Large-time behavior of perturbed diffusion markov processes with applications to the second eigenvalue problem for fokker-planck operators and simulated annealing

We study the large-time behavior and rate of convergence to the invariant measures of the processes dX (t)=b(X) (t)) dt + (X (t)) dB(t). A crucial constant appears naturally in our study. Heuristically, when the time is of the order exp( – )/² , the transition density has a good lower bound and when the process has run for about exp( – )/², it is very close to the invariant measure. LetL =(²/2) – U · be a second-order differential operator on ^d. Under suitable conditions,L ^z has the discrete spectrum

Variations on the theme of repeated distances

We give an asymptotically sharp estimate for the error term of the maximum number of unit distances determined byn points in ^{d, d}4. We also give asymptotically tight upper bounds on the total number of occurrences of the favourite distances fromn points in ^{d, d}4. Related results are proved for distances determined byn disjoint compact convex sets in ².At the time this paper was written, both authors were visiting the Technion — Israel Institute of Technology.     

Sphere orders

Ann-sphere order is a finite partially ordered set representable by containment ofn-spheres in Euclidean (n+1)-space. We present a sequence {P _i } of ordered sets such that eachP _i is ann-sphere order only forni; one consequence is that we are able to determine the dimension of a Euclidean space-time manifold from the finite suborders of its causality order.Research supported by ONR grant N00014 85-K-0769.     

Heat “polynomials” for a singular differential operator on (0, ∞)

We generalize the theory of the heat polynomials introduced by P. V. Rosenbloom and D. V. Widder for a more general class of singular differential operator on (0, ). The heat polynomials associated with the Bessel operator and studied by D. T. Haimo appear as a particular case in this paper. In the special cases of second derivative and Bessel operators the heat polynomials are in fact polynomials inx andt, however, this property does not hold in general.Communicated by Tom. H. Koornwinder.     

蛋白质—四氯苯醌荷移反应的分光光度研究

本文用分光光度法研究了蛋白质—四氯苯醌荷移反应。通过对影响反应各因素的研究,确立了以四氯苯醌形成荷移络合物的方法测定蛋白质的最佳条件,测定了最大结合数及反应平衡常数。     

碱土金属邻苯二甲酸盐的振动光谱

测定了CaPHT·H2O和两种CaPHT的晶体结构, 其空间群分别属于P21/c(C2h^5,Z=4), P21/m(C2h^2, Z=8)和P2/m(C2h^1, Z=6), 研究CaPHT·H2O、CaPHT(A)、CaPHT(B)、MgPHT、SrPHT和BaPHT的IR及CaPHT·H2O的拉曼光谱, 讨论了固体样品中PHT与碱土金属离子的配位结构及其对光谱的影响。     

1-氨基环丙烷-1-羧酸的合成: 新型植物生长调节剂

本文报道了合成1-氨基环丙烷-1-羧酸的简便而价廉的方法,即乙酰乙酸乙酯法和α-氰乙酸乙酯法;并测定了产品的结构。     

Clathrate formation in water-cyclic ether systems at high pressures

Experimental data on the investigation of the water-trimethyleneoxide system,P, t, x phase diagram (up to 6 kbar) are presented. The results are compared with those on water systems with ethyleneoxide, 1,3- and 1,4-dioxane, 1,3-dioxolane and tetrahydrofuran, on the basis of which a summarizedP, t, x diagram is plotted for water-cyclic ether systems. It is shown that in all the systems in which a cubic structure II hydrate forms at 1 bar, it eventually turns to cubic structure I under pressure. The nature of high pressure hydrates is discussed.Dedicated to the memory of D. W. Davidson.     

复合蛋白锌在儿科疾患方面的应用

儿童缺锌是较普遍的社会现象，济南泉城微量元素生命研究所研制的复合蛋白锌系采用生物技术转化而得到的一种蛋白复合物，属生物合成的有机微量元素，经急性和长期毒性试验均未发现毒副作用，经检测不含兴奋剂，用于临床后，对纠正偏食厌食，反复呼吸道感染和智力低下等近千例儿童疾患，显示了可喜的临床效果，证明是优质有机补锌剂。