Computation and Mathieu Functions
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The History and Development of Numerical Analysis in Scotland: a Personal Perspective∗
The history and development of numerical analysis in Scotland: a personal perspective∗ G. A. Watson, Division of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland. Abstract An account is given of the history and development of numerical analysis in Scotland. This covers, in particular, activity in Edinburgh in the first half of the 20th century, the collaboration between Edinburgh and St Andrews in the 1960s, and the role played by Dundee from the 1970s. I will give some reminiscences from my own time at both Edinburgh and Dundee. 1 Introduction To provide a historical account of numerical analysis (or of anything else), it is necessary to decide where to begin. If numerical analysis is defined to be the study of algorithms for the problems of continuous mathematics [16], then of course it has a very long history (see, for example, [6], [13]). But \modern" numerical analysis is inextricably linked with computing machines. It is usually associated with programmable electronic computers, and is often said to have its origins in the 1947 paper by von Neumann and Goldstine [10]. The name apparently was first used around that time, and was given formal recognition in the setting up of the Institute for Numerical Analysis, located on the campus of the University of California at Los Angeles [3]. This was a section of the National Applied Mathematics Laboratories of the National Bureau of Standards, headed by J. H. Curtiss, who is often given credit for the name. Others consider modern numerical analysis to go back further than this; for example Todd [15] suggests it begins around 1936, and cites papers by Comrie and Turing. -
Mathieu Functions for Purely Imaginary Parameters
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Journal of Computational and Applied Mathematics 236 (2012) 4513–4524 Contents lists available at SciVerse ScienceDirect Journal of Computational and Applied Mathematics journal homepage: www.elsevier.com/locate/cam Mathieu functions for purely imaginary parameters C.H. Ziener a,d,∗, M. Rückl b,c, T. Kampf c, W.R. Bauer d, H.P. Schlemmer a a German Cancer Research Center - DKFZ, Department of Radiology, Im Neuenheimer Feld 280, 69120 Heidelberg, Germany b Humboldt-University Berlin, Department of Physics, Newtonstraße 15, 12489 Berlin, Germany c Julius-Maximilians-Universität Würzburg, Experimentelle Physik 5, Am Hubland, 97074 Würzburg, Germany d Julius-Maximilians-Universität Würzburg, Medizinische Klinik I, Oberdürrbacher Straße 6, 97080 Würzburg, Germany article info a b s t r a c t Article history: For the Mathieu differential equation y00.x/CTa−2q cos.x/Uy.x/ D 0 with purely imaginary Received 23 December 2011 parameter q D is, the characteristic value a exhibits branching points. We analyze the Received in revised form 24 April 2012 properties of the Mathieu functions and their Fourier coefficients in the vicinity of the branching points. Symmetry relations for the Mathieu functions as well as the Fourier Keywords: coefficients behind a branching point are given. A numerical method to compute Mathieu Mathieu functions functions for all values of the parameter s is presented. Numerical computation ' 2012 Elsevier B.V. All rights reserved. 1. Introduction Many problems in physics can be expressed as partial differential equations and the main task that remains is to find mathematical solutions of these equations that fit the physical initial and boundary conditions. -
James Clerk Maxwell
James Clerk Maxwell JAMES CLERK MAXWELL Perspectives on his Life and Work Edited by raymond flood mark mccartney and andrew whitaker 3 3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries c Oxford University Press 2014 The moral rights of the authors have been asserted First Edition published in 2014 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2013942195 ISBN 978–0–19–966437–5 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. -
William Robertson Smith, Solomon Schechter and Contemporary Judaism
https://doi.org/10.14324/111.444.jhs.2016v48.026 William Robertson Smith, Solomon Schechter and contemporary Judaism bernhard maier University of Tübingen, Germany* During Solomon Schechter’s first years in the University of Cambridge, one of his most illustrious colleagues was the Scottish Old Testament scholar and Arabist William Robertson Smith (1846–1894), who is today considered to be among the founding fathers of comparative religious studies. Smith was the son of a minister of the strongly evangelical Free Church of Scotland, which had constituted itself in 1843 as a rival to the state-controlled established Church of Scotland. Appointed Professor of Old Testament Exegesis in the Free Church College Aberdeen at the early age of twenty-four, Smith soon came into conflict with the conservative theologians of his church on account of his critical views. After a prolonged heresy trial, he was finally deprived of his Aberdeen chair in 1881. In 1883 he moved to Cambridge, where he served, successively, as Lord Almoner’s Reader in Arabic, University Librarian, and Thomas Adams’s Professor of Arabic. Discussing Schechter’s relations with Robertson Smith, one has to bear in mind that direct contact between Schechter and Smith was confined to a relatively short period of less than five years (1890–94), during which Smith was frequently ill and consequently not resident in Cambridge at all.1 Furthermore, there is not much written evidence, so that several hints and clues that have come down to us are difficult to interpret, our understanding being sometimes based on inference and reasoning by analogy rather than on any certain knowledge. -
Former Fellows Biographical Index Part
Former Fellows of The Royal Society of Edinburgh 1783 – 2002 Biographical Index Part Two ISBN 0 902198 84 X Published July 2006 © The Royal Society of Edinburgh 22-26 George Street, Edinburgh, EH2 2PQ BIOGRAPHICAL INDEX OF FORMER FELLOWS OF THE ROYAL SOCIETY OF EDINBURGH 1783 – 2002 PART II K-Z C D Waterston and A Macmillan Shearer This is a print-out of the biographical index of over 4000 former Fellows of the Royal Society of Edinburgh as held on the Society’s computer system in October 2005. It lists former Fellows from the foundation of the Society in 1783 to October 2002. Most are deceased Fellows up to and including the list given in the RSE Directory 2003 (Session 2002-3) but some former Fellows who left the Society by resignation or were removed from the roll are still living. HISTORY OF THE PROJECT Information on the Fellowship has been kept by the Society in many ways – unpublished sources include Council and Committee Minutes, Card Indices, and correspondence; published sources such as Transactions, Proceedings, Year Books, Billets, Candidates Lists, etc. All have been examined by the compilers, who have found the Minutes, particularly Committee Minutes, to be of variable quality, and it is to be regretted that the Society’s holdings of published billets and candidates lists are incomplete. The late Professor Neil Campbell prepared from these sources a loose-leaf list of some 1500 Ordinary Fellows elected during the Society’s first hundred years. He listed name and forenames, title where applicable and national honours, profession or discipline, position held, some information on membership of the other societies, dates of birth, election to the Society and death or resignation from the Society and reference to a printed biography. -
Combinatorial Approach to Mathieu and Lam\'E Equations
Combinatorial approach to Mathieu and Lam´eequations Wei He1, a) 1Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China 2Instituto de F´ısica Te´orica, Universidade Estadual Paulista, Barra Funda, 01140-070, S˜ao Paulo, SP, Brazil Based on some recent progress on a relation between four dimensional super Yang- Mills gauge theory and quantum integrable system, we study the asymptotic spec- trum of the quantum mechanical problems described by the Mathieu equation and the Lam´eequation. The large momentum asymptotic expansion of the eigenvalue is related to the instanton partition function of supersymmetric gauge theories which can be evaluated by a combinatorial method. The electro-magnetic duality of gauge theory indicates that in the parameter space there are three asymptotic expansions for the eigenvalue, we confirm this fact by performing the WKB analysis in each asymptotic expansion region. The results presented here give some new perspective on the Floquet theory about periodic differential equation. PACS numbers: 12.60.Jv, 02.30.Hq, 02.30.Mv Keywords: Seiberg-Witten theory, instanton partition function, Mathieu equation, Lam´eequation, WKB method arXiv:1108.0300v6 [math-ph] 27 Jul 2015 a)Electronic mail: [email protected] 1 CONTENTS I. Introduction 3 II. Differential equations and gauge theory 4 A. The Mathieu equation 4 B. The Lam´eequation 5 C. The spectrum of Schr¨odinger operator and quantum gauge theory 8 III. Spectrum of the Mathieu equation 9 A. Combinatorial evaluating in the electric region 10 B. Extension to other regions 11 IV. Combinatorial approach to the Lam´eeigenvalue 13 A. Identify parameters 14 B. -
Computer Oral History Collection, 1969-1973, 1977
Computer Oral History Collection, 1969-1973, 1977 Interviewee: John H. Curtiss Interviewer: Henry S. Tropp Date: March 9, 1973 Repository: Archives Center, National Museum of American History TROPP: This is a discussion with Professor John H. Curtiss in his office at the University of Miami in Coral Gables. Professor Curtiss is Professor of Mathematics here at the University of Miami. [Recorder off]. I guess the first question is really quite a general one and that is: You were in the Navy during the war and on leave of absence from Cornell as a mathematician. How did you end up at the Bureau of Standards? CURTISS: Dr. W. Edward Deming, who is one of my best friends in Washington, at that time was a senior adviser, statistical adviser, at the Bureau of the Budget -- was friendly with Dr. E. U. Condon. Dr. Deming, like some other great statisticians at the time and before, was himself a trained physicist. I believe Karl Pearson was a physicist and I believe also R. A. Fisher was a physicist; and naturally the physicists more or less knew each other, and so Dr. Deming felt that there should be a statistical adviser in the Bureau of Standards just as there was one in the Census Bureau -- that is, a person qualified statistically who had the ... who had publications and who might, say, be a Fellow of the Institute and the Association, just as Morris Hanson had the same qualifications for a parallel job with Census. I believe that Dr. Deming actually brought Hanson, Mr. Hanson, to the Census Bureau. -
RM Calendar 2017
Rudi Mathematici x3 – 6’135x2 + 12’545’291 x – 8’550’637’845 = 0 www.rudimathematici.com 1 S (1803) Guglielmo Libri Carucci dalla Sommaja RM132 (1878) Agner Krarup Erlang Rudi Mathematici (1894) Satyendranath Bose RM168 (1912) Boris Gnedenko 1 2 M (1822) Rudolf Julius Emmanuel Clausius (1905) Lev Genrichovich Shnirelman (1938) Anatoly Samoilenko 3 T (1917) Yuri Alexeievich Mitropolsky January 4 W (1643) Isaac Newton RM071 5 T (1723) Nicole-Reine Etable de Labrière Lepaute (1838) Marie Ennemond Camille Jordan Putnam 2002, A1 (1871) Federigo Enriques RM084 Let k be a fixed positive integer. The n-th derivative of (1871) Gino Fano k k n+1 1/( x −1) has the form P n(x)/(x −1) where P n(x) is a 6 F (1807) Jozeph Mitza Petzval polynomial. Find P n(1). (1841) Rudolf Sturm 7 S (1871) Felix Edouard Justin Emile Borel A college football coach walked into the locker room (1907) Raymond Edward Alan Christopher Paley before a big game, looked at his star quarterback, and 8 S (1888) Richard Courant RM156 said, “You’re academically ineligible because you failed (1924) Paul Moritz Cohn your math mid-term. But we really need you today. I (1942) Stephen William Hawking talked to your math professor, and he said that if you 2 9 M (1864) Vladimir Adreievich Steklov can answer just one question correctly, then you can (1915) Mollie Orshansky play today. So, pay attention. I really need you to 10 T (1875) Issai Schur concentrate on the question I’m about to ask you.” (1905) Ruth Moufang “Okay, coach,” the player agreed. -
Hannes Werthner Frank Van Harmelen Editors
Hannes Werthner Frank van Harmelen Editors Informatics in the Future Proceedings of the 11th European Computer Science Summit (ECSS 2015), Vienna, October 2015 Informatics in the Future Hannes Werthner • Frank van Harmelen Editors Informatics in the Future Proceedings of the 11th European Computer Science Summit (ECSS 2015), Vienna, October 2015 Editors Hannes Werthner Frank van Harmelen TU Wien Vrije Universiteit Amsterdam Wien, Austria Amsterdam, The Netherlands ISBN 978-3-319-55734-2 ISBN 978-3-319-55735-9 (eBook) DOI 10.1007/978-3-319-55735-9 Library of Congress Control Number: 2017938012 © The Editor(s) (if applicable) and The Author(s) 2017. This book is an open access publication. Open Access This book is licensed under the terms of the Creative Commons Attribution- NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this book are included in the book’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the book’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. This work is subject to copyright. All commercial rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. -
The Logarithmic Tables of Edward Sang and His Daughters
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Historia Mathematica 30 (2003) 47–84 www.elsevier.com/locate/hm The logarithmic tables of Edward Sang and his daughters Alex D.D. Craik School of Mathematics & Statistics, University of St Andrews, St Andrews, Fife KY16 9SS, Scotland, United Kingdom Abstract Edward Sang (1805–1890), aided only by his daughters Flora and Jane, compiled vast logarithmic and other mathematical tables. These exceed in accuracy and extent the tables of the French Bureau du Cadastre, produced by Gaspard de Prony and a multitude of assistants during 1794–1801. Like Prony’s, only a small part of Sang’s tables was published: his 7-place logarithmic tables of 1871. The contents and fate of Sang’s manuscript volumes, the abortive attempts to publish them, and some of Sang’s methods are described. A brief biography of Sang outlines his many other contributions to science and technology in both Scotland and Turkey. Remarkably, the tables were mostly compiled in his spare time. 2003 Elsevier Science (USA). All rights reserved. Résumé Edward Sang (1805–1890), aidé seulement par sa famille, c’est à dire ses filles Flora et Jane, compila des tables vastes des logarithmes et des autres fonctions mathématiques. Ces tables sont plus accurates, et plus extensives que celles du Bureau du Cadastre, compileés les années 1794–1801 par Gaspard de Prony et une foule de ses aides. On ne publia qu’une petite partie des tables de Sang (comme celles de Prony) : ses tables du 1871 des logarithmes à 7-places décimales. -
Lettere Tra LUIGI CREMONA E Corrispondenti in Lingua Inglese
Lettere tra LUIGI CREMONA e corrispondenti in lingua inglese CONSERVATE PRESSO L’ISTITUTO MAZZINIANO DI GENOVA a cura di Giovanna Dimitolo Indice Presentazione della corrispondenza 1 J.W. RUSSELL 47 Criteri di edizione 1 G. SALMON 49 A.H.H. ANGLIN 2 H.J.S. SMITH 50 M.T. BEIMER 3 R.H. SMITH 55 BINNEY 4 Smithsonian Institution 57 J. BOOTH 5 W. SPOTTISWOODE 58 British Association 6 C.M. STRUTHERS 67 W.S. BURNSIDE 7 J.J. SYLVESTER 68 CAYLEY 8 M.I. TADDEUCCI 69 G. CHRYSTAL 10 P.G. TAIT 70 R.B. CLIFTON 16 W. THOMSON (Lord Kelvin) 74 R. CRAWFORD 17 R. TUCKER 75 A.J.C. CUNNINGHAM 18 G. TYSON-WOLFF 76 C.L. DODGSON (Lewis Carrol) 19 R.H. WOLFF 90 DULAN 20 J. WILSON 93 H.T. EDDY 21 Tabella: i dati delle lettere 94 S. FERGUSON 22 Biografie dei corrispondenti 97 W.T. GAIRDNER 23 Indice dei nomi citati nelle lettere 99 J.W.L. GLAISHER 29 Bibliografia 102 A.B. GRIFFITHS 30 T. HUDSON BEARE 34 W. HUGGINS 36 M. JENKINS 37 H. LAMB 38 C. LEUDESDORF 39 H.A. NEWTON 41 B. PRICE 42 E.L. RICHARDS 44 R.G. ROBSON 45 Royal Society of London 46 www.luigi-cremona.it – aprile 2017 Presentazione della corrispondenza La corrispondenza qui trascritta è composta da 115 lettere: 65, in inglese, sono di corrispondenti stranieri e 50 (48 in inglese e 2 in italiano) sono bozze delle lettere di Luigi Cremona indirizzate a stranieri. I 43 corrispondenti stranieri sono per la maggior parte inglesi, ma vi sono anche irlandesi, scozzesi, statunitensi, australiani e un tedesco, l’amico compositore Gustav Tyson-Wolff che, per un lungo periodo visse in Inghilterra. -
Projects and Publications of the National Applied
NATIONAL BUREAU OF STANDARDS REPORT 2688 PROJECTS and PUBLICATIONS « of the NATIONAL APPLIED MATHEMATICS LABORATORIES A Quarterly Report April through June 1953 <NBp> U. S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS U. S. DEPARTMENT OF COMMERCE Sinclair Weeks, Secretary NATIONAL BUREAU OF STANDARDS A. V. Astin, Director THE NATIONAL BUREAU OF STANDARDS The scope of activities of the National Bureau of Standards is suggested in the following listing of the divisions and sections engaged in technical work. In general, each section is engaged in special- ized research, development, and engineering in the field indicated by its title. A brief description of the activities, and of the resultant reports and publications, appears on the inside of the back cover of this report. Electricity. Resistance Measurements. Inductance and Capacitance. Electrical Instruments. Magnetic Measurements. Applied Electricity. Electrochemistry. Optics and Metrology. Photometry and Colorimetry. Optical Instruments. Photographic Technology. Length. Gage. Heat and Power. Temperature Measurements. Thermodynamics. Cryogenics. Engines and Lubrication. Engine Fuels. Cryogenic Engineering. Atomic and Radiation Physics. Spectroscopy. Radiometry. Mass Spectrometry. Solid State Physics. Electron Physics. Atomic Physics. Neutron Measurements. Infrared Spectroscopy. Nuclear Physics. Radioactivity. X-Rays. Betatron. Nucleonic Instrumentation. Radio- logical Equipment. Atomic Energy Commission Instruments Branch. Chemistry. Organic Coatings. Surface Chemistry. Organic