相关系数与相关性度量

研究了度量相关性的两个主要工具:线性相关系数和尾部相关系数.线性相关系数反映了变量间的线性相关性,这对于一般的椭圆型分布是合适的.但如果随机变量具有不对称的尾部变化特征时,要用尾部相关系数描述它们之间的相关性.通过相关函数C opu la,对沪深股市的尾部相关系数进行了定量分析.结果表明:沪深股市具有较强的相关性.     

Linear least squares problems with data over incomplete grids

The paper addresses bivariate surface fitting problems, where data points lie on the vertices of a rectangular grid. Efficient and stable algorithms can be found in the literature to solve such problems. If data values are missing at some grid points, there exists a computational method for finding a least squares spline by fixing appropriate values for the missing data. We extended this technique to arbitrary least squares problems as well as to linear least squares problems with linear equality constraints. Numerical examples are given to show the effectiveness of the technique presented. AMS subject classification (2000)  65D05, 65D07, 65D10, 65F05, 65F20     

Some geometrical aspects of semidefinite linear complementarity problems

This article studies some geometrical aspects of the semidefinite linear complementarity problem (SDLCP), which can be viewed as a generalization of the well-known linear complementarity problem (LCP). SDLCP is a special case of a complementarity problem over a closed convex cone, where the cone considered is the closed convex cone of positive semidefinite matrices. It arises naturally in the unified formulation of a pair of primal-dual semidefinite programming problems. In this article, we introduce the notion of complementary cones in the semidefinite setting using the faces of the cone of positive semidefinite matrices and show that unlike complementary cones induced by an LCP, semidefinite complementary cones need not be closed. However, under R₀-property of the linear transformation, closedness of all the semidefinite complementary cones induced by L is ensured. We also introduce the notion of a principal subtransformation with respect to a face of the cone of positive semidefinite matrices and show that for a self-adjoint linear transformation, strict copositivity is equivalent to strict semimonotonicity of each principal subtransformation. Besides the above, various other solution properties of SDLCP will be interpreted and studied geometrically.     

Linear Relations, Differential Inclusions, and Degenerate Semigroups

A generalized linear differential equation in a Banach space is studied. The construction of a phase space and solutions with the help of the spectral theory of linear operators, ergodic theorems, and degenerate semigroups of linear operators is carried out.     

Bayes估计的进一步研究及其Pitman最优性

对线性模型参数,讨论了Bayes估计的Pitman最优性,将已有结果进行了改进,去掉了附加条件,证明了在Pitman准则下,Bayes估计一致优于最小二乘估计(LSE),在此基础上,提出了一种基于先验信息的方差分量估计,通过和基于LSE的方差分量估计作比较,证明了新估计是无偏估计且有更小的均方误差．最后,证明了在Pitman准则下生长曲线模型参数的Bayes估计优于最佳线性无偏估计．     

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??We study the linear quadratic optimal stochastic control problem which is jointly driven by Brownian motion and L\'{e}vy processes. We prove that the new affine stochastic differential adjoint equation exists an inverse process by applying the profound section theorem. Applying for the Bellman's principle of quasilinearization and a monotone iterative convergence method, we prove the existence and uniqueness of the solution of the backward Riccati differential equation. Finally, we prove that the optimal feedback control exists, and the value function is composed of the initial value of the solution of the related backward Riccati differential equation and the related adjoint equation.     

电火花铣削钛合金电极损耗在线补偿研究

根据电火花铣削等损耗理论，对用电火花铣削钛合金的加工中电极损耗补偿作了分析阐述。并根据正交试验的数据对理论分析结果进行对比，同时给出了一定的结论和建议。     

Vector-Orthogonality and Lanczos-Type Methods

A method for solving a linear system is defined. It is a Lanczos-type method, but it uses formal vector orthogonality instead of scalar orthogonality. Moreover, the dimension of vector orthogonality may vary which gives a large freedom in leading the algorithm, and controlling the numerical problems. The ideas of truncated and restarted methods are revisited. The obtained residuals are exactly orthogonal to a space of increasing dimension. Some experiments are done, the problem of finding automaticaly good directions of projection remains partly open.     

基于单纯形方法的双层线性规划全局优化算法

通过分析双层线性规划可行域的结构特征和全局最优解在约束域的极点上达到这一特性,对单纯形方法中进基变量的选取法则进行适当修改后,给出了一个求解双层线性规划局部最优解方法,然后引进上层目标函数对应的一种割平面约束来修正当前局部最优解,直到求得双层线性规划的全局最优解.提出的算法具有全局收敛性,并通过算例说明了算法的求解过程.     

Restorations of punctured languages and similarity of languages

Punctured languages are languages whose words are partial words in the sense that the letters at some positions are unknown. We investigate to which extent restoration of punctured languages is possible if the number of unknown positions or the proportion of unknown positions per word, respectively, is bounded, and we study their relationships for different boundings. The considered restoration classes coincide with similarity classes according to some kind of similarity for languages. Thus all results we can also formulate in the language of similarity. We show some hierarchies of similarity classes for each class from the Chomsky hierarchy and prove the existence of linear languages which are not δ ‐similar to any regular language for any δ < ½. For δ ≥ ½ this is unknown but it could only be possible in the case of non‐slender linear languages. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)