Improved results on the robustness of stochastic approximation algorithms

This paper is a continuation of the research carried out in [1]–[2], where the robustness analysis for stochastic approximation algorithms is given for two cases: 1. The regression function and the Liapunov function are not zero at the sought-forx ⁰; 2. lim sup _n a131_{n i=1} ⁿ _i+1 is not zero, where { _i } are the measurement errors and {a _n} are the weighting coefficients in the algorithm. Allowing these deviations from zero to occur simultaneously but to remain small, this paper shows that the estimation error is still small even for a class of measurement errors more general than that considered in [2].This project is supported by the National Natural Science Foundation of China.     

A path following algorithm for a class of convex programming problems

We present a primal-dual path following interior algorithm for a class of linearly constrained convex programming problems with non-negative decision variables. We introduce the definition of a Scaled Lipschitz Condition and show that if the objective function satisfies the Scaled Lipschitz Condition then, at each iteration, our algorithm reduces the duality gap by at least a factor of (1–/n), where is positive and depends on the curvature of the objective function, by means of solving a system of linear equations which requires no more than O(n³) arithmetic operations. The class of functions having the Scaled Lipschitz Condition includes linear, convex quadratic and entropy functions.     

Adsorption Heat Pump Using an Innovative Coupling Refrigeration Cycle

An adsorption heat pump system using a new binary coupling adsorptive cycle is developed and tested. Experimental results show that the COP of the binary coupling cycle is higher than that of a pure zeolite-water system. The system operating pressure is found to be moderate (close to the ambient pressure) when a proper concentration of ammonia is used in the system. The moderate operating pressure of the new coupling cycle results in low leakage to the system, achieving long life and the light design of the system vessels. The use of the new binary adsorption cycle greatly improves the feasibility and reliability of the adsorption heat pumps, providing essential benefits for the industrialisation of adsorption heat pumps.     

New Approach to Synthesis of 6,7—Dimethoxyisatin

A new approach to synthesis of 6,7-dimethoxyisatin is reported.2-nitro-3,4-dimethoxy mandelonitrile in glacial acetic acid was treated with the solution of stannous chloride in hydrochloric acid to give 6,7-dimethoxyisatin in a high yield.     

Electrochemical Immunoassay for Carbohydrate Antigen‐125 Based on Polythionine and Gold Hollow Microspheres Modified Glassy Carbon Electrodes

A new electrochemical immunosensor for the detection of carbohydrate antigen‐125 (CA125), a carcinoma antigen, was developed by immobilization CA125 antibody (anti‐CA125) on gold hollow microspheres and porous polythionine (PTH) modified glassy carbon electrodes (GCE). The gold hollow microspheres provided a biocompatible microenvironment for proteins, and greatly amplified the coverage of anti‐CA125 molecules on the electrode surface. The performance and factors influencing the immunosensor were investigated in detail. The detection is based on the current change before and after the antigen‐antibody interaction. Under optimal conditions, the amperometric changes were proportional to CA125 concentration ranging from 4.5 to 36.5 U/mL with a detection limit of 1.3 U/mL (at 3σ). The CA125 immunosensor exhibited good precision, high sensitivity, acceptable stability, accuracy and reproducibility. The as‐prepared immunosensors were used to analyze CA125 in human serum specimens. Analytical results suggest that the developed immunoassay has a promising alternative approach for detecting CA125 in the clinical diagnosis.     

N,N′-bis(1-ferrocenyl-1-oxo-3-methyl)propenylethylenediamine and its metal complexes

Summary A new Schiff base ligand, N,N-bis(l-ferrocenyl-1-oxo-3-methyl)propenylethylenediamine (H₂L) and its copper(II), zinc(II), cobalt(II), nickel(II), cadmium(II) and manganese(II) complexes have been prepared, and the structure of the copper complex has been determined by single crystal X-ray techniques and refined to R = 0.041 for 7403 independent reflections. The copper atom is situated in a distorted planar environment. The dihedral angle between planes of two chelating rings which do not contain the metal is 33.5°. Two substituted Cp rings are conjugated with two chelating acacim rings. The iron-centroid forms an angle of 179.4°. The Cp rings are twisted from the eclipsed conformation.