Harnack Inequalities for Functional SDEs Driven by Subordinate Brownian Motions

Potential Analysis - Using coupling by change of measure and an approximation technique, Wang’s Harnack inequalities are established for a class of functional SDEs driven by subordinate...     

An approach for solving fuzzy multi-criteria decision problem under linguistic information

Fuzzy Optimization and Decision Making - Linguistic information processing exists in multi-criteria decision making, and linguistic truth-valued lattice implication algebra (LTV-LIA) has definite...     

Stochastic flows on the boundaries of SL(n,R)

Summary We study the asymptotic stability of the stochastic flows on a class of compact spaces induced by a diffusion process in SL(n, R) or GL(n, R). These compact spaces are called boundaries of SL(n, R), which include SO(n), the flag manifold, the sphereS ⁿ–1 and the Grassmannians. The one point motions of these flows are Brownian motions. For almost every, , we determine the set of stable points. This is a random open set whose complement has zero Lebesgue measure. The distance between any two points in the same component of this set tends to zero exponentially fast under the flow. The Lyapunov exponents at stable points are computed explicitly. We apply our results to a stochastic flow onS ⁿ–2 generated by a stochastic differential equation which exhibits some nice symmetry.Research supported in part by Hou Yin Dong Education Foundation of China On leave from Nankai University, Tianjin, China     

HIGHLY SENSITIVE SPECTROPHOTOMETRY OF NIOBIUM

In pH2.0-3.0,niobium(V)forms molybdonlobic acid with sodiummolybdate.A spectrophotometric method has been developed for the deter-mination of niobium based on the formation of ion-associate compound ofmolybdoniobate with Butyl Rhodamine B in aqueous solution in the presenceof polyvinyl alcohol and 0.4-0.7 mol/L H_2SO_4.The maximum absorption ofion-associate compound exhioits at 85 nm and the molar absorptivity is7.5×1.0~5 L.mol~(-1).cm~(-1)for niobium.The new method has been applied tothe determination of microamounts niobium in silicate rock,when niobiumcontent is at the level of 8×10~(-3)%,with the relative standard deviationof about 3%.     

Highly regioselective rearrangement of 2-substituted vinylepoxides catalyzed by gallium(III) triflate

Gallium(III) triflate catalyzed the rearrangement of 2-substituted vinylepoxides into beta,gamma-unsaturated carbonyl compounds with high regio- and chemoselectivity (>97/3) in low catalyst loading (1-5 mol %). The alkyl-substituted trimethylsilylvinyl epoxides gave beta,gamma-unsaturated ketone, but aryl-substituted vinylepoxides gave the aldehydes instead.     

Asymmetric synthesis of cis-5-tert-butylproline with metal carbenoid NH insertion

The highly stereoselective intramolecular metal carbenoid insertion reaction of sulfinimine-derived delta-amino alpha-diazoesters is used to prepare cis-5-tert-butylproline. A concerted or nearly concerted metal carbenoid N-H insertion reaction mechanism is proposed.     

含羟基的青蒿倍半萜内酯差向异构体的合成

本文报道以青蒿酸(2)为原料合成了一些含羟基的青蒿倍半萜内酯差向异构体9与10、11与12、13与14。其中9已从青蒿中分离到。