### White Noise Calculus and Fock Space

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White Noise Calculus is a distribution theory on

**Gaussian**space, proposed by T. Hida in 1975. This approach enables us to use pointwise defined creation and annihilation operators as well as the well-established theory of nuclear space.This self-contained monograph presents, for the first time, a systematic introduction to operator theory on fock space by means of white noise calculus. The goal is a comprehensive account of general expansion theory of Fock space operators and its applications. In particular,first order differential operators, Laplacians, rotation group, Fourier transform and their interrelations are discussed in detail w.r.t. harmonic analysis on**Gaussian**space. The mathematical formalism used here is based on distribution theory and functional analysis , prior knowledge of white noise calculus is not required.Category: Science. ISBN: 9783540579854

### Econometrics of Risk

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This edited book contains several state-of-the-art papers devoted to econometrics of risk. Some papers provide theoretical analysis of the corresponding mathematical, statistical, computational, and economical models. Other papers describe applications of the novel risk-related econometric techniques to real-life economic situations. The book presents new methods developed just recently, in particular, methods using non-

**Gaussian**heavy-tailed distributions, methods using non-**Gaussian**copulas to properly take into account dependence between different quantities, methods taking into account imprecise ("fuzzy") expert knowledge, and many other innovative techniques. This versatile volume helps practitioners to learn how to apply new techniques of econometrics of risk, and researchers to further improve the existing models and to come up with new ideas on how to best take into account economic risks.Category: Business. ISBN: 9783319134482

### Geophysical Data Analysis: Discrete Inverse Theory

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Geophysical Data Analysis: Discrete Inverse Theory is an introductory text focusing on discrete inverse theory that is concerned with parameters that either are truly discrete or can be adequately approximated as discrete. Organized into 12 chapters, the book's opening chapters provide a general background of inverse problems and their corresponding solution, as well as some of the basic concepts from probability theory that are applied throughout the text. Chapters 3-7 discuss the solution of the canonical inverse problem, that is, the linear problem with

**Gaussian**statistics, and discussions on problems that are non-**Gaussian**and nonlinear are covered in Chapters 8 and 9. Chapters 10-12 present examples of the use of inverse theory and a discussion on the numerical algorithms that must be employed to solve inverse problems on a computer. This book is of value to graduate students and many college seniors in the applied sciences.Category: Science. ISBN: 9780124909205

### Explicit Formulas

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The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These explicit formulas can be used to describe the quantitative behavior of various objects in analytic number theory and spectral theory. The present book deals with other applications arising from

**Gaussian**test functions, leading to theta inversion formulas and corresponding new types of zeta functions which are**Gaussian**transforms of theta series rather than Mellin transforms, and satisfy additive functional equations. Their wide range of applications includes the spectral theory of a broad class of manifolds and also the theory of zeta functions in number theory and representation theory. Here the hyperbolic 3-manifolds are given as a significant example.Category: Mathematics. ISBN: 9783540586739

### Random Matrix Theory with an External Source

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This is a first book to show that the theory of the

**Gaussian**random matrix is essential to understand the universal correlations with random fluctuations and to demonstrate that it is useful to evaluate topological universal quantities. We consider**Gaussian**random matrix models in the presence of a deterministic matrix source. In such models the correlation functions are known exactly for an arbitrary source and for any size of the matrices. The freedom given by the external source allows for various tunings to different classes of universality. The main interest is to use this freedom to compute various topological invariants for surfaces such as the intersection numbers for curves drawn on a surface of given genus with marked points, Euler characteristics, and the GromovWitten invariants. A remarkable duality for the average of characteristic polynomials is essential for obtaining such topological invariants. The analysis is extended to nonorientable surfaces and to surfaces with boundaries.Category: Science. ISBN: 9789811033155

### Fundamentals of Ultrasonic Nondestructive Evaluation

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This extensively revised and updated second edition of a widely read classic presents the use of ultrasound in nondestructive evaluation (NDE) inspections. Retaining the first edition's use of wave propagation /scattering theory and linear system theory, this volume also adds significant new material including: the introduction of MATLAB functions and scripts that evaluate key results involving beam propagation and scattering, flaw sizing, and the modeling of ultrasonic systems. elements of

**Gaussian**beam theory and a multi-**Gaussian**ultrasonic beam model for bulk wave transducers. a new chapter on the connection between ultrasonic modeling and probability of detection (POD) and reliability models. new and improved derivations of ultrasonic measurement models. updated coverage of ultrasonic simulators that have been developed around the world. Students, engineers, and researchers working in the ultrasonic NDE field will find a wealth of information on the modeling of ultrasonic inspections and the fundamental ultrasonic experiments that support those models in this new edition.Category: Technology. ISBN: 9783319304618

### Students t-Distribution and Related Stochastic Processes

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This brief monograph is an in-depth study of the infinite divisibility and self-decomposability properties of central and noncentral Student's distributions, represented as variance and mean-variance mixtures of multivariate

**Gaussian**distributions with the reciprocal gamma mixing distribution. These results allow us to define and analyse Student-Lvy processes as Thorin subordinated**Gaussian**Lvy processes. A broad class of one-dimensional, strictly stationary diffusions with the Student's t -marginal distribution are defined as the unique weak solution for the stochastic differential equation. Using the independently scattered random measures generated by the bi-variate centred Student-Lvy process, and stochastic integration theory, a univariate, strictly stationary process with the centred Student's t- marginals and the arbitrary correlation structure are defined. As a promising direction for future work in constructing and analysing new multivariate Student-Lvy type processes, the notion of Lvy copulas and the related analogue of Sklar's theorem are explained.Category: Mathematics. ISBN: 9783642311451

### An Introduction to the Locally-Corrected Nystrom Method

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This lecture provides a tutorial introduction to the Nystrm and locally-corrected Nystrm methods when used for the numerical solutions of the common integral equations of two-dimensional electromagnetic fields. These equations exhibit kernel singularities that complicate their numerical solution. Classical and generalized

**Gaussian**quadrature rules are reviewed. The traditional Nystrm method is summarized, and applied to the magnetic field equation for illustration. To obtain high order accuracy in the numerical results, the locally-corrected Nystrm method is developed and applied to both the electric field and magnetic field equations. In the presence of target edges, where current or charge density singularities occur, the method must be extended through the use of appropriate singular basis functions and special quadrature rules. This extension is also described.Table of Contents: Introduction / Classical Quadrature Rules / The Classical Nystrm Method / The Locally-Corrected Nystrm Method / Generalized**Gaussian**Quadrature / LCN Treatment of Edge SingularitiesCategory: Technology. ISBN: 9781608452996

### Advances in Chemical Physics

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This series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. Volume 131 includes chapters on: Polyelectrolyte Dynamics; Hydrodynamics and Slip at the Liquid-Solid Interface; Structure of Ionic Liquids and Ionic Liquid Compounds: Are Ionic Liquids Genuine Liquids in the Conventional Sense?; Chemical Reactions at Very High Pressure; Classical Description of Nonadiabatic Quantum Dynamics; and Non-Born Oppenheimer Variational Calculations of Atoms and Molecules with Explicitly Correlated

**Gaussian**Basis Functions.Category: Science. ISBN: 9780471445265

### Robot Learning by Visual Observation

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This book presents programming by demonstration for robot learning from observations with a focus on the trajectory level of task abstraction Discusses methods for optimization of task reproduction, such as reformulation of task planning as a constrained optimization problem Focuses on regression approaches, such as

**Gaussian**mixture regression, spline regression, and locally weighted regression Concentrates on the use of vision sensors for capturing motions and actions during task demonstration by a human task expertCategory: Technology. ISBN: 9781119091806