Randomly chosen chaotic maps can give rise to nearly ordered behavior

Parrondo’s paradox [J.M.R. Parrondo, G.P. Harmer, D. Abbott, New paradoxical games based on Brownian ratchets, Phys. Rev. Lett. 85 (2000), 5226–5229] (see also [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68–72]) states that two losing gambling games when combined one after the other (either deterministically or randomly) can result in a winning game: that is, a losing game followed by a losing game = a winning game. Inspired by this paradox, a recent study [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] asked an analogous question in discrete time dynamical system: can two chaotic systems give rise to order, namely can they be combined into another dynamical system which does not behave chaotically? Numerical evidence is provided in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] that two chaotic quadratic maps, when composed with each other, create a new dynamical system which has a stable period orbit. The question of what happens in the case of random composition of maps is posed in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] but left unanswered. In this note we present an example of a dynamical system where, at each iteration, a map is chosen in a probabilistic manner from a collection of chaotic maps. The resulting random map is proved to have an infinite absolutely continuous invariant measure (acim) with spikes at two points. From this we show that the dynamics behaves in a nearly ordered manner. When the foregoing maps are applied one after the other, deterministically as in [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68–72], the resulting composed map has a periodic orbit which is stable.     

Racah operators for the group of motions

The author [5] introduced Racah operators for unitary representations of topological groups of type I. In the present paper, we indicate the explicit form of these operators for representations of the group of motions of three-dimensional Euclidean space.     

基于微分算子的边缘检测法在基因芯片图像识别中的应用

一种基于梯度算子和拉普拉斯算子检测医学基因芯片荧光数字图像边缘的方法．数字图像经过图像增强等预处理以后，突出了我们感兴趣的数字图像特征，根据数字图像灰度变化的趋势，用灰度变化的一阶导数(梯度算子)检测图象中的边缘区域；用灰度变化的二阶导数确定图像边缘的中心位置．最后根据某些预定的准则把满足这些准则的象素组成一条边缘．     

On Hill's operator with a matrix potential

In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the self‐adjoint operator generated by a system of Sturm–Liouville equations with summable coefficients and quasiperiodic boundary conditions. Then using these asymptotic formulas, we find conditions on the potential for which the number of gaps in the spectrum of the Hill's operator with matrix potential is finite. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces

In this paper, we study the existence of solutions and approximation of the solutions by using a Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces. The results presented in this paper generalize the corresponding results of J. Li [J. Li, On the existence of solutions of variational inequalities in Banach spaces, J. Math. Anal. Appl. 295 (2004) 115-126].     

模糊线性系统的扰动分析

使用谱范数分析了模糊线性系统在三种情形下的扰动: (1)右端模糊向量有扰动, 系数矩阵不变; (2)系数矩阵有扰动,右端模糊向量不变; (3)系数矩阵和右端模糊向量都有扰动,并通过数值实例验证给出的扰动界的估计.     

求线性规划问题可行基的一种方法

文章给出了一般情形下从线性规划问题的标准型求可行基的一种方法，并通过与大Ｍ法、两阶段法及文［１］方法进行对比分析，说明这是一种有效可行且有可能较简便的方法     

A note on optimality conditions for the Euclidean. Multifacility location problem

Thekey problem of the Euclidean multifacility location (EMFL) problem is to decide whether a givendead point is optimal. If it is not optimal, we wish to compute a descent direction. This paper extends the optimality conditions of Calamai and Conn and Overton to the case when the rows of the active constraints matrix are linearly dependent. We show that linear dependence occurs wheneverG, the graph of the coinciding facilities, has a cycle. In this case the key problem is formulated as a linear least squares problem with bounds on the Euclidean norms of certain subvectors.     

On the problem of crack system with an elliptic hole

The problem of cracks with an elliptic hole in an infinite plane is investigated. By introducing the fictitious loads on the hole edge and using the Muskhelishvili method, the problem is reduced to solving a system of mixed-type integral equations in which some are Fredholm equations but others Cauchy-type singular ones. A numerical method is suggested and can be used for the treatment of other similar equations. The numerical results for some typical examples are given, showing that the method is really effective.