21. Chebyshev Expansions And Rational Approximations For Some Special Functions And Let A(z) = (A sub m)(z) + (a sub m)(z sup m)B(z,m) where (A sub m)(z) is a polynomial in z of degree m1. Suppose A(z) and B(z,m) are approximated by main http://stinet.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA

22. Asymptotic Expansions For The Laplace Approximations Of Sums Of Keywords Laplace approximation; asymptotic expansions; i.i.d. random vectors; Banach spacevalued random variables. Full-text Access by subscription http://projecteuclid.org/handle/euclid.aop/1108141728

Log in RSS Title Author(s) Abstract Subject Keyword All Fields FullText more options Home Browse Search ... next Asymptotic expansions for the Laplace approximations of sums of Banach space-valued random variables Sergio Albeverio and Song Liang Source: Ann. Probab. Volume 33, Number 1 (2005), 300-336. Abstract Let X i i N , be i.i.d. B -valued random variables, where B B into R . An asymptotic evaluation of Z n E (exp( n i n X i n ))), up to a factor (1+ o (1)), has been gotten in Bolthausen [ Probab. Theory Related Fields Probab. Theory Related Fields Z n as n Primary Subjects: Keywords: Laplace approximation; asymptotic expansions; i.i.d. random vectors; Banach space-valued random variables Full-text: Access granted (open access) Screen Optimized PDF File (260 KB) Links and Identifiers Permanent link to this document: http://projecteuclid.org/euclid.aop/1108141728 Digital Object Identifier: doi:10.1214/009117904000001017 Mathematical Reviews number (MathSciNet): back to Table of Contents previous next The Annals of Probability Current Issue All Issues Search this Journal Editorial Board ... Log in RSS Cornell University Library

23. Stochastic Expansions And Asymptotic Approximations Author(s) Magdalinos, Michael A. 1992 Abstract No abstract is available for this item. http://ideas.repec.org/a/cup/etheor/v8y1992i3p343-67.html

This file is part of IDEAS , which uses RePEc data Papers Articles Software Books ... Help! Stochastic Expansions and Asymptotic Approximations Author info Abstract Publisher info Download info ... Statistics Author Info Magdalinos, Michael A Abstract No abstract is available for this item. Download Info To our knowledge, this item is not available for download . To find whether it is available, there are three options: 1. Check below under "Related research" whether another version of this item is available online. 2. Check on the provider's web page whether it is in fact available. 3. Perform a search for a similarly titled item that would be available. Publisher Info Article provided by Cambridge University Press in its journal Econometric Theory Volume (Year): Issue (Month): 3 (September) Pages: Download reference. The following formats are available: HTML plain text BibTeX RIS (EndNote), ReDIF Handle: RePEc:cup:etheor:v:8:y:1992:i:3:p:343-67 Contact details of provider: Postal: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK Fax: +44 (0)1223 325150 Email: liame2('org','cambridge','m7i7','journals')

24. Expansions, Inequalities And Approximations (Univerity Of Sydney, 2007): Travel expansions, inequalities and approximations. On the occasion of Gavin Brown’s 65th Birthday University of Sydney, Australia, 56 March 2007 http://www.maths.usyd.edu.au/u/donaldc/gbrown/travel.html

Expansions, inequalities and approximations. University of Sydney, Australia, 5-6 March 2007 Participants List of talks pdf files of talks Registration ... Schedule Travel and Accommodation Print version (PDF) Travel and Accommodation Arrival Information Hotel Accommodation Immigration and Customs Arrival Information For more information on public transport, see www.sydneytransport.net.au and the Transport Infoline website (which has a Trip Planner and Timetables Here is a map of the campus of the University of Sydney Overview Map The venue of the conference talks within the University of Sydney will be given to the registered participants. It will be near the School of Mathematics and Statistics , which is located in the Carslaw Building (L19 on the Campus Map ), very close to the City Road entrance. Hotel Accommodation Unilodge Hotel Corner of Broadway and Bay Streets, NSW 2007, Telephone (02) 9338 5000 (D26 on the Campus Map ) email: sydney.hotel@unilodge.com.au ($115/night, room only); Oakford Apartments Campus Map ) email: frontoffice.ocw@the-ascot.com (starting at $125/night, for a studio apartment). Rydges Camperdown 9 Missenden Road, Camperdown NSW 2050, Telephone (02) 9516 1522. (Opposite Sancta Sophia College, F1 on the

25. Cookies Required The subject of this paper is the construction of the exponential asymptotic expansions of the unstable and stable manifolds of the areapreserving Hénon map http://link.aip.org/link/?CHAOEH/8/665/1

26. Constructive Approximation : An International Journal For Approximations And Exp Title, Constructive approximation an international journal for approximations and expansions. Publisher, New York etc. Springer. Publication year, ? http://library.wur.nl/WebQuery/catalog/1764357?wq_sfx=lang

27. MSC2000 41XX approximations and expansions ( 0 Dok.) 41-00 General reference works (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok. http://darwin.bth.rwth-aachen.de/opus3/msc_ebene2.php?zahl=41&anzahl=0&la=de

28. Front: Mathematics Categories orthogonal polynomials, harmonic analysis, ODE s, differential relations, calculus of variations, approximations, expansions, asymptotics http://front.math.ucdavis.edu/categories/math

Front for the arXiv Front math categories search register submit journals ... iFAQ Here are the categories and category groups in the mathematics arXiv listed with sample topics. Please use restraint when cross-listing new submissions. The moderators for each category are listed in parentheses. math.** All Mathematics math.AC Commutative Algebra (Irena Swanson, Anurag Singh, David R. Morrison) commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics math.AG Algebraic Geometry (David R. Morrison, Irena Swanson, Anurag Singh, Bill McCallum) Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology math.AP Analysis of PDEs (Christopher Sogge) Existence and uniquness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE's, conservation laws, qualitative dynamics math.AT Algebraic Topology (Mark Hovey, Mark Steinberger) Homotopy theory, homological algebra, algebraic treatments of manifolds

29. Paper Info Special functions, orthogonal polynomials, harmonic analysis, ODE s, differential relations, calculus of variations, approximations, expansions, asymptotics http://math.ucr.edu/home/baez/paper.info.html

Paper Info John Baez You can get a bunch of math and physics papers electronically by going to the xxx e-print archives . There is a lot of information to read if you're having trouble figuring out how it works. Once you know what you're doing, it's easy to download papers using the xxx `form interface'. From there, you can easily get ahold of papers in the following physics archives: astro-ph Astrophysics cond-mat Condensed Matter gr-qc hep-th High Energy Physics - Experiment hep-lat High Energy Physics - Lattice hep-ph High Energy Physics - Phenomenology hep-th High Energy Physics - Theory math-ph Mathematical Physics nucl-ex Nuclear Experiment nucl-th Nuclear Theory quant-ph Quantum Physics physics Physics (various topics not covered above) as well as those in the math archive: math Another nice interface to the math archive is the U.C. Davis front end Math papers are divided into the following subject classifications. (Some of these subject classifications subsume the old math archives alg-geom, dg-ga, funct-an, and q-alg.) AG - Algebraic Geometry subsumes alg-geom Real and complex algebraic geometry, schemes, stacks, commutative rings, local rings

30. KryssTal : Pascal's Triangle The Binomial Theorem used for algebraic expansions and finding roots. when the Binomial Series can be used for calculations of approximations. http://www.krysstal.com/binomial.html

[Home Page] [Mathematics Page] [Introduction to Numbers] [Introduction to Algebra] ... [Other] Pascal's Triangle combinations : algebra : probability : binomial theorem : roots var site="sm4krysstal" Support this web site by making a donation Introduction to Pascal's Triangle Mathematics is the language of science. Something that may be difficult to picture, may be easy to understand mathematically. A mathematical equation may take up a single line whereas the same thing written in words may take up a large paragraph. In this essay I'd like to introduce some clever ways of doing algebra and of calculations using a simple calculator. By simple calculator I mean one that does only the basics (plus, minus, multiply and divide). At the end, you should be able to calculate quite difficult roots with this calculator. Blaise Pascal (1623 - 1662) was a French mathematician. His surname is used as the unit of pressure. One of his sayings was to note that 'had Cleopatra's nose been differently shaped, the history of the world would have been different'. He is most famous for the triangle named after him, Pascal's Triangle . In fact, the triangle was known to both the Chinese and the Arabs for several hundred years previously.

31. CCA: Center For Constructive Approximation - Home The Center also houses the editorial headquarters of Constructive Approximation, an international journal for approximations and expansions. http://www.math.vanderbilt.edu/~cca/

Home People Visitors Seminars ... Recent Papers The Center for Constructive Approximation comprises faculty, students, and visiting researchers working in Approximation Theory and related areas in Analysis, Spline and Wavelet Theory, and Numerical Analysis. The list of people includes: Akram Aldroubi, Doug Hardin, Mike Neamtu, Alex Powell, Ed Saff, Larry Schumaker, and also other faculty with interest in this general area. The Center also houses the editorial headquarters of Constructive Approximation , an international journal for approximations and expansions. CA Editor Emmanuel Candes Wins $500,000 NSF Award The National Science Foundation has chosen CA Editorial Board Member Emmanuel J. Candes , a professor of applied and computational mathematics at the California Institute of Technology, as the winner of the Alan T. Waterman Award for 2006. The award is given annually to a young researcher not more than 35 years old. It carries a $500,000 award for continued research. Candes, 35, was selected for his work in harmonic analysis. NSF officials cited his development of new mathematical tools that allow efficient digital representation of wave signals and his discovery of new, improved methods for translating analog data into digital form. His work has the potential to improve the digital processing of signals in a vast array of modern technologies, including electronic devices, medical technology, aircraft safety, and DNA analysis. More Information: NSF Website CA Editors Among ICM Plenary Speakers

32. Phys. Rev. C 25 (1982): A. Casel, H. Haberzettl, And W. Sandhas - Unitary Pole A Unitary pole approximations and expansions in fewbody systems The unitary pole approximations or expansions of the two-body subsystem operators are http://link.aps.org/doi/10.1103/PhysRevC.25.1738

Physical Review Online Archive Physical Review Online Archive AMERICAN PHYSICAL SOCIETY Home Browse Search Members ... Help Abstract/title Author: Full Record: Full Text: Title: Abstract: Cited Author: Collaboration: Affiliation: PACS: Phys. Rev. Lett. Phys. Rev. A Phys. Rev. B Phys. Rev. C Phys. Rev. D Phys. Rev. E Phys. Rev. ST AB Phys. Rev. ST PER Rev. Mod. Phys. Phys. Rev. (Series I) Phys. Rev. Volume: Page/Article: MyArticles: View Collection Help (Click on the to add an article.) Phys. Rev. C 25, 1738 - 1750 (1982) Previous article Next article Issue 4 View Page Images PDF (1688 kB), or Buy this Article Use Article Pack Export Citation: BibTeX EndNote (RIS) Unitary pole approximations and expansions in few-body systems A. Casel H. Haberzettl , and W. Sandhas Physikalisches Institut der Universit¤t Bonn, D-5300 Bonn 1, West Germany Received 10 August 1981 The unitary pole approximations or expansions of the two-body subsystem operators are well known, and particularly efficient and practical, methods to reduce the three-body problem to an effective two-body theory. In the present investigation we develop generalizations of these approximation techniques to the subsystem amplitudes of problems with higher particle numbers. They are based on the expansion of effective potentials which, in contrast to the genuine two-body interactions, are now energy dependent. Despite this feature our generalizations require only energy independent form factors, thus preserving one of the essential advantages of the genuine two-body approach. The application of these techniques to the four-body case is discussed in detail.

33. Local Approximations Based On Orthogonal Differential Operators chromatic expansions. Like truncations of a Taylor expansion, truncations of a chromatic expansion are local approximations; http://www.cse.unsw.edu.au/db/ai/seminars/info/32784.html

Home People Publications AI Seminars ... Contact TITLE: Local Approximations Based on Orthogonal Differential Operators PRESENTER: Aleksandar Ignjatovic, http://www.cse.unsw.edu.au/~ignjat , ignjat@cse.unsw.edu.au AFFILIATION: School of Computer Science and Engineering, UNSW, http://www.cse.unsw.edu.au DATE: Friday 24th August 2007 TIME: PLACE: CSE Seminar Room, Level 1, K17 ABSTRACT: This is a replay of the talk I gave at the Analysis Seminar (School of Mathematics at UNSW), but was asked for a replay by two colleagues. I will present some generalizations of the Neumann expansion of analytic functions (as a series of Bessel functions), called the chromatic expansions. Like truncations of a Taylor expansion, truncations of a chromatic expansion are local approximations; they converge uniformly for important classes of analytic functions. The coefficients of a chromatic expansion of an analytic function f(t) are of the form K_n[f](0), where K_n are linear differential operators, orthogonal with respect to a suitably defined scalar product. A family of such orthogonal operators K_n can be described using a three-term recurrence formula, akin to the recurrence formulas for

34. Analytical Approximations Of Fractional Delays: Lagrange Interpolators And Allpa Analytical approximations of Fractional Delays Lagrange Interpolators and Padé approximations series expansions and continued fraction expansions, http://recherche.ircam.fr/anasyn/tassart/these/icassp97/article.html

Next: Introduction S. Tassart, Ph. Depalle IRCAM, Analysis/Synthesis Team 1 place Igor-Stravinsky, 75004 PARIS, FRANCE tassartircam.fr, phdircam.fr Analytical Approximations of Fractional Delays: Lagrange Interpolators and Allpass Filters Abstract: Introduction Ideal Fractional Delay From Continuous to Discrete An Ideal Transfer Function ... About this document ... Stephan Tassart Wed May 21 17:49:28 MET DST 1997

35. First Order Approximation Of An Elliptic 3D Singular Perturbation Problem (cwi R A saddle point analysis is used to obtain a first approximation, elliptic equations;Asymptotic approximations, asymptotic expansions (steepest descent, http://repos.project.cwi.nl:8080/nl/repository_db/all_publications/10929/

Login Nederlands repository db jump-off pages (all publications) ... Powered by entire cwi repository site fuzzy match First order approximation of an elliptic 3D singular perturbation problem Print View Creator L³pez, J. L. Creator P©rez Sinus­a, E. Creator Temme, N. M. Abstract A three-dimensional elliptic singular perturbation problem with discontinuous boundary values is considered. The solution of the problem is written in terms of a double integral. A saddle point analysis is used to obtain a first approximation, which is expressed in terms of a function that can be viewed as a generalization of the complementary error function Publisher CWI Date Type preprint Source CWI. Modeling, Analysis and Simulation [MAS] ; E 0518. ISSN: 1386-3703 Language en Rights IPR: CWI Identifier(s) http://www.cwi.nl/ftp/CWIreports/MAS/MAS-E0518.pdf (publisher site) Class SMC Singular perturbations;Asymptotic behavior of solutions;Solutions in closed form;Asymptotic expansions;Boundary value problems for second-order, elliptic equations;Asymptotic approximations, asymptotic expansions (steepest descent, etc.);Computation of special functions, construction of tables Last modified: 08-01-2006 00:10

36. Infinite Series Expansions Apart from their uses in calculators and computers, infinite series expansions are used. To find approximations for special numbers like and e. http://www.intmath.com/Series-expansion/Infinite-series-expansion.php

This is interactive mathematics where you learn math by playing with it! home sitemap LiveMath info Flash highlights ... feedback Infinite Series Expansions - Introduction By M. Bourne Ever wondered: How a calculator can give you the value of sine (or cos, or cot) of any angle? How it can give you the square root (or cube root, or 4th root) of any positive number? How it can find the logarithm of any (positive) number you give it? Does a calculator store every answer that every human may ever ask it? Actually, no. The pocket calculator just remembers special polynomials and substitutes whatever you give it into that polynomial. It keeps substituting into terms of that polynomial until it reaches the required number of decimal places. It then displays the answer on the screen. [See the definition of a polynomial So what are these special polynomials? In this chapter, we learn that they are infinite series expansions . We also learn how to obtain such expansions, using differentiation. Why Study Series Expansions? Revision Tip Need some background information? See

37. Second-order And Resampling Approximation Of Finite Population U-statistics Base The expansions provide secondorder approximations that improve upon the normal approximation. Theoretical results are illustrated by a simulation study http://www.informaworld.com/smpp/content~content=a778859601~db=all~jumptype=rss

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38. List KWIC DDC And MSC Lexical Connection approximations discrete 49M25 approximations methods of successive 49Mxx approximations smooth 57R12 approximations and expansions 511.4 http://www.mi.imati.cnr.it/~alberto/dml_11_03.htm

approximation # etale and flat extensions; Henselization; Artin approximation # numerical approximation # simultaneous approximation # spline approximation # stochastic approximation # trigonometric approximation # uniqueness of best approximation algorithms approximation and computational geometry (primarily algorithms) # numerical approximation and interpolation # trigonometric approximation by arbitrary linear expressions approximation by arbitrary nonlinear expressions; widths and entropy approximation by convex sets approximation by numbers from a fixed field approximation by operators (in particular, by integral operators) approximation by other special function classes approximation by polynomials approximation by positive operators approximation by rational functions approximation formulas # remainders in approximation in non-Archimedean valuations approximation in normed linear spaces and other abstract spaces) # abstract approximation theory ( approximation in the complex domain approximation methods (nonlinear Galerkin, etc.)

39. Distributed System Simulation Using Infinite Product Expansions -- Goodson 15 (6 Comparisons are made between the classi cal eigenvalue and product expansion approximations. It is concluded that the product expansion is an ex tremum http://sim.sagepub.com/cgi/content/abstract/15/6/255

SAGE Website Help Contact Us Home ... Sign In to gain access to subscriptions and/or personal tools. SIMULATION Quick Search this Journal Advanced Search Journal Navigation Journal Home Subscriptions Archive Contact Us ... Sign In to gain access to subscriptions and/or personal tools. This Article Full Text (PDF) References Alert me when this article is cited ... Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to Saved Citations ... Add to My Marked Citations Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Goodson, R.E. Search for Related Content Social Bookmarking What's this? SIMULATION, Vol. 15, No. 6, 255-263 (1970) DOI: 10.1177/003754977001500603 Distributed system simulation using infinite product expansions R.E. Goodson School of Mechanical Engineering Purdue University Lafayette, Indiana Infinite product expansions for the transcendental terms in the transfer functions for linear distributed systems are developed. Simulation of the dynamic re sponse of such systems is indicated

40. Introduction To Perturbation Methods By Mark H. Holmes Department 1.4 Asymptotic approximations. 1.4.1 Asymptotic expansions. 1.4.2 Accuracy vs Convergence of an Asymptotic Series. 1.4.3 Manipulating Asymptotic expansions http://www.rpi.edu/~holmes/Perturbation/TC.html

Introduction to Perturbation Methods by Mark H. Holmes Department of Mathematical Sciences Rensselaer Polytechnic Institute Troy, NY 12180 Preface The methods covered in the text vary widely in their applicability. The first chapter introduces the fundamental ideas underlying asymptotic approximations. This includes their use in constructing approximate solutions of transcendental equations as well as differential equations. In the second chapter, matched asymptotic expansions are used to analyze problems with layers. Chapter Three describes a method for dealing with problems with more than one time scale. In Chapter Four, the WKB method for analyzing linear singular perturbation problems is developed, while in Chapter Five a method for dealing with materials containing disparate spatial scales (e.g., microscopic vs. macroscopic) is discussed. The last chapter examines the topics of multiple solutions and stability. The mathematical prerequisites for this text include a basic background in differential equations and advanced calculus. In terms of difficulty, the chapters are written so the first sections are either elementary or intermediate, while the later sections are somewhat more advanced. Also, the ideas developed in each chapter are applied to a spectrum of problems, including ordinary differential equations, partial differential equations, and difference equations. Scattered through the exercises are applications to integral equations, integro-differential equations, differential-difference equations, and delay equations. What will not be found is an in-depth discussion of the theory underlying the methods. This aspect of the subject is important and references to the more theoretical work in the area are given in each chapter.

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