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This volume studies characteristic functions--which play an essential role in probability and statistics-- for their intrinsic, mathematical interest.
Book Synopsis Characteristic Functions by : E. Lukacs
Download or read book Characteristic Functions written by E. Lukacs and published by Oxford University Press. This book was released on 1987-03-01 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume studies characteristic functions--which play an essential role in probability and statistics-- for their intrinsic, mathematical interest.
This book contains basic information on characteristic functions and moment sequences that is frequently used in probability theory. Characteristic functions and moment sequences are viewed as special cases of positive definite functions. Positive definite functions occur in diverse parts of mathematics, e.g. in operator theory, moment problems, complex function theory, embedding problems, integral equations, and other areas. However, the area of mathematics in which the largest number of people use positive definite functions (some without knowing it) seems to be that of probability theory.
Book Synopsis Characteristic Functions and Moment Sequences by : Torben Maack Bisgaard
Download or read book Characteristic Functions and Moment Sequences written by Torben Maack Bisgaard and published by Nova Publishers. This book was released on 2000 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains basic information on characteristic functions and moment sequences that is frequently used in probability theory. Characteristic functions and moment sequences are viewed as special cases of positive definite functions. Positive definite functions occur in diverse parts of mathematics, e.g. in operator theory, moment problems, complex function theory, embedding problems, integral equations, and other areas. However, the area of mathematics in which the largest number of people use positive definite functions (some without knowing it) seems to be that of probability theory.
The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
Book Synopsis Selected Topics in Characteristic Functions by : Nikolai G. Ushakov
Download or read book Selected Topics in Characteristic Functions written by Nikolai G. Ushakov and published by Walter de Gruyter. This book was released on 2011-11-02 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
In a certain sense characteristic functions and correlation functions are the same, the common underlying concept is positive definiteness. Many results in probability theory, mathematical statistics and stochastic processes can be derived by using these functions. While there are books on characteristic functions of one variable, books devoting some sections to the multivariate case, and books treating the general case of locally compact groups, interestingly there is no book devoted entirely to the multidimensional case which is extremely important for applications. This book is intended to fill this gap at least partially. It makes the basic concepts and results on multivariate characteristic and correlation functions easily accessible to both students and researchers in a comprehensive manner. The first chapter presents basic results and should be read carefully since it is essential for the understanding of the subsequent chapters. The second chapter is devoted to correlation functions, their applications to stationary processes and some connections to harmonic analysis. In Chapter 3 we deal with several special properties, Chapter 4 is devoted to the extension problem while Chapter 5 contains a few applications. A relatively large appendix comprises topics like infinite products, functional equations, special functions or compact operators.
Book Synopsis Multivariate Characteristic and Correlation Functions by : Zoltán Sasvári
Download or read book Multivariate Characteristic and Correlation Functions written by Zoltán Sasvári and published by Walter de Gruyter. This book was released on 2013-03-22 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a certain sense characteristic functions and correlation functions are the same, the common underlying concept is positive definiteness. Many results in probability theory, mathematical statistics and stochastic processes can be derived by using these functions. While there are books on characteristic functions of one variable, books devoting some sections to the multivariate case, and books treating the general case of locally compact groups, interestingly there is no book devoted entirely to the multidimensional case which is extremely important for applications. This book is intended to fill this gap at least partially. It makes the basic concepts and results on multivariate characteristic and correlation functions easily accessible to both students and researchers in a comprehensive manner. The first chapter presents basic results and should be read carefully since it is essential for the understanding of the subsequent chapters. The second chapter is devoted to correlation functions, their applications to stationary processes and some connections to harmonic analysis. In Chapter 3 we deal with several special properties, Chapter 4 is devoted to the extension problem while Chapter 5 contains a few applications. A relatively large appendix comprises topics like infinite products, functional equations, special functions or compact operators.
Transfer functions and characteristic functions proved to be key in operator theory and system theory. Moshe Livic played a major role in developing these functions, and this book of papers dedicated to his memory covers a wide variety of topics in the field.
Book Synopsis Characteristic Functions, Scattering Functions and Transfer Functions by : Daniel Alpay
Download or read book Characteristic Functions, Scattering Functions and Transfer Functions written by Daniel Alpay and published by Springer Science & Business Media. This book was released on 2010-01-12 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transfer functions and characteristic functions proved to be key in operator theory and system theory. Moshe Livic played a major role in developing these functions, and this book of papers dedicated to his memory covers a wide variety of topics in the field.
Book Synopsis Characteristic Functions of Real Resonators by : V. M. Vakhnin
Download or read book Characteristic Functions of Real Resonators written by V. M. Vakhnin and published by . This book was released on 1954 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Tables are presented containing 69,000 values of a set of characteristic functions which first arose in problems of supersonic wing-body interference. The tables are useful in problems of supersonic flow involving aerodynamic shapes which are wholly or in part quasi-cylinders of nearly circular cross section. A number of uses are described in the aerodynamics of bodies alone, body-body or shock-body interference, wing-body interference, the vortex-panel interference. Three illustrative examples are worked out in detail. First, the pressure field due to fuselage indentation is calculated and presented in a form independent of Mach number. Secondly, the tables are applied to a problem involving a previously unpublished solution to the Navier-Stokes equations; namely, the boundary-layer profiles of a circular cylinder moved impulsively with a constant axial force in a viscous incompressible fluid. In the final example, the wave drag of corrugated circular cylinders is calculated as a function of the number of corrugations and their wave length. Several nonaerodynamic applications are pointed out in the fields of acoustics and heat conduction. Generally speaking, the tables are applicable to boundary-value problems of the second kind involving the wave equation in three dimensions with approximately circular cylindrical boundaries or involving the unsteady heat-conduction equation in two space dimensions with nearly circular boundaries.
Book Synopsis Tables of Characteristic Functions for Solving Boundary-value Problems of the Wave Equation with Application to Supersonic Interference by : Jack Norman Nielsen
Download or read book Tables of Characteristic Functions for Solving Boundary-value Problems of the Wave Equation with Application to Supersonic Interference written by Jack Norman Nielsen and published by . This book was released on 1957 with total page 682 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tables are presented containing 69,000 values of a set of characteristic functions which first arose in problems of supersonic wing-body interference. The tables are useful in problems of supersonic flow involving aerodynamic shapes which are wholly or in part quasi-cylinders of nearly circular cross section. A number of uses are described in the aerodynamics of bodies alone, body-body or shock-body interference, wing-body interference, the vortex-panel interference. Three illustrative examples are worked out in detail. First, the pressure field due to fuselage indentation is calculated and presented in a form independent of Mach number. Secondly, the tables are applied to a problem involving a previously unpublished solution to the Navier-Stokes equations; namely, the boundary-layer profiles of a circular cylinder moved impulsively with a constant axial force in a viscous incompressible fluid. In the final example, the wave drag of corrugated circular cylinders is calculated as a function of the number of corrugations and their wave length. Several nonaerodynamic applications are pointed out in the fields of acoustics and heat conduction. Generally speaking, the tables are applicable to boundary-value problems of the second kind involving the wave equation in three dimensions with approximately circular cylindrical boundaries or involving the unsteady heat-conduction equation in two space dimensions with nearly circular boundaries.
This work aims to give a systematic presentation of methods used in the spectral theory of nonself-adjoint, generally unbounded, operators. Subjects treated include the wide class of both selfadjoint and nonself-adjoint extensions of Hermitian operators; characteristic functions of a regular extension; the construction of some operator models for different classes of nonself-adjoint operators; the construction of the selfadjoint dilation of an arbitrary dissipative operator and J-unitary and J-selfadjoint dilations of linear operators; the abstract Lax Phillips scheme in scattering theory for spaces with indefinite metric (Pontryagin spaces); the relation between scattering matrix and the characteristic function of J-nonexpansive operators; a structure of J-nonexpansive operators; and contractions and their triangulation.
Book Synopsis Characteristic Functions and Models of Nonself-Adjoint Operators by : A. Kuzhel
Download or read book Characteristic Functions and Models of Nonself-Adjoint Operators written by A. Kuzhel and published by Springer. This book was released on 1996 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work aims to give a systematic presentation of methods used in the spectral theory of nonself-adjoint, generally unbounded, operators. Subjects treated include the wide class of both selfadjoint and nonself-adjoint extensions of Hermitian operators; characteristic functions of a regular extension; the construction of some operator models for different classes of nonself-adjoint operators; the construction of the selfadjoint dilation of an arbitrary dissipative operator and J-unitary and J-selfadjoint dilations of linear operators; the abstract Lax Phillips scheme in scattering theory for spaces with indefinite metric (Pontryagin spaces); the relation between scattering matrix and the characteristic function of J-nonexpansive operators; a structure of J-nonexpansive operators; and contractions and their triangulation.
Download or read book Probability written by Alan F. Karr and published by . This book was released on 1993-08-01 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
An Essential Reference for Intermediate and Advanced R Programmers Advanced R presents useful tools and techniques for attacking many types of R programming problems, helping you avoid mistakes and dead ends. With more than ten years of experience programming in R, the author illustrates the elegance, beauty, and flexibility at the heart of R. The book develops the necessary skills to produce quality code that can be used in a variety of circumstances. You will learn: The fundamentals of R, including standard data types and functions Functional programming as a useful framework for solving wide classes of problems The positives and negatives of metaprogramming How to write fast, memory-efficient code This book not only helps current R users become R programmers but also shows existing programmers what’s special about R. Intermediate R programmers can dive deeper into R and learn new strategies for solving diverse problems while programmers from other languages can learn the details of R and understand why R works the way it does.
Book Synopsis Advanced R by : Hadley Wickham
Download or read book Advanced R written by Hadley Wickham and published by CRC Press. This book was released on 2015-09-15 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Essential Reference for Intermediate and Advanced R Programmers Advanced R presents useful tools and techniques for attacking many types of R programming problems, helping you avoid mistakes and dead ends. With more than ten years of experience programming in R, the author illustrates the elegance, beauty, and flexibility at the heart of R. The book develops the necessary skills to produce quality code that can be used in a variety of circumstances. You will learn: The fundamentals of R, including standard data types and functions Functional programming as a useful framework for solving wide classes of problems The positives and negatives of metaprogramming How to write fast, memory-efficient code This book not only helps current R users become R programmers but also shows existing programmers what’s special about R. Intermediate R programmers can dive deeper into R and learn new strategies for solving diverse problems while programmers from other languages can learn the details of R and understand why R works the way it does.
