A note on an SOR-like method for augmented systems

Golub et al. (2001, BIT, 41, 71–85) gave a generalizedsuccessive over-relaxation method for the augmented systems.In this paper, the connection between the SOR-like method andthe preconditioned conjugate gradient (PCG) method for the augmentedsystems is investigated. It is shown that the PCG method isat least as accurate (fast) as the SOR-like method. Numericalexamples demonstrate that the PCG method is much faster thanthe SOR-like method.     

精确搜索下的非线性共轭梯度法

该文提出一种无约束优化非线性共轭梯度法，证明了精确线性 搜索下的全局收敛性。当目标函数为一致凸函数时，证明了算法具有线性收敛速度。数值实验表明算法对于求解实际问题是有效的。     

On the Existence of Focal Points near Closed Geodesics on Surfaces

We establish some criteria for the existence or nonexistence of focal points near closed geodesics on surfaces. These criteria are in terms of the curvature of the manifold along the closed geodesic and the average values of the partial derivatives of the curvature in the direction perpendicular to the geodesic. Our criteria lead to a new family of examples of surfaces with no focal points. We also show that if S is a compact surface with no focal points and an inequality relating the curvature of the surface to the curvature of the horocycles holds, then the horocycles (considered as curves in S) are uniformly C ^2+Lipschitz.     

Reference priors for exponential families with simple quadratic variance function

Reference analysis is one of the most successful general methods to derive noninformative prior distributions. In practice, however, reference priors are often difficult to obtain. Recently developed theory for conditionally reducible natural exponential families identifies an attractive reparameterization which allows one, among other things, to construct an enriched conjugate prior. In this paper, under the assumption that the variance function is simple quadratic, the order-invariant group reference prior for the above parameter is found. Furthermore, group reference priors for the mean- and natural parameter of the families are obtained. A brief discussion of the frequentist coverage properties is also presented. The theory is illustrated for the multinomial and negative-multinomial family. Posterior computations are especially straightforward due to the fact that the resulting reference distributions belong to the corresponding enriched conjugate family. A substantive application of the theory relates to the construction of reference priors for the Bayesian analysis of two-way contingency tables with respect to two alternative parameterizations.     

Flow Search Approach and New Bounds for the m-Step Linear Conjugate Gradient Algorithm

A flow search approach is presented in this paper. In the approach, each iterative process involves a subproblem, whose variables are the stepsize parameters. Every feasible solution of the subproblem corresponds to some serial search stages, the stepsize parameters in different search stages may interact mutually, and their optimal values are determined by evaluating the total effect of the interaction. The main idea of the flow search approach is illustrated via the minimization of a convex quadratic function. Based on the flow search approach, some properties of the m-step linear conjugate gradient algorithm are analyzed and new bounds on its convergence rate are also presented. Theoretical and numerical results indicate that the new bounds are better than the well-known ones.     

Modifications of the Wolfe Line Search Rules to Satisfy Second-Order Optimally Conditions in Unconstrained Optimization

The line search method incorporating the Wolfe conditions is modified to ensure that a descent algorithm terminates in a finite number of steps at an approximate stationary point where the second-order conditions of optimality are satisfied. A simple procedure based on conjugate directions is proposed to determine directions of negative curvature.     

乌骨鸡磷脂侧链脂肪酸的GC-MS分析

用氯仿:甲醇(2:1)超声提取乌骨鸡总磷脂,丙酮脱油精制后,经皂化、甲酯化处理,应用GC-MS联用技术对其侧链脂肪酸组成进行分析,并以面积归一法,计算各脂肪酸的相对百分含量.结果显示,乌骨鸡总磷脂中含有硬脂酸27.46%、花生四烯酸21.39%、油酸18.22%、亚油酸16.67%、棕榈酸12.13%、二十二碳六烯酸(DHA) 2.26%、二十碳三烯酸1.71%、棕榈油酸0.16%.不饱和脂肪酸和多不饱和脂肪酸的含量分别为60.41%和42.03%.乌骨鸡磷脂侧链脂肪酸中高比例的多不饱和脂肪酸和花生四烯酸含量是乌骨鸡磷脂的显著特征.     

关于正定可对称化线性代数方程组的预对称正则化算法

1引言考虑线性代数方程组A_x=b,A∈R~(n×n)非奇异,x,b∈R~n(1)的求解．当系数矩阵是大型稀疏的正定可对称化矩阵,文[1,2]讨论了一类预对称共轭梯度算法(LRSCG算法是其中之一),这类算法的实质是利用非对称的系数矩阵可对称化的性质,并结合共轭梯度法而构造的一种预处理的共轭梯度法[12,16,17]．但非对称的系数     

Zn/AlCl3促进下二硫醚与α,β-不饱和化合物的共轭加成

二芳基二硫醚与锌粉在DMF 中110 ℃反应, 生成二硫醚与锌的复合物; 后者在无水AlCl₃存在下与丙烯酸酯、丙烯腈反应分别生成β-芳硫基丙酸酯和相应的腈, 产率48%～91%.