Описание: Uses the method of maximum likelihood to a large extent to ensure reasonable, and in some cases optimal procedures. This work treats the basic and important topics in multivariate statistics.
Описание: Dimensional analysis is a magical way of finding useful results with almost no effort. It makes it possible to bring together the results of experiments and
computations in a concise but exact form, so that they can be used efficiently and economically to make predictions. It takes advantage of the fact that phenomena go their way
independently of the units we measure them with, because the units have nothing to do with the underlying physics.
This simple idea turns out to be unexpectedly
powerful.Students often fail to gain from dimensional analysis, because bad teaching has led them to suppose it cannot be used to derive new results, and can only confirm results that
have been secured by some other route. That notion is false. This book demonstrates what can be done with dimensional analysis through a series of examples, starting with
Pythagoras' theorem and the simple pendulum, and going on to a number of practical examples, many from the author's experience in ocean engineering.
In parallel, the book
explains the underlying theory, starting with Vaschy's elegant treatment, whilst avoiding unnecessary complexity. It also explores the use and misuse of models, which can be useful but
can also be seriously misleading.
Описание: There is almost no field in mathematics that does not use mathematical analysis. Computer methods in applied mathematics are often based on statements and procedures of mathematical analysis as well. An important part of mathematical analysis is complex analysis because it has many applications in various branches of math. Present trends in complex analysis, which are reflected in the book, are mainly concentrated on the following four research directions: -Value distribution theory and its applications, -Holomorphic functions in several (finitely or infinitely many) complex variables, -Clifford analysis, I.e., complex methods in higher-dimensional real Euclidian spaces, -Generalized analytic functions. A specific feature of today's complex analysis is combining methods of Clifford analysis. This leads to a theory of multi-regular functions.
Описание: Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as
stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well
established, the study of their stability properties has grown rapidly only in the past 20 years, and most results have remained scattered in journals and conference proceedings.This
book offers a systematic presentation of the modern theory of the stability of stochastic differential equations in infinite dimensional spaces - particularly Hilbert spaces. The treatment
includes a review of basic concepts and investigation of the stability theory of linear and nonlinear stochastic differential equations and stochastic functional differential equations in
The final chapter of this title explores topics and applications such as stochastic optimal control and feedback stabilization, stochastic reaction-diffusion,
Navier-Stokes equations, and stochastic population dynamics. In recent years, this area of study has become the focus of increasing attention, and the relevant literature has
expanded greatly. "Stability of Infinite Dimensional Stochastic Differential Equations with Applications" makes up-to-date material in this important field accessible even to newcomers
and lays the foundation for future advances.
Описание: The lectures this volume collects were designed for an audience having basic knowledge of Functional Analysis and Measure Theory, but not familiar with Probability. The main aim is to give an introduction to Analysis in separable infinite-dimensional Hilbert spaces. The arguments the book deals with are: Gaussian measures, reproducing kernels, Cameron-Martin formula, Brownian motion, Wiener integral, invariant measures, ergodicity, mixing, Ito-Wiener decomposition.
Описание: In this revised and extended version of his course notes from a 1-year course at Scuola Normale Superiore, Pisa, the author provides an introduction вЂ“ for an audience knowing basic functional analysis and measure theory but not necessarily probability theory вЂ“ to analysis in a separable Hilbert space of infinite dimension. Starting from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate some basic stochastic dynamical systems (including dissipative nonlinearities) and Markov semi-groups, paying special attention to their long-time behavior: ergodicity, invariant measure. Here fundamental results like the theorems of Prokhorov, Von Neumann, Krylov-Bogoliubov and Khas'minski are proved. The last chapter is devoted to gradient systems and their asymptotic behavior.
Описание: This volume consists of 18 research papers reflecting the impressive progress made in the field of quantum probability and infinite-dimensional analysis. It
includes results on quantum stochastic integration, the stochastic limit, quantum teleportation, and other areas.
Описание: This volume contains the latest results in the fields of quantum probability and infinite dimensional analysis. The contributions range from classical probability,
'pure' functional analysis and foundations of quantum mechanics to applications in mathematical physics, quantum information theory and modern mathematical finance. This diversity
illustrates that research in
uantum probability and infinite dimensional analysis is very active and strongly involved in modern mathematical developments and applications.
Описание: This valuable collection of articles presents the latest methods and results in complex analysis and its applications. The present trends in complex analysis
reflected in the book are concentrated in the following research directions: Clifford analysis, complex dynamical systems, complex function spaces, complex numerical analysis,
qusiconformal mapping, Riemann surfaces, Teichmuller theory and Klainian groups, several complex variables, and value distribution theory.
Описание: This book introduces the reader to the basic principles of functional analysis and to areas of Banach space theory that are close to nonlinear analysis and
topology. In the first part, the book develops the classical theory, including weak topologies, locally convex spaces, Schauder bases, and compact operator theory. The presentation is
self-contained, including many folklore results, and the proofs are accessible to students with the usual background in real analysis and topology.
The second part covers
topics in convexity and smoothness, finite representability, variational principles, homeomorphisms, weak compactness and more. Several results are published here for the first time in a
monograph. The text can be used in graduate courses or for independent study.
It includes a large number of exercises of different levels of difficulty, accompanied by hints.
The book is also directed to young researchers in functional analysis and can serve as a reference book.
Автор: Aliprantis Название: Infinite Dimensional Analysis ISBN: 3540295860 ISBN-13(EAN): 9783540295860 Издательство: Springer Рейтинг: Цена: 21412 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This monograph presents a complete and rigorous study of modern functional analysis. It is intended for the student or researcher who could benefit from functional analytic methods, but does not have an extensive background and does not plan to make a career as a functional analyst. It develops the topological structures in connection with measure theory, convexity, Banach lattices, integration, correspondences (multifunctions), and the analytic approach to Markov processes. Many of the results were previously available only in works scattered throughout the literature. The choice of material was motivated from problems in control theory and economics, although the material is more applicable than applied.
Описание: Demonstrates what can be done with dimensional analysis through a series of examples, starting with Pythagoras` theorem and the simple pendulum, and going on to a number of practical examples. This book explains the underlying theory, starting with Vaschy`s elegant treatment and also explores the use and misuse of models.
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