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10 Asia Pacific Mathematics Newsletter [2] G. Galperin and A. Zemlyakov, Mathematical Billiards (Nauka, Moscow, 1990) (in Russian). [3] G. A. Galperin and N. I. Chernov, Billiards and Chaos (Znanie, Moscow, 1991) (in Russian). [4] A. B. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems (Cambridge University Press, 1995). [5] A. B. Katok, Billiard Table as a Mathematician’s Playground, Surveys in Modern Mathematics (Cambridge University Press, 2005), pp. 216–242. [6] V. V. Kozlov and D. V. Treshchev, Billiards: A Genetic Introduction to the Dynamics of Systems with Impacts, Translations of Mathematical Monographs, Vol. 89 (American Mathematical Society, 1991). April 2012, Volume 2 No 2 [7] H. Masur and S. Tabachnikov, Rational Billiards and Flat Structures, Handbook in Dynamical Systems, Vol. 1A (Elsevier, 2002), pp. 1015–1089. [8] Ya. G. Sinai, Dynamical systems with elastic reflections, Russian Math. Surv. 25 (1970) 137–191. [9] D. Szász (Editor), Hard Ball Systems and the Lorentz Gas (Springer-Verlag, Berlin, 2000). (Encyclopedia of Mathematical Sciences, 101, Mathematical Physics, II.) [10] S. Tabachnikov, Billiards, Societe Mathematique de France, “Panoramas et Syntheses,” No. 1 (1995). Utkir Rozikov Institute of Mathematics and Information Technologies U A Rozikov 29, Do’rmon Yo’li str. Institute of Mathematics and Information Technologies, Uzbekistan 100125, Tashkent, Uzbekistan rozikovu@yandex.ru email: rozikovu@yandex.ru U A Rozikov is a professor at the Institute of Mathematics and Information Technologies, Tashkent, Uzbekistan. He graduated from the Samarkand State University in 1993. He obtained PhD in 1995 and Doctor of Sciences in physics and mathematics (2001) from the Institute of Mathematics, Tashkent. Professor Rozikov is known for his works on the theory of Gibbs measures of models on trees of statistical mechanics. He developed a contour method to study the models on trees and described complete set of periodic Gibbs measures. He and his coworkers obtained some important results in non-Archimedean theory of phase transitions and dynamical systems, non-Volterra quadratic operators, and a quadratic operator which connects phases of the models of statistical mechanics with models of genetics. He had been invited to several leading universities and research centres in the UK, France, Italy, Germany, Spain, etc., and he has published about 80 papers in front-line journals. 5
Indo–French Cooperation Asia Pacific Mathematics Newsletter 1 Indo–French Cooperation in Mathematics Abstract. Links between mathematicians from India and France are old, strong and fruitful. We present a short survey of these relations. We start with a brief overview of the mathematical heritage of India. The stay of A Weil as a Professor in Aligarh Muslim University from 1930 to 1931 was the first outstanding event in the Franco–Indian relationship. A few years later, the French Jesuit Father Racine came to India where he played a major role in the development of mathematics in this country, as well as in its relations with French mathematicians. Now, there are many collaborations and exchanges of visitors between both countries. This is one of the most flourishing bilateral cooperations and plays a unique role both for French and Indian mathematicians. 1. Indian Tradition in Mathematics Mathematics has been studied in India since ancient times. There are many references on the subject; among the reliable ones are the books of G R Kaye [5] in 1915, C N Srinivasiengar [13] in 1967, A K Bag [1] in 1979 and A Weil [19] in 1984. References on the more recent period are the papers by R Narasimhan [8] in 1991, V S Varadarajan [14] in 1998, M S Raghunathan [10] in 2003 and K Plofker in 2009. According to the Hindu tradition, the most important work on astronomy, Surya Siddhānta, is supposed to have been written more than two thousand years ago. However, it seems more likely that this treatise is only about 1200 years old. As a matter of fact there is no proof of mathematical activity in India before 1500 BC. The Indus civilisation (around 3000 BC) was discovered less than one century ago, the writings have not yet been deciphered; there are weights and objects which seem to be devoted to measure and hence maybe to a numerical system, but nothing else is known yet. The Sulvasūtras (cord manuals) were written by Baudhāyana, Apastamba and Katyayana not earlier than between the 8th and the 4th Century BC. From 500 to 200 BC, Vedic mathematics continued to be developed before declining and leaving place to the mathematics of the Jains: number Michel Waldschmidt∗ in Mathematics Michel Waldschmidt* theory, permutations and combinations, binomial theorem and, as always, astronomy. A decimal number system existed in India in the 3rd Century BC, during the time of the King Ashoka. On the pillars he erected are found inscriptions in Brahmi with early ancestors of our numerical decimal system of writing in the socalled arabic digits. This way of writing would be an indispensable tool for the later developments of mathematics in India: it enabled Jain mathematicians to write out very large numbers by which they were fascinated. It is probably between the 2nd and 4th Century AD that the manuscript Bakhs.h ā l īshould be dated; it introduces algebraic operations, decimal notations, zero, quadratic equations, square roots, indeterminates and the minus sign. The classical period of mathematics in India extends from 600 to 1200 AD. The major works are named Āryabhat.ī y a, Pan¯casiddhāntikā, Āryabhat.ī y a Bhasya, Mahā Bhāskariya, Brāhmasput.asiddhānta, P ā t.ī g a n. ita, Gan. itasārasa¯ngraha, Gan. italaka, L ī l ā v a t ī, Bijagan. ita, and the authors are Āryabhat . a I (476– 550), Varāhamihira (505–587), Bhāskara I (∼600– ∼680), Brahmagupta (598–670), Mahāvīracarya (∼800 –∼870), Āryabhat . a II (∼920–∼1000), ´Srı.dhara (∼870–∼930), Bhāskarācārya (Bhāskara II, 1114– 1185). Mahāvīra, a Jain from the region of Mysore, one of the few Indian mathematicians of that time who was not an astronomer, wrote one among the first courses of arithmetic. Bhāskara II (also named Bhāskarācārya, or Professor Bhāskara), belonged to the Ujjain school, like Varāhamihira and Brahmagupta. His treatise of astronomy called Siddhānta´siroman. i (1150) contains chapters on geometry (Lī l ā v a t ī) and on algebra (Bījagan . ita). While the mathematical school was declining in the rest of India, it flourished in Kerala between the 14th and the 17th Century. After the work on astronomy and on series by Madhava of Sangamagramma (1350–1425), the four most important works on astronomy and mathematics from that April 2012, Volume 2 No 2 11
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Page 5 and 6: Compressive Sensing and Application
Page 7 and 8: matrix A is the smallest number sat
Page 9 and 10: [18] T. Cai, G. Xu and J. Zhang, On
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Page 41 and 42: Endre Szemerédi Receives 2012 Abel
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Page 53 and 54: Other News Chinese Undergraduate So
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Mathematical Societies in Asia Paci
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Mathematical Society of the Philipp
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