Nonstandard Methods For Stochastic Fluid Mechanics
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Nonstandard Methods For Stochastic Fluid Mechanics
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Author : Marek Capinski
language : en
Publisher: World Scientific
Release Date : 1995-03-16
Nonstandard Methods For Stochastic Fluid Mechanics written by Marek Capinski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-16 with Mathematics categories.
This book is an exposition of a new approach to the Navier-Stokes equations, using powerful techniques provided by nonstandard analysis, as developed by the authors. The topics studied include the existence and uniqueness of weak solutions, statistical solutions and the solution of general stochastic equations.The authors provide a self-contained introduction to nonstandard analysis, designed with applied mathematicians in mind and concentrated specifically on techniques applicable to the Navier-Stokes equations. The subsequent exposition shows how these new techniques allow a quick and intuitive entrance into the mathematical theory of hydrodynamics, as well as provide a research tool that has proven useful in solving open problems concerning stochastic equations.
Nonstandard Methods For Stochastic Fluid Mechanics
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Author : Marek Capi?ski
language : en
Publisher: World Scientific
Release Date : 1995
Nonstandard Methods For Stochastic Fluid Mechanics written by Marek Capi?ski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.
This book is an exposition of a new approach to the Navier-Stokes equations, using powerful techniques provided by nonstandard analysis, as developed by the authors. The topics studied include the existence and uniqueness of weak solutions, statistical solutions and the solution of general stochastic equations.The authors provide a self-contained introduction to nonstandard analysis, designed with applied mathematicians in mind and concentrated specifically on techniques applicable to the Navier-Stokes equations. The subsequent exposition shows how these new techniques allow a quick and intuitive entrance into the mathematical theory of hydrodynamics, as well as provide a research tool that has proven useful in solving open problems concerning stochastic equations.
Nonstandard Analysis
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Author : Leif O. Arkeryd
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonstandard Analysis written by Leif O. Arkeryd and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of appli cability of NSA more widely known and available to research mathemati cians.
Nonstandard Analysis For The Working Mathematician
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Author : Peter A. Loeb
language : en
Publisher: Springer
Release Date : 2015-08-26
Nonstandard Analysis For The Working Mathematician written by Peter A. Loeb and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-26 with Mathematics categories.
Starting with a simple formulation accessible to all mathematicians, this second edition is designed to provide a thorough introduction to nonstandard analysis. Nonstandard analysis is now a well-developed, powerful instrument for solving open problems in almost all disciplines of mathematics; it is often used as a ‘secret weapon’ by those who know the technique. This book illuminates the subject with some of the most striking applications in analysis, topology, functional analysis, probability and stochastic analysis, as well as applications in economics and combinatorial number theory. The first chapter is designed to facilitate the beginner in learning this technique by starting with calculus and basic real analysis. The second chapter provides the reader with the most important tools of nonstandard analysis: the transfer principle, Keisler’s internal definition principle, the spill-over principle, and saturation. The remaining chapters of the book study different fields for applications; each begins with a gentle introduction before then exploring solutions to open problems. All chapters within this second edition have been reworked and updated, with several completely new chapters on compactifications and number theory. Nonstandard Analysis for the Working Mathematician will be accessible to both experts and non-experts, and will ultimately provide many new and helpful insights into the enterprise of mathematics.
Microscopic Theory Of Condensation In Gases And Plasma
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Author : Andrey Itkin
language : en
Publisher: World Scientific
Release Date : 1997-06-16
Microscopic Theory Of Condensation In Gases And Plasma written by Andrey Itkin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-16 with Science categories.
This book summarizes results on the creation of a new theory of condensation which has an impact on consideration of some microscopic effects left aside in the usual nucleation theories. In particular, the main idea of the authors' microscopic condensation theory is that it considers the violation of the equilibrium cluster distribution over the internal degrees of freedom due to co-occurring condensation and decay reactions of the clusters.
Advanced Mathematical Computational Tools In Metrology Vii
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Author : P. Ciarlini
language : en
Publisher: World Scientific
Release Date : 2006
Advanced Mathematical Computational Tools In Metrology Vii written by P. Ciarlini and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This volume collects the refereed contributions based on the presentations made at the Seventh Workshop on Advanced Mathematical and Computational Tools in Metrology, a forum for metrologists, mathematicians and software engineers that will encourage a more effective synthesis of skills, capabilities and resources. The volume contains articles by world renowned metrologists and mathematicians involved in measurement science and, together with the six previous volumes in this series, constitutes an authoritative source of the mathematical, statistical and software tools necessary in modern metrology. Sample Chapter(s). Chapter 1: Modelling Measurement Processes in Complex Systems with Partial Differential Equations: From Heat Conduction to the Heart (537 KB). Contents: Modeling Measurement Processes in Complex Systems with Partial Differential Equations: From Heat Conduction to the Heart (M Bnr et al.); Mereotopological Approach for Measurement Software (E Benoit & R Dapoigny); Data Evaluation of Key Comparisons Involving Several Artefacts (M G Cox et al.); Box-Cox Transformations and Robust Control Charts in SPC (M I Gomes & F O Figueiredo); Multisensor Data Fusion and Its Application to Decision Making (P S Giruo et al.); Generic System Design for Measurement Databases OCo Applied to Calibrations in Vacuum Metrology, Bio-Signals and a Template System (H Gross et al.); Evaluation of Repeated Measurements from the Viewpoint of Conventional and Bayesian Statistics (I Lira & W WAger); Detection of Outliers in Interlaboratory Testing (C Perruchet); On Appropriate Methods for the Validation of Metrological Software (D Richter et al.); Data Analysis OCo A Dialogue with the Data (D S Sivia); Validation of Soft Sensors in Monitoring Ambient Parameters (P Ciarlini et al.); Evaluation of Standard Uncertainties in Nested Structures (E Filipe); Measurement System Analysis and Statistical Process Control (A B Forbes); Monte Carlo Study on Logical and Statistical Correlation (B Siebert et al.); Some Problems Concerning the Estimate of the Degree of Equivalence in MRA Key Comparisons and of Its Uncertainty (F Pavese); Preparing for a European Research Area Network in Metrology: Where are We Now? (M Khne et al.); and other papers. Readership: Researchers, graduate students, academics and professionals in metrology."
On The Way To Understanding The Time Phenomenon
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Author : A. P. Levich
language : en
Publisher: World Scientific
Release Date : 1996
On The Way To Understanding The Time Phenomenon written by A. P. Levich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Science categories.
Time is considered as an independent entity which cannot be reduced to the concept of matter, space or field. The point of discussion is the ?time flow? conception of N A Kozyrev (1908-1983), an outstanding Russian astronomer and natural scientist. In addition to a review of the experimental studies of ?the active properties of time?, by both Kozyrev and modern scientists, the reader will find different interpretations of Kozyrev's views and some developments of his ideas in the fields of geophysics, astrophysics, general relativity and theoretical mechanics.
Constrained Control Problems Of Discrete Processes
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Author : Ngoc Phat Vu
language : en
Publisher: World Scientific
Release Date : 1996
Constrained Control Problems Of Discrete Processes written by Ngoc Phat Vu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
The book gives a novel treatment of recent advances on constrained control problems with emphasis on the controllability, reachability of dynamical discrete-time systems. The new proposed approach provides the right setting for the study of qualitative properties of general types of dynamical systems in both discrete-time and continuous-time systems with possible applications to some control engineering models. Most of the material appears for the first time in a book form. The book is addressed to advanced students, postgraduate students and researchers interested in control system theory and optimal control.
On The Way To Understanding The Time Phenomenon The Constructions Of Time In Natural Science Part 2
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Author : A P Levich
language : en
Publisher: World Scientific
Release Date : 1996-05-15
On The Way To Understanding The Time Phenomenon The Constructions Of Time In Natural Science Part 2 written by A P Levich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05-15 with Science categories.
Time is considered as an independent entity which cannot be reduced to the concept of matter, space or field. The point of discussion is the “time flow” conception of N A Kozyrev (1908-1983), an outstanding Russian astronomer and natural scientist. In addition to a review of the experimental studies of “the active properties of time”, by both Kozyrev and modern scientists, the reader will find different interpretations of Kozyrev's views and some developments of his ideas in the fields of geophysics, astrophysics, general relativity and theoretical mechanics.
Multigroup Equations For The Description Of The Particle Transport In Semiconductors
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Author : Martin Galler
language : en
Publisher: World Scientific
Release Date : 2005
Multigroup Equations For The Description Of The Particle Transport In Semiconductors written by Martin Galler and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Technology & Engineering categories.
Deterministic simulation of the particle transport in semiconductor devices is an interesting alternative to the common Monte Carlo approach. In this book, a state-of-the-art technique called the multigroup approach is presented and applied to a variety of transport problems in bulk semiconductors and semiconductor devices. High-field effects as well as hot-phonon phenomena in polar semiconductors are studied in detail. The mathematical properties of the presented numerical method are studied, and the method is applied to simulating the transport of a two-dimensional electron gas formed at a semiconductor heterostructure. Concerning semiconductor device simulation, several diodes and transistors fabricated of silicon and gallium arsenide are investigated. For all of these simulations, the numerical techniques employed are discussed in detail. This unique study of the application of direct methods for semiconductor device simulation provides the interested reader with an indispensable reference on this growing research area.