Computation of the eigenvalues of Sturm-Liouville problems with parameter dependent boundary conditions using the regularized sampling method

The purpose in this paper is to compute the eigenvalues of Sturm-Liouville problems with quite general separated boundary conditions nonlinear in the eigenvalue parameter using the regularized sampling method, an improvement on the method based on Shannon sampling theory, which does not involve any multiple integration and provides higher order estimates of the eigenvalues at a very low cost. A few examples shall be presented to illustrate the power of the method and a comparison made with the the exact eigenvalues obtained as squares of the zeros of the exact characteristic functions.

     

最小费用k度限制树对策

本在Glover—Klingman算法及最小费用支撑树对策的基础上，讨论了最小费用k度限制树对策问题．利用威胁、旁支付理论制订了两种规则，并利用优超、策略等价理论分别给出了在这两种规则下最小费用k度限制树对策核心中的解，从而证明了在这两种规则下其核心非空．     

一般非均匀凸介质迁移算子本征值的分布

本文讨论一般非均匀凸介质所确定的迁移算子的本征值的分布问题，利用Ｈｉｌｂｅｒｔ空间的Ｈ算子理论，完整地解决了一般非均匀凸介质中迁移算子本征值的分布问题，若｛λｎ｝ｎ＝１＾∞是迁移算子本征值的一种计数，我们证明了Σ↓ｎ＝１↑∞ｅ＾６Ｒｅλｎτ〈＋∞，其中τ是粒子的最大逃逸时间，并对本征值的发散程度以及本征值的个数函数作了相应的讨论。     

Hermitian阵的 Hadamard积的Schur补的一些不等式（英文）

本文得到了正定Hermitian阵的Hadamard积的Schur补的一些不等式，进而，给出了他们的一些应用，这些改进了近期的一些结束．     

The Two-Point Codes with the Designed Distance on a Hermitian Curve in Even Characteristic

In Homma M and Kim SJ [2], the authors considered two-point codes on a Hermitian curve defined over fields of odd characteristic. In this paper, we study the geometry of a Hermitian curve over fields of even characteristic and classify the two-point codes whose minimum distances agree with the designed ones.     

An Improved Extra-Gradient Method for Minimizing a Sum of p-norms—A Variational Inequality Approach

This paper presents a variational inequality (VI) approach to the problem of minimizing a sum of p-norms. First the original problem is reformulated as an equivalent linear VI. Then an improved extra-gradient method is presented to solve the linear VI. Applications to the problem of p-norm Steiner Minimum Trees (SMT) shows that the proposed method is effective. Comparison with the general extra-gradient method is also provided to show the improvements of the new method.     

半线性方程组边界层解的存在性

本文利用隐函数定理讨论了含小参数的半线性椭圆方程组边界层解的存在性．     

Quadratically constrained minimum cross-entropy analysis

Quadratically constrained minimum cross-entropy problem has recently been studied by Zhang and Brockett through an elaborately constructed dual. In this paper, we take a geometric programming approach to analyze this problem. Unlike Zhang and Brockett, we separate the probability constraint from general quadratic constraints and use two simple geometric inequalities to derive its dual problem. Furthermore, by using the dual perturbation method, we directly prove the strong duality theorem and derive a dual-to-primal conversion formula. As a by-product, the perturbation proof gives us insights to develop a computation procedure that avoids dual non-differentiability and allows us to use a general purpose optimizer to find an-optimal solution for the quadratically constrained minimum cross-entropy analysis.     

甲烷—空气燃烧中NOx生成的简化模型研究

用特征值－特征向量法对甲烷－空气燃烧时ＮＯＸ生成的化学反应机理进行了简化，得到了仅由１５个基元以应组成的简化反应模型。对比计算结果表明，该模型能在较宽燃空比内与全面模型很好吻合，因而可望用于燃烧过程数值模拟时对ＮＯＸ生成的预测     

TB-curve, a New 2-D Graphical Representation of DNA Sequences

Based on the classifications of the four nucleic acid bases, we introduce a new 2-D method of DNA representation: TB-curve, which avoids loss of information accompanying alternative 2-D representation in which the curve standing for DNA overlaps and intersects itself. The method is illustrated on the coding sequence of the first exon of human beta-globin gene.