A Strong Limit Theorem on Random Selection

In this paper, the idea of random selection in the theorem on gambling system is extended to Markov chains, by using the notion likelihood ratio and an analytic technique. A strong limit theorem on the relative frequency of ordered couple under random selection is established.AMS Subject Classification (2001) primary 60F15 Secondary 60J10     

Inexpensive d‐dimensional matchings

Suppose that independent U(0, 1) weights are assigned to the ${d\choose 2}n^{2}$ edges of the complete d‐partite graph with n vertices in each of the d maximal independent sets. Then the expected weight of the minimum‐weight perfect d‐dimensional matching is at least $\frac{3}{16}n^{1-(2/d)}$. We describe a randomized algorithm that finds a perfect d‐dimensional matching whose expected weight is at most 5d³n^1?(2/d)+d¹⁵ for all d≥3 and n≥1. © 2002 John Wiley & Sons, Inc. Random Struct. Alg., 20, 50–58, 2002     

A combination of potential reduction steps and steepest descent steps for solving convex programming problems

This paper studies the possibility of combining interior point strategy with a steepest descent method when solving convex programming problems, in such a way that the convergence property of the interior point method remains valid but many iterations do not request the solution of a system of equations. Motivated by this general idea, we propose a hybrid algorithm which combines a primal–dual potential reduction algorithm with the use of the steepest descent direction of the potential function. The complexity of the potential reduction algorithm remains valid but the overall computational cost can be reduced. Our numerical experiments are also reported. Copyright © 2002 John Wiley & Sons, Ltd.     

Synthesis of single crystal BaWO4 nanowires in catanionic reverse micelles

High aspect-ratio, single crystal BaWO4 nanowires with diameters as small as 3.5 nm and lengths up to more than 50 microns were synthesized in catanionic reverse micelles formed by an equimolar mixture of two surfactants: undecylic acid and decylamine.     

Electrophilic aromatic nitration using perfluorinated rare earth metal salts in fluorous phase

In this paper, we describe a practical, useful electrophilic aromatic nitration process in fluorous phase by using perfluorodecalin (C10F18, cis- and trans-mixture) as a fluorous solvent and perfluorinated rare earth metal salt [Yb(OSO2C8F17)3] as a catalyst for the electrophilic aromatic nitration.     

Efficient soluble polymer-supported sharpless alkene epoxidation catalysts

High chemical yields and good enantiomeric excesses are obtained by using soluble polymer-supported tartrate ester in the epoxidation of trans-hex-2-en-1-ol using Ti(OPri)4/tert-butyl hydroperoxide.     

The Number of Isomorphism Classes of Finite Groups with Given Element Orders

Let G be a finite group and _e(G) the set of element orders of G. Denote by h( _e(G)) the number of isomorphism classes of finite groups H satisfying _e(H) = _e(G). We prove that if G has at least three prime graph components, then h( _e (G)){1, }.     

High-efficiency coupling structure for a single-line-defect photonic-crystal waveguide

We present the design and fabrication of a planar structure for coupling light from a multimode feed waveguide into a single-line-defect photonic-crystal waveguide. Finite-difference time-domain calculations predict a coupling efficiency of greater than 90%, and preliminary experimental results indicate successful coupling through a single-line-defect photonic-crystal waveguide. Device design, fabrication, and characterization are presented.