Generalized Solution of a Kind of Nonparametric Curvature Evolution with Boundary Condition

The existence and uniqueness of the generalized solution for a kind of nonparametric curvature flow problem are obtained. This kind of curvature flow problem describes the evolution of graphs with speed depending on the reciprocal of the Gauss curvature.     

On the cover time of random walks on graphs

This article deals with random walks on arbitrary graphs. We consider the cover time of finite graphs. That is, we study the expected time needed for a random walk on a finite graph to visit every vertex at least once. We establish an upper bound ofO(n ²) for the expectation of the cover time for regular (or nearly regular) graphs. We prove a lower bound of (n logn) for the expected cover time for trees. We present examples showing all our bounds to be tight.Mike Saks was supported by NSF-DMS87-03541 and by AFOSR-0271. Jeff Kahn was supported by MCS-83-01867 and by AFOSR-0271.     

Small random perturbations of finite- and infinite-dimensional dynamical systems: Unpredictability of exit times

We apply previous results on the pathwise exponential loss of memory of the initial condition for stochastic differential equations with small diffusion to the problem of the asymptotic distribution of the first exit times from an attracted domain. We show under general hypotheses that the suitably rescaled exit time converges in the zero-noise limit to an exponential random variable. Then we extend the results to an infinite-dimensional case obtained by adding a small random perturbation to a nonlinear heat equation.     

应用分子图形学、分子力学、量子化学及静电势研究农药分子结构与性能关系(X)──磺酰脲分子内旋转通道的分子力学研究

磺酞豚分子是一类极其重要的低毒超高效除草剂，有着十分重要的用途．研究分子的空间结构对于了解分子的构效关系十分重要．最近，我们测定的一系列分子的晶体结构［‘－’1表明，分子1、2、3晶体结构的空间群分别为PZ；儿、Pz、Pz，说明晶体中分别有对称元素（对称面或者对称中心），分子以对映体的形式存在于晶体中．由于磺酸豚分子本身不存在手性原子，由此推断磺酷服分子在晶体中存在的对映异构体是由内旋转阻碍产生的，因而应是构象异构体．本项研究工作的目的是应用分子力学方法，计算阻碍内旋转的能垒，从而找出分子内旋转时的最低…     

Zur Theorie der Chiralitätsfunktionen

The Algebraic Theory of Chirality Functions is derived by means of exclusively qualitative considerations. Hence, the significance of quantitative results is questionable. Moreover the construction of “Näherungsansätze” (”Approximation-Ansatz”), which may be interpreted as semiempirical methods, is achieved on the basis of plausibility and mathematical simplicity. Since physical arguments are not included, the consistency or inconsistency of “Näherungsansätze” with experimental results do not justify direct physical conclusions.     

Structural and magnetic characterization of Mn3IrGe and Mn3Ir(Si1−xGex): experiments and theory

The structural and magnetic properties of a new ternary Ir-Mn-Ge phase, Mn₃IrGe, as well as the solid solution Mn₃Ir(Si_1−xGe_x), 0?x?1, have been investigated by means of X-ray and neutron powder diffraction, magnetization measurements and first principles calculations. The crystal structure is cubic, of the AlAu₄-type (an ordered form of the β-Mn structure), Z=4, space group P2₁3, and the unit-cell dimension varies linearly with the silicon content. For all compositions, antiferromagnetic ordering is found below a critical temperature of about 225 K. The magnetic structure is noncollinear, as a result of frustrated magnetic interactions on a triangular network of Mn atoms, on which the moments rotate 120° around the triangle axes. The magnitude of the magnetic moment at 10 K is 3.39(4) μ_B for Mn₃IrGe. The theoretical calculations reproduce with very good accuracy the magnitudes as well as the directions of the experimentally observed magnetic moments.     

Critical behavior of the two-dimensional first passage time

We study the two-dimensional first passage problem in which bonds have zero and unit passage times with probabilityp and 1–p, respectively. We prove that as the zero-time bonds approach the percolation thresholdp _c, the first passage time exhibits the same critical behavior as the correlation function of the underlying percolation problem. In particular, if the correlation length obeys(p) ¦p–p _c¦^–v, then the first passage time constant satisfies(p)¦p–p _c¦^v. At p_c, where it has been asserted that the first passage time from 0 tox scales as ¦x¦ to a power with 0<<1, we show that the passage times grow like log ¦x¦, i.e., the fluid spreads exponentially rapidly.     

一阶导数分光光度法测定血中一氧化碳含量的研究

本文通过理论推导及实验证明CO饱和血与正常血一阶导数的振幅高度比为一常数。将CO中毒检血氨稀释液取一半通CO至饱和,与另一半分别加入Na_2S_2O_4后在500～600nm测定一阶导数光谱在579nm处量出振幅值经计算可得CO在血中含量。     

热动力学的研究 X. 一级反应的热谱峰高法

本文根据一级反应的热谱曲线方程、建立了速度常数的一种新算法。这种新方法,只需要热谱曲线在各个特征时刻的峰高,而不需要任何峰面积,即可算得反应体系的无量纲参数和速度常数,称为一级反应的热谱峰高法。     

一阶导数吸光光度法测定碘酸钾碘盐中碘

采用一阶导数吸光光度法测定碘酸钾碘盐中碘 ,线性范围为 0～ 12 μg·ml-1,检出限为1.6μg·ml-1,对盐样进行重复测定 ,相对标准偏差≤ 1.9% ,对样品进行加标回收试验 ,回收率在 97.0 %～ 10 2 .5 % ,结果良好