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.     

Inorganic nanocrystal-dynamic porous polymer assemblies with effective energy transfer for sensitive diagnosis of urine copper

Despite their remarkable mechanical, optical, and electrical properties, inorganic particles and dynamic polymer assemblies encounter difficulties in their compatibility with regards to structural order and complexity. Here, covalent organic frameworks (COFs) constructed through reversible coupling reactions were exploited as dynamic porous polymers to prepare inorganic nanocrystal-polymer assemblies. Under an in situ growth process, carbon quantum dots (CDs) were gradually prepared in the COF cavity, with a narrow size distribution (2 ± 0.5 nm). The well-established assemblies achieve effective energy transfer from the inorganic to the organic part (efficiency > 80%), thus rendering a ∼130% increase in quantum yield compared with the pristine COF network. Notably, the hybrid material realizes a simple, selective, and sensitive diagnostic tool for urine copper, surpassing the detection limit of COF solid by 150 times. Beyond the scientific and fundamental interests, such hybrid assemblies are attractive from technological perspectives as well, for example, in energy storage, electronics, catalysis, and optics.

Despite their remarkable mechanical, optical, and electrical properties, inorganic particles and dynamic polymer assemblies encounter difficulties in their compatibility with regards to structural order and complexity.     

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.     

Flash photolytic generation and study of p-quinone methide in aqueous solution. An estimate of rate and equilibrium constants for heterolysis of the carbon-bromine bond in p-hydroxybenzyl bromide

Flash photolysis of p-hydroxybenzyl acetate in aqueous perchloric acid solution and formic acid, acetic acid, biphosphate ion, and tris(hydroxymethyl)methylammonium ion buffers produced p-quinone methide as a short-lived species that underwent hydration to p-hydroxybenzyl alcohol in hydronium ion catalyzed (k(H(+)) = 5.28 x 10(4) M(-1) s(-1)) and uncatalyzed (k(uc) = 3.33 s(-1)) processes. The inverse nature of the solvent isotope effect on the hydronium ion-catalyzed reaction, k(H(+))/k(D(+)) = 0.41, indicates that this process occurs by rapid and reversible protonation of the quinone methide on its carbonyl carbon atom, followed by rate-determining capture of the p-hydroxybenzyl carbocation so produced by water, while the magnitude of the rate constant on the uncatalyzed process indicates that this reaction occurs by simple nucleophilic addition of water to the methylene group of the quinone methide. p-Quinone methide also underwent hydronium ion-catalyzed and uncatalyzed nucleophilic addition reactions with chloride ion, bromide ion, thiocyanate ion, and thiourea. The solvent isotope effects on the hydronium ion-catalyzed processes again indicate that these reactions occurred by preequilibrium mechanisms involving a p-hydroxybenzyl carbocation intermediate, and assignment of a diffusion-controlled value to the rate constant for reaction of this cation with thiocyanate ion led to K(SH) = 110 M as the acidity constant of oxygen-protonated p-quinone methide. In a certain perchloric acid concentration range, the bromide ion reaction became biphasic, and least-squares analysis of the kinetic data using a double-exponential function provided k(Br(-)) = 3.8 x 10(8) M(-1) s(-1) as the rate constant for nucleophilic capture of the p-hydroxybenzyl carbocation by bromide ion, k(ionz) = 8.5 x 10(2) s(-1) for ionization of the carbon-bromine bond of p-hydroxybenzyl bromide, and K = 4.5 x 10(5) M(-1) as the equilibrium constant for the carbocation-bromide ion combination reaction, all in aqueous solution at 25 degrees C. Comparisons are made of the reactivity of p-quinone methide with p-quinone alpha,alpha-bis(trifluoromethyl)methide as well as p-quinone methide with o-quinone methide.