Semi-infinite homology and 2D gravity. I

In [33], we studied the constraint problem for two-dimensional quantum gravity in the conformal gauge. In this gauge, we proposed an ansatz for the gravitational sector. Using this ansatz, we established a striking connection between the matrix models and continuum 2D gravity. We also announced several results on semi-infinite homology of the Virasoro algebra with coefficients in a suitable class of positive energy modules. In this article, we will provide details of the proof of the announced results.Supported in part by the Alfred P. Sloan FoundationSupported by NSF Grant DMS-8703581     

在有限执行假设下对最优契约的扩展模型研究

本文运用违约保证金条款改进了代理人事前报酬契约；在契约有限执行的假设下，扩展了代理人的逆向选择模型，并运用扩展逆向选择模型分析了改进后的最优报酬契约。文章指出，改进后的最优报酬契约严格优于委托人为防范代理人违约而被迫采用的非负参与性约束条件下的最优报酬契约。     

HL－1装置中LHCD和等离子体参数的关系

本文研究了在ＨＬ－１托卡马克的不同放电阶段的低混杂波驱动特性。给出了驱动电流及驱动效率和等离子体参数，如电子平均密度ｎｅ、等离子体电流Ｉｐ及纵向磁场的关系。也给出和分析了波驱动和入射波功率的关系。在放电平段，对正反向驱动效率进行了研究和比较。     

Toeplitz矩阵乘积的封闭性

本文建立了两个Toeplitz矩阵之积仍为Toeplitz矩阵的一个充分必要条件,由此也立即获得了循环矩阵的乘积及其逆也是循环矩阵的已知结果。     

微分脉冲溶出伏安法同时测定食品中的锌铁锰

在1％乙二胺-0．1mol／L酒石酸钠-pH11．82 Britton—Robinson缓冲溶液体系中用微分脉冲溶出伏安法同时测定锌、铁、锰三种微量元素。它们的峰电位分别为-1184，-1392和-1456mV(vs．Ag/AgCl)；线性范围分别为：0.001—0.015，0．005—0．05和0．04—0．7μg／mL，最低检出浓度分别为0．0007，0．0014和0．0193μg／mL。本法操作简便、准确、灵敏度较高，用于食品中这三种元素的分析，结果令人满意。     

Metallothionein as a biomarker for mercury in tissues of rat fed orally with cinnabar

Cinnabar, as one of the most widely used mineral drugs in traditional Chinese medicines, has been proven to have prominent curative effects in clinical use for more than 2000 years. But the safety and toxicity of the drug has been under constant debate in clinic usage. Metallothionein (MT) contains about 30% of cysteine in the molecule, and plays an important detoxification role against heavy metals. In this study, it was used as a biomarker to assess mercurial accumulation in rats fed orally with cinnabar. After feeding rats with cinnabar by gastric gavage at different dosages and at different times, the distribution of heavy metals (including mercury, copper and zinc) and MT was investigated among rat tissues, including liver, kidney, heart, brain, testis and blood. Metals and MT determinations were carried out using inductively coupled plasma mass spectrometry (ICP‐MS) and a modified mercury saturation assay technique respectively. The results indicated that mercury was easily accumulated in the tissues of rats exposed to cinnabar, especially in kidney. For example: at a feeding dosage of 5 g kg^?1 (bw) for 4 weeks, the mercury concentrations in kidney were 13, 8.7, 21.6 and 26 times those in liver, testis, brain and heart respectively; and at 2.5 g kg^?1 (bw) for 2 weeks, the mercury concentrations in kidney were 21, 2.1, 3 and 21 times those in liver, testis, brain and heart respectively. In addition, mercury in kidney and liver of all cinnabar groups was significantly higher than that of the control group (P < 0.01). A high positive correlation observed between MT concentrations and mercury levels in both liver and kidney (R² = 0.9299, P < 0.02 for liver; R² = 0.9923, P < 0.0008 for kidney) indicated that MT could be used as a biomarker for mercury in tissues. Copyright © 2004 John Wiley & Sons, Ltd.     

A projection method for solving incompressible viscous flows on domains with moving boundaries

In this paper, a projection method is presented for solving the flow problems in domains with moving boundaries. In order to track the movement of the domain boundaries, arbitrary‐Lagrangian–Eulerian (ALE) co‐ordinates are used. The unsteady incompressible Navier–Stokes equations on the ALE co‐ordinates are solved by using a projection method developed in this paper. This projection method is based on the Bell's Godunov‐projection method. However, substantial changes are made so that this algorithm is capable of solving the ALE form of incompressible Navier–Stokes equations. Multi‐block structured grids are used to discretize the flow domains. The grid velocity is not explicitly computed; instead the volume change is used to account for the effect of grid movement. A new method is also proposed to compute the freestream capturing metrics so that the geometric conservation law (GCL) can be satisfied exactly in this algorithm. This projection method is also parallelized so that the state of the art high performance computers can be used to match the computation cost associated with the moving grid calculations. Several test cases are solved to verify the performance of this moving‐grid projection method. Copyright © 2004 John Wiley Sons, Ltd.     

Correlation between Al2O3 particles and interface of Al-Al2O3 coatings by cold spray

Al-Al₂O₃ composite coatings with different Al₂O₃ particle shapes were prepared on Si and Al substrate by cold spray. The powder compositions of metal (Al) and ceramic (Al₂O₃) having different sizes and agglomerations were varied into ratios of 10:1 wt% and 1:1 wt%. Al₂O₃ particles were successfully incorporated into the soft metal matrix of Al. It was found that crater formation between the coatings and substrate, which is typical characteristic signature of cold spray could be affected by initial starting Al₂O₃ particles. In addition, when the large hard particles of fused Al₂O₃ were employed, the deep and big craters were generated at the interface between coatings and hard substrates. In the case of pure soft metal coating such as Al on hard substrate, it is very hard to get proper adhesion due to lack of crater formation. Therefore, the composite coating would have certain advantages.     

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     

New Compacton-Like and Solitary Pattern-Like Solutions of （2＋1）-Dimensional Generalization of Modified KdV Equation

Recently some （1＋1）-dimensional nonlinear wave equations with linearly dispersive terms were shown to possess compacton-like and solitary pattern-like solutions. In this paper, with the aid of Maple, new solutions of （2＋1）- dimensional generalization of mKdV equation, which is of only linearly dispersive terms, are investigated using three new transformations. As a consequence, it is shown that this （2＋1）-dimensional equation also possesses new compacton-like solutions and solitary pattern-like solutions.