Postponing the choice of the barrier parameter in Mehrotra-type predictor–corrector algorithms

Recently Salahi et al. have considered a variant of Mehrotra’s celebrated predictor–corrector algorithm. By a numerical example they showed that this variant might make very small steps in order to keep the iterate in a certain neighborhood of the central path, that itself implies the inefficiency of the algorithm. This observation motivated them to incorporate a safeguard in their algorithmic scheme that gives a lower bound for the step size at each iteration and thus imply polynomial iteration complexity. In this paper we propose a different approach that enables us to have control on the iterates.     

Criss-cross methods: A fresh view on pivot algorithms

Criss-cross methods are pivot algorithms that solve linear programming problems in one phase starting with any basic solution. The first finite criss-cross method was invented by Chang, Terlaky and Wang independently. Unlike the simplex method that follows a monotonic edge path on the feasible region, the trace of a criss-cross method is neither monotonic (with respect to the objective function) nor feasibility preserving. The main purpose of this paper is to present mathematical ideas and proof techniques behind finite criss-cross pivot methods. A recent result on the existence of a short admissible pivot path to an optimal basis is given, indicating shortest pivot paths from any basis might be indeed short for criss-cross type algorithms. The origins and the history of criss-cross methods are also touched upon.     

线性模型中误差为相依情形下误差方差估计的Berry—Esseen界限

本文主要讨论了线性模型中误差为α－混合强一稳序列情形下，误差方差估计的Ｂｅｒｒｙ－Ｅｓｓｅｅｎ界限，其阶为ｎ＾－１／２＋λ。     

Recrystallization of germanium surfaces by femtosecond laser pulses

The damage morphology of germanium surfaces using femtosecond laser pulses of various fluences and number of pulses is reported. The single pulse damage threshold in the present experiment was 9.7±4.0×10⁻¹³ W/cm². The experimental threshold value was compared with theory, considering the damage threshold as the melting threshold. The cooling rate calculated on the basis of present results is 2.4×10^15°C/s. Recrystallization was the common feature of the damage morphology. For fluences greater than the single pulse damage-threshold micropits and spherical grains of micron size were formed in the damaged surface. Ablation (surface removal) was also observed at higher fluences (at two or three times of damage threshold value). The damage morphology, induced by multiple pulses, was unaffected for linear and circular polarization.     

A new algorithm of non-Gaussian component analysis with radial kernel functions

We consider high-dimensional data which contains a linear low-dimensional non-Gaussian structure contaminated with Gaussian noise, and discuss a method to identify this non-Gaussian subspace. For this problem, we provided in our previous work a very general semi-parametric framework called non-Gaussian component analysis (NGCA). NGCA has a uniform probabilistic bound on the error of finding the non-Gaussian components and within this framework, we presented an efficient NGCA algorithm called Multi-index Projection Pursuit. The algorithm is justified as an extension of the ordinary projection pursuit (PP) methods and is shown to outperform PP particularly when the data has complicated non-Gaussian structure. However, it turns out that multi-index PP is not optimal in the context of NGCA. In this article, we therefore develop an alternative algorithm called iterative metric adaptation for radial kernel functions (IMAK), which is theoretically better justifiable within the NGCA framework. We demonstrate that the new algorithm tends to outperform existing methods through numerical examples.     

线性规划Karmarkar算法的一种改进算法及其数值检验

本文给出求解线性规划问题的一种改进的Karmarkar算法IKA.本算法通过施行仿射变换,将已给定的一个可行内点,变成另一空间可行域中所有分量为1的点e,然后从e出发,沿梯度方向进行一维搜索,使问题的目标函数单调下降,并收敛于最优值,因而不需假定目标函数最优值为已知.几个有数百个约束方程和变量的实际算例表明本算法比Karmarkar算法有效.     

Characterization of a dual wavelength fibre laser based-on dumbbell configuration

This paper reports the design of a dual wavelength fibre laser system using a dumbbell shaped configuration. The oscillation of the lasing wavelength is completed via fibre loop mirrors with a tuneable bandpass filter. The output power, side mode suppression ratio and wavelength spacing of the lasers were investigated against the pump power for forward and backward pumping schemes. The output powers of 4.99 and 3.69 dBm at 1545.08 and 1547.28 nm, respectively, for forward pumping scheme. On contrary, the output powers of 1.93 and 2.14 dBm at 1546.12 and 1551.48 nm, respectively, for backward pumping scheme. The peak output powers of less than 1 dB difference are obtained without any adjustment of the intra-cavity loss over a wider spectral range.     

A linear Bragg–Fresnel optics fabricated for 1D focusing of 18 nm X-ray radiation

The theoretical and technique results of a 1D focusing linear Bragg–Fresnel optics working at 18 nm X-ray radiation are given in the present paper. A theoretical method describing its optical performances is introduced briefly, the parameters of the diffraction pattern are presented. The preparation of multilayer mirrors, the decision of X-ray absorber layer thickness and the fabrication process of the diffraction pattern are described. The studied results of thermal and chemical stabilities for Mo/Si multilayer structure are shown. Some measured results for the 1D focusing linear Bragg–Fresnel optics are given.     

A fundamental relationship between the relaxation spectra and the tangent distribution function in the theory of linear viscoelasticity

The tangent distribution function (TDF) is analyzed within the theory of linear viscoelasticity on mechanical properties. A proof is given that both the relaxation and retardation spectra can be derived from the TDF, through a Fredholm integral equation. Furthermore, the relaxation strength can be calculated as a consequence of this relationship. Finally, as an example, the relationship is applied to discrete spectra.     

12 MeV直线感应加速器主开关的优化设计

 介绍了12MeV直线感应加速器主开关的一种优化设计。在保持原有主开关的设计风格和接口结构的条件下，通过优化设计局部结构和调整开关电极尺寸，把主开关的结构电感从63.7nH减小到35nH，使得加速腔的高压脉冲前沿从39.6ns减小到27ns，从而有利于提高12MeV直线感应加速器的性能，验证了优化设计的可行性。