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25 October 2010, Volume 30 Issue 5 Previous Issue    Next Issue

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深切缅怀李国平院士——纪念李国平院士诞辰100周年 FAN Wen-Tao, LIU Pei-De, OU Yang Cai-Heng Acta mathematica scientia,Series A. 2010, 30 (5):  1185-1189.  Abstract ( 1472 )   RICH HTML PDF (457KB) ( 1922 )   Save 2010年11月15日, 是我们的恩师李国平院士诞辰100周年纪念日. 我们师从李先生凡数十年, 每聆教诲, 获益良多, 春风化雨, 受用终身. 今距李先生仙逝, 又过去了十四年, 先生的音容笑貌与人格魅力仍时时浮现于眼前. 值此先生百年诞辰之际, 谨以此文深切缅怀敬爱的李老师. Related Articles | Metrics

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新中国偏微分方程事业的奠基人——纪念吴新谋教授诞生100周年 LI Wen-Lin, LIU Zhu-Jia Acta mathematica scientia,Series A. 2010, 30 (5):  1190-1193.  Abstract ( 1446 )   RICH HTML PDF (433KB) ( 1549 )   Save 我们怀着尊敬与怀念的心情,纪念数学家吴新谋教授诞生100周年暨逝世21周年.  吴新谋, 1910年4月14日生于江苏省江阴县, 父亲是江阴县礼延高小历史教员. 吴新谋13岁时父亲不幸早亡, 不久母亲亦病故. 孤苦无靠的吴新谋由舅家收养. 他自幼勤奋好学, 14岁考上江苏省立第三师范学校, 班主任就是后来名声斐然的国学大师钱穆. 吴新谋在校成绩优良, 数学更是名列前茅. 1928年吴新谋考入中央大学数学系, 大学期间在高等代数、几何与分析方面受业于何鲁先生. 1932年大学毕业后回家乡在县立中学教数学. 1934年由何鲁推荐到清华大学数学系任助教, 并在熊庆来先生指导下研习微分方程论. 1937年公费留学法国, 先从师H.$.\!$维拉(Villat)研究粘性流体力学, 后转随J.阿达玛(Hadamard)从事偏微分方程论研究. 侨居法国期间, 吴新谋教授在开展数学研究的同时, 积极参加了我党领导下的抗日爱国运动. 早在1939年, 他就担任我党旅法 支部主办的进步刊物《祖国抗日情报》编辑, 并在艰苦的条件下多方支援我旅法党组织的革命活动. 1945年, 吴新谋正式加入中国共产党, 曾任中共旅法支部委员和旅法侨联秘书等职, 先后在邓发、刘宁一同志领导下开展党的工作, 认真完成了党组织交托的各项任务. Related Articles | Metrics

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Reconsideration on a Periodic Contact Problem in Anisotropic Plane Elasticity LU Jian-Ke, CAI Hai-Tao Acta mathematica scientia,Series A. 2010, 30 (5):  1194-1197.  Abstract ( 1570 )   RICH HTML PDF (242KB) ( 1405 )   Save The following elastic contact problem is reconsidered. A series of periodic rigid stamps is pressed to the boundary of an anisotropic half-plane with friction. Find the stresses in equilibrium. The problem was considered and solved in [1, 2]. However, the method of solution is not exact. In this note, it is modified so that the exact solution is obtained in closed form. References | Related Articles | Metrics

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On the Problem of Isometric Extension between the Unit Spheres in Banach Spaces DING Guang-Gui Acta mathematica scientia,Series A. 2010, 30 (5):  1198-1209.  Abstract ( 1394 )   RICH HTML PDF (398KB) ( 1516 )   Save In this paper, we introduce the problem of isometric extension between the unit spheres in normed spaces. Some important results and recent advances of this problem are also presented. References | Related Articles | Metrics

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An Introduction to Markov Process in Random Environment HU Di-He Acta mathematica scientia,Series A. 2010, 30 (5):  1210-1241.  Abstract ( 2029 )   RICH HTML PDF (628KB) ( 1556 )   Save We will introduce some results on Markov processes in random environments in this paper, there are four chapters in it. In chapter 1, we introduce the Markov chains in time random environments, including existence and equivalence; the chassification of states, ergodic theory and invariant measure, the central limit theorem and invariance principle for p-θ chain. In chapter 2, we introduce the Markov processes in time random environments, including some basic concepts, the exsistence and uniqueness for q-process in random environment, homogenious q-q-processes in random environments, the construction theorem and equivalence. In chapter 3 we introduce the branching chains in time random environments, including the models for finite dimension and infinite dimension, the extinction probability and palarization and proliferattion rate are introduced. In chapter 4, we introduce the Markov chains in space time random environments, including basic concepts, central limit theorem and invariance priciple for RWSTRE. References | Related Articles | Metrics

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Some Topics in the Mathematical Theory of Brownian Motion WANG Zi-Kun Acta mathematica scientia,Series A. 2010, 30 (5):  1242-1247.  Abstract ( 1286 )   RICH HTML PDF (335KB) ( 1351 )   Save The paper is a survey of some new results for Brownian Motion (Br.M.), including the joint distributions of first hitting, last exit, maximum excursion; the behavior of approach to infinity; and some properties of multiparameter infinite dimensional Br.M.. References | Related Articles | Metrics

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Enumerating Characteristics of a kind of Chain-like Graphs WANG Zhen-Yu Acta mathematica scientia,Series A. 2010, 30 (5):  1248-1253.  Abstract ( 1387 )   RICH HTML PDF (289KB) ( 1332 )   Save We defined the so-called B graph in research on concurrent program complexity metrics as one the models of rendezvous relations in Ada programs. In this paper, we investigate a special case of  B graph ----- BB graph, and call it chain-like graph. A BB graph of order n is the oriented tree of order n and height n-1by adding some edges with the constraint that both of the in-degree and out-degree for every node are two at most. The paper gives some enumerating characteristics of BB Graph, and points out the closed relationship with the Stirling numbers of second kind. References | Related Articles | Metrics

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The Warrant Pricing Model with Transaction Costs in Fuzzy Environment JIAN Ming, BIAN Xiao-Nan Acta mathematica scientia,Series A. 2010, 30 (5):  1254-1262.  Abstract ( 1740 )   RICH HTML PDF (661KB) ( 1549 )   Save Taking the so-called invisible costs which widely exist in the Chinese security market, this paper builds the fuzzy warrant pricing model with transaction costs. Under the assumption that the rate of transaction costs is a triangle fuzzy number, a new warrant price interval is obtained. Applying the concept of fuzzy-expectation, this paper gets the theoretical warrant price by converting the interval number to a crisp number which is independent to the investor's subject judgments. Based on this model, this paper makes the sensitivity analysis of some key parameters of the triangle fuzzy number, and the analysis of investment strategies is also made. References | Related Articles | Metrics

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Some Advances on Theory of Noncommutative Hp Spaces CHEN Ze-Qian, Turdebek N.Bekjan Acta mathematica scientia,Series A. 2010, 30 (5):  1263-1275.  Abstract ( 2118 )   RICH HTML PDF (496KB) ( 1550 )   Save We give a survey on theory of noncommutative Hp spaces. These include noncommutative Szeg\"o and Riesz theorems, H1-BMO duality, noncommutative Burkholder-Gundy martingale inequalitity, noncommutative Burkholder martingale inequality, atomic decomposition for Hardy spaces of noncommutative martingales and so on. We also mention some open problems in the fileds. References | Related Articles | Metrics

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Information Architecture and Its Impact on the Equilibrium for |All Pay Auction Model WANG Xian-Jia, CHEN Wen-Lei Acta mathematica scientia,Series A. 2010, 30 (5):  1276-1282.  Abstract ( 1591 )   RICH HTML PDF (327KB) ( 1269 )   Save All pay auction  are situations in which players spend bids  in order to win the contest. This paper characterize the all pay auction architecture and the equilibrium for the auction. First we give each player's  expenditure distributed function when facing different player. Player use cutoff strategies to decide whether they will participate in the all pay auction. Then we give the equilibrium when player are homogeneous or heterogeneous. Finally, when the equilibrium exists, from the point of competitor, we give the  the equilibrium distribution  estimates. References | Related Articles | Metrics

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Remarks on the Regularity and Global Structure of Solutions WANG Jing-Hua, ZHAO Yin-Chuan, WEN Hai-Rui Acta mathematica scientia,Series A. 2010, 30 (5):  1283-1287.  Abstract ( 2225 )   RICH HTML PDF (277KB) ( 1383 )   Save The paper is concerned with the Cauchy problem for the Hamilton-Jacobi equations of multi-dimensional space variables. We prove the sufficient and necessary condition for that a characteristic emanating from a given point never touches the set of singularity points is that the initial function attains its minimum at this point. Finally, we prove there exists one-to-one correspondence between the path connected components of the set of singularity points and  the path connected components of the set on which the initial function does not attain  its minimum. Each path connected component of the set of the singularity points never terminates at a finite time. In particularly, it is worth pointing out that our results are obtained without assuming that the gradient of the initial function tends to zero at infinity under which the important proposition 2.7 and theorem 3.3, one of the main results in [12] are obtained. References | Related Articles | Metrics

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A Fundamental Inequality in the Theory of Meromorphic Functions LI Xue-Quan, TAN Wei-Ping, CAI Hai-Tao Acta mathematica scientia,Series A. 2010, 30 (5):  1288-1291.  Abstract ( 1940 )   RICH HTML PDF (199KB) ( 1289 )   Save This paper explores an upper bound of the characteristic function of meromorphic function by using the method of Professor Hiong Kinglai and Professor Li Guoping. The abtained results are more general than those of Professor Hiong Kinglai, thus more general and more accurate than those of Professor Valiron and Professor Milloux. References | Related Articles | Metrics

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The Martingale Inequalities in Weak-type Spaces and Their Applications LIU Pei-De Acta mathematica scientia,Series A. 2010, 30 (5):  1292-1305.  Abstract ( 1965 )   RICH HTML PDF (456KB) ( 1453 )   Save In recent years, the weak-type spaces have received more and more attention in Harmonic analysis and Martingale theory. In the paper, we intend to clarify some our study results in weak-type martingale spaces. It consists of four aspects: (1) The atomic decomposition of Lourentz martingale spaces; (2) The strong-type and weak-type weighted inequality for Orlicz martingales; (3) The weak-Orlicz martingale spaces and their quasi-normed   inequalities; (4) Some applications in Banach space theory and the dyadic harmonic analysis. References | Related Articles | Metrics

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Some Inequalities for the Functions in Weighted Bergman Spaces ZHAO Ru-Han Acta mathematica scientia,Series A. 2010, 30 (5):  1306-1312.  Abstract ( 1314 )   RICH HTML PDF (219KB) ( 1232 )   Save Some strict inequalities for the integrals of the functions in weighted Bergman spaces are given. References | Related Articles | Metrics

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The Mathematical Foundation of the BA Model HOU Zhen-Ting, KONG Xiang-Xing, SHI Ding-Hua, CHEN Guan-Rong Acta mathematica scientia,Series A. 2010, 30 (5):  1313-1321.  Abstract ( 2055 )   RICH HTML PDF (363KB) ( 1429 )   Save Based on the concept and techniques of Markov chain, this letter provides a rigorous proof for the existence of the steady-state degree distribution of the scale-free network generated by the Barabàsi-Albert (BA) model, and mathematically re-derives the exact analytic formulas of the distribution. The approach developed here is quite general, applicable to many other scale-free types of complex networks. References | Related Articles | Metrics

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Geometric Inequalities-From Integral Geometry Point of View ZHOU Jia-Zu, REN De-Lin Acta mathematica scientia,Series A. 2010, 30 (5):  1322-1339.  Abstract ( 3145 )   RICH HTML PDF (482KB) ( 1796 )   Save This paper first surveys geometric inequalities achieved mainly by the Chinese mathematicians. By estimating the containment measure of a random convex body to be contained in, or to contain, another convex body via the fundamental kinematic formula of Blaschke and the formula of Poincarè in plane integral geometry, we obtain the classical isoperimetric inequality and some Bonnesen-style inequalities. Then some new geometric inequalities, such as the symmetric mixed isoperimetric inequality, Minkowski  and Bonnesen style symmetric mixed isohomothetic inequalities, are obtained. We also investigate the Gage type isoperimetric inequalities and the Ros type isoperimetric inequalities. References | Related Articles | Metrics

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The Distribution of Zeros for Differential Polynomials f kQ [ f ]+P [ f ] in Function f(z) ZHAN Xiao-Ping, TAN Wei-Ping Acta mathematica scientia,Series A. 2010, 30 (5):  1340-1346.  Abstract ( 1809 )   RICH HTML PDF (301KB) ( 1384 )   Save This paper discusses the evolution of exceptional set theory of differential polynomials f kQ[ f ]+P[ f ] in meromorphic function f(z), and introduces its recent progress, and also presents proposals for further study. References | Related Articles | Metrics

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The Estimate of a Quadratic Functional DING Xia-Qi Acta mathematica scientia,Series A. 2010, 30 (5):  1347-1353.  Abstract ( 1359 )   RICH HTML PDF (193KB) ( 1430 )   Save This paper gives the lower bound estimate of a quadratic functional related with Rimann Hypothesis. It is devided into two parts. Part (I) gives some related formulas. Part (II) gives the estimate explicitly. References | Related Articles | Metrics

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Tent Embedding of Forelli-Rudin Integral and Integral Operators from Qp to α-Bloch Spaces Ouyang Caiheng Acta mathematica scientia,Series A. 2010, 30 (5):  1354-1363.  Abstract ( 1907 )   RICH HTML PDF (390KB) ( 1358 )   Save In this paper, the boundedness and compactness of the extended Cesàro operator,  from Qp spaces to α-Bloch spaces in the unit ball of Cn, are characterized by means of an embedding theorem for the non-isotropic tent type spaces and Carleson type measure. References | Related Articles | Metrics

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Nonstationarity Measure of Data Stream DING Yi-Ming, FAN Wen-Tao, TAN Qiu-Heng, WU Ke-Kun, ZOU Yong-Jie Acta mathematica scientia,Series A. 2010, 30 (5):  1364-1376.  Abstract ( 2411 )   RICH HTML PDF (681KB) ( 1370 )   Save We study the nonstationarity measure for data streams by integration ideas from ergodic theory, coarse grain and information theory. We introduce nonstationarity measure for data streams. An effective approximation algorithm is designed for implementation. The nonstationarity measure is a real number between 0 and 1. The nonstationarity measure is smaller for a more stationary data stream. We apply the nonstationarity measure to model selection, and propose a criterion for model selection which requires least nonstationarity measure for residual sequence. Numerical experiments are performed to test our approximation algorithm and to validate the least nonstationarity measure as a criterion for model selection. The numerical results indicate that the nonstationarity measure is a sound index to compare the level of nonstationarity among data streams. By comparing the nonstationarity measure, we can distinguish trend-stationary process and difference-stationary process effectively, and discern i.i.d. sequence, white noise sequence and martingale difference sequence. References | Related Articles | Metrics

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Quaternion Representation of Lorentz Transformation WANG Zhen-Yu, FAN Wen-Tao Acta mathematica scientia,Series A. 2010, 30 (5):  1377-1381.  Abstract ( 1555 )   RICH HTML PDF (266KB) ( 1484 )   Save A special quaternion representation with a simple form is constructed for general Lorentz transformations. A unique character of the representation lies in that all components of the quaternions used are either real numbers or pure imaginary numbers. The construction has considerable advantages over the conventional vector-tensor and biquaternion description. References | Related Articles | Metrics