界面反射偏振象差分析

在光学没计中,一般认为在同一光波面上,光束具有相同的振幅和偏振状态。事实上,光束经过许多光学元件后,偏振状态会发生变化,特别是入射角和光程的不同,会导致出射光波面上偏振分布不再均匀,形成偏振象差。本文主要就轴上物点发出的光束经过界面反射后的偏振象差方面进行了分析。     

Two differential equation systems for equality-constrained optimization

This paper presents two differential systems, involving first and second order derivatives of problem functions, respectively, for solving equality-constrained optimization problems. Local minimizers to the optimization problems are proved to be asymptotically stable equilibrium points of the two differential systems. First, the Euler discrete schemes with constant stepsizes for the two differential systems are presented and their convergence theorems are demonstrated. Second, we construct algorithms in which directions are computed by these two systems and the stepsizes are generated by Armijo line search to solve the original equality-constrained optimization problem. The constructed algorithms and the Runge–Kutta method are employed to solve the Euler discrete schemes and the differential equation systems, respectively. We prove that the discrete scheme based on the differential equation system with the second order information has the locally quadratic convergence rate under the local Lipschitz condition. The numerical results given here show that Runge–Kutta method has better stability and higher precision and the numerical method based on the differential equation system with the second information is faster than the other one.     

局部对称共形平坦黎曼流形中的极小子流形

对局部对称共形平坦黎曼流形中具有平坦法丛的极小子流形作了一些讨论，得到了极小子流形是全测地的两个充分条件。     

2‐Cyanoprop‐2‐yl dithiobenzoate mediated reversible addition–fragmentation chain transfer polymerization of acrylonitrile targeting a polymer with a higher molecular weight

The reversible addition–fragmentation chain transfer (RAFT) polymerization of acrylonitrile (AN) mediated by 2‐cyanoprop‐2‐yl dithiobenzoate was first applied to synthesize polyacrylonitrile (PAN) with a high molecular weight up to 32,800 and a polydispersity index as low as 1.29. The key to success was ascribed to the optimization of the experimental conditions to increase the fragmentation reaction efficiency of the intermediate radical. In accordance with the atom transfer radical polymerization of AN, ethylene carbonate was also a better solvent candidate for providing higher controlled/living RAFT polymerization behaviors than dimethylformamide and dimethyl sulfoxide. The various experimental parameters, including the temperature, the molar ratio of dithiobenzoate to the initiator, the molar ratio of the monomer to dithiobenzoate, the monomer concentration, and the addition of the comonomer, were varied to improve the control of the molecular weight and polydispersity index. The molecular weights of PANs were validated by gel permeation chromatography along with a universal calibration procedure and intrinsic viscosity measurements. ¹H NMR analysis confirmed the high chain‐end functionality of the resultant polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1272–1281, 2007     

热等离子体裂解天然气制备C2烃

采用氮气热等离子体来裂解天然气制备乙炔乙烯,着重研究了天然气转化率和乙炔、乙烯收率随氮气流量和天然气流量的变化.结果表明,天然气流量与氮气流量之比为11时,可得到较好的结果.当等离子体功率为15kW、天然气流量为3Nm3*h-1、氮气流量为3Nm3*h-1时得到最好的结果.这时天然气转化率为57%,乙炔、乙烯的收率分别为34%和9%;乙炔在反应气中的体积浓度为7.5%,与部分氧化法相似;扣除不参加反应的氮气,乙炔在气相产品中的体积浓度为13.2%,与热力学平衡计算结果基本符合.     

有限混合Gamma分布的拓扑稠密性证明

首先给出了有限混合Erlang分布在正实数轴上所有概率分布中稠密的理论证明,进而给出了混合Gamma分布具有稠密性的结论,说明有限混合Gamma分布具有广泛的适用性,可以用来刻画正实数轴上的任意随机变量.     

Ring head and single pole head recording performance on 3D random SOMA media

Currently, self-organized magnetic array (SOMA) is a non-oriented media, with randomly distributed easy axis directions. We investigate the recording performance of SOMA under two different head types—Ring Head (RH) and single pole head (SPH). Our results show an interesting dependence of the recorded transition pattern on the field strength of RH, where a weak RH field generates longitudinal transition pattern and a strong RH field generates a perpendicular transition pattern in the media. The SPH only generates perpendicular transition patterns and has a higher signal-to-noise ratio (SNR) than that of the RH.     

The compound binomial risk model with time-correlated claims

In this paper, we consider the compound binomial risk model with the time-correlated claims. It is assumed that every main claim will produce a by-claim but the occurrence of the by-claim may be delayed. We obtain the recursive formula of the joint distribution of the surplus immediately prior to ruin and deficit at ruin. Furthermore, the ruin probability is given by means of ruin probability and the deficit at ruin of the classical compound binomial risk model. Finally, we derive an upper bound for the ruin probability.     

Horizontal Connection and Horizontal Mean Curvature in Carnot Groups

In this paper we give a geometric interpretation of the notion of the horizontal mean curvature which is introduced by Danielli Garofalo-Nhieu and Pauls who recently introduced sub- Riemannian minimal surfaces in Carnot groups. This will be done by introducing a natural nonholonomic connection which is the restriction （projection） of the natural Riemannian connection on the horizontal bundle. For this nonholonomic connection and （intrinsic） regular hypersurfaces we introduce the notions of the horizontal second fundamental form and the horizontal shape operator. It turns out that the horizontal mean curvature is the trace of the horizontal shape operator.     

Bivariate Recursive Equations on Excess-of-loss Reinsurance

This paper investigates bivariate recursive equations on excess-of-loss reinsurance. For an insurance portfolio, under the assumptions that the individual claim severity distribution has bounded continuous density and the number of claims belongs to R1 （a, b） family, bivariate recursive equations for the joint distribution of the cedent＇s aggregate claims and the reinsurer＇s aggregate claims are obtained.