Series: Monographs and Surveys in Pure and Applied Math
ISBN: 9781439836903
Publication Date: 03/05/2010
Pages: 280
Binding(s): Hardback
A self-contained discussion of quasilinear hyperbolic PDEs and systems, this book includes carefully chosen physical examples in gas dynamics and shallow water theory. It introduces the necessary mathematical concepts in the first three chapters, which cover wave propagation problems and the issues to be developed in the remainder of the text. The book describes the applications of the characteristic approach, singular surface theory, asymptotic methods, self-similarity and group theoretic methods, and the theory of generalized functions to several concrete physical examples from radiation gas dynamics, magneto gas dynamics, and nonequilibrium flows.
Hyperbolic Systems of Conservation Laws. Scalar Hyperbolic Equations in One-dimension. Hyperbolic Systems in one space Dimension. Evolution of Weak Waves in Hyperbolic Systems. Asymptotic Waves for Quasilinear Systems. Self-similar Solutions involving Discontinuities & their Interaction. Kinematics of a Shock of Arbitrary Strength.
Series: Chapman Hall/CRC Mathematics Series
ISBN: 9781439835982
Publication Date: 15/09/2010
Pages: 266
Binding(s): Hardback
A Concise Introduction to Pure Mathematics, Second Edition provides a robust bridge between high school and university mathematics, expanding upon basic topics in ways that will interest first-year students in mathematics and related fields and stimulate further study. Divided into 22 short chapters, this textbook offers a selection of exercises ranging from routine calculations to quite challenging problems.
The author discusses real and complex numbers and explains how these concepts are applied in solving natural problems. He introduces topics in analysis, geometry, number theory, and combinatorics.
The textbook allows for the design of courses with various points of emphasis, because it can be divided into four fairly independent sections related to: an introduction to number systems and analysis; theory of the integers; an introduction to discrete mathematics; and functions, relations, and countability.
Sets and proofs. Number systems. Decimals. Inequalities. nth Roots and Rational Powers. Complex numbers. Polynomial equations. Induction. Euler's formula and platonic solids. Introduction to analysis. The integers. Prime factorization. More on prime numbers. Congruence of integers. More on congruence. Secret codes. Counting and choosing. More on sets. Equivalence relations. Functions. Permutations. Infinity.
Series: Chapman & Hall/CRC Texts in Statistical Science
ISBN: 9781439816806
Publication Date: 17/07/2011
Pages: 544
Binding(s): Hardback
Computer-Aided Multivariate Analysis, Fourth Edition enables researchers and students with limited mathematical backgrounds to understand the concepts underlying multivariate statistical analysis, perform analysis using statistical packages, and understand the output. New topics include Loess and Poisson regression, nominal and ordinal logistic regression, interpretation of interactions in logistic and survival analysis, and imputation for missing values. This book includes new exercises and references, and updated options in the latest versions of the statistical packages. All data sets and codebooks are available for download.
The authors explain the assumptions made in performing each analysis and test, how to determine if your data meets those assumptions, and what to do if they do not. What to Watch out for sections in each chapter warn of common difficulties. By reading this text, you will know what method to use with your data set, how to get the results, and how to interpret them and explain them to others.
PREPARATION FOR ANALYSIS: What is Multivariate Analysis? Characterizing Data for Future Analyses. Preparing for Data Analysis. Data Screening and Data Transformation. Selecting Appropriate Analyses. APPLIED REGRESSION ANALYSIS: Simple Linear Regression and Correlation. Multiple Regression and Correlation. Variable Selection in Regression Analysis. Special Regression Topics. MULTIVARIATE ANALYSIS: Canonical Correlation Analysis. Discriminant Analysis. Logistic Regression. Regression Analysis Using Survival Data. Principal Components Analysis. Factor Analysis. Cluster Analysis. Log-Linear Analysis. APPENDICES.
Abstract
Property testing algorithms are ?ultra"-efficient algorithms that decide whether a given object (e.g., a graph) has a certain property (e.g., bipartiteness), or is significantly different from any object that has the property. To this end property testing algorithms are given the ability to perform (local) queries to the input, though the decisions they need to make usually concern properties with a global nature. In the last two decades, property testing algorithms have been designed for many types of objects and properties, amongst them, graph properties, algebraic properties, geometric properties, and more. In this article we survey results in property testing, where our emphasis is on common analysis and algorithmic techniques. Among the techniques surveyed are the following:
a) The self-correcting approach, which was mainly applied in the study of property testing of algebraic properties;
b) The enforce and test approach, which was applied quite extensively in the analysis of algorithms for testing graph properties (in the dense-graphs model), as well as in other contexts;
c) Szemeredi's Regularity Lemma, which plays a very important role in the analysis of algorithms for testing graph properties (in the dense-graphs model);
d) The approach of Testing by implicit learning, which implies efficient testability of membership in many functions classes.
e) Algorithmic techniques for testing properties of sparse graphs, which include local search and random walks.
Abstract 1 Introduction 2 Preliminaries 3 The Self-Correcting Approach 4 The Enforce-and-Test Approach 5 Testing by Implicit Learning 6 The Regularity Lemma 7 Local-Search Algorithms 8 Random Walks Algorithms 9 Lower Bounds 10 Other Results 11 Extensions, Generalizations, and Related Problems References