A Limited-Memory Multipoint Symmetric Secant Method for Bound Constrained Optimization

A new algorithm for solving smooth large-scale minimization problems with bound constraints is introduced. The way of dealing with active constraints is similar to the one used in some recently introduced quadratic solvers. A limited-memory multipoint symmetric secant method for approximating the Hessian is presented. Positive-definiteness of the Hessian approximation is not enforced. A combination of trust-region and conjugate-gradient approaches is used to explore useful information. Global convergence is proved for a general model algorithm. Results of numerical experiments are presented.     

Nonlinear heave-roll coupling and ship rolling

A nonlinear model for simulating the heave-roll motions of ships in following waves is presented. The parametric excitation is modeled by a Hill's type equation, instead of the conventional Mathieu's equation. The model includes not only the linear but also the quadratic coupling term. Instability conditions for parametrically excited rolling motions are derived using the harmonic balance method. The results are verified by numerical analyses. The effects of including the quadratic coupling term on the instability conditions and nonlinear responses are studied. The complex dynamic behaviour of the coupled system in the various instability regions is also investigated. Bifurcations of the flip, fold and pitchfork types are observed in the Poincaré mapping of the numerically simulated responses. Chaotic motions leading to boundary crises and inevitable capsize are also reported.     

Statistical inference based on aligned ranks for two-way MANOVA with interaction

Multiresponse experiments in two-way layouts with interactions, having equal number of observations per cell, are considered. Robust procedures based on aligned ranks for statistical inference of interactions, main effects and an overall mean response in the models are proposed. Large sample properties of the proposed tests, estimators and confidence regions as the cell size tends to infinity are investigated. For the univariate case, it is found that the asymptotic relative efficiencies (ARE's) of the proposed procedures relative to classical procedures agree with the ARE-results of the two-sample rank test relative to the t-test. In addition, robustness due to Huber (1981, Robust Statistics, Wiley, New York) can be drawn.     

Convergence Properties of a Self-adaptive Levenberg-Marquardt Algorithm Under Local Error Bound Condition

We propose a new self-adaptive Levenberg-Marquardt algorithm for the system of nonlinear equations F(x) = 0. The Levenberg-Marquardt parameter is chosen as the product of ‖F_k‖^δ with δ being a positive constant, and some function of the ratio between the actual reduction and predicted reduction of the merit function. Under the local error bound condition which is weaker than the nonsingularity, we show that the Levenberg-Marquardt method converges superlinearly to the solution for δ∈ (0, 1), while quadratically for δ∈ [1, 2]. Numerical results show that the new algorithm performs very well for the nonlinear equations with high rank deficiency. This work is supported by Chinese NSFC grants 10401023 and 10501013, Research Grants for Young Teachers of Shanghai Jiao Tong University, and E-Institute of Shanghai Municipal Education Commission, N. E03004.     

非晶态HoP5O14的蓝绿波段上转换发光的分析

本文报道了脉冲ＤＣＭ染料激光导致的非晶态ＨｏＰ５Ｏ１４的兰绿波段的上转换发光现象，从实验和理论上对其上转换发光的现象，机理和能道行了测量，分析和计算；结果表明对＾５Ｆ３和Ｓ２能级，其上转换发光主要由离间能量传递机理导致；对５Ｇ４和（５Ｇ３Ｇ）５能级，则步进双光子吸收和离子间能量传递共同参与导致了它们的上转换发光。     

Laplacian第一特征值整体曲率Pinching的一个结果

紧致流形上Laplacian的第一特征值的下界估计一直以来是人们非常感兴趣的问题之一.本文在整体曲率Pinching较小的条件之下考虑这个问题,得到了相应几何条件之下的Laplacian第一特征值的一个下界估计.     

A modified trust region method with Beale’s PCG technique for optimization

It is well-known that the conjugate gradient method is widely used for solving large scale optimization problems. In this paper a modified trust-region method with Beale’s Preconditioned Conjugate Gradient (BPCG) technique is developed for solving unconstrained optimization problems. The modified version adopts an adaptive rule and retains some useful information when an unsuccessful iteration occurs, and therefore improves the efficiency of the method. The behavior and the convergence properties are discussed. Some numerical experiments are reported. This work was partially supported by Grant of the National Natural Science Foundation of China, Grant: 20040319003 of the Doctoral Site of the Education Ministry of China, and SRG: 7001428 of City University of Hong Kong.     

A filter-trust-region method for <Emphasis Type="Italic">LC</Emphasis><Superscript>1</Superscript> unconstrained optimization and its global convergence

In this paper we present a filter-trust-region algorithm for solving LC1 unconstrained optimization problems which uses the second Dini upper directional derivative.We establish the global convergence of the algorithm under reasonable assumptions.     

The crossover from classical to quantum regime in the problem of the decay of the metastable state

The probability of the decay of the metastable state has been found as a function of viscosity and temperature. At low temperatures, a classical overbarrier transition changes to the quantum tunneling. At low viscosity in classical and transitive semiquantum region of temperatures a depopulation of the distribution function is significant. The distribution function is shown to satisfy the integral kinetic equation, the kernel of which equals the transition probability. The probability of transitions, induced by the red noise, with the frequency comparable to the transition frequency, is found.     

Design of axisymmetric sandwich plates for alternative loads

The minimal-weight design of sandwich plates whose rigidplastic face sheets obey the Tresca yield condition and which are subjected to two alternative loads is systematically determined by the method of stress variation. It is shown that, when the loads are unidirectional, the general solution for a certain class of edge conditions consists of five fundamentally different designs. The totality of optimal design solutions is depicted in the form of a design chart. A comprehensive example is presented to illustrate the method.This paper is based in part upon a dissertation submitted by the first author to The University of Iowa in partial fulfillment of requirements for the PhD Degree.