A conformational analysis method for understanding the energy landscapes of clusters.

A newly developed unbiased structural optimization method, named dynamic lattice searching (DLS), is proposed as an approach for conformational analysis of atomic/molecular clusters and used in understanding the energy landscape of large clusters. The structures of clusters are described in terms of the number of basic tetrahedron (BT) units they contain. We found that the hit numbers of different structural motifs in DLS runs is proportional to the number of BTs. A parameter T(max) is defined to limit the maximal number of atoms moved in a structural transition. Results show that T(max) is a key parameter for modulating the efficiency of the DLS method and has a great influence on the hit number of different motifs in DLS runs. Finally, the effect of potential range on the conformational distribution of the (Morse)(98) cluster is also discussed with different potential-range parameters.     

Global Forcing Number of Benzenoid Graphs

A global forcing set in a simple connected graph G with a perfect matching is any subset S of E(G) such that the restriction of the characteristic function of perfect matchings of G on S is an injection. The number of edges in a global forcing set of the smallest cardinality is called the global forcing number of G. In this paper we prove several results concerning global forcing sets and numbers of benzenoid graphs. In particular, we prove that all catacondensed benzenoids and catafused coronoids with n hexagons have the global forcing number equal to n, and that for pericondensed benzenoids the global forcing number is always strictly smaller than the number of hexagons.     

杂合型全局优化法优化水分子团簇结构

基于遗传算法、快速模拟退火及共轭梯度方法提出了一种快速的杂合型全局优化方法(fast hybrid global optimization algorithm, FHGOA),并将这一方法应用于TIP3P和TIPS2模型水分子团簇(H2O)n结构的优化.在进行TIP3P模型水分子团簇结构的优化过程中,发现了能量比文献值更低的团簇结构,且执行效率有较大提高.把该方法应用到优化TIPS2模型的水分子团簇,发现最优结构和采用TTM2-F模型优化的水分子团簇结构在n < 17时完全相同,为全表面结构;而在n=17、19、22时为单中心水分子笼状结构;在n=25、27时为双中心水分子笼状结构.说明随着团簇中水分子个数的增加,采用TIPS2和TTM2-F势能函数优化的团簇最优结构有相同的变化趋势.     

Resolution of global signals using ratio differential pulse polarograms: Determination of p-nitroaniline and p-nitrotoluene in their mixture

Ratio differential pulse polarograms obtained by dividing the multianalyte and single analyte signals are proposed as a tool for resolution of global signals and quantification of the analytes from a qualitatively known mixture by differential pulse polarography (DPP) and related electroanalytical techniques. The influences of shape and position of the resolving function (DP polarograms of individual analyte) on the efficiency of resolution are discussed on simulated and experimental results. The method is applied for the determination of p-nitroaniline (NA) and p-nitrotoluene (NT) from their mixture in N,N′-dimethylformamide solutions with 0.1 M tetrabutylammonium iodide as supporting electrolyte, using an external calibration diagram and internal standard addition methods. NA and NT give one-electron DP polarographic peaks with 93 mV of peak separation and, therefore, show significant overlapping which depends on the concentration ratio of NA and NT in the mixture. The method is especially suitable for quantification of one analyte in the presence of a large excess of another analyte, because by division the component in excess is removed and the pseudo-ratio DPP of the minor component is clearly revealed in a way which is not possible by deconvolution using polynomial division or deconvolution by Fourier transforms.     

Fractal phenomena in molecular mechanics calculation

It is proposed that in molecular mechanics calculation points belonging to various stable or meta-sta-ble conformtrs are mixed up and form fractal structures in conformation space.The calculation results show the following two phenomena:(i)Two levels of structure with fractal feature were observed.Around the conformer without mirror symmetry points belonging to the conformer and its enantiomer are mixed up and form the first level of fractal structure; on the boundary of the attractive basin o{ each atlractor,points belonging to different attractors form the second level of fractal structure.(ii) The variation of molecular mechanics parameters will influence the structure and area of each attractive basin significantly The above phenomena may become the basis of a new method for solving the troublesome multi-minimum-point problem in molecular mechanics calculation.     

带有随机初值的复值Ginzburg-Landau方程的弱平均动力学*

本文研究了无界域上的带有随机初值的复值Ginzburg-Landau方程.首先, 基于解过程的全局适定性, 建立了带有随机初值的Ginzburg-Landau方程的平均随机动力系统.然后, 证明了弱拉回平均随机吸引子的存在唯一性以及随机吸引子的周期性,并将其进一步推广到加权空间L²(?, L²_σ(R)).     

修正PRP共轭梯度方法求解无约束最优化问题

基于著名的PRP共轭梯度方法,利用CG_DESCENT共轭梯度方法的结构,本文提出了一种求解大规模无约束最优化问题的修正PRP共轭梯度方法。该方法在每一步迭代中均能够产生一个充分下降的搜索方向,且独立于任何线搜索条件。在标准Wolfe线搜索条件下,证明了修正PRP共轭梯度方法的全局收敛性和线性收敛速度。数值结果展示了修正PRP方法对给定的测试问题是非常有效的。     

求解张量随机互补问题的光滑牛顿算法

近年来, 越来越多的人意识到随机互补问题在经济管理中具有十分重要的作用。有学者已将随机互补问题由矩阵推广到张量, 并提出了张量随机互补问题。本文通过引入一类光滑函数, 提出了求解张量随机互补问题的一种光滑牛顿算法, 并证明了算法的全局和局部收敛性, 最后通过数值实验验证了算法的有效性。     

Nonmonotone stabilization methods for nonlinear equations

We are concerned with defining new globalization criteria for solution methods of nonlinear equations. The current criteria used in these methods require a sufficient decrease of a particular merit function at each iteration of the algorithm. As was observed in the field of smooth unconstrained optimization, this descent requirement can considerably slow the rate of convergence of the sequence of points produced and, in some cases, can heavily deteriorate the performance of algorithms. The aim of this paper is to show that the global convergence of most methods proposed in the literature for solving systems of nonlinear equations can be obtained using less restrictive criteria that do not enforce a monotonic decrease of the chosen merit function. In particular, we show that a general stabilization scheme, recently proposed for the unconstrained minimization of continuously differentiable functions, can be extended to methods for the solution of nonlinear (nonsmooth) equations. This scheme includes different kinds of relaxation of the descent requirement and opens up the possibility of describing new classes of algorithms where the old monotone linesearch techniques are replace with more flexible nonmonotone stabilization procedures. As in the case of smooth unconstrained optimization, this should be the basis for defining more efficient algorithms with very good practical rates of convergence.This material is partially based on research supported by the Air Force Office of Scientific Research Grant AFOSR-89-0410, National Science Foundation Grant CCR-91-57632, and Istituto di Analisi dei Sistemi ed Informatica del CNR.     

Existence and asymptotic results for a system of integro-partial differential equations

A non-Fourier phase field model is considered. A global existence result for a Dirichlet, or generalized Neumann, initial-boundary value problem is obtained, followed by a discussion of the regularity and asymptotic properties of solutions ast.This research was supported in part by the National Science Foundation under Grant DMS 91-11794 and in part by the Italian M.U.R.S.T. project Problemi non lineari...Part of this author's work was done while visiting Ohio University.