On moments based Padé approximations of ruin probabilities

In this paper, we investigate the quality of the moments based Padé approximation of ultimate ruin probabilities by exponential mixtures. We present several numerical examples illustrating the quick convergence of the method in the case of Gamma processes. While this is not surprising in the completely monotone case (which holds when the shape parameter is less than 1), it is more so in the opposite case, for which we improve even further the performance by a fix-up which may be of special importance due to its potential use in the four moments Gamma approximation.We also review the connection of the exponential mixtures approximation to Padé approximation, orthogonal polynomials, and Gaussian quadrature. These connections may turn out useful for providing rates of convergence.     

范德蒙德行列式与多项式的不动点

以范德蒙德行列式为工具,得到关于多项式不动点的两个新结论,以及线性代数中某已知结论的一个新证明,另外提供实例说明多项式不动点的应用．     

多项式不动点的进一步研究

对文[1]中关于多项式不动点的主要定理进行了修正和发展,进而研究了多项式的广义(高阶)不动点,证明了对任意给定的n个点t_1≤t_2≤…≤t_n,存在唯一的首项系数为α∈R(α≠0)的n次多项式P(x)以它们为广义不动点.     

A note on backward errors for structured linear systems

Let x? be a computed solution to a linear system Ax=b with , where is a proper subclass of matrices in . A structured backward error (SBE) of x? is defined by a measure of the minimal perturbations and such that (1) and that the SBE can be used to distinguish the structured backward stability of the computed solution x?. For simplicity, we may define a partial SBE of x? by a measure of the minimal perturbation such that (2) Can one use the partial SBE to distinguish the structured backward stability of x?? In this note we show that the partial SBE may be much larger than the SBE for certain structured linear systems such as symmetric Toeplitz systems, KKT systems, and dual Vandermonde systems. Besides, certain backward errors for linear least squares are discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

ERROR ANALYSIS FOR SOLVING VANDERMONDE SYSTEM WITH SPECIAL POINTS

The Bjorck and Pereyra algorithms used for solving Vandermonde system of equation are modified for the case where the points are symmetricly situated around zero. The working operation is saved about half. A forward error analysis is presented for the modified algorithms, and it's shown that if the points are situated in some order, the error bound are as good as Higham's result in 1987.     

Estimation of the Combined Effect of Temperature and Carbon Dioxide Pressure on Dissolved Calcium Carbonate Concentration in Oilfield Brines

Calcium carbonate, or calcite, scale is frequently encountered in oilfield operations. In a reservoir, when brine is produced, it is disturbed because the brine is moved to lower temperature and pressure areas. The dissolved concentration of calcium carbonate is greatly influenced by temperature and the partial pressure of carbon dioxide gas over the water. The net result of a drop in temperature and pressure may therefore be an increase or a decrease in the calcium carbonate saturation ratio as determined by the temperature change relative to the pressure change. In this article, a simple Arrhenius-type function is developed to estimate the combined effect of temperature and carbon dioxide pressure on calcium carbonate dissolved concentration in oilfield brines. Estimations are found to be in excellent agreement with reported data in the literature with average absolute deviation being less than 2%. The tool developed in this study can be of immense practical value for engineers to have a quick check of combined effect of temperature and carbon dioxide pressure on calcium carbonate dissolved concentration at various conditions without opting for any field or experimental trials. In particular, engineers would find the approach to be user friendly with transparent calculations involving no complex expressions.     

有限域上的逻辑函数与其Chrestenson谱的关系

本文首先给出了有限域上逻辑函数的Chrestenson线性谱的新定义(不同于文献[1]所给出的),如同Chrestenson循环谱一样,重新定义的Chrestenson线性谱也是有限域Fq到复数域的映射,且证明了它们之间在实质意义下可以相互线性表出;最后我们还用重新定义的Chrestenson线性谱给出了有限域上逻辑函数的反演公式.