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Ramanujan As a Patient
Proc. Indian Acad. Sci. (Math. Sci.), Voi. 93, Nos 2 & 3, December 1984, pp. 79-100 Printed in India. Ramanujan as a patient R A RANKIN Department of Mathematics, University of Glasgow, Glasgow GI2 8QW, Scotland 1. Introduction In this article I attempt to give as full a picture as possible of Srinivasa Ramanujan's medical history during his time in England. The account is based largely on unpublished letters and documents housed in various libraries, and on information extracted from the records of public bodies. In my earlier paper [12] I was concerned mainly with his notebooks and manuscripts, although I did give a brief description of the nursing homes in which he was a patient, based on information available to me at the time. What might be called Ramanujan's domestic history is well documented [1, 5, 7, 8, 9, 10, 14], at any rate as regards incident, if not exact date, so that, in the interests of brevity, I recall only those events that have a direct bearing on my subject. I also take the opportunity (in w to amplify and extend some of the material included in [12], in the light of information more recently received, and to make a number of general comments. The source to which most frequent reference is made is the collection of unpublished papers and documents written by, or concerning, Ramanujan (1887-1920), which were passed on by G H Hardy (1877-1947) and J E Littlewood (1885-1977) to G N Watson (1886-1965) and are now housed in the Wren Library of Trinity College, Cambridge, where at one time all four were Fellows. -
Ramanujan: Matemático Genial Desde La Pobreza Extrema
Rev.R.Acad.Cienc.Exact.Fís.Nat. (Esp) Vol. 107, Nº. 1-2, pp 43-54, 2014 XVI Programa de Promoción de la Cultura Científica y Tecnológica RAMANUJAN: MATEMÁTICO GENIAL DESDE LA POBREZA EXTREMA. MANUEL LÓPEZ PELLICER Real Academia de Ciencias Exactas, Físicas y Naturales. Valverde, 22. 28004 Madrid. 1. ENTORNO FAMILIAR. Srinivasa Aiyangar Ramanujan nació en Erode, cer- ca de Madrás, el 22 de diciembre de 1887. La India luchaba por su independencia desde 1857, mediante revueltas contra los ingleses. El héroe pacifista de la independencia fue Mohandas Karamchand Gandhi1, héroe pacifista de la independencia de la India, cono- cido como Mahatma Gandhi, que vivió entre 1869 y 1948. Ramanujan no conoció la independencia de la India, que se produjo el 15 de agosto de 1947. Su familia era muy pobre, aunque pertenecía a la casta Brahmin, que era una casta alta. Su padre era contable en un comercio de telas de Kumbakonam y su madre, apreciada por su buen criterio derivado de su gran sentido común, era hija de un modesto oficial del juzgado de Erodo. Su abuelo sufrió la lepra. Figura 1. Srinivasa Aiyangar Ramanujan. 1887-1920. 1 Desde 1918 perteneció al movimiento nacionalista hindú, utilizó la huelga de hambre como método de lucha social. Influido por León Tolstoi rechazó la lucha armada, predicando la no violencia para vencer al dominio británico, defendiendo la fidelidad a los dictados de la conciencia y el retorno a las tradiciones hinduistas. Su encarcelamiento en varias ocasiones le convirtió en un héroe nacional. En 1944 Gandi y su esposa Kasturba sufrieron arresto domiciliario en el Palacio del Aga Khan, donde ella murió en 1944, mientras que Gandhi realizaba veintiún días de ayuno. -
The Case of George Ernest Thompson Edalji
THE CASE OF GEORGE ERNEST THOMPSON EDALJI In 1903, Staffordshire Police arrested George Edalji of Great Wyrley (near Birmingham) on charges of wounding a pony and writing a threatening letter under a pseudonym (which strangely accused Edalji himself of the mutilations). Edalji, the eldest of three children, was at the time a twenty-seven-year old solicitor still living with his parents, and commuting by train to Birmingham to practice law. Although his father Shapurji Edalji (the vicar of Great Wyrley), who had converted to Church of England from Parsi, the family had suffered a great deal of abuse (including racial abuse) for many years from colleagues and local people perhaps because of Shapurji’s Indian origin and his marriage to an Englishwoman. Over a period of six months, 16 animals were found brutally slashed to death and mutilated with shallow slits along their stomach. Despite him having no possible involvement (Davenport-Hines 2008) George Edalji was convicted of the 8th animal outrage, when a pit-pony was discovered in a field not far from the Edalji home with a savage wound across its belly. The police suspected that he was also responsible for the other slayings. Although his father testified that George was fast asleep at the time of the crime, his testimony was disregarded. Instead, dubious circumstantial evidence such as razor blades found in the vicarage and spots of blood on his coat were counted as evidence that his had committed the crime. The fact that the animal outrages continued after George Edalji’s imprisonment was disregarded and it was claimed that George was just a member of a gang. -
Arthur & George
The Game Is On—for Real. Arthur & George With Martin Clunes as Sir Arthur Conan Doyle Adapted from Julian Barnes’s acclaimed novel Sundays, September 6 - 20, 2015 at the special time of 8pm ET on MASTERPIECE on PBS Martin Clunes (Doc Martin) stars as Sir Arthur Conan Doyle, the creator of Sherlock Holmes, in a real-life case that inspired the great author to put down his pen and turn detective. Tracing a string of notorious animal mutilations alleged to involve an attorney named George Edalji, Arthur & George airs in three gripping episodes on MASTERPIECE, Sundays, September 6-20, 2015 at the special time of 8pm ET on PBS (check local listings). Arthur & George is adapted from Julian Barnes’s acclaimed novel of the same name, which was a finalist for the Man Booker Prize, the most prestigious literary award in the English-speaking world. Co-starring are Arsher Ali (The Missing) as George Edalji, a mixed-race solicitor living in the English Midlands; Art Malik (Upstairs Downstairs) as his Indian father, an Anglican minister; and Emma Fielding (Cranford) as his Scottish mother. Also appearing are Charles Edwards (Downton Abbey) as Alfred Wood, Sir Arthur’s private secretary; and Hattie Morahan (Sense and Sensibility) as Jean Leckie, the woman that Doyle befriended while his wife was gravely ill. The three-part drama won plaudits from the press during its recent UK broadcast, with The Sunday Telegraph (London) hailing it as “thoroughly enjoyable … Clunes proves exceptionally winning as the widowed writer and sometime crusader for justice, Arthur Conan Doyle, who finds a new zest for life when he comes across the curious case of George Edalji.” The Edalji case saw an improbable defendant, mild-mannered lawyer George Edalji, convicted for mutilating a pony and, by implication, a host of other farm animals in a slashing spree known as the Great Wyrley Outrages. -
Who, Where and When: the History & Constitution of the University of Glasgow
Who, Where and When: The History & Constitution of the University of Glasgow Compiled by Michael Moss, Moira Rankin and Lesley Richmond © University of Glasgow, Michael Moss, Moira Rankin and Lesley Richmond, 2001 Published by University of Glasgow, G12 8QQ Typeset by Media Services, University of Glasgow Printed by 21 Colour, Queenslie Industrial Estate, Glasgow, G33 4DB CIP Data for this book is available from the British Library ISBN: 0 85261 734 8 All rights reserved. Contents Introduction 7 A Brief History 9 The University of Glasgow 9 Predecessor Institutions 12 Anderson’s College of Medicine 12 Glasgow Dental Hospital and School 13 Glasgow Veterinary College 13 Queen Margaret College 14 Royal Scottish Academy of Music and Drama 15 St Andrew’s College of Education 16 St Mungo’s College of Medicine 16 Trinity College 17 The Constitution 19 The Papal Bull 19 The Coat of Arms 22 Management 25 Chancellor 25 Rector 26 Principal and Vice-Chancellor 29 Vice-Principals 31 Dean of Faculties 32 University Court 34 Senatus Academicus 35 Management Group 37 General Council 38 Students’ Representative Council 40 Faculties 43 Arts 43 Biomedical and Life Sciences 44 Computing Science, Mathematics and Statistics 45 Divinity 45 Education 46 Engineering 47 Law and Financial Studies 48 Medicine 49 Physical Sciences 51 Science (1893-2000) 51 Social Sciences 52 Veterinary Medicine 53 History and Constitution Administration 55 Archive Services 55 Bedellus 57 Chaplaincies 58 Hunterian Museum and Art Gallery 60 Library 66 Registry 69 Affiliated Institutions -
Several New Product Identities in Relation to Two-Variable Rogers–Ramanujan Type Sums and Mock Theta Functions
SEVERAL NEW PRODUCT IDENTITIES IN RELATION TO TWO-VARIABLE ROGERS–RAMANUJAN TYPE SUMS AND MOCK THETA FUNCTIONS ALEXANDRU PASCADI Abstract. Product identities in two variables x; q expand infinite products as infinite sums, which are linear combinations of theta functions; famous examples include Jacobi’s triple product identity, Watson’s quintuple identity, and Hirschhorn’s septuple identity. We view these series expansions as representations in canonical bases of certain vector spaces of quasiperiodic meromorphic functions (related to sections of line and vector bundles), and find new identities for two nonuple products, an undecuple product, and several two-variable Rogers–Ramanujan type sums. Our main theorem explains a correspondence between the septuple product identity and the two original Rogers– Ramanujan identities, involving two-variable analogues of fifth-order mock theta functions. We also prove a similar correspondence between an octuple product identity of Ewell and two simpler variations of the Rogers–Ramanujan identities, which is related to third-order mock theta functions, and conjecture other occurrences of this phenomenon. As applications, we specialize our results to obtain identities for quotients of generalized Dedekind eta functions and mock theta functions. 1. Introduction 2πiτ 2πiz Q1 n Fix τ 2 C with Im τ > 0, and let z 2 C. Denote q := e , x := e , (x; q) := n=0 (1 − q x), and hx; qi := (x; q)(q=x; q) (the standard notations have a subscript of 1, which we drop for brevity; this will be helpful in identities like (1.4)). Then Jacobi’s triple product identity [13, p. 10] reads X n n n (q; q) hx; qi = (−1) q(2)x : (1.1) n2Z As functions of z, both sides of (1.1) converge absolutely and locally uniformly to entire 1-periodic functions, and satisfy the τ-quasiperiodicity F (z) = −xF (z + τ); in geometric language, F is a section of a certain holomorphic line bundle over the complex torus C=(Z + Zτ). -
Arthur & George Por Julian Barnes – Na Pista De Um Crime Sem Castigo
UNIVERSIDADE DE TRÁS-OS-MONTES E ALTO DOURO Arthur & George por Julian Barnes – na Pista de um Crime sem Castigo DISSERTAÇÃO DE MESTRADO EM CULTURA E LITERATURA INGLESAS ANABELA CRISTINA ANTUNES PEREIRA Vila Real, 2008 1 Dissertação elaborada no âmbito do Mestrado em Cultura e Literatura Inglesas e apresentada à Universidade de Trás-os-Montes e Alto Douro. Trabalho orientado pela Professora Doutora Laura Fernanda Bulger. 2 Ao meu avô, José da Costa. 3 ÍNDICE Agradecimentos 5 Resumo 6 Abstract 7 Introdução 8 1. Os caminhos tortuosos do Realismo Inglês 10 1.1 - A problemática em torno do Realismo 10 1.2- Intimismo e auto-reflexão 13 1.3 - O romance não-realista de Julian Barnes 16 2. Arthur & George e a ficção da Pós-Modernidade 19 2.1 - A questão da pós-modernidade 19 2.2 - Ambiguidades narrativas 24 2.3 - A reconstituição paródica do passado 35 3. “The Englishness” 38 3.1- England, England - Uma visão paródica de “Englishness” 38 3.2- Arthur and George, “the unoficial Englishmen” 46 4. Perspectivas Dialógicas 52 4.1- A narração omnisciente em Arthur and George 52 4.2- Arthur 58 4.3- George 66 4.4- Arthur and George 75 5. Subversão da lógica detectivesca 83 5.1- Romance Policial 83 5.2- Veredicto 93 5.3- A verdade póstuma do crime 98 Conclusão 104 Referências bibliográficas 107 4 AGRADECIMENTOS Os meus sinceros agradecimentos à Professora Doutora Laura Bulger pelos seus ensinamentos e pela sua orientação atenta durante todos estes meses. A todos os meus Professores de Mestrado, pelo seu profissionalismo e disponibilidade. -
Julian Barnes, Arthur & George
ACTA LITTERARIA COMPARATIVA The Anonymous Letter in the Construction of Racial Prejudice (Julian Barnes, Arthur & George) Anoniminio laiško vaidmuo konstruojant rasizmą Juliano Barneso romane Arthuras & George‘as Oksana WERETIUK University of Rzeszow Institute of English Studies Comparative Literary and Cultural Studies Al. mjr. W. Kopisto 2B 35-315 Rzeszów, Poland [email protected] Summary The article is an attempt to provide a postcolonial interpretation of racism in Arthur & George, a historical novel by Julian Barnes. The main character, George Edalji, the son of an English pastor of Indian descent and a Scottish mother identi- fies himself as “full English.” His birth, citizenship, education, religion, profes- sion confirm his British status. More and more often, the intelligent, slow, too much introverted “hybrid” is exposed to acts fueled by the racial intolerance of the local community members, which occur behind the rectory fence of the vicar- age. All the time the Edalji family suffers from the attacks of a poisonous racist’s anonymous letters. In Arthur & George, the author of Sherlock Holmes runs a private investigation in defense of George. He carefully reads all the letters and becomes certain of a growing aversion to the Edaljis and especially to the intelli- gent George, a solicitor. The novel shows race-based aversion to the dark-skinned neighbor, whose otherness was sufficient evidence of his guilt, not only for the local community, but also for most of British society, including public institutions such as the police, courts, and even the government. With the help of the anony- mous letters, introduced into the plot, Barnes does not present racism as an act of overt discrimination or aggression, as Victorian-era British society is apparently free from racial prejudice. -
The Mathematical Gazette Index for 1894 to 1908
The Mathematical Gazette Index for 1894 to 1908 AUTHOR TITLE PAGE Issue Category C.W.Adams Stability of cube floating in liquid p. 388 Dec 1908 MNote 285 V.Ramaswami Aiyar Extension of Euclid I.47 to n-sided regular polygons p. 109 June 1897 MNote 41 V.Ramaswami Aiyar On a fundamental theorem in inversion p. 88 Oct 1904 MNote 153 V.Ramaswami Aiyar On a fundamental theorem in inversion p. 275 Jan 1906 MNote 183 V.Ramaswami Aiyar Note on a point in the demonstration of the binomial theorem p. 276 Jan 1906 MNote 185 V.Ramaswami Aiyar Note on the power inequality p. 321 May 1906 MNote 192 V.Ramaswami Aiyar On the exponential inequalities and the exponential function p. 8 Jan 1907 Article V.Ramaswami Aiyar The A, B, C of the higher analysis p. 79 May 1907 Article V.Ramaswami Aiyar On Stolz and Gmeiner’s proof of the sine and cosine series p. 282 June 1908 MNote 259 V.Ramaswami Aiyar A geometrical proof of Feuerbach’s theorem p. 310 July 1908 MNote 264 A.O.Allen On the adjustment of Kater’s pendulum p. 307 May 1906 Article A.O.Allen Notes on the theory of the reversible pendulum p. 394 Dec 1906 Article Anonymous Proof of a well-known theorem in geometry p. 64 Oct 1896 MNote 30 Anonymous Notes connected with the analytical geometry of the straight line p. 158 Feb 1898 MNote 49 Anonymous Method of reducing central conics p. 225 Dec 1902 MNote 110B (note) Anonymous On a fundamental theorem in inversion p. -
Additive Combinatorics and Its Applications in Theoretical Computer Science
THEORY OF COMPUTING LIBRARY GRADUATE SURVEYS 887 (2016), pp. 1–53 www.theoryofcomputing.org Additive Combinatorics and its Applications in Theoretical Computer Science Shachar Lovett∗ Received October 1, 2013; Published August 21, 2016 Abstract: Additive combinatorics (or perhaps more accurately, arithmetic combinatorics) is a branch of mathematics which lies at the intersection of combinatorics, number theory, Fourier analysis and ergodic theory. It studies approximate notions of various algebraic structures, such as vector spaces or fields. In recent years, several connections between additive combinatorics and theoretical computer science have been discovered. Techniques and results in additive combinatorics were applied to problems in coding theory, property testing, hardness of approximation, computational complexity, communication complexity, randomness extraction and pseudo-randomness. The goal of this survey is to provide an introduction to additive combinatorics for students and researchers in theoretical computer science, to illustrate some of the exciting connections to classical problems in computer science, and to describe the many open problems that remain. 1 Introduction Additive combinatorics (or perhaps more accurately, arithmetic combinatorics) is a branch of mathematics which lies at the intersection of combinatorics, number theory, Fourier analysis and ergodic theory. It ∗Supported by NSF CAREER award 1350481. ACM Classification: F.2.2, G.2.3 AMS Classification: 68Q17, 68Q25 Key words and phrases: additive combinatorics, theoretical computer science © 2016 Shachar Lovett cb Licensed under a Creative Commons Attribution License (CC-BY) DOI: 10.4086/toc.gs.2016.887 SHACHAR LOVETT studies approximate notions of algebraic structures. As an illustrative example, consider the following problem. Let G be an Abelian group, and let A be a subset of G. -
The Life and Work of Ra Rankin
THE LIFE AND WORK OF R. A. RANKIN (1915–2001) BRUCE C. BERNDT1, WINFRIED KOHNEN, AND KEN ONO2 Robert Alexander Rankin, an eminent Scottish number theorist and, for several decades, one of the world’s foremost experts in modular forms, died on January 27, 2001 in Glasgow at the age of 85. He was one of the founding editors of The Ramanujan Journal. For this and the next issue of the The Ramanujan Journal, several well-known mathematicians have prepared articles in Rankin’s memory. In this opening paper, we provide a short biography of Rankin and discuss some of his major contributions to mathematics. At the conclusion of this article, we provide a complete bibliography of all of Rankin’s writings divided into five categories: 1) Research and Expository Papers; 2) Books; 3) Books Edited; 4) Obituaries; 5) Other Writings. 1. His Life Robert Rankin was born on October 27, 1915 at Garlieston, Wigtownshire, Scotland. His father, Reverend Oliver Shaw Rankin, was a parish minister in Sorbie, Wigtown- shire between 1912 and 1937. His mother was Olivia Teresa Shaw Rankin born in 1884 in W¨urzburg,Germany. Oliver and Olivia were first cousins, their mothers be- ing sisters. Robert was named after his paternal grandfather, who was a pastor in Lamington, Lanarkshire, when his grandson was born. He attended Garlieston School and already at a young age developed an affinity for the Gaelic culture and language. Late in his teenage years, he spent four to six weeks working in a general store on the island of Barra in the Outer Hebrides in order to learn spoken Gaelic. -
Reading Group Guide Spotlight
Spotlight on: Reading Group Guide Arthur & George Author: Julian Barnes Born January 9, 946, in Leicester, England; son of Name: Julian Barnes Albert Leonard (a French teacher) and Kaye (a French Born: January 9, 946 teacher) Barnes; married Pat Kavanagh (a literary Education: Magdalen agent), 979. Education: Magdalen College, Oxford, College, Oxford, B.A. B.A. (with honors), 968. Addresses: Agent: Peters, (with honors) Fraser, and Dunlop Ltd., Drury House, 34-43 Russell St., Address: Peters, Fraser, and London WC2B 5HA, England. Dunlop Ltd., Drury House, 34-43 Russell St., London WC2B 5HA, England. Career: Freelance writer, 972—. Lexicographer for Oxford English Dictionary Supplement, Oxford, England, 969-72; New Statesman, London, England, assistant literary editor, 977-78, television critic, 977-8; Sunday Times, London, deputy literary editor, 979-8; Observer, London, television critic, 982-86; London correspondent for New Yorker magazine, 990-94. Awards: Somerset Maugham Prize, 980, for Metroland; Booker Prize nomination, 984, Geoffrey Faber Memorial Prize, and Prix Medicis, all for Flaubert’s Parrot; American Academy and Institute of Arts and Letters award, 986, for work of distinction; Prix Gutembourg, 987; Premio Grinzane Carour, 988; Prix Femina for Talking It Over, 992; Shakespeare Prize (Hamburg), 993; Officier de l’Ordre des Arts et des Lettres; shortlisted for Booker Prize, 998, for England, England. Writings: Novels Metroland, St. Martin’s Press (New York, NY), 980. Before She Met Me, Jonathan Cape (London, England), 982, McGraw-Hill (New York, NY), 986. Flaubert’s Parrot, Jonathan Cape (London, England), 984, Knopf (New York, NY), 985. Staring at the Sun, Jonathan Cape (London, England), 986, Knopf (New York, NY), 987.