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Academic Press

A First Course in Stochastic Processes
1st Edition
May 12, 2014
Samuel Karlin
English
A First Course in Stochastic Processes focuses on several principal areas of stochastic processes and the diversity of applications of stochastic processes, including Markov chains, Brownian motion, and Poisson processes. The publication first takes a look at the elements of stochastic processes, Markov chains, and the basic limit theorem of Markov chains and applications. Discussions focus on criteria for recurrence, absorption probabilities, discrete renewal equation, classification of states of a Markov chain, and review of basic terminologies and properties of random variables and distribution functions. The text then examines algebraic methods in Markov chains and ratio theorems of transition probabilities and applications. The manuscript elaborates on the sums of independent random variables as a Markov chain, classical examples of continuous time Markov chains, and continuous time Markov chains. Topics include differentiability properties of transition probabilities, birth and death processes with absorbing states, general pure birth processes and Poisson processes, and recurrence properties of sums of independent random variables. The book then ponders on Brownian motion, compounding stochastic processes, and deterministic and stochastic genetic and ecological processes. The publication is a valuable source of information for readers interested in stochastic processes.
Group Theory and Its Applications
1st Edition
May 12, 2014
Ernest M. Loebl
English
Group Theory and Its Applications focuses on the applications of group theory in physics and chemistry. The selection first offers information on the algebras of lie groups and their representations and induced and subduced representations. Discussions focus on the functions of positive type and compact groups; orthogonality relations for square-integrable representations; group, topological, Borel, and quotient structures; and classification of semisimple lie algebras in terms of their root systems. The text then takes a look at the generalization of Euler's angles and projective representation of the Poincare group in a quaternionic Hilbert space. The manuscript ponders on group theory in atomic spectroscopy, group lattices and homomorphism, and group theory in solid state physics. Topics include band theory of solids, lattice vibrations in solids, stationary states in the quantum theory of matter, coupled tensors, and shell structure. The text then examines the group theory of harmonic oscillators and nuclear structure and de Sitter space and positive energy. The selection is a dependable reference for physicists and chemists interested in group theory and its applications.
Introductory Statistics for Psychology
The Logic and the Methods
1st Edition
May 12, 2014
Gustav Levine
English
Introductory Statistics for Psychology: The Logic and the Methods presents the concepts of experimental design that are carefully interwoven with the statistical material. This book emphasizes the verbalization of conclusions to experiments, which is another means of communicating the reasons for statistical analyses. Organized into 17 chapters, this book begins with an overview of alternative ways of stating the conclusions from a significant interaction. This text then presents the analysis of variance and introduces the summation sign and its use. Other chapters consider frequency distribution as any presentation of data that offers the frequency with which each score occurs. This book discusses as well the differences in and among people, which are a constant source of variability in test scores, and in most other measurements of people. The final chapter deals with the working knowledge of arithmetic and elementary algebra. This book is a valuable resource for students and psychologists.
Functional Equations in Probability Theory
1st Edition
May 12, 2014
Ramachandran Balasubrahmanyan + 1 more
English
Functional Equations in Probability Theory deals with functional equations in probability theory and covers topics ranging from the integrated Cauchy functional equation (ICFE) to stable and semistable laws. The problem of identical distribution of two linear forms in independent and identically distributed random variables is also considered, with particular reference to the context of the common distribution of these random variables being normal. Comprised of nine chapters, this volume begins with an introduction to Cauchy functional equations as well as distribution functions and characteristic functions. The discussion then turns to the nonnegative solutions of ICFE on R+; ICFE with a signed measure; and application of ICFE to the characterization of probability distributions. Subsequent chapters focus on stable and semistable laws; ICFE with error terms on R+; independent/identica... distributed linear forms and the normal laws; and distribution problems relating to the arc-sine, the normal, and the chi-square laws. The final chapter is devoted to ICFE on semigroups of Rd. This book should be of interest to mathematicians and statisticians.
Graph Theory and Computing
1st Edition
May 12, 2014
Ronald C. Read
English
Graph Theory and Computing focuses on the processes, methodologies, problems, and approaches involved in graph theory and computer science. The book first elaborates on alternating chain methods, average height of planted plane trees, and numbering of a graph. Discussions focus on numbered graphs and difference sets, Euclidean models and complete graphs, classes and conditions for graceful graphs, and maximum matching problem. The manuscript then elaborates on the evolution of the path number of a graph, production of graphs by computer, and graph-theoretic programming language. Topics include FORTRAN characteristics of GTPL, design considerations, representation and identification of graphs in a computer, production of simple graphs and star topologies, and production of stars having a given topology. The manuscript examines the entropy of transformed finite-state automata and associated languages; counting hexagonal and triangular polyominoes; and symmetry of cubical and general polyominoes. Graph coloring algorithms, algebraic isomorphism invariants for graphs of automata, and coding of various kinds of unlabeled trees are also discussed. The publication is a valuable source of information for researchers interested in graph theory and computing.
Recombinant DNA Laboratory Manual
1st Edition
May 12, 2014
Judith W. Zyskind + 1 more
English
Recombinant DNA Laboratory Manual is a laboratory manual on the fundamentals of recombinant DNA techniques such as gel electrophoresis, in vivo mutagenesis, restriction mapping, and DNA sequencing. Procedures that are useful for studying either prokaryotes or eukaryotes are discussed, and experiments are included to teach the fundamentals of recombinant DNA technology. Hands-on computer sessions are also included to teach students how to enter and manipulate sequence information. Comprised of nine chapters, this book begins with an introduction to bacterial growth parameters, how to measure bacterial cell growth, and how to plot cell growth data. The discussion then turns to the isolation and analysis of chromosomal DNA in bacteria and Drosophila; plasmid DNA isolation and agarose gel analysis; and introduction of DNA into cells. Subsequent chapters deal with Tn5 mutagenesis of pBR329; DNA cloning in M13; DNA sequencing; and DNA gel blotting, probe preparation, hybridization, and hybrid detection. The book concludes with an analysis of lambda phage manipulations. This manual is intended for advanced undergraduate or beginning graduate students and should also be helpful to established investigators who are changing their research focus.
Random Matrices and the Statistical Theory of Energy Levels
1st Edition
May 12, 2014
M. L. Mehta
English
Random Matrices and the Statistical Theory of Energy Levels focuses on the processes, methodologies, calculations, and approaches involved in random matrices and the statistical theory of energy levels, including ensembles and density and correlation functions. The publication first elaborates on the joint probability density function for the matrix elements and eigenvalues, including the Gaussian unitary, symplectic, and orthogonal ensembles and time-reversal invariance. The text then examines the Gaussian ensembles, as well as the asymptotic formula for the level density and partition function. The manuscript elaborates on the Brownian motion model, circuit ensembles, correlation functions, thermodynamics, and spacing distribution of circular ensembles. Topics include continuum model for the spacing distribution, thermodynamic quantities, joint probability density function for the eigenvalues, stationary and nonstationary ensembles, and ensemble averages. The publication then examines the joint probability density functions for two nearby spacings and invariance hypothesis and matrix element correlations. The text is a valuable source of data for researchers interested in random matrices and the statistical theory of energy levels.
Pathology, Vector Studies, and Culture
1st Edition
May 12, 2014
Julius P. Kreier
English
Malaria: Volume 2, Pathology, Vector Studies, and Culture is a collection of papers that deals with erythrocyte destruction mechanism in malaria, the pathology of malaria, colonization of laboratory mosquitoes, and their transmission of plasmodia. Other papers describe the culture of the invertebrate stages of plasmodia, of mosquito tissues, and also of erythrocytic and exoerythrocytic stages of plasmodia. One paper constructs a model to show the roles of the different destructive and regenerative processes in the mechanisms of erythrocyte destruction in malaria. Another paper describes the organ changes and physiopathological mechanism connected with Plasmodium infection. These organs concern the spleen, liver, heart, and vascular system. One paper reviews the procedures involved in malaria transmission by mosquitoes, as well as some specialized procedures unique in avian, rodent, simian, and human malarias. Another paper discusses the benefits and drawbacks of a culture medium based on the composition of adult anopheline hemolymph. This medium should lead to a rapid growth rate in primary cultures of mosquito cells and a shorter interval of adaptation for continuous cell lines. The collection can prove useful for pharmacologists, general medical practitioners, investigators, and laboratory technicians involved in mosquito borne diseases or tropical medicine research.
A First Course in Linear Algebra
1st Edition
May 12, 2014
Daniel Zelinsky
Samuel S. Saslaw
English
A First Course in Linear Algebra provides an introduction to the algebra and geometry of vectors, matrices, and linear transformations. This book is designed as a background for second-year courses in calculus of several variables and differential equations where the theory of linear differential equations parallels that of linear algebraic equations. The topics discussed include the multiplication of vectors by scalars, vectors in n-space, planes and lines, and composites of linear mappings. The symmetric matrices and mappings, quadratic forms, change of coordinates, and effect of change of basis on matrices of linear functions are also described. This text likewise considers the computation of determinants, diagonalizable transformations, computation of eigenvalues and eigenvectors, and principal axis theorem. This publication is suitable for college students taking a course in linear algebra.
An Introduction to Numerical Mathematics
1st Edition
May 12, 2014
Eduard L. Stiefel
English
An Introduction to Numerical Mathematics provides information pertinent to the fundamental aspects of numerical mathematics. This book covers a variety of topics, including linear programming, linear and nonlinear algebra, polynomials, numerical differentiation, and approximations. Organized into seven chapters, this book begins with an overview of the solution of linear problems wherein numerical mathematics provides very effective algorithms consisting of finitely many computational steps. This text then examines the method for the direct solution of a definite problem. Other chapters consider the determination of frequencies in freely oscillating mechanical or electrical systems. This book discusses as well eigenvalue problems for oscillatory systems of finitely many degrees of freedom, which can be reduced to algebraic equations. The final chapter deals with the approximate representation of a function f(x) given by I-values as in the form of a table. This book is a valuable resource for physicists, mathematicians, theoreticians, engineers, and research workers.

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