,
concentrating on differential, integral and finite difference
equations. It contains many inequalities which have only recently
appeared in the literature and which can be used as powerful
tools and will be a valuable source for a long time to come. It
is self-contained and thus should be useful for those who are
interested in learning or applying the inequalities with explicit
estimates in their studies.
- Contains a variety of inequalities discovered which find
numerous applications in various branches of differential,
integral and finite difference equations.
- Many inequalities which have only recently discovered in the
literature and can not yet be found in bother book.
- A valuable reference for someone requiring results about
inequalities for use in some applications in various other
branches of mathematics.
- Will be of interest to researchers working both in pure and
applied mathematics and other areas of science and technology,
and it could also be used as a text for an advanced graduate
course.
Contents
Preface
Introduction
Chapter 1. Integral inequalities in one variable
Chapter 2. Integral inequalities in two variables
Chapter 3. Retarded integral inequalities
Chapter 4. Finite difference inequalities in one variable
Chapter 5. Finite difference inequalities in two variables
References
Index
Bibliographic & ordering Information
Hardbound, ISBN: 0-444-52762-1, 320 pages, publication date: 2006
Description
This handbook is volume III in a series devoted to stationary
partial differential quations. Similarly as volumes I and II, it
is a collection of self contained state-of-the-art surveys
written by well known experts in the field. The topics covered by
this handbook include singular and higher order equations,
problems near critically, problems with anisotropic
nonlinearities, dam problem, T-convergence and Schauder-type
estimates.
These surveys will be useful for both beginners and experts and
speed up the progress of corresponding (rapidly developing and
fascinating) areas of mathematics.
Key features:
- Written by well-known experts in the field
- Self-contained volume in series covering one of the most rapid
developing topics in mathematics
Audience
Graduate students and academics
Contents
Preface
Contributors
1. S. Antontsev and S. Shmarev: Elliptic equations with
anisotropic nonlinearity and nonstandard growth conditions.
2. A. Braides: A Handbook of T-convergence.
3. M. del Pino and M. Musso: Bubbling in nonlinear elliptic
problems near criticality.
4. J. Hernandez and F.J. Mancebo: Singular elliptic and parabolic
equations.
5. S. Kichenassamy: Schauder-type estimates and applications.
6. A. Lyaghfouri: The Dam problem.
7. L.A. Peletier: Nonlinear eigenvalue problems for higher order
model equations.
Index
Bibliographic & ordering Information
Hardbound, ISBN: 0-444-52846-6, publication date: 2006
Description
This handbook is the third volume in a series of volumes devoted
to self contained and up-to-date surveys in the tehory of
ordinary differential equations, written by leading researchers
in the area. All contributors have made an additional effort to
achieve readability for mathematicians and scientists from other
related fields so that the chapters have been made accessible to
a wide audience.
These ideas faithfully reflect the spirit of this multi-volume
and hopefully it becomes a very useful tool for reseach, learing
and teaching. This volumes consists of seven chapters covering a
variety of problems in ordinary differential equations. Both pure
mathematical research and real word applications are reflected by
the contributions to this volume.
Key features
- Written by leading experts in the area
- Seven chapters covering a variety of problems in ordinary
differential equations
- Pure mathematical and real word applications are well reflected
Audience
Mathematicians, Researchers, (post-)graduate students
Contents
Preface
1. Topological Principles for Ordinary Differential Equations (J.
Andres).
2. Heteroclinic Orbtis for Some Classes of Second and Fourth
Order Differential Equations (D. Bonheure and L. Sanchez).
3. A Qualitative Analysis, via Lower and Upper Solutions, of
First Order Periodic Evolutionary Equations with Lack of
Uniqueness (C. DeCoster, F. Obersne and P. Omari).
4. Bifurcation Theory of Limit Cycles of Planar Systems (M. Han).
5. Functional Differential Equations with State-Dependent Delays:
Theory and Applications (F. Hartung, T. Krisztin, H.O. Walther
and J. Wu).
6. Global Solutions Branches and Exact Multiplicity of Solutions
for Two Point Boundary Value Problems (I. Rachunkova, S. Stanek
and M. Tvrdy).
7. Singularities and Laplacians in Boundary Value Problems for
Nonlinear Ordinary Differential Equations.
Index
Bibliographic & ordering Information
Hardbound, ISBN: 0-444-52849-0, 640 pages, publication date: 2006
Audience
This one-semester basic probability textbook is written for
students in mathematics, physics, engineering, statistics,
actuarial science, operations research, and computer science with
a background in elementary calculus taking upper level or
graduate level introduction to probability courses.
Contents
1. SOME MOTIVATING EXAMPLES 2. SOME FUNDAMENTAL CONCEPTS 3. THE
CONCEPT OF PROBABILITY AND BASIC RESULTS 4. CONDITIONAL
PROBABILITY AND INDEPENDENCE 5. NUMERICAL CHARACTERISTICS OF A
RANDOM VARIABLE 6. SOME SPECIAL DISTRIBUTIONS 7. JOINT
PROBABILITY DENSITY FUNCTION OF TWO RANDOM VARIABLES AND RELATED
QUANTITIES 8. JOINT MOMENT GENERATING FUNCTION, COVARIANCE AND
CORRELATION COEFFICIENT OF TWO RANDOM VARIABLES 9. SOME
GENERALIZATIONS TO k RANDOM VARIABLES, AND THREE MULTIVARIATE
DISTRIBUTIONS 10. INDEPENDENCE OF RANDOM VARIABLES AND SOME
APPLICATIONS 11. TRANSFORMATION OF RANDOM VARIABLES 12. TWO MODES
OF CONVERGENCE, THE WEAK LAW OF LARGE NUMBERS, THE CENTRAL LIMIT
THEOREM, AND FURTHER RESULTS 13. AN OVERVIEW OF STATISTICAL
INFERENCE APPENDIX TABLES 1. The Cumulative Binomial Distribution
2. The Cumulative Poisson Distribution 3. The Normal Distribution
4. Critical Values of the Chi-Square Distribution 5. Table of
Selected Discrete and Continuous Distributions and Some of Their
Characteristics 6. Handy Reference to Some Formulas Used in the
Text SOME NOTATION AND ABBREVIATIONS ANSWERS TO THE EVEN-NUMBERED
EXERCISES
Bibliographic & ordering Information
Hardbound, ISBN: 0-12-088595-6, 416 pages, publication date: 2007
Included in series
Mathematics in Science and Engineering, 207
Description
Mixing up various disciplines frequently produces something that
are profound and far-reaching. Cybernetics is such an often-quoted
example. Mix of information theory, statistics and computing
technology proves to be very useful, which leads to the recent
development of information-theory based methods for estimating
complicated probability distributions.
Estimating probability distribution of a random variable is the
fundamental task for quite some fields besides statistics, such
as reliability, probabilistic risk analysis (PSA), machine
learning, pattern recognization, image processing, neural
networks and quality control. Simple distribution forms such as
Gaussian, exponential or Weibull distributions are often employed
to represent the distributions of the random variables under
consideration, as we are taught in universities. In engineering,
physical and social science applications, however, the
distributions of many random variables or random vectors are so
complicated that they do not fit the simple distribution forms at
al.
Exact estimation of the probability distribution of a random
variable is very important. Take stock market prediction for
example. Gaussian distribution is often used to model the
fluctuations of stock prices. If such fluctuations are not
normally distributed, and we use the normal distribution to
represent them, how could we expect our prediction of stock
market is correct? Another case well exemplifying the necessity
of exact estimation of probability distributions is reliability
engineering. Failure of exact estimation of the probability
distributions under consideration may lead to disastrous designs.
There have been constant efforts to find appropriate methods to
determine complicated distributions based on random samples, but
this topic has never been systematically discussed in detail in a
book or monograph. The present book is intended to fill the gap
and documents the latest research in this subject.
Determining a complicated distribution is not simply a multiple
of the workload we use to determine a simple distribution, but it
turns out to be a much harder task. Two important mathematical
tools, function approximation and information theory, that are
beyond traditional mathematical statistics, are often used.
Several methods constructed based on the two mathematical tools
for distribution estimation are detailed in this book. These
methods have been applied by the author for several years to many
cases. They are superior in the following senses:
(1) No prior information of the distribution form to be
determined is necessary. It can be determined automatically from
the sample; (2) The sample size may be large or small; (3) They
are particularly suitable for computers.
It is the rapid development of computing technology that makes it
possible for fast estimation of complicated distributions.
The methods provided herein well demonstrate the significant
cross influences between information theory and statistics, and
showcase the fallacies of traditional statistics that, however,
can be overcome by information theory.
Key Features:
- Density functions automatically determined from samples
- Free of assuming density forms
- Computation-effective methods suitable for PC
Audience
Statisticians and academic researchers.
Contents
Preface
Chapter 1. Randomness and probability
Chapter 2. Inference and statistics
Chapter 3. Random numbers and their applications
Chapter 4. Approximation and B-spline function
Chapter 5. Disorder, entropy and entropy estimation
Chapter 6. Estimation of 1-D complicated distributions based on
large samples
Chapter 7. Estimation of 2-D complicated distributions based on
large samples
Chapter 8. Estimation of 1-D complicated distribution based on
small samples
Chapter 9. Estimation of 2-D complicated distribution based on
small samples
Chapter 10. Estimation of the membership function
Chapter 11. Code specifications
Bibliography
Index
Bibliographic & ordering Information
Hardbound, ISBN: 0-444-52796-6, publication date: 2006