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

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.     

二价稀土金属有机配合物的合成及反应

本文将试图对二价的铕、镱、和钐的有机配合物的合成,结构及反应性能作了较为全面的综述。     

芳烃金属配合物在有机合成中的应用

本文讨论了芳烃金属配合物中的芳香部份在与金属配合后性质上的变化,以及这些变化后的性质在有机合成中的应用。     

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.     

12,14-二羟基紫韧革烯的分离和结构测定

由紫韧革菌(Stereum purpureum)代谢产物中分离出一个新的三环倍半萜烯醇(sterpurenol), 12,14-二羟基紫韧革烯。用二维核磁共振确定了它具有紫韧革烯(sterpurene,1)的骨架及它的整个分子结构。     

Iodination of alcohols using triphenylphosphine/iodine under solvent-free conditions using microwave irradiation

A straightforward and effective procedure for the conversion of benzylic, allylic and aliphatic alcohols to the corresponding iodides using Ph₃P/I₂ under solvent-free conditions using microwave irradiation is reported.     

铜催化下格氏试剂与α,ω-二溴代烷的偶合反应

七十年代发展了铜催化下格氏试剂与卤代物、磺酸酯、酰卤的选择性交叉偶合反应,以后对这类反应并未深入研究。我们以几种铜