Johan Gielis Riccione 2012
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Right Ideals of a Ring and Sublanguages of Science
RIGHT IDEALS OF A RING AND SUBLANGUAGES OF SCIENCE Javier Arias Navarro Ph.D. In General Linguistics and Spanish Language http://www.javierarias.info/ Abstract Among Zellig Harris’s numerous contributions to linguistics his theory of the sublanguages of science probably ranks among the most underrated. However, not only has this theory led to some exhaustive and meaningful applications in the study of the grammar of immunology language and its changes over time, but it also illustrates the nature of mathematical relations between chunks or subsets of a grammar and the language as a whole. This becomes most clear when dealing with the connection between metalanguage and language, as well as when reflecting on operators. This paper tries to justify the claim that the sublanguages of science stand in a particular algebraic relation to the rest of the language they are embedded in, namely, that of right ideals in a ring. Keywords: Zellig Sabbetai Harris, Information Structure of Language, Sublanguages of Science, Ideal Numbers, Ernst Kummer, Ideals, Richard Dedekind, Ring Theory, Right Ideals, Emmy Noether, Order Theory, Marshall Harvey Stone. §1. Preliminary Word In recent work (Arias 2015)1 a line of research has been outlined in which the basic tenets underpinning the algebraic treatment of language are explored. The claim was there made that the concept of ideal in a ring could account for the structure of so- called sublanguages of science in a very precise way. The present text is based on that work, by exploring in some detail the consequences of such statement. §2. Introduction Zellig Harris (1909-1992) contributions to the field of linguistics were manifold and in many respects of utmost significance. -
Academic Genealogy of the Oakland University Department Of
Basilios Bessarion Mystras 1436 Guarino da Verona Johannes Argyropoulos 1408 Università di Padova 1444 Academic Genealogy of the Oakland University Vittorino da Feltre Marsilio Ficino Cristoforo Landino Università di Padova 1416 Università di Firenze 1462 Theodoros Gazes Ognibene (Omnibonus Leonicenus) Bonisoli da Lonigo Angelo Poliziano Florens Florentius Radwyn Radewyns Geert Gerardus Magnus Groote Università di Mantova 1433 Università di Mantova Università di Firenze 1477 Constantinople 1433 DepartmentThe Mathematics Genealogy Project of is a serviceMathematics of North Dakota State University and and the American Statistics Mathematical Society. Demetrios Chalcocondyles http://www.mathgenealogy.org/ Heinrich von Langenstein Gaetano da Thiene Sigismondo Polcastro Leo Outers Moses Perez Scipione Fortiguerra Rudolf Agricola Thomas von Kempen à Kempis Jacob ben Jehiel Loans Accademia Romana 1452 Université de Paris 1363, 1375 Université Catholique de Louvain 1485 Università di Firenze 1493 Università degli Studi di Ferrara 1478 Mystras 1452 Jan Standonck Johann (Johannes Kapnion) Reuchlin Johannes von Gmunden Nicoletto Vernia Pietro Roccabonella Pelope Maarten (Martinus Dorpius) van Dorp Jean Tagault François Dubois Janus Lascaris Girolamo (Hieronymus Aleander) Aleandro Matthaeus Adrianus Alexander Hegius Johannes Stöffler Collège Sainte-Barbe 1474 Universität Basel 1477 Universität Wien 1406 Università di Padova Università di Padova Université Catholique de Louvain 1504, 1515 Université de Paris 1516 Università di Padova 1472 Università -
Mathematical Genealogy of the Wellesley College Department Of
Nilos Kabasilas Mathematical Genealogy of the Wellesley College Department of Mathematics Elissaeus Judaeus Demetrios Kydones The Mathematics Genealogy Project is a service of North Dakota State University and the American Mathematical Society. http://www.genealogy.math.ndsu.nodak.edu/ Georgios Plethon Gemistos Manuel Chrysoloras 1380, 1393 Basilios Bessarion 1436 Mystras Johannes Argyropoulos Guarino da Verona 1444 Università di Padova 1408 Cristoforo Landino Marsilio Ficino Vittorino da Feltre 1462 Università di Firenze 1416 Università di Padova Angelo Poliziano Theodoros Gazes Ognibene (Omnibonus Leonicenus) Bonisoli da Lonigo 1477 Università di Firenze 1433 Constantinople / Università di Mantova Università di Mantova Leo Outers Moses Perez Scipione Fortiguerra Demetrios Chalcocondyles Jacob ben Jehiel Loans Thomas à Kempis Rudolf Agricola Alessandro Sermoneta Gaetano da Thiene Heinrich von Langenstein 1485 Université Catholique de Louvain 1493 Università di Firenze 1452 Mystras / Accademia Romana 1478 Università degli Studi di Ferrara 1363, 1375 Université de Paris Maarten (Martinus Dorpius) van Dorp Girolamo (Hieronymus Aleander) Aleandro François Dubois Jean Tagault Janus Lascaris Matthaeus Adrianus Pelope Johann (Johannes Kapnion) Reuchlin Jan Standonck Alexander Hegius Pietro Roccabonella Nicoletto Vernia Johannes von Gmunden 1504, 1515 Université Catholique de Louvain 1499, 1508 Università di Padova 1516 Université de Paris 1472 Università di Padova 1477, 1481 Universität Basel / Université de Poitiers 1474, 1490 Collège Sainte-Barbe -
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. -
![Arxiv:2106.01162V1 [Math.HO] 27 May 2021 Shine Conference in Kashiwa” 1 and Contain a Number of New Perspectives and Ob- Servations on Monstrous Moonshine](https://docslib.b-cdn.net/cover/0845/arxiv-2106-01162v1-math-ho-27-may-2021-shine-conference-in-kashiwa-1-and-contain-a-number-of-new-perspectives-and-ob-servations-on-monstrous-moonshine-950845.webp)
Arxiv:2106.01162V1 [Math.HO] 27 May 2021 Shine Conference in Kashiwa” 1 and Contain a Number of New Perspectives and Ob- Servations on Monstrous Moonshine
Kashiwa Lectures on New Approaches to the Monster John McKay1 edited and annotated by Yang-Hui He2;3;4;5 1 CICMA & Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8, Canada 2 London Institute for Mathematical Sciences, Royal Institution of Great Britain, 21 Albemarle Street, Mayfair, London W1S 4BS, UK; 3 Merton College, University of Oxford, OX14JD, UK; 4 Department of Mathematics, City, University of London, EC1V 0HB, UK; 5 School of Physics, NanKai University, Tianjin, 300071, P.R. China [email protected] [email protected] Abstract These notes stem from lectures given by the first author (JM) at the 2008 \Moon- arXiv:2106.01162v1 [math.HO] 27 May 2021 shine Conference in Kashiwa" 1 and contain a number of new perspectives and ob- servations on Monstrous Moonshine. Because many new points have not appeared anywhere in print, it is thought expedient to update, annotate and clarify them (as footnotes), an editorial task which the second author (YHH) is more than delighted to undertake. We hope the various puzzles and correspondences, delivered in a personal and casual manner, will serve as diversions intriguing to the community. 1Organized by the Institute for the Physics and Mathematics of the Universe (IPMU) under the support of the Graduate School of Mathematical Sciences, the University of Tokyo. 1 Contents 1 Introduction 3 1.1 Resources . 3 1.2 Talk Outline . 5 1.3 Where to Start ? . 6 2 Monstrous Moonshine 9 2.1 Primes in the Monster's Order . 10 2.2 Balance . -
Fundamental Theorems in Mathematics
SOME FUNDAMENTAL THEOREMS IN MATHEMATICS OLIVER KNILL Abstract. An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 243 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [6] without leading to panic. The order is not a ranking but ordered along a time-line when things were writ- ten down. Since [556] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context" we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The num- ber of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable" theorems with included proofs. More comments on the choice of the theorems is included in an epilogue. For literature on general mathematics, see [193, 189, 29, 235, 254, 619, 412, 138], for history [217, 625, 376, 73, 46, 208, 379, 365, 690, 113, 618, 79, 259, 341], for popular, beautiful or elegant things [12, 529, 201, 182, 17, 672, 673, 44, 204, 190, 245, 446, 616, 303, 201, 2, 127, 146, 128, 502, 261, 172]. For comprehensive overviews in large parts of math- ematics, [74, 165, 166, 51, 593] or predictions on developments [47]. For reflections about mathematics in general [145, 455, 45, 306, 439, 99, 561]. Encyclopedic source examples are [188, 705, 670, 102, 192, 152, 221, 191, 111, 635]. -
Mathematical Sciences Meetings and Conferences Section
OTICES OF THE AMERICAN MATHEMATICAL SOCIETY Richard M. Schoen Awarded 1989 Bacher Prize page 225 Everybody Counts Summary page 227 MARCH 1989, VOLUME 36, NUMBER 3 Providence, Rhode Island, USA ISSN 0002-9920 Calendar of AMS Meetings and Conferences This calendar lists all meetings which have been approved prior to Mathematical Society in the issue corresponding to that of the Notices the date this issue of Notices was sent to the press. The summer which contains the program of the meeting. Abstracts should be sub and annual meetings are joint meetings of the Mathematical Associ mitted on special forms which are available in many departments of ation of America and the American Mathematical Society. The meet mathematics and from the headquarters office of the Society. Ab ing dates which fall rather far in the future are subject to change; this stracts of papers to be presented at the meeting must be received is particularly true of meetings to which no numbers have been as at the headquarters of the Society in Providence, Rhode Island, on signed. Programs of the meetings will appear in the issues indicated or before the deadline given below for the meeting. Note that the below. First and supplementary announcements of the meetings will deadline for abstracts for consideration for presentation at special have appeared in earlier issues. sessions is usually three weeks earlier than that specified below. For Abstracts of papers presented at a meeting of the Society are pub additional information, consult the meeting announcements and the lished in the journal Abstracts of papers presented to the American list of organizers of special sessions. -
RM Calendar 2011
Rudi Mathematici x4-8.212x3+25.286.894x2-34.603.963.748x+17.756.354.226.585 =0 Rudi Mathematici January 1 S (1894) Satyendranath BOSE Putnam 1996 - A1 (1878) Agner Krarup ERLANG (1912) Boris GNEDENKO Find the least number A such that for any two (1803) Guglielmo LIBRI Carucci dalla Sommaja RM132 squares of combined area 1, a rectangle of 2 S (1822) Rudolf Julius Emmanuel CLAUSIUS area A exists such that the two squares can be (1938) Anatoly SAMOILENKO packed in the rectangle (without interior (1905) Lev Genrichovich SHNIRELMAN overlap). You may assume that the sides of 1 3 M (1917) Yuri Alexeievich MITROPOLSKY the squares are parallel to the sides of the rectangle. 4 T (1643) Isaac NEWTON RM071 5 W (1871) Federigo ENRIQUES RM084 Math pickup lines (1871) Gino FANO (1838) Marie Ennemond Camille JORDAN My love for you is a monotonically increasing 6 T (1807) Jozeph Mitza PETZVAL unbounded function. (1841) Rudolf STURM MathJokes4MathyFolks 7 F (1871) Felix Edouard Justin Emile BOREL (1907) Raymond Edward Alan Christopher PALEY Ten percent of all car thieves are left-handed. 8 S (1924) Paul Moritz COHN All polar bears are left-handed. (1888) Richard COURANT If your car is stolen, there’s a 10% chance it (1942) Stephen William HAWKING was taken by a polar bear. 9 S (1864) Vladimir Adreievich STEKLOV The description of right lines and circles, upon 2 10 M (1905) Ruth MOUFANG which geometry is founded, belongs to (1875) Issai SCHUR mechanics. Geometry does not teach us to 11 T (1545) Guidobaldo DEL MONTE RM120 draw these lines, but requires them to be (1734) Achille Pierre Dionis DU SEJOUR drawn. -
RM Calendar 2015
Rudi Mathematici x4–8228 x3+25585534 x2–34806653332 x+17895175197705=0 www.rudimathematici.com 1 G (1803) Guglielmo Libri Carucci dalla Sommaja RM132 (1878) Agner Krarup Erlang Rudi Mathematici (1894) Satyendranath Bose RM168 (1912) Boris Gnedenko 2 V (1822) Rudolf Julius Emmanuel Clausius (1905) Lev Genrichovich Shnirelman (1938) Anatoly Samoilenko 3 S (1917) Yuri Alexeievich Mitropolsky Gennaio 4 D (1643) Isaac Newton RM071 2 5 L (1723) Nicole-Reine Etable de Labrière Lepaute (1838) Marie Ennemond Camille Jordan Putnam 2000, A1 (1871) Federigo Enriques RM084 Sia A un numero reale positivo. Quali sono i possibili (1871) Gino Fano ∞ 6 M (1807) Jozeph Mitza Petzval valori di x , se x0, x1, … sono numeri positivi per cui ∑ i2 (1841) Rudolf Sturm =i 0 7 M (1871) Felix Edouard Justin Emile Borel ∞ ? (1907) Raymond Edward Alan Christopher Paley ∑ i A=x 8 G (1888) Richard Courant RM156 =i 0 (1924) Paul Moritz Cohn (1942) Stephen William Hawking Barzellette per élite 9 V (1864) Vladimir Adreievich Steklov È difficile fare giochi di parole con i cleptomani. (1915) Mollie Orshansky Prendono tutto alla lettera . 10 S (1875) Issai Schur (1905) Ruth Moufang 11 D (1545) Guidobaldo del Monte RM120 Titoli da un mondo matematico (1707) Vincenzo Riccati Con il passaggio ai nuovi test, le valutazioni crollano. (1734) Achille Pierre Dionis du Sejour Mondo matematico: Con il passaggio ai nuovi test, i 3 12 L (1906) Kurt August Hirsch risultati non sono più confrontabili. (1915) Herbert Ellis Robbins RM156 13 M (1864) Wilhelm Karl Werner Otto Fritz Franz Wien (1876) Luther Pfahler Eisenhart Alice rise: “È inutile che ci provi”, disse; “non si può (1876) Erhard Schmidt credere a una cosa impossibile”. -
![Arxiv:1402.4957V3 [Math.HO] 12 Sep 2014 .INTRODUCTION I](https://docslib.b-cdn.net/cover/1629/arxiv-1402-4957v3-math-ho-12-sep-2014-introduction-i-3211629.webp)
Arxiv:1402.4957V3 [Math.HO] 12 Sep 2014 .INTRODUCTION I
Cauchy’s almost forgotten Lagrangian formulation of the Euler equation for 3D incompressible flow Uriel Frisch UNS, CNRS, OCA, Lab. Lagrange, B.P. 4229, 06304 Nice Cedex 4, France Barbara Villone INAF, Osservatorio Astrofisico di Torino, Via Osservatorio, 20, 10025 Pino Torinese, Italy (Dated: September 16, 2014) Two prized papers, one by Augustin Cauchy in 1815, presented to the French Academy and the other by Hermann Hankel in 1861, presented to G¨ottingen University, contain major discover- ies on vorticity dynamics whose impact is now quickly increasing. Cauchy found a Lagrangian formulation of 3D ideal incompressible flow in terms of three invariants that generalize to three dimensions the now well-known law of conservation of vorticity along fluid particle trajectories for two-dimensional flow. This has very recently been used to prove analyticity in time of fluid particle trajectories for 3D incompressible Euler flow and can be extended to compressible flow, in particular to cosmological dark matter. Hankel showed that Cauchy’s formulation gives a very simple Lagrangian derivation of the Helmholtz vorticity-flux invariants and, in the middle of the proof, derived an intermediate result which is the conservation of the circulation of the velocity around a closed contour moving with the fluid. This circulation theorem was to be rediscovered independently by William Thomson (Kelvin) in 1869. Cauchy’s invariants were only occasionally cited in the 19th century — besides Hankel, foremost by George Stokes and Maurice L´evy — and even less so in the 20th until they were rediscovered via Emmy Noether’s theorem in the late 1960, but reattributed to Cauchy only at the end of the 20th century by Russian scientists. -
~2 Q ! / Date an EXPOSITION on the KRONECKER-WEBER THEOREM
An exposition on the Kronecker-Weber theorem Item Type Thesis Authors Baggett, Jason A. Download date 24/09/2021 09:05:39 Link to Item http://hdl.handle.net/11122/11349 AN EXPOSITION ON THE KRONECKER-WEBER THEOREM By Jason A. Baggett RECOMMENDED: Advisory Committee Chair Chair, Department of Mathematics APPROVED: Dean, College of Natural §sztfmce and Mathematics ; < r Dean of the Graduate School ~2 Q_! / Date AN EXPOSITION ON THE KRONECKER-WEBER THEOREM A THESIS Presented to the Faculty of the University of Alaska Fairbanks in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE By Jason A. Baggett, B.S. Fairbanks, Alaska May 2011 iii Abstract The Kronecker-Weber Theorem is a classification result from Algebraic Number Theory. Theorem (Kronecker-Weber). Every finite, abelian extension Qof is contained in a cyclo- tomic field. This result was originally proven by Leopold Kronecker in 1853. However, his proof had some gaps that were later filled by Heinrich Martin Weber in 1886 and David Hilbert in 1896. Hilbert's strategy for the proof eventually led to the creation of the field of mathematics called Class Field Theory, which is the study of finite, abelian extensions of arbitrary fields and is still an area of active research. Not only is the Kronecker-Weber Theorem surprising, its proof is truly amazing. The idea of the proof is that for a finite, Galois extension K of Q, there is a connection be tween the Galois group Gal(K/Q) and how primes of Z split in a certain subring R of K corresponding to Z in Q. -
Takagi's Class Field Theory
RIMS Kôkyûroku Bessatsu B25 (2011), 125160 Takagis Class Field Theory ‐ From where? and to where? ‐ By * Katsuya MIYAKE §1. Introduction After the publication of his doctoral thesis [T‐1903] in 1903, Teiji Takagi (1875‐ 1960) had not published any academic papers until1914 when World War I started. In the year he began his own investigation on class field theory. The reason was to stay in the front line of mathematics still after the cessation of scientific exchange between Japan and Europe owing to World War I; see [T‐1942, Appendix I Reminiscences and Perspectives, pp.195196] or the quotation below from the English translation [T‐1973, p.360] by Iyanaga. The last important scientific message he received at the time from Europe should be Fueters paper [Fu‐1914] which contained a remarkable result on Kroneckers Ju‐ gendtraum (Kroneckers dream in his young days): Kroneckers Jugendtraum The roots of an Abelian equation over an imagi‐ nary quadratic field k are contained in an extension field of k generated by the singular moduli of elliptic functions with complex multiplication in k and values of such elliptic functions at division points of their periods. (See Subsections 3.2 and 3.3 in Section 3.) K. Fueter treated Abelian extensions of k of odd degrees. Theorem 1.1 (Fueter). Every abelian extension of an imaginary quadratic num‐ ber field k with an odd degree is contained in an extension of k generated by suitable roots of unity and the singular moduli of elliptic functions with complex multiplication in k. Received March 31, 2010. Revised in final form February 17, 2011.