The Legacy of Alladi Ramakrishnan in the Mathematical Sciences

ISBN-13: 9781441962621 / Angielski / Twarda / 2010 / 575 str.

Krishnaswami Alladi; John R. Klauder; Calyampudi R. Rao

Opis

Alladi Ramakrishnan (1923-2008) was an eminent scientist who had a wide range of research interests in theoretical and mathematical physics. Professor Ramakrishnan made signi?cant contributions to probability and statistics, elem- tary particle physics, cosmic rays and astrophysics, matrix theory, and the special theory of relativity. Ramakrishnan believedstrongly that in addition to doing fun- mental research, one must contribute to the advancementof the profession. Inspired by his visit to the Institute for Advanced Study in Princeton in 1957-1958, he returned to Madras and began the Theoretical Physics Seminar at his family home Ekamra Nivas. These seminars were ultimately responsible for the creation of MATSCIENCE, The Institute of Mathematical Sciences in 1962. This institute, of which he was the Director for its ?rst 21years, has grown steadily in size and stature, and is his monumental contribution to the profession. In a distinguished scienti?c life that has spanned more than ?ve decades, Professor Ramakrishnan has come into close contact with, and was in?uenced by, several eminent mathema- cians and physicists, and has moulded the careers of his several students and young researchers. This volume, which is a tribute to his great legacy, not only deals with his signi?cant contributions to research and the profession, but also contains a ?ne collection of research and survey papers by leading physicists and mathematicians that cover a broad range of areas in the mathematical sciences.

Spis treści

- Preface Part I. The Legacy of Alladi Ramakrishnan - Contributions of Alladi Ramakrishnan to the Mathematical Sciences. - Alladi Ramakrishnan's Theoretical Physics Seminar. - Telegrams received for the MATSCIENCE inauguration. - The miracle has happened, speech given by Alladi Ramakrishnan at the inauguration of MATSCIENCE. - Overseas Trips of Alladi Ramakrishnan. - List of publications of Alladi Ramakrishnan. - List of PhD students of Alladi Ramakrishnan. Part II. Pure Mathematics - Inversion and invariance of characteristic terms - part I (Abhyankar). - Partitions with non-repeating odd parts and q-hypergeometric identities (Alladi). - q-Catalan identities (Andrews). - Completing Brahmagupta's extension of Ptolemy's theorem (Askey). - A transformation formula involving the gamma and Riemann zeta functions in Ramanujan's Lost Notebook (Berndt and Dixit). - Ternary quadratic forms, modular equations, and certain positivity conjectures (Berkovich and Jagy). - How often is n! a sum of three squares? (Deshouillers and Luca).- Crystal symmetry viewed as zeta symmetry - II (Kanemitsu and Tsukuda). - Eulerian polynomials: From Euler’s time to the present (Foata). - Crystal symmetry viewed as zeta symmetry II (Kanemitsu and Tsukada). - Positive homogeneous minima for a system of linear forms (Raghavan). - The divisor matrix, Dirichlet series, and SL(2,Z)(Sin and Thompson). - Proof of a conjecture of Alladi Ramakrishnan on circulants (Waldschmidt). Part III. Probability and Statistics - Branching random walks (Athreya). - A commentary on the logistic distribution (Ghosh, Choi, and Li). - Entropy and cross entropy characterizations and applications (Rao). - Optimal weights for a class of rank tests for censored bivariate data (Rao, Raychaudhuri, and Wu). - Connections between Bernoulli strings and random permutations (Sethuraman and Sethuraman). - Storage models for a class of master equations with separable kernels (Vittal, Jayasankar, and Muralidhar). Part IV. Theoretical Physics and Applied Mathematics - Inverse consistent deformable image registration (Chen and Ye). - A statistical model for the quark structure of the nucleon (Devanathan and Karthiyayini). - On generalized Clifford algebras and their physical applications (Jagannathan). - (p,q)-Rogers-Szegö polynomial and the (p,q)-oscillator (Jagannathan and Sridhar). - Rethinking renormalization (Klauder). - Magnetism, FeS celluloids, and origins of life (Mitra-Delmotte and Mitra). - The Ehrenfest theorem in quantum field theory (Parthasarathy).

O autorze

Krishnaswami Alladi is the editor in Chief of Springer's Ramanujan Journal, and the Development in Mathematics Book series. He was chair of the mathematics department of the University of Florida. In addition to his contributions of bibliographic material about his father, Krishnaswami Alladi has directed and organized the development of this tribute volume. C.R. Rao is inarguably the most prominent academic in the field of Statistics in current times. John Klauder has served on the Physics Advisory Panel of the NSF and been Editor of the Journal of Mathematical Physics, and as President of the International Association of Mathematical Physics.

Blurb

In a distinguished scientific life that had spanned over five decades, Alladi Ramakrishnan made significant contributions to probability and statistics, elementary particle physics, cosmic rays and astrophysics, matrix theory, and the special theory of relativity. Inspired by his visit to the Institute of Advanced Study during 1957-1958, and the direct influences of Robert Oppenheimer, Niels Bohr, Sir C.V. Raman, S. Chandrasekhar, and other notable contemporaries, he later founded the Institute of Mathematical Sciences (MATSCIENCE) in Madras, India. In the spirit of Alladi Ramakrishnan’s profound interest and contributions to three fields of science — Mathematics, Statistics, and Physics — this volume contains invited surveys and research articles from prominent members of these communities who also knew Ramakrishnan personally and greatly respected his influence in these areas of science. Historical photos, telegrams, and biographical narratives of Alladi Ramakrishnan’s illustrious career of special interest are included as well.