Pit your wits against young minds!

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.     

Ruin Probability with Variable Premium Rate and Disturbed by Diffusion in a Markovian Environment

We consider a risk model with a premium rate which varies with the level of free reserves. In this model, the occurrence of claims is described by a Cox process with Markov intensity process, and the influence of stochastic factors is considered by adding a diffusion process. The integro-differential equation for the ruin probability is derived by a infinitesimal method.     

中国入世对政府的影响及政府应对问题

中国成功入世后，各行各业和各市场主体都面临新的机遇和挑战，以及自我适应和应对的问题。相对而言，政府受到的影响是首要的、最为全面而深远的，政府率先入世既十分必要又相当紧迫。政府要实现真正意义上的入世，关键是要转变公务员队伍观念，提高公务员队伍的整体综合素质，转变政府职能，转变行政方式，实现依法行政。     

α—珠蛋白基因的PCR检测

用多对引物的复合ＰＣＲ技术，分别扩增α－珠蛋白基因族中α１和α２基因片段；参照β－珠蛋白基因ＰＣＲ扩增产物量，判断α１和α２基因是否正常，是否为缺失的纯合子或杂合子，对α－地中海贫血症先征者家系基因型进行ＰＣＲ分型诊断。     

Atomistic phenomena in dense fluid shock waves

The shock structure problem is one of the classical problems of fluid mechanics and at least for non-reacting dilute gases it has been considered essentially solved. Here we present a few recent findings, to show that this is not the case. There are still new physical effects to be discovered provided that the numerical technique is general enough to not rule them out a priori. While the results have been obtained for dense fluids, some of the effects might also be observable for shocks in dilute gases.     

Approximation of transient temperatures in complex geometries using fractional derivatives

It is shown that time-dependent temperatures in a transient, conductive system can be approximately modeled by a fractional-order differential equation, the order of which depends on the Biot number. This approximation is particularly suitable for complex shapes for which a first-principles approach is too difficult or computationally time-consuming. Analytical solutions of these equations can be written in terms of the Mittag-Leffler function. The approximation is especially useful if a suitable fractional-order controller is to be designed for the system.     

Damage and fracture evaluation of granular composite materials by digital image correlation method

This paper presents the applications of digital image correlation technique to the mesoscopic damage and fracture study of some granular based composite materials including steelfiber reinforced concrete, sandstone and crystal-polymer composite. The deformation fields of the composite materials resulted from stress localization were obtained by the correlation computation of the surface images with loading steps and thus the related damage prediction and fracture parameters were evaluated. The correlation searching could be performed either directly based on the gray levels of the digital images or from the wavelet transform (WT) coefficients of the transform spectrum. The latter was developed by the authors and showed higher resolution and sensitivity to the singularity detection. Because the displacement components came from the rough surfaces of the composite materials without any coats of gratings or fringes of optical interferometry, both surface profiles and the deformation fields of the composites were visualized which was helpful to compare each other to analyze the damage of those heterogeneous materials. The project supported by the National Natural Science Foundation of China (10125211 and 10072002), the Scientific Committee of Yunnan Province for the Program of Steel Fiber Reinforced Concrete, and the Institute of Chemical Materials, CAEP at Mianyang