Audet, Charles; Hansen, Pierre; Savard, Gilles (Eds.)
Essays and Surveys in Global Optimization
2005, XIV, 298 p. 15 illus., Hardcover
ISBN: 0-387-25569-9
About this book
Global optimization aims at solving the most general problem of
deterministic mathematical programming: to find the global
optimum of a nonlinear, nonconvex, multivariate function of
continuous and/or integer variables subject to constraints which
may be themselves nonlinear and nonconvex. In addition, once the
solution is found, proof of its optimality is also expected from
this methodology. ESSAYS AND SURVEYS IN GLOBAL OPTIMIZATION is
the most recent examination of its mathematical capability,
power, and wide ranging solution to many fields in the applied
sciences.
In a series of topical chapters, the first section of the book
appraises the mathematical properties and algorithms for general
global optimization problems. These include chapters on "Unilateral
Analysis and Duality"; "Monotonic Optimization: Branch
and Cut Methods"; "Duality Bound Methods in Global
Optimization"; "General Quadratic Programming";
"On Solving Polynomial, Factorable, and Black-Box
Optimization Problems using the RLT Methodology"; and "Bilevel
Programming." The book’s second section offers a variety
of current application chapters where global optimization has
been applied to assorted problems in diverse fields. These
include chapters on "Application of Global Optimization to
Portfolio Analysis"; "Optimization Techniques in
Medicine"; "Global Optimization in Geometry?Circle
Packing into the Square"; and "A Deterministic Global
Optimization Algorithm for Design Problems."
Table of contents
Foreword.- Avant-propos.- Contributing Authors.- Preface.-
Unilaterial Analysis and Duality.- Monotonic Optimization: Branch
and Cut Methods.- Duality Bound Methods in Global Optimization.-
General Quadratic Programming.- On Solving Polynomial,
Factorable, and Black-box Optimization Problems Using the RLT
Methodology.- Bilevel Programming.- Applications of Global
Optimization to Portfolio Analysis.- Optimization Techniques in
Medicine.- Global Optimization in Geometry - Circle Packing into
the Square.- A Deterministic Global Optimization Algorithm for
Design Problems.
Lurie, A.I.
Theory of Elasticity
Series: Foundations of Engineering Mechanics
2005, IV, 1050 p., Hardcover
ISBN: 3-540-24556-1
About this book
This invaluable treatise belongs to the cultural heritage of mechanics.
It is an encyclopaedia of the classic and analytic approaches of continuum
mechanics and of many domains of natural science. The book is unique also
because an impressive number of methods and approaches it displays have
been worked out by the author himself. In particular, this implies a full
consistency of notation, ideas and mathematical apparatus which results
in a unified approach to a broad class of problems. The book is of great
interest for engineers who will find a lot of analytical formulae for very
different problems covering nearly all aspects of the elastic behavior
of materials. In particular, it fills the gap between the well-developed
numerical methods and sophisticated methods of elasticity theory. It is
also intended for researchers and students taking their first steps in
continuum mechanics as it offers a carefully written and logically substantiated
basis of both linear and nonlinear continuum mechanics.
Table of contents
Stress Tensor.- Deformation of a Continuum.- The Constitutive
Laws of the Linear Theory of Elasticity.- Governing Relationships
in the Linear Theory of Elasticity.- Three-dimensional Problems
in the Theory of Elasticity.- Saint-Venant's Problem.- The Plane
Problem of the Theory of Elasticity.- Constitutive Laws for
Nonlinear Elastic Bodies.- Problems and Methods of the Nonlinear
Theory of Elasticity.
Duchesne, Pierre; Remillard, Bruno (Eds.)
Statistical Modeling and Analysis for Complex Data Problems
2005, XIV, 330 p. 35 illus., Hardcover
ISBN: 0-387-24554-5
About this book
Statistical Modeling and Analysis for Complex Data Problems
treats some of today’s more complex problems and it reflects
some of the important research directions in the field. Twenty-nine
authors ? largely from Montreal’s GERAD Multi-University
Research Center and who work in areas of theoretical statistics,
applied statistics, probability theory, and stochastic processes
? present survey chapters on various theoretical and applied
problems of importance and interest to researchers and students
across a number of academic domains.
Table of contents
Foreword.- Contributing Authors.- Preface.- Dependence Properties
of Meta-Elliptical Distributions.- The Statistical Significance
of Palm Beach County.- Bayesian Functional Estimation of Hazard
Rates for Randomly Right Censored Data Using Fourier Series
Methods.- Conditions for the Validity of F-Ratio Tests for
Treatment and Carryover Effects in Crossover Designs.- Bias in
Estimating the Variance of K-Fold Cross Validation.- Effective
Construction of Modified Histograms in Higher Dimensions.- On
Robust Diagnostics at Individual Lags Using RA-ARX Estimators.-
Bootstrap Confidence Intervals for Periodic Preventive
Replacement Policies.- Statistics for Comparison of Two
Independent cDNA Filter Microarrays.- Large Deviations for
Interacting Processes in the Strong Topology.- Asymptotic
Distribution of a Simple Linear Estimator for VARMA Models in
Echolon Form.- Recent Results for Linear Time Series Models with
Non Independent Innovations.- Filtering of Images for Detecting
Multiple Targets Trajectories.- Optimzal Detection of
Periodicities in Vector Autoregressive Models.- The Wilcoxon
Signed-Rank Test for Cluster Correlated Data.
SITU, Rong
Theory of Stochastic Differential Equations with Jumps and
Applications
Mathematical and Analytical Techniques with Applications to
Engineering
2005, XX, 434 p., Hardcover
ISBN: 0-387-25083-2
About this book
Stochastic differential equations (SDEs) are a powerful tool in
science, mathematics, economics and finance. This book will help
the reader to master the basic theory and learn some applications
of SDEs. In particular, the reader will be provided with the
backward SDE technique for use in research when considering
financial problems in the market, and with the reflecting SDE
technique to enable study of optimal stochastic population
control problems. These two techniques are powerful and
efficient, and can also be applied to research in many other
problems in nature, science and elsewhere.
Table of contents
Martingale Theory and the Stochastic Integral for Point Processes.-
Brownian Motion, Stochastic Integral and Ito’s Formula.-
Stochastic Differential Equations.- Some Useful Tools in
Stochastic Differential Equations.- Stochastic Differential
Equations with Non-Lipschitzian Coefficients.- How to Use the
Stochastic Calculus to Solve SDE.- Linear and Non-Linear
Filtering.- Option Pricing in a Financial Market and BSDE.-
Optimal Consumption by H-J-B Equation and Lagrange Method.-
Comparison Theorem and Stochastic Pathwise Control.- Stochastic
Population Control and Reflecting SDE.- Maximum Principle for
Stochastic Systems with Jumps.- Short Review on Basic Probability
Theory.- Space D and Skorohod’s Metric.- Monotone Class
Theorems. Convergence of Random Processes.
D. M.Y. Sommerville
The Elements of Non-Euclidean Geometry
ISBN: 0-486-44222-5
Page Count: 288
Dimensions: 5 3/8 x 8 1/2
This volume became the standard text in the field almost immediately upon
its original publication. Renowned for its lucid yet meticulous exposition,
it can be appreciated by anyone familiar with high school algebra and geometry.
Its arrangement follows the traditional pattern of plane and solid geometry,
allowing students to follow the development of non-Euclidean geometry from
a fundamental analysis of the concept of parallelism to such advanced topics
as inversion and transformations. Although geared toward undergraduates,
it treats such topics as the relation between parataxy and parallelism,
the absolute measure, the pseudosphere, and Gauss’ proof of the defect-area
theorem. 1914 ed. 133 figures.
Table of Contents
I. Historical
II. Elementary Hyperbolic Geometry
III. Elliptic Geometry
IV. Analytical Geometry
V. Representations of Non-Euclidean Geometry in Euclidean Space
VI. “Space-Curvature” and the Philosophical Bearing of Non-Euclidean
Geometry
VII. Radical Axes, Homothetic Centres, and Systems of Circles
VIII. Inversion and Allied Transformations
IX. The Conic
Index