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Writing the History of Dynamical Systems and Chaos
Historia Mathematica 29 (2002), 273–339 doi:10.1006/hmat.2002.2351 Writing the History of Dynamical Systems and Chaos: View metadata, citation and similar papersLongue at core.ac.uk Dur´ee and Revolution, Disciplines and Cultures1 brought to you by CORE provided by Elsevier - Publisher Connector David Aubin Max-Planck Institut fur¨ Wissenschaftsgeschichte, Berlin, Germany E-mail: [email protected] and Amy Dahan Dalmedico Centre national de la recherche scientifique and Centre Alexandre-Koyre,´ Paris, France E-mail: [email protected] Between the late 1960s and the beginning of the 1980s, the wide recognition that simple dynamical laws could give rise to complex behaviors was sometimes hailed as a true scientific revolution impacting several disciplines, for which a striking label was coined—“chaos.” Mathematicians quickly pointed out that the purported revolution was relying on the abstract theory of dynamical systems founded in the late 19th century by Henri Poincar´e who had already reached a similar conclusion. In this paper, we flesh out the historiographical tensions arising from these confrontations: longue-duree´ history and revolution; abstract mathematics and the use of mathematical techniques in various other domains. After reviewing the historiography of dynamical systems theory from Poincar´e to the 1960s, we highlight the pioneering work of a few individuals (Steve Smale, Edward Lorenz, David Ruelle). We then go on to discuss the nature of the chaos phenomenon, which, we argue, was a conceptual reconfiguration as -
Evidence and Counter-Evidence : Essays in Honour of Frederik
Evidence and Counter-Evidence Studies in Slavic and General Linguistics Series Editors: Peter Houtzagers · Janneke Kalsbeek · Jos Schaeken Editorial Advisory Board: R. Alexander (Berkeley) · A.A. Barentsen (Amsterdam) B. Comrie (Leipzig) - B.M. Groen (Amsterdam) · W. Lehfeldt (Göttingen) G. Spieß (Cottbus) - R. Sprenger (Amsterdam) · W.R. Vermeer (Leiden) Amsterdam - New York, NY 2008 Studies in Slavic and General Linguistics, vol. 32 Evidence and Counter-Evidence Essays in honour of Frederik Kortlandt Volume 1: Balto-Slavic and Indo-European Linguistics edited by Alexander Lubotsky Jos Schaeken Jeroen Wiedenhof with the assistance of Rick Derksen and Sjoerd Siebinga Cover illustration: The Old Prussian Basel Epigram (1369) © The University of Basel. The paper on which this book is printed meets the requirements of “ISO 9706: 1994, Information and documentation - Paper for documents - Requirements for permanence”. ISBN: set (volume 1-2): 978-90-420-2469-4 ISBN: 978-90-420-2470-0 ©Editions Rodopi B.V., Amsterdam - New York, NY 2008 Printed in The Netherlands CONTENTS The editors PREFACE 1 LIST OF PUBLICATIONS BY FREDERIK KORTLANDT 3 ɽˏ˫˜ˈ˧ ɿˈ˫ː˧ˮˬː˧ ʡ ʤʡʢʡʤʦɿʄʔʦʊʝʸʟʡʞ ʔʒʩʱʊʟʔʔ ʡʅʣɿʟʔʱʔʦʊʝʸʟʷʮ ʄʣʊʞʊʟʟʷʮ ʤʡʻʒʡʄ ʤʝɿʄʼʟʤʘʔʮ ʼʒʷʘʡʄ 23 Robert S.P. Beekes PALATALIZED CONSONANTS IN PRE-GREEK 45 Uwe Bläsing TALYSCHI RöZ ‘SPUR’ UND VERWANDTE: EIN BEITRAG ZUR IRANISCHEN WORTFORSCHUNG 57 Václav Blažek CELTIC ‘SMITH’ AND HIS COLLEAGUES 67 Johnny Cheung THE OSSETIC CASE SYSTEM REVISITED 87 Bardhyl Demiraj ALB. RRUSH, ON RAGUSA UND GR. ͽΚ̨ 107 Rick Derksen QUANTITY PATTERNS IN THE UPPER SORBIAN NOUN 121 George E. Dunkel LUVIAN -TAR AND HOMERIC ̭ш ̸̫ 137 José L. García Ramón ERERBTES UND ERSATZKONTINUANTEN BEI DER REKON- STRUKTION VON INDOGERMANISCHEN KONSTRUKTIONS- MUSTERN: IDG. -
Lewis Fry Richardson: Scientist, Visionary and Pacifist
Lett Mat Int DOI 10.1007/s40329-014-0063-z Lewis Fry Richardson: scientist, visionary and pacifist Angelo Vulpiani Ó Centro P.RI.ST.EM, Universita` Commerciale Luigi Bocconi 2014 Abstract The aim of this paper is to present the main The last of seven children in a thriving English Quaker aspects of the life of Lewis Fry Richardson and his most family, in 1898 Richardson enrolled in Durham College of important scientific contributions. Of particular importance Science, and two years later was awarded a grant to study are the seminal concepts of turbulent diffusion, turbulent at King’s College in Cambridge, where he received a cascade and self-similar processes, which led to a profound diverse education: he read physics, mathematics, chemis- transformation of the way weather forecasts, turbulent try, meteorology, botany, and psychology. At the beginning flows and, more generally, complex systems are viewed. of his career he was quite uncertain about which road to follow, but he later resolved to work in several areas, just Keywords Lewis Fry Richardson Á Weather forecasting Á like the great German scientist Helmholtz, who was a Turbulent diffusion Á Turbulent cascade Á Numerical physician and then a physicist, but following a different methods Á Fractals Á Self-similarity order. In his words, he decided ‘‘to spend the first half of my life under the strict discipline of physics, and after- Lewis Fry Richardson (1881–1953), while undeservedly wards to apply that training to researches on living things’’. little known, had a fundamental (often posthumous) role in In addition to contributing important results to meteo- twentieth-century science. -
EGU 2018 EGU – Abstracts
CEN @ EGU 2018 EGU – abstracts Summary of Presentations, Sessions, Orals, PICOs and Posters by CEN/ CliSAP Scientists www.clisap.de www.cen.uni-hamburg.de https://twitter.com/CENunihh Presentations @ EGU 2018 CliSAP/CEN/UHH Member/Presenter; CliSAP/CEN/UHH Member Monday, 9th of April Sessions TS10.2 Hypervelocity impact cratering: Mechanics and environmental consequences Convener: Ulrich Riller | Co-Convener: Michael Poelchau Orals / Mon, 09 Apr, 10:30–12:00 / Room 1.61 Posters / Attendance Mon, 09 Apr, 17:30–19:00 / Hall X2 Orals BG1.1, Application of stable isotopes in Biogeosciences (co-organized by the European Association of Geochemistry (EAG) , Orals, 08:30–10:00, Room 2.20 09:00– EGU2018-19620 Nitrate sources in the catchment basin of the Rhône River by 09:15 Alexander Bratek, Kirstin Daehnke, Tina Sanders, and Jürgen Möbius OS2.4, Oceanography at coastal scales. Modelling, coupling, observations and benefits from coastal Research Infrastructures , Orals, 10:30–12:00, Room 1.85 EGU2018-7112 Synergy between satellite observations and model simulations 11:15– during extreme events by Anne Wiese, Joanna Staneva, Arno Behrens, Johannes 11:30 Schulz-Stellenfleth, and Luciana Fenoglio-Marc Sessions / Orals / Posters TS10.2, Hypervelocity impact cratering: Mechanics and environmental consequences , Orals, 10:30–12:00, Room 1.61 11:30– EGU2018-4309 Dynamics of the thermal aureole of the Sudbury impact melt 11:45 sheet, Canada by Paul Göllner and Ulrich Riller GD8.3/GMPV9.4/TS9.10, The geology of the Azores: a comprehensive approach to understanding a unique geological, geochemical and geodynamic setting (co-organized) , PICO, 15:30–17:00, PICO spot 3 15:30– EGU2018-8375 The submarine geology of the Azores Plateau – insights from 15:32 marine reflection seismic and multi-beam imaging by Christian Huebscher PICO3.1 15:56– EGU2018-9441 Extensional forces in intraplate magmatism: constraints from 15:58 Faial Island, Azores by René H.W. -
Montana Throne Molly Gupta Laura Brannan Fractals: a Visual Display of Mathematics Linear Algebra
Montana Throne Molly Gupta Laura Brannan Fractals: A Visual Display of Mathematics Linear Algebra - Math 2270 Introduction: Fractals are infinite patterns that look similar at all levels of magnification and exist between the normal dimensions. With the advent of the computer, we can generate these complex structures to model natural structures around us such as blood vessels, heartbeat rhythms, trees, forests, and mountains, to name a few. I will begin by explaining how different linear transformations have been used to create fractals. Then I will explain how I have created fractals using linear transformations and include the computer-generated results. A Brief History: Fractals seem to be a relatively new concept in mathematics, but that may be because the term was coined only 43 years ago. It is in the century before Benoit Mandelbrot coined the term that the study of concepts now considered fractals really started to gain traction. The invention of the computer provided the computing power needed to generate fractals visually and further their study and interest. Expand on the ideas by century: 17th century ideas • Leibniz 19th century ideas • Karl Weierstrass • George Cantor • Felix Klein • Henri Poincare 20th century ideas • Helge von Koch • Waclaw Sierpinski • Gaston Julia • Pierre Fatou • Felix Hausdorff • Paul Levy • Benoit Mandelbrot • Lewis Fry Richardson • Loren Carpenter How They Work: Infinitely complex objects, revealed upon enlarging. Basics: translations, uniform scaling and non-uniform scaling then translations. Utilize translation vectors. Concepts used in fractals-- Affine Transformation (operate on individual points in the set), Rotation Matrix, Similitude Transformation Affine-- translations, scalings, reflections, rotations Insert Equations here. -
International Standard ISO/IEC 14977
ISO/IEC 14977 : 1996(E) Contents Page Foreword ................................................ iii Introduction .............................................. iv 1Scope:::::::::::::::::::::::::::::::::::::::::::::: 1 2 Normative references :::::::::::::::::::::::::::::::::: 1 3 Definitions :::::::::::::::::::::::::::::::::::::::::: 1 4 The form of each syntactic element of Extended BNF :::::::::: 1 4.1 General........................................... 2 4.2 Syntax............................................ 2 4.3 Syntax-rule........................................ 2 4.4 Definitions-list...................................... 2 4.5 Single-definition . 2 4.6 Syntactic-term...................................... 2 4.7 Syntacticexception.................................. 2 4.8 Syntactic-factor..................................... 2 4.9 Integer............................................ 2 4.10 Syntactic-primary.................................... 2 4.11 Optional-sequence................................... 3 4.12 Repeatedsequence................................... 3 4.13 Grouped sequence . 3 4.14 Meta-identifier...................................... 3 4.15 Meta-identifier-character............................... 3 4.16 Terminal-string...................................... 3 4.17 First-terminal-character................................ 3 4.18 Second-terminal-character . 3 4.19 Special-sequence.................................... 3 4.20 Special-sequence-character............................. 3 4.21 Empty-sequence.................................... -
Fighting for Tenure the Jenny Harrison Case Opens Pandora's
Calendar of AMS Meetings and Conferences This calendar lists all meetings and conferences approved prior to the date this issue insofar as is possible. Instructions for submission of abstracts can be found in the went to press. The summer and annual meetings are joint meetings with the Mathe January 1993 issue of the Notices on page 46. Abstracts of papers to be presented at matical Association of America. the meeting must be received at the headquarters of the Society in Providence, Rhode Abstracts of papers presented at a meeting of the Society are published in the Island, on or before the deadline given below for the meeting. Note that the deadline for journal Abstracts of papers presented to the American Mathematical Society in the abstracts for consideration for presentation at special sessions is usually three weeks issue corresponding to that of the Notices which contains the program of the meeting, earlier than that specified below. Meetings Abstract Program Meeting# Date Place Deadline Issue 890 t March 18-19, 1994 Lexington, Kentucky Expired March 891 t March 25-26, 1994 Manhattan, Kansas Expired March 892 t April8-10, 1994 Brooklyn, New York Expired April 893 t June 16-18, 1994 Eugene, Oregon April4 May-June 894 • August 15-17, 1994 (96th Summer Meeting) Minneapolis, Minnesota May 17 July-August 895 • October 28-29, 1994 Stillwater, Oklahoma August 3 October 896 • November 11-13, 1994 Richmond, Virginia August 3 October 897 • January 4-7, 1995 (101st Annual Meeting) San Francisco, California October 1 December March 4-5, 1995 -
Fractals Dalton Allan and Brian Dalke College of Science, Engineering & Technology Nominated by Amy Hlavacek, Associate Professor of Mathematics
Fractals Dalton Allan and Brian Dalke College of Science, Engineering & Technology Nominated by Amy Hlavacek, Associate Professor of Mathematics Dalton is a dual-enrolled student at Saginaw Arts and Sciences Academy and Saginaw Valley State University. He has taken mathematics classes at SVSU for the past four years and physics classes for the past year. Dalton has also worked in the Math and Physics Resource Center since September 2010. Dalton plans to continue his study of mathematics at the Massachusetts Institute of Technology. Brian is a part-time mathematics and English student. He has a B.S. degree with majors in physics and chemistry from the University of Wisconsin--Eau Claire and was a scientific researcher for The Dow Chemical Company for more than 20 years. In 2005, he was certified to teach physics, chemistry, mathematics and English and subsequently taught mostly high school mathematics for five years. Currently, he enjoys helping SVSU students as a Professional Tutor in the Math and Physics Resource Center. In his spare time, Brian finds joy playing softball, growing roses, reading, camping, and spending time with his wife, Lorelle. Introduction For much of the past two-and-one-half millennia, humans have viewed our geometrical world through the lens of a Euclidian paradigm. Despite knowing that our planet is spherically shaped, math- ematicians have developed the mathematics of non-Euclidian geometry only within the past 200 years. Similarly, only in the past century have mathematicians developed an understanding of such common phenomena as snowflakes, clouds, coastlines, lightning bolts, rivers, patterns in vegetation, and the tra- jectory of molecules in Brownian motion (Peitgen 75). -
Lewis Fry Richardson's Forecast Factory for Real
Lewis Fry Richardson’s forecast factory – for real Andrew Charlton-Perez horizontal momentum, pressure, humidity 1. Forecasts are made by solving math- and stratospheric temperature over central ematical equations which represent and Helen Dacre Europe, using initial conditions from an the physical laws governing the University of Reading analysis by Bjerknes for 20 May 1910. This atmosphere. forecast was manually computed by 2. Forecasts are often made on a grid of The idea that supercomputers are an impor- Richardson between 1916 and 1918, when, points which represent different geo- tant part of making forecasts of the weather as a Quaker (and therefore a pacifist), he graphical locations. and climate is well known amongst the gen- served as an ambulance driver in Cham- eral population. However, the details of their pagne, France. Famously, his forecast pro- use are somewhat mysterious. A concept duced very large tendencies in most of its A scaled-down forecast factory Weather – February 2011, Vol. 66, No. 2 66, No. Vol. 2011, – February Weather used to illustrate many undergraduate components – much larger than those In order to make the problem tractable for numerical weather prediction courses is the observed in the real atmosphere (Lynch, secondary-school-age children and to make idea of a giant ‘forecast factory’, conceived 2006, p.133, discusses the reasons for this). it possible to complete the activity in a rea- by Lewis Fry Richardson in 1922. In this Nonetheless, the principles of Richardson’s sonably short time (~30 minutes) it was article, a way of using the same idea to forecast, particularly the application of math- necessary to design a forecast factory which communicate key ideas in numerical ematical techniques to solving the primi - solved a much simpler problem than that weather prediction to the general public is tive equations on a grid representing the used by Richardson. -
RM Calendar 2013
Rudi Mathematici x4–8220 x3+25336190 x2–34705209900 x+17825663367369=0 www.rudimathematici.com 1 T (1803) Guglielmo Libri Carucci dalla Sommaja RM132 (1878) Agner Krarup Erlang Rudi Mathematici (1894) Satyendranath Bose (1912) Boris Gnedenko 2 W (1822) Rudolf Julius Emmanuel Clausius (1905) Lev Genrichovich Shnirelman (1938) Anatoly Samoilenko 3 T (1917) Yuri Alexeievich Mitropolsky January 4 F (1643) Isaac Newton RM071 5 S (1723) Nicole-Reine Etable de Labrière Lepaute (1838) Marie Ennemond Camille Jordan Putnam 1998-A1 (1871) Federigo Enriques RM084 (1871) Gino Fano A right circular cone has base of radius 1 and height 3. 6 S (1807) Jozeph Mitza Petzval A cube is inscribed in the cone so that one face of the (1841) Rudolf Sturm cube is contained in the base of the cone. What is the 2 7 M (1871) Felix Edouard Justin Emile Borel side-length of the cube? (1907) Raymond Edward Alan Christopher Paley 8 T (1888) Richard Courant RM156 Scientists and Light Bulbs (1924) Paul Moritz Cohn How many general relativists does it take to change a (1942) Stephen William Hawking light bulb? 9 W (1864) Vladimir Adreievich Steklov Two. One holds the bulb, while the other rotates the (1915) Mollie Orshansky universe. 10 T (1875) Issai Schur (1905) Ruth Moufang Mathematical Nursery Rhymes (Graham) 11 F (1545) Guidobaldo del Monte RM120 Fiddle de dum, fiddle de dee (1707) Vincenzo Riccati A ring round the Moon is ̟ times D (1734) Achille Pierre Dionis du Sejour But if a hole you want repaired 12 S (1906) Kurt August Hirsch You use the formula ̟r 2 (1915) Herbert Ellis Robbins RM156 13 S (1864) Wilhelm Karl Werner Otto Fritz Franz Wien (1876) Luther Pfahler Eisenhart The future science of government should be called “la (1876) Erhard Schmidt cybernétique” (1843 ). -
17191931.Pdf
PDF hosted at the Radboud Repository of the Radboud University Nijmegen The following full text is a publisher's version. For additional information about this publication click this link. http://hdl.handle.net/2066/113622 Please be advised that this information was generated on 2017-12-06 and may be subject to change. Description and Analysis of Static Semantics by Fixed Point Equations Description and Analysis of Static Semantics by Fixed Point Equations Een wetenschappelijke proeve op het gebied van de Wiskunde en Natuurwetenschappen Proefschrift ter verkrijging van de graad van doctor aan Katholieke Universiteit te Nijmegen, volgens besluit van college van decanen in het openbaar te verdedigen maandag 3 april 1989, des namiddags te 1.30 uur precies door Matthias Paul Gerhard Moritz geboren op 13 mei 1951 te Potsdam-Babelsberg druk: Bloembergen Santee bv, Nijmegen Promotor: Prof. C.H.A. Koster ISBN 90-9002752-1 © 1989, M. Moritz, The Netherlands I am grateful to many present and former members of the Nijmegen Informatics Department for numerous constructive dis cussions and for their comments on earlier drafts of this thesis. Contents Contents 1 1 Introduction 5 1.1 A Personal View 6 1.2 Description and Implementation 9 1.2.1 Syntax of Programming Languages 10 1.2.2 Semantics of Programming Languages ... 11 1.2.3 Static Semantics of Programming Languages 12 1.3 Our Aim 13 1.4 Overview 14 1.5 Related Work 15 2 Posets and Lattices 19 2.1 Partially Ordered Sets 19 2.2 Functions on Partially Ordered Sets 24 2.3 Construction of Posets 25 2.4 Lattices 29 2.5 Construction of Complete Lattices 31 2.6 Reflexive Lattices 34 1 2 CONTENTS 2.7 Functions on Lattices 35 2.8 Fixed Points 38 3 Description of Systems by Graphs 41 3.1 Graphs and Systems 42 3.1.1 Graph Schemes 42 3.1.2 Graph Structures 44 3.2 Functions on Graphs . -
Asymptotology of Chemical Reaction Networks
Chemical Engineering Science 65 (2010) 2310-2324 Asymptotology of Chemical Reaction Networks A. N. Gorban ∗ University of Leicester, UK O. Radulescu IRMAR, UMR 6625, University of Rennes 1, Campus de Beaulieu, 35042 Rennes, France A. Y. Zinovyev Institut Curie, U900 INSERM/Curie/Mines ParisTech, 26 rue d’Ulm, F75248, Paris, France Abstract The concept of the limiting step is extended to the asymptotology of multiscale reaction networks. Complete theory for linear networks with well separated reaction rate constants is developed. We present algorithms for explicit approximations of eigenvalues and eigenvectors of kinetic matrix. Accuracy of estimates is proven. Performance of the algorithms is demonstrated on simple examples. Application of algorithms to nonlinear systems is discussed. Key words: Reaction network, asymptotology, dominant system, limiting step, multiscale asymptotic, model reduction PACS: 64.60.aq, 82.40.Qt, 82.39.Fk, 82.39.Rt 87.15.R-, 89.75.Fb 1. Introduction was proposed by Kruskal (1963), but fundamental research in this direction are much older, and many Most of mathematical models that really work fundamental approaches were developed by I. New- are simplifications of the basic theoretical models ton (Newton polyhedron, and many other things). Following Kruskal (1963), asymptotology is “the arXiv:0903.5072v2 [physics.chem-ph] 14 Jun 2010 and use in the backgrounds an assumption that some terms are big, and some other terms are small art of describing the behavior of a specified solution enough to neglect or almost neglect them. The closer (or family of solutions) of a system in a limiting case. consideration shows that such a simple separation ..