非线性最小二乘问题的信赖域方法

本文提出一个新的非线性最小二乘的信赖域方法,在该方法中每个信赖域子问题只需要一次求解,而且每次迭代的一维搜索步长因子是给定的,避开一维搜索的环节,大大地提高了算法效率.文中证明了在一定的条件下算法的全局收敛性.     

统计深度的几何推广

改进统计深度的定义,并将点的深度概念推广到直线与平面的深度,由此得到深度计算的基本定理和深度的一系列性质.最后讨论应用展望.     

Enhanced nonlinearity in photonic crystal fiber by germanium doping in the core region

Germanium doping in silica can be used as a method for nonlinearity enhancement.Properties of the enhanced nonlinearity in photonic crystal fiber(PCF)with a GeO2-doped core are investigated theoretically by using all-vector finite element method.Numerical result shows that the nonlinear coefficient of PCF is greatly enhanced with increasing doping concentration,furthermore,optimal radius of the doped region should be considered for the desired operating wavelength.     

An explanation for deviations from the quark number scaling of elliptic flows in low pT region

We carry out a systematic study of the different contributions to the deviations of the elliptic flows from the quark number scaling in high energy heavy ion collision in a quark combination model.The effects that we considered are:the resonance decay,the flavor dependence of the quark elliptic flow and the combination of quarks/antiquarks with slightly different transverse momenta.Our results show that the deviations observed in experiments can be well reproduced within the combination framework if all the three effects are considered. We make a detailed analysis of the different contributions using a Monte-Carlo program and suggest measuring the quark number scaling in intermediate pT range more precisely.     

Systematics on fission fragment mass distribution of neutron induced 235U fission

Based on the neutron induced fission fragment mass distribution data up to neutron energy 20 MeV measured with the double kinetic energy method (KEM) and the radio active method (RAM), the systematics of fission fragment mass distribution was investigated by using 5 Gaussian model and the systematics parameters were obtained by fitting the experimental data. With the systematics, the yields of any mass A and at any energy in the region from 0 to 20 MeV of neutron energy can be calculated. The calculated results could well reproduce the experimental data measured with KEM, but show some systematical deviation from the data measured by RAM, which reflects some systematical deviations between the two kinds of measured data.The error of systematics yield was calculated in an exact error transformation way, including from the error of the experimental yield data to the error of the discrete parameters, then to the systematics parameters,and at last to the yield calculated with systematics.     

SUPPLEMENT TO “PASSAGE, BLOCKADE, SINK AND SOURCE OF A PLANAR DYNAMICAL SYSTEM”

A Theorem is given on the number of passages passing throgh a multiply-connected region,which corrects a wrong conjecture in a former paper of the author.     

Numerical experience with the truncated Newton method for unconstrained optimization

The truncated Newton algorithm was devised by Dembo and Steihaug (Ref. 1) for solving large sparse unconstrained optimization problems. When far from a minimum, an accurate solution to the Newton equations may not be justified. Dembo's method solves these equations by the conjugate direction method, but truncates the iteration when a required degree of accuracy has been obtained. We present favorable numerical results obtained with the algorithm and compare them with existing codes for large-scale optimization.     

A CLASS OF TRUST REGION METHODS FOR LINEAR INEQUALITY CONSTRAINED OPTIMIZATION AND ITS THEORY ANALYSIS Ⅱ. LOCAL CONVERGENCE RATE AND NUMERICAL TESTS

In this paper we prove that a class of trust region methods presented in part Ⅰ is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatures have demonstrated that our algorithm is effective.     

An optimum tolerance region for multivariate regression

A tolerance region is a map from the sample space of one statistical model to the event space of a second statistical model having the same parameter. This paper derives an optimum β-expectation tolerance region for the multivariate regression model. A measure of power is proposed and evaluated.