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ISSN: 0025-5742 THE MATHEMATICS STUDENT Volume 76, Numbers 1 - 4, (2007) copy- Edited by J. R. PATADIA circulation (Issued: October, 2008) Member'sfor not PUBLISHED BY THE INDIAN MATHEMATICAL SOCIETY (In the memory of late Professor M. K. Singal) THE MATHEMATICS STUDENT Edited by J. R. PATADIA In keeping with the current periodical policy, THE MATHEMATICS STUDENT (STUDENT) will seek to publish material of interest not just to mathematicians with specialized interest but to undergraduate and postgraduate students and teachers of mathematics in India. With this in view, it will publish material of the following type: 1. Expository articles and popular (not highly technical) articles. 2. Classroom notes (this can include hints on teaching certain topics or filling vital gaps in the usual treatments of topics to be found in text-books or how some execises can and should be made an integral part of teaching, etc.) 3. Problems and solutions, News and Views. 4. Information on articles of common interest published in other periodicals, 5. Proceedings of IMS Conferences. Expository articles, classroom notes, news and announcements and research papers are invited for publication in THE MATHEMATICS STUDENT. Manuscripts intended for publication should preferably be submitted online in the LaTeX .pdf file or in the standard word processing format (Word or Word Perfect) including figures and tables. In case of hard copy submission, three copies of the manuscripts along with the Compact Disc (CD) copy should be submitted to the Editor Dr. J. R. Patadia, Department of Mathematics, faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara-390 002 (Gujarat),copy- India. E-mail: [email protected]. Manuscripts (including bibliographies, tables, etc.) should be typed double spaced on A4 size white paper with 1 inch (2.5 cm.) margins on all sides with font size 11 pt., preferably in LaTeX. Sections should appear in the following order: Title Page, Abstract, Text, Notes and References. Comments or replies to previously published articles should also follow this format with the exception of abstracts. In LaTeX, the following preamble be used as is required by the Press: n documentclass[11 pt]amsart n usepackage amsfonts, amssymb, amscd, amsmath, enumerate, verbatim, calc n renewcommand fnbaselinestretchgf1.1g n textwidth=11.5 cm circulation n textheight=19.5 cm n topmargin=1.5 cm n oddsidemargin=1.5 cm n evensidemargin=1.5 cm nMember'spagestylefheadingsg for For more details refer IMS website: www.indianmathsociety.org.in Authors of articles/research papers printed in the STUDENT are entitled to 50 reprints free of charge. Additional copies (in integral mulyiples of 50) will be supplid at cost, if orders are placed at the time of proof correction. Authors of articles/research papers printed in the STUDENT are chargednot page charges at the rate of US dollars Thirty-five per page (Rs. 100 per page for authors in India). Business correspondence relating to the STUDENT should be addressed to Dr. (Miss) S. P. Arya, Treasurer, Indian Mathematical Society, Dept. of Mathematics, Maitryi College, Bapu Dham Complex, New Delhi - 110 021, India. ISSN: 0025-5742 THE MATHEMATICS STUDENT Volume 76, Numbers 1 - 4, (2007) copy- Edited by J. R. PATADIA circulation (Issued: October, 2008) Member'sfor not PUBLISHED BY THE INDIAN MATHEMATICAL SOCIETY (In the memory of late Professor M. K. Singal) c THE INDIAN MATHEMATICAL SOCIETY, 2008. This volume or any part there of may not be reproduced in any form without the written permission of the publisher. This volume is not to be sold outside the Country to which it is consigned by the copy- Indian Mathematical Society. Member's copy is strictly for personal use. It is not intended for sale. circulation Member'sfor not Published by V. M. Shah for the Indian Mathematical Society, type set by Sunil B. Thakare, at the Department of Mathematics, University of Pune, Pune-411 007 and printed by Dinesh Barve at Parashuram Process, Shed No. 1246/3, S. No. 129/5/2, Dalviwadi Road, Barangani Mala, Wadgaon Dhayari, Pune - 411 041 (India). Printed in India. The Mathematics Student Vol. 76, Nos. 1-4, (2007) CONTENTS ASHA RANI: OBITUARY - Professor Mahendra Kumar Singal (1932-2006). 01 SATYA DEO: Professor M. K. Singal: An organizer par excellence. 05 A. N. MITRA: A date with Mahendra Kumar Singal. 07 N. K. THAKARE: Professor M. K. Singal: A tribute. 09 SUNDER LAL: Professor M. K. Singal: A life devoted to mathematics. 13 R. S. PATHAK and S. R. VERMA: Jacobi Convolution of Distributions. 17 ARUN M. VAIDYA: S. Chowlas Contributions to Combinatorics. 29 PREM NARAIN: The Transmission/Disequilibrium Test (TDT) used in Human Genetics. 39 R. B. BAPAT: Challenges and Frustrations of being a Mathematician. 49 R. B. BAPAT: Recent Developments and Open Problems in the Theory of Permanents. 55 Abstracts of Papers Presented at the 73rd Annual Conference of The Indian Mathe- 71 matical Society held at Pune University, Pune during December 27 30, 2007. SHING-TUNG YAU: The Past, Present and Future of Mathematics in China and 103 India. S. R. S. VARADHAN: Homogenization. copy- 129 DINESH SINGH: Harmonic Analysis on the Unit Circle: A Personal Perspective. 137 DANIEL WULBERT: The Locator Problem. 157 D. S. THAKUR: Recent Developments in Function Field Theory. 163 S. S. ABHYANKAR: Conics as Axis and Jacobian Problem. 171 K. VARADARAJAN: Anti Hopfian and Anti Co-Hopfian Modules. 185 AJAY KUMAR: Operator Space Structure of Banach Spaces. 195 A. K. Lal: Graph structure via its Laplaciancirculation matrix. 203 B. CHOUDHARY: On Sequence Spaces defined by Orlicz Function. 217 Member'sfor not iv KANTI PANDEY: Burgers Equations: Introduction and Applicability. 225 S. K. VAIDYA: Cordial Labeling for Two-Cycle Related Graphs. 237 AJAI CHOUDHRY: On Squares of Squares. 247 R. S. KULKARNI: Book Review: Collected Work of Patodi. 257 B. N. WAPHARE: 73rd I. M. S. Conference: A brief Report. 267 ******* copy- circulation Member'sfor not Mahendra Kumar Singal (November 10, 1932 - July 16, 2006) OBITUARY Professor Mahendra Kumar Singal (1932-2006) Where do you begin to describe a man likecopy- Dr M K Singal? Do you talk about his life, his strong yet kind character, his indefatigable enthusiasm for work and his passion for Mathematics, or about the people whose lives he touched every day? Born on November 10, 1932, Professor M K Singal passed his Matricu- lation Examination at the early age of 12 years. He got one of the five All India Entrance Scholarships. At the B.A. (Mathematics Honours) Exami- nation, he was awarded the Bholanath Gold Medal and the Rabikanta Debi Prize. In his B.A. Examination, he toppedcirculation in seven of the eight papers but by some incomprehensible happenings somewhere, he got only 80 marks instead of a 100 in one paper. Frustrated, he left Mathematics and joined Law instead. In the BCL Examination, it was compulsory to clear the Marriage Law paper infor order to pass. Unfortunately he had a bad boil in hisMember's right hand and could not write this paper. He still got the highest marks with a zero counted in this paper. There was no provision for a re-examination in Delhi University at that time but on a request from his father on the plea of still highest marks, the Vice Chancellor Sir Maurice Gwayr allowed a re-examination. This created history. After obtaining an L.L.B., henot came back to Mathematics. He had realized that Law was not a career for him as that often involved working in favour of the client by hook or by crook. He opted for an honest career. On the performance of his M. A. (Mathematics) Examination, he was awarded a scholarship to carry out research. However, at the request of the Principal of Ramjas College, Delhi University, he forsook the research c Indian Mathematical Society-2007. 1 2 scholarship and took up a Lectureship at Ramjas College to which he was invited without application and interview. He appeared for the IAS Examination but was rejected in personal in- terview. At that time, one had to clear both the theory and the personal interview separately. Yet he had obtained the 5th position in aggregate marks among all the students that appeared that year. That started a pub- lic debate. Should such a brilliant student be rejected just because, may be, some of the interviewers were biased? The matter reached the Parlia- ment and an act was passed whereby only the aggregate marks were to be considered. Fortunately for the Mathematics Community, the rule was not applied retrospectively and he became a mathematician rather than an IAS Officer. He pursued research along with his heavy work-load of teaching 32 pe- riods a week. He obtained his Ph.D. degree in Differential Geometry. His research interests were in the area of Differential Geometry, General Topol- ogy and Mathematics Education. He supervised the Ph.D. research work of more than a dozen students and published 75 research papers. He became a Reader in Mathematics at Delhicopy- University in 1964. In 1969, he was invited to set up the Mathematics Department at the newly formed Meerut University. He joined Meerut University as Founder-Professor and Head of the Mathematics Department and also served tenure at the same University as the Vice-Chancellor. Professor Singal was a Fellow of the National Academy of Sciences (India) and also that of the Institute of Mathematics and its Applications, UK. He travelled and lectured in dozens of countries. At the home front also, he lectured in a large number of cities, Staffcirculation Academic Colleges, as well as in most of the colleges and a large number of schools in Delhi. He was also a reputed author.
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