Creative Contribution of D. Ya. Petrina to the Development of Contemporary Mathematical Physics

This is a brief survey of the results obtained by Prof. D. Ya. Petrina in various branches of contemporary mathematical physics.     

On the 75th Birthday of Vladimir Semenovich Korolyuk

Ukrainian Mathematical Journal -     

B.V. Gnedenko: Classic of Limit Theorems in the Theory of Probability

B.V. Gnedenko is an outstanding scientist-mathematician, who worked in the area of probability theory and its applications. B.V. Gnedenko deserved world-wide popularity by his investigations of limit distributions for sums of independent random variables (Gnedenko and Kolmogorov 1954) that completed a long period of probability theory development up to the middle of XX-th century. The main idea of “accompanied infinitely divisible distributions” developed by B.V. Gnedenko, became a guidance in the limit theory of semimartingales as it is presented by Jacod and Shiryaev (1987) and others (Çinlar et al. 1980). The triplet of predictable characteristics for semimartingale is the main idea in investigation the limit behavior for the random evolutions in the scheme of Poisson approximation (Koroliuk and Limnios, Theory Probab Appl 49(4):629–644, 2005b).     

浅谈概率论与数理统计的教学

概率论与数理统计跟其它的数学分支课程相比,有其特殊的思维模式．本文主要从激发学生学习兴趣、平行概念类比教学、锻炼概率思维,N重视“辨误”数学四个方面阐述了如何搞好概率统计课的教学．     

On the 80th Birthday of Academician V. S. Vladimirov

Theoretical and Mathematical Physics -     

On a theorem of V. V. Filippov

A new characterization of spaces having a point-countable basis is obtained. This characterization is used in giving a simpler proof of a recent theorem of Filippov. Partly supported by an N.S.F. grant.     

Probability of Winning at Tennis I. Theory and Data

The probability of winning a game, a set, and a match in tennis are computed, based on each player's probability of winning a point on serve, which we assume are independent identically distributed (iid) random variables. Both two out of three and three out of five set matches are considered, allowing a 13-point tiebreaker in each set, if necessary. As a by-product of these formulas, we give an explicit proof that the probability of winning a set, and hence a match, is independent of which player serves first. Then, the probability of each player winning a 128-player tournament is calculated. Data from the 2002 U.S. Open and Wimbledon tournaments are used both to validate the theory as well as to show how predictions can be made regarding the ultimate tournament champion. We finish with a brief discussion of evidence for non-iid effects in tennis, and indicate how one could extend the current theory to incorporate such features.