A stochastic algorithm using one sample point per iteration and diminishing stepsizes

A stochastic algorithm for finding stationary points of real-valued functions defined on a Euclidean space is analyzed. It is based on the Robbins-Monro stochastic approximation procedure. Gradient evaluations are done by means of Monte Carlo simulations. At each iteratex _i , one sample point is drawn from an underlying probability space, based on which the gradient is approximated. The descent direction is against the approximation of the gradient, and the stepsize is 1/i. It is shown that, under broad conditions, w.p.1 if the sequence of iteratesx ₁,x ₂,...generated by the algorithm is bounded, then all of its accumulation points are stationary.     

Adaptive Algorithm for Constrained Least-Squares Problems

This paper is concerned with the implementation and testing of an algorithm for solving constrained least-squares problems. The algorithm is an adaptation to the least-squares case of sequential quadratic programming (SQP) trust-region methods for solving general constrained optimization problems. At each iteration, our local quadratic subproblem includes the use of the Gauss–Newton approximation but also encompasses a structured secant approximation along with tests of when to use this approximation. This method has been tested on a selection of standard problems. The results indicate that, for least-squares problems, the approach taken here is a viable alternative to standard general optimization methods such as the Byrd–Omojokun trust-region method and the Powell damped BFGS line search method.     

Algebraic methods in quantum mechanics: from molecules to polymers

We present a brief review of algebraic techniques developed and applied in molecular spectroscopy in the last five years. We also outline perspectives for new applications of the Lie algebraic method in the first decade of the new century. Received 21 November 2001     

Discretization of the solutions to Poisson’s equation

Sharp estimates (in the power scale) are obtained for the discretization error in the solutions to Poisson’s equation whose right-hand side belongs to a Korobov class. Compared to the well-known Korobov estimate, the order is almost doubled and has an ultimate value in the power scale.     

Differential Entropy and Dynamics of Uncertainty

We analyze the functioning of Gibbs-type entropy functionals in the time domain, with emphasis on Shannon and Kullback-Leibler entropies of time-dependent continuous probability distributions. The Shannon entropy validity is extended to probability distributions inferred from L ²(R ⁿ ) quantum wave packets. In contrast to the von Neumann entropy which simply vanishes on pure states, the differential entropy quantifies the degree of probability (de)localization and its time development. The associated dynamics of the Fisher information functional quantifies nontrivial power transfer processes in the mean, both in dissipative and quantum mechanical cases. PACS NUMBERS: 05.45.+b, 02.50.-r, 03.65.Ta, 03.67.-a     

电子回旋共振放电的电离特性PIC/MCC模拟(Ⅰ)——物理模型与理论方法

采用粒子模拟与蒙特卡罗相结合(PIC/MCC)的方法对电子回旋共振(ECR)放电中的电离过程进行了模拟，其中带电粒子与微波的相互作用由PIC方法的电磁模型描述，粒子间的碰撞过程由MCC方法描述.考虑的碰撞类型有电子与中性粒子的弹性、激发、电离碰撞，离子与中性粒子的弹性、电荷交换碰撞，碰撞截面均依赖于能量而变化.阐述了理论分析的过程，为数值模拟ECR放电奠定了基础. 关键词： 电子回旋共振放电 粒子模拟 蒙特卡罗 电离     

Approximate Inverse Preconditioners for Some Large Dense Random Electrostatic Interaction Matrices

A sparse mesh-neighbour based approximate inverse preconditioner is proposed for a type of dense matrices whose entries come from the evaluation of a slowly decaying free space Green’s function at randomly placed points in a unit cell. By approximating distant potential fields originating at closely spaced sources in a certain way, the preconditioner is given properties similar to, or better than, those of a standard least squares approximate inverse preconditioner while its setup cost is only that of a diagonal block approximate inverse preconditioner. Numerical experiments on iterative solutions of linear systems with up to four million unknowns illustrate how the new preconditioner drastically outperforms standard approximate inverse preconditioners of otherwise similar construction, and especially so when the preconditioners are very sparse. AMS subject classification (2000) 65F10, 65R20, 65F35, 78A30     

Correlation between the Mechanical Properties and the Amount of Desorbed Water for Composites Based on Low-Density Polyethylene and Linen Yarn Production Waste

The effect of the amount of desorbed water on the mechanical properties of composites based on low-density polyethylene and linen yarn production waste (LW) is analyzed by statistical methods. It is shown that the amount of absorbed water decreases during the desorption process at room temperature both for specimens modified and unmodified with diphenylmethane diisocyanate (DIC.) The most sensitive to the action of water is the elastic modulus, which decreases considerably under the effect of water and is fully restored in the desorption process. The tensile strain also increases with the amount of absorbed water. It is found that the elastic modulus of the unmodified composite correlates linearly with the amount of desorbed water. Between the amount of desorbed water and the tensile strain, as well the specific work of deformation, a negative linear correlation is revealed. After water desorption, all strength and deformation characteristics of both the modified and unmodified composites are fully recovered.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 515–524, July–August, 2005.     

Convergence analysis of a modified inexact implicit method for general mixed monotone variational inequalities

We consider a useful modification of the inexact implicit method with a variable parameter in Wang et al. J Optim Theory 111: 431–443 (2001) for generalized mixed monotone variational inequalities. One of the contributions of the proposed method in this paper is that the restrictions imposed on the variable parameter are weaker than the ones in Wang et al. J Optim Theory 111: 431–443 (2001). Another contribution is that we establish a sufficient and necessary condition for the convergence of the proposed method to a solution of the general mixed monotone variational inequality.     

An AFM, XPS and electrochemical study of molecular electroactive monolayers formed by wet chemistry functionalization of H-terminated Si(1 0 0) with vinylferrocene

Molecular electroactive monolayers have been produced from vinylferrocene (VFC) via light-assisted surface anchoring to H-terminated n- and p-Si(1 0 0) wafers prepared via wet chemistry, in a controlled atmosphere. The resulting Si-C bound hybrids have been characterized by means of XPS and AFM. Their performance as semiconductor functionalized electrodes and their surface composition have been followed by combining electrochemical and XPS measurements on the same samples, before and after use in an electrochemical cell. White-light photoactivated anchoring at short (1 h) exposure times has resulted in a mild route, with a very limited impact on the initial quality of the silicon substrate. In fact, the functionalized Si surface results negligibly oxidized, and the C/Fe atomic ratio is close to the value expected for the pure molecular species. The VFC/Si hybrids can be described as (η⁵-C₅H₅)Fe²⁺(η⁵-C₅H₄)-CH₂-CH₂-Si species, on the basis of XPS results. Electrochemical methods have been applied in order to investigate the role played by a robust, covalent Si-C anchoring mode towards substrate-molecule electronic communication, a crucial issue for a perspective development of molecular electronics devices. The response found from cyclic voltammograms for p-Si(1 0 0) functionalized electrodes, run in the dark and under illumination, has shown that the electron transfer is not limited by the number of charge carriers, confirming the occurrence of electron transfer via the Si valence band. The hybrids have shown a noticeable electrochemical stability and reversibility under cyclic voltammetry (cv), and the trend in peak current intensity vs. the scan rate was linear. The molecule-Si bond is preserved even after thousands of voltammetric cycles, although the surface coverage, evaluated from cv and XPS, decreases in the same sequence. An increasingly larger surface concentration of Fe³⁺ at the expenses of Fe²⁺ redox centers has been found at increasing number of cv’s, experimentally associated with the growth of silicon oxide. Surface SiO⁻ groups from deprotonated silanol termination, induced by the electrochemical treatments, are proposed as the associated counterions for the Fe³⁺ species. They could be responsible for the observed decrease in the electron transfer rate constant with electrode ageing.