Lower bounds for densities of uniformly elliptic random variables on Wiener space

 In this article, we generalize the lower bound estimates for uniformly elliptic diffusion processes obtained by Kusuoka and Stroock. We define the concept of uniform elliptic random variable on Wiener space and show that with this definition one can prove a lower bound estimate of Gaussian type for its density. We apply our results to the case of the stochastic heat equation under the hypothesis of unifom ellipticity of the diffusion coefficient. Received: 6 November 2001 / Revised version: 27 February 2003 / Published online: 12 May 2003 Key words or phrases: Malliavin Calculus – Density estimates – Aronson estimates     

变In组分沟道的MM-HEMT材料电子输运特性研究

在变缓冲层高迁移率晶体管（MM_HEMT）器件中，二维电子气的输运性质对器件性能起着决定作用.通过低温下二维电子气横向电阻的量子振荡现象，结合变温度的Hall测量，系统研究了不同In组分沟道MM_HEMT器件中子带电子迁移率和浓度随温度的变化关系.结果表明，沟道中In组分为0.65的样品，材料电学性能最好，In组分高于0.65的样品，严重的晶格失配将产生位错，引起迁移率下降，大大影响材料和器件的性能. 关键词： 变缓冲层高迁移率晶体管 Shubnikov_de Hass 振荡     

Local effect of electric and magnetic fields on the position of an attached shock in a supersonic diffuser

Effective ways for controlling shock wave configurations by means of external actions are sought. One such way is a local effect of electric and magnetic fields. In this paper, the local effect of external fields is implemented by current localization in a limited region of a diffuser. The experiment is carried out in a diffuser providing the complete internal compression of the gas with a Mach number at the inlet M=4.3. As a working medium, a xenon plasma is used. The plasma flow is formed in a shock tube equipped with an accelerating nozzle. Two ways of current localization are tested. In the first one, the diffuser inlet is a short channel of Faraday generator type. In this case, the ponderomotive force basically decelerates or accelerates the flow depending on the direction of the electric field. In the second way, the current flows through a narrow near-wall region between adjacent electrodes. In this case, the ponderomotive force compresses or expands the gas. In both cases, it is shown that the angle of an attached shock due to MHD interaction can be both decreased and increased. The central problem with the MHD control of shock waves is near-electrode and near-wall phenomena.     

Development of a Millimeter Wave Compact Equipment for NDT of Materials

We developed a compact equipment working at 94 GHz to replace the commonly used network analyzer for nondestructive testing of materials. The compact equipment was designed to measure the variations in the amplitude and phase of the reflected signal from the material relative to a reference signal. A good accuracy of the amplitude and phase measurement of the equipment was obtained in the confirmative experiments. The distribution of a drop of water in a wood plate is clearly visible in the millimeter wave images obtained by the amplitude and phase measurement.     

The negative gradient flow for the <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-integral of Ricci curvature

 In this paper, the negative gradient flow for the L ²-integral of Ricci curvature on a 3-manifold is considered. It is not known whether the solution to this fourth order geometric evolution equation exists, and whether it will develop singularities in finite time. Based on the trick of De Turck and the idea of Hamilton on the flow of Ricci curvature, the local existence on any compact Riemannian manifold is obtained. In addition, the conditions for the occurences of singularities in finite time during the evolution and the asymptotic behavior of the flow on a 3-manifold are discussed. Received: 22 April 2002 / Revised version: 5 January 2003 Published online: 24 April 2003 This work is partially supported by the Foundations of NNSF of China, the Foundation for University Key Teacher by MEC and Shanghai Priority Academic Discipline.     

The fabrication and characterization of poly(lactic acid) scaffolds for tissue engineering by improved solid–liquid phase separation

In this article a new technique was developed to fabricate scaffolds with a unique microstructure by solid–liquid separation in combination with particulate-leaching. Firstly, the effects of polymer concentration, quenching temperature on the porous morphology and the mechanical property of obtained scaffolds during solid–liquid separation have been investigated. Then, salt granules as porogen were introduced into the solid–liquid phase separation to produce the unique pore structure of the scaffold. The pore diameter of the scaffold could be controlled with the particulate size and the wall of pores possessed special microstructure, which enhanced the pore interconnectivity. The cell culture results confirmed that a good interconnectivity of the scaffold prepared by the improved solid–liquid separation was useful for nutrition transportation and cell proliferation. Copyright © 2003 John Wiley & Sons, Ltd.     

Some sufficient conditions for oscillation of impulsive delay hyperbolic systems with Robin boundary conditions

This paper deals with the oscillation problems of delay hyperbolic systems with impulses. Some sufficient conditions for oscillations of impulsive delay hyperbolic systems with Robin boundary conditions are obtained and the criteria of oscillation of the systems are established.     

Ritt’s theorem and the Heins map in hyperbolic complex manifolds

Let X be a Kobayashi hyperbolic complex manifold, and assume that X does not contain compact complex submanifolds of positive dimension (e.g., X Stein). We shall prove the following generalization of Ritt’s theorem: every holomorphic self-map f:X→X such that f(X) is relatively compact in X has a unique fixed point τ(f) ∈ X, which is attracting. Furthermore, we shall prove that τ(f) depends holomorphically on f in a suitable sense, generalizing results by Heins, Joseph-Kwack and the second author.     

The speed of biased random walk on percolation clusters

 We consider biased random walk on supercritical percolation clusters in ℤ². We show that the random walk is transient and that there are two speed regimes: If the bias is large enough, the random walk has speed zero, while if the bias is small enough, the speed of the random walk is positive. Received: 20 November 2002 / Revised version: 17 January 2003 Published online: 15 April 2003 Research supported by Microsoft Research graduate fellowship. Research partially supported by the DFG under grant SPP 1033. Research partially supported by NSF grant #DMS-0104073 and by a Miller Professorship at UC Berkeley. Mathematics Subject Classification (2000): 60K37; 60K35; 60G50 Key words or phrases: Percolation – Random walk     

数学建模与素质教育

面对二十一世纪知识经济的挑战 ,我国高等教育模式应由应试教育 ,专业教育向素质教育转变 ,培养学生自主意识 ,效率意识 ,竞争意识 ,创新意识和民主意识 ,即高校教育应重视大学生的创新能力、实践能力和创业精神 ,普遍提高大学生的人文素质和科学素质 .本文拟就提高大学生素质的有效层面 ,对开展数学建模教学与实践进行深入分析 ,以窥探数学建模与素质教育之关系 .在深入把握数学建模教学与实践内涵的同时 ,分析得出这种以不打扰现行正常秩序的教育是提高大学生素质的有效途径之一