How likely is Polya's drunkard to stay in x⩾ y⩾z?

In his celebrated paper, Polya has considered the random walk in the three-dimensional (cubic) lattice and showed that the probability of return to the origin is less than 1. Subsequent authors have shown that the probability is %34.053.... Here we consider the same random walk, with the restriction that the drunkard is only allowed to stay inxyz. It is shown that his probability of returning to the originand staying in the allowed region is %6.4844....     

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.     

载波钝化和钼酸盐后处理对不锈钢钝化膜性能的影响

一般认为交流电对金属的腐蚀过程具有加速作用,但我们发现,在直流电位基础上叠加适当波形、幅值和频率的交流电对不锈钢进行载波钝化,尔后再进行适当后处理可使钝化膜的稳定性提高,我们曾就不经后处理的载波钝化过程进行过探讨,本文着重探讨钼酸盐后处理对载波钝化膜表面状态和化学稳定性改善的作用机理。     

过渡金属钼钒砷杂多化合物的合成与TPR,TPD研究

Seven transition metal molybdovanadoarsenic heteropoly compounds have been synthesized and characterized using IR, UV, TG-DTA, pH potential titration techniques. The molecular formulae of these compounds are pro-posed to be H_xM_yAsMO₁₀V₂O₄₀·zH₂O(x=1～3, y=1,2, M=Cr, Mn, Fe, Co, Ni, Cu, Zn).They are all keggin structure. Surface nature of these compounds have been investigated by temperature programmed desorption and temperature programmed reduction techniques. NH₃-TPD results show that in TPD profiles of the compounds there are two desorption peaks corresponding to weak acid sites of desorption, respectively. Desorbing activativon energy and preexponential factor of weak acid site of desorption for compounds have been calculated. H₂-TPR re-sults show that introducting transtion metal to molybdovanarsenic acid, the reduction peak temperatures of H₂-TPR shift regularly with increasing d electron numbers of transition metals. In addition, Zn and Cu heteropoly com-pounds have yet apparent effect of hydrogen spill over.     

Convergence of optimal stochastic bin packing

Consider independent identically distributed random variables (X_i) valued in [0,1]. Let B(n) be the optimal (minimum) number of unit size bins needed to pack n items of size X₁, X₂,…,X_n. We prove that there exists a numerical constant C such that for t > 0,

$\text{Pr(∣B(n)?E(B(n))∣>t}\text{n}\text{)≤ C exp(? t).}$

The constant C does not depend on the distribution of X.     

水溶性聚合物和两亲聚合物:12.环氧乙烷-环氧丙烷无规共聚醚结构与性能的关系

来用连续加料法,以二元醇-KOH为引发剂合成一组不同组成的环氧乙烷-环氧丙烷无规共聚醚,并用核磁共振、红外光谱、示差扫描量热计和热失重等方法对其本体聚合物,用浊点和表面张力测定的方法对其水溶液,进行系统的表征。     

Excess molar heat capacities of ((<Emphasis Type="Italic">R</Emphasis>)-(+)-α-pinene+(<Emphasis Type="Italic">S</Emphasis>)-(-)- α-pinene) at temperatures between 293.15-308.15 K

Summary {\rtf1\ansi\ansicpg1250\deff0\deflang1038\deflangfe1038\deftab708{\fonttbl{\f0\froman\fprq2\fcharset238{\*\fname Times New Roman;}Times New Roman CE;}} \viewkind4\uc1\pard\f0\fs20 New explanations are given for two types of irregular thermogravimetric (TG) data. A TG relationship between mass and temperature is derived on the basis of migration behavior of bubbles generated in bulk of sample system, and superposed on that derived on the basis of kinetics of the 4\super th\nosupersub order event, which is superposed on the experimental TG data obtained from three reference papers. This suggests that these TG data are reflecting migration of bubbles. A dependence of TG behavior on heating rate, which is contrary to usual that, is shown and is explained in terms of event-rate determination by boiling. \par }     

On the invariant measures for the two-dimensional euler flow

It is proven that the canonical Gibbs measure associated with a gas of vortices of intensity ± converges, in the limitN, 0,Nconst, to a Gaussian measure, which is invariant for the two-dimensional Euler equation.On leave from Dipartimento di Matematica Università di Roma Tor Vergata Roma, Italy.On leave from Dipartimento di Matematica Università di Roma La Sapienza, Roma, Italy.     

On the existence of thermodynamics for the generalized random energy model

Derrida's generalized random energy model is considered. Almost sure andL ^p convergence of the free energy at any inverse temperature are proven for an arbitrary numbern of hierarchical levels. The explicit form of the free energy is given in the most general case and the limitn is discussed.