CBMS-NSF Regional Conference Series in Applied Mathematics – serie
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52 produkter
52 produkter
674 kr
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An exploration of the interrelated fields of design of experiments and sequential analysis with emphasis on the nature of theoretical statistics and how this relates to the philosophy and practice of statistics.
554 kr
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Presents a coherent body of theory for the derivation of the sampling distributions of a wide range of test statistics. Emphasis is on the development of practical techniques. A unified treatment of the theory was attempted, e.g., the author sought to relate the derivations for tests on the circle and the two-sample problem to the basic theory for the one-sample problem on the line. The Markovian nature of the sample distribution function is stressed, as it accounts for the elegance of many of the results achieved, as well as the close relation with parts of the theory of stochastic processes.
612 kr
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This monograph provides a relatively brief introduction to conjugate duality in both finite- and infinite-dimensional problems. Emphasizes the fundamental importance of the concepts of Lagrangian function, saddle-point, and saddle-value. General examples are drawn from nonlinear programming, approximation, stochastic programming, the calculus of variations, and optimal control.
426 kr
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Presents a theory of indexing capable of ranking index terms, or subject identifiers in decreasing order of importance. This leads to the choice of good document representations, and also accounts for the role of phrases and of thesaurus classes in the indexing process.This study is typical of theoretical work in automatic information organization and retrieval, in that concepts are used from mathematics, computer science, and linguistics. A complete theory of information retrieval may emerge from an appropriate combination of these three disciplines.
370 kr
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Solutions of the wave equation or Maxwell's equations in boundary value and free space problems are analyzed. Hyperbolic systems in domains going off to infinity are studied. New results on Maxwell's equations and nonstar shaped reflecting bodies are included.
344 kr
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Mathematical theories of populations have appeared both implicitly and explicitly in many important studies of populations, human populations as well as populations of animals, cells and viruses. They provide a systematic way for studying a population's underlying structure.In this book, a basic model in population age structure is studied and then applied, extended and modified, to several population phenomena such as stable age distributions, self-limiting effects, and two-sex populations. Population genetics are studied with special attention to derivation and analysis of a model for a one-locus, two-allele trait in a large randomly mating population. The dynamics of contagious phenomena in a population are studied in the context of epidemic diseases.
370 kr
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Lectures on a unified theory of and practical procedures for the numerical solution of very general classes of linear and nonlinear two point boundary-value problems.
647 kr
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An introduction to aspects of the theory of dynamical systems based on extensions of Liapunov's direct method. The main ideas and structure for the theory are presented for difference equations and for the analogous theory for ordinary differential equations and retarded functional differential equations. The latest results on invariance properties for non-autonomous time-varying systems processes are presented for difference and differential equations.
807 kr
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A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.
901 kr
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Topics include: ways modern statistical procedures can yield estimates of pi more precisely than the original Buffon procedure traditionally used; the question of density and measure for random geometric elements that leave probability and expectation statements invariant under translation and rotation; the number of random line intersections in a plane and their angles of intersection; developments due to W. L. Stevens's ingenious solution for evaluating the probability that n random arcs of size a cover a unit circumference completely; the development of M. W. Crofton's mean value theorem and its applications in classical problems; and an interesting problem in geometrical probability presented by a karyograph.
794 kr
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Explores modern topics in graph theory and its applications to problems in transportation, genetics, pollution, perturbed ecosystems, urban services, and social inequalities. The author presents both traditional and relatively atypical graph-theoretical topics to best illustrate applications.
Integer Programming
Facets, Subadditivity, and Duality for Group and Semi-Group Problems
Häftad, Engelska, 1987
581 kr
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This monograph considers pure integer programming problems which concern packing, partitioning or covering. For this class of problems, an algorithmic framework using a duality approach is offered. Furthermore, the author proposes for the first time a general framework for both packing and covering problems characterizing the convex whole of integer solutions.
694 kr
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Focuses on finding the minimum number of arithmetic operations needed to perform the computation and on finding a better algorithm when improvement is possible. The author concentrates on that class of problems concerned with computing a system of bilinear forms.Results that lead to applications in the area of signal processing are emphasized, since (1) even a modest reduction in the execution time of signal processing problems could have practical significance; (2) results in this area are relatively new and are scattered in journal articles; and (3) this emphasis indicates the flavor of complexity of computation.
687 kr
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Draws together some mathematical ideas that are useful in population genetics, concentrating on a few aspects which are both biologically relevant and mathematically interesting.
687 kr
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A monograph on some of the ways geometry and analysis can be used in mathematical problems of physical interest. The roles of symmetry, bifurcation, and Hamiltonian systems in diverse applications are explored.
527 kr
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A treatment of the convergence of probability measures from the foundations to applications in limit theory for dependent random variables. Mapping theorems are proved via Skorokhod's representation theorem; Prokhorov's theorem is proved by construction of a content. The limit theorems at the conclusion are proved under a new set of conditions that apply fairly broadly, but at the same time make possible relatively simple proofs.
Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves
Häftad, Engelska, 1987
554 kr
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This book deals with the mathematical side of the theory of shock waves. The author presents what is known about the existence and uniqueness of generalized solutions of the initial value problem subject to the entropy conditions. The subtle dissipation introduced by the entropy condition is investigated and the slow decay in signal strength it causes is shown.
687 kr
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The jackknife and the bootstrap are nonparametric methods for assessing the errors in a statistical estimation problem. They provide several advantages over the traditional parametric approach: the methods are easy to describe and they apply to arbitrarily complicated situations; distribution assumptions, such as normality, are never made.This monograph connects the jackknife, the bootstrap, and many other related ideas such as cross-validation, random subsampling, and balanced repeated replications into a unified exposition. The theoretical development is at an easy mathematical level and is supplemented by a large number of numerical examples.The methods described in this monograph form a useful set of tools for the applied statistician. They are particularly useful in problem areas where complicated data structures are common, for example, in censoring, missing data, and highly multivariate situations.
491 kr
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Provides a comprehensive theory of the approximations of quantile processes in light of recent advances, as well as some of their statistical applications.
741 kr
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An introduction to far reaching developments in theoretical combustion, with special emphasis on flame stability, a topic that has, to date, benefited most from the application of modern asymptotic methods. The authors provide a modern view of flame theory, and a complete description of the longstanding ignition and explosion problems, including the solutions that were made available independently by Kapila and Kassoy through activation energy asymptotics, the main theme of this monograph.
763 kr
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There has been an explosive growth in the field of combinatorial algorithms. These algorithms depend not only on results in combinatorics and especially in graph theory, but also on the development of new data structures and new techniques for analyzing algorithms.Four classical problems in network optimization are covered in detail, including a development of the data structures they use and an analysis of their running time.Data Structures and Network Algorithms attempts to provide the reader with both a practical understanding of the algorithms, described to facilitate their easy implementation, and an appreciation of the depth and beauty of the field of graph algorithms.
607 kr
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Uses fundamental ideas in dynamical systems to answer questions of a biological nature, in particular, questions about the behavior of populations given a relatively few hypotheses about the nature of their growth and interaction. The principal subject treated is that of coexistence under certain parameter ranges, while asymptotic methods are used to show competitive exclusion in other parameter ranges. Finally, some problems in genetics are posed and analyzed as problems in nonlinear ordinary differential equations.
607 kr
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Many situations exist in which solutions to problems are represented as function space integrals. Such representations can be used to study the qualitative properties of the solutions and to evaluate them numerically using Monte Carlo methods. The emphasis in this book is on the behavior of solutions in special situations when certain parameters get large or small.
Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces
Häftad, Engelska, 1985
647 kr
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A systematic, self-contained treatment of the theory of stochastic differential equations in infinite dimensional spaces. Included is a discussion of Schwartz spaces of distributions in relation to probability theory and infinite dimensional stochastic analysis, as well as the random variables and stochastic processes that take values in infinite dimensional spaces.
1 061 kr
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The soliton is a dramatic concept in nonlinear science. What makes this book unique in the treatment of this subject is its focus on the properties that make the soliton physically ubiquitous and the soliton equation mathematically miraculous. Here, on the classical level, is the entity field theorists have been postulating for years: a local traveling wave pulse; a lump-like coherent structure; the solution of a field equation with remarkable stability and particle-like properties. It is a fundamental mode of propagation in gravity-driven surface and internal waves; in atmospheric waves; in ion acoustic and Langmuir waves in plasmas; in some laser waves in nonlinear media; and in many biologic contexts, such as alpha-helix proteins.This is not an encyclopedia of information on solitons in which every sentence is interrupted by either a caveat or a reference. Rather, Newell has tried to tell the story of the soliton as he would have liked to have heard it as a graduate student, with some historical development, lots of motivation, and frequent attempts to relate the topic at hand to the big picture.The book begins with a history of the soliton from its first sighting to the discovery of the inverse scattering method and recent ideas on the algebraic structure of soliton equations. Chapter 2 focuses on the universal nature of these equations and how and why they arise in physical and engineering contexts as asymptotic solvability conditions. The third chapter deals with the inverse scattering method and perturbation theories. Chapter 4 introduces the t-function and discusses the relations between the various methods for constructing solutions to the soliton equations and their various properties. Finally, an algebraic structure for the equations is provided in Chapter 5.
607 kr
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Interfacial phenomena are commonplace in physics, chemistry, biology, and in various disciplines bridging these fields. They occur whenever a continuum is present which can exist in at least two different chemical or physical ""states"", and there is some mechanism which generates or enforces a spatial separation between these states. The separation boundary is then called an interface. In the examples studied here, the separation boundary, and its internal structure, result from the balance between two opposing tendencies: a diffusive effect which attempts to mix and smooth the properties of the material, and a physical or chemical mechanism which works to drive it to one or the other pure state.This volume is unique in that the treatment of flames, as well as internal layer dynamics ""including curvature effects"", is more detailed and systematic than in most other publications. Mathematicians and natural scientists interested in interfacial phenomena, especially flame theory, the mathematics of excitable media, electrophoresis, and phase change problems, will find Dynamics of Internal Layers and Diffusive Interfaces exceptionally useful.
558 kr
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The subject of multivariate splines has become a rapidly growing field of mathematical research. The author presents the subject from an elementary point of view that parallels the theory and development of univariate spline analysis. To compensate for the missing proofs and details, an extensive bibliography has been included. There is a presentation of open problems with an emphasis on the theory and applications to computer aided design, data analysis, and surface fitting. Applied mathematicians and engineers working in the areas of curve fitting, finite element methods, computer aided geometric design, signal processing, mathematical modelling, computer aided design, computer aided manufacturing, and circuits and systems will find this monograph essential to their research.
554 kr
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This monograph is a survey of some of the work that has been done since the appearance of the second edition of Combinatorial Algorithms. Topics include progress in: Gray Codes, listing of subsets of given size of a given universe, listing rooted and free trees, selecting free trees and unlabeled graphs uniformly at random, and ranking and unranking problems on unlabeled trees.
821 kr
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This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. The estimate is a polynomial smoothing spline. By placing this smoothing problem in the setting of reproducing kernel Hilbert spaces, a theory is developed which includes univariate smoothing splines, thin plate splines in d dimensions, splines on the sphere, additive splines, and interaction splines in a single framework. A straightforward generalization allows the theory to encompass the very important area of (Tikhonov) regularization methods for ill posed inverse problems.Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a wide variety of problems which fall within this framework. Methods for including side conditions and other prior information in solving ill posed inverse problems are included. Data which involves samples of random variables with Gaussian, Poisson, binomial, and other distributions are treated in a unified optimization context. Experimental design questions, i.e., which functionals should be observed, are studied in a general context. Extensions to distributed parameter system identification problems are made by considering implicitly defined functionals.
1 114 kr
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Winner of the 1994 Leroy P. Steele Prize for excellence in expository writing.Ingrid Daubechies received the 2000 National Academy of Sciences (NAS) Award in Mathematics, which is given every four years for excellence in published mathematical research. Daubechies was chosen “for fundamental discoveries on wavelets and wavelet expansions and for her role in making wavelet methods a pracical basic tool of applied mathematics”.Wavelets are a mathematical development that may revolutionize the world of information storage and retrieval according to many experts. They are a fairly simple mathematical tool now being applied to the compression of data--such as fingerprints, weather satellite photographs, and medical x-rays--that were previously thought to be impossible to condense without losing crucial details.This monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMS-NSF Conference on Wavelets and Applications. The author has worked on several aspects of the wavelet transform and has developed a collection of wavelets that are remarkably efficient.The opening chapter provides an overview of the main problems presented in the book. Following chapters discuss the theoretical and practical aspects of wavelet theory, including wavelet transforms, orthonormal bases of wavelets, and characterization of functional spaces by means of wavelets. The last chapter presents several topics under active research, as multidimensional wavelets, wavelet packet bases, and a construction of wavelets tailored to decompose functions defined in a finite interval. Because of their interdisciplinary origins, wavelets appeal to scientists and engineers of many different backgrounds.Special Features:Only comprehensive book in English on this subject.Ideal for mapping out a graduate course or a seminar on the subject.Includes an extensive bibliography.