新的对角形式快速多极边界元法求解声学Helmholtz方程

传统外部声学Helmholtz边界积分方程无法在个人计算机上求解大规模工程问题. 为了有效解决这个问题, 将快速多极方法引入到边界积分方程中, 加速系统矩阵方程组的迭代求解. 由于在边界积分方程中引入基本解的对角形式多极扩展, 新的快速多极边界元法的计算效率与传统边界元相比显著提高, 计算量和存储量减少到O(N)量级(N为问题的自由度数). 包括含有420000个自由度的大型潜艇模型数值算例验证了快速多极边界元法的准确性和高效性, 清楚表明新算法在求解大规模声学问题中的优势,     

利用凸优化进行多用户OFDM通信系统的简化设计

以有限发射功率、迫零均衡为限定条件,利用现代凸优化理论和算法进一步进行多用户通信系统收发器的简化设计。将半正定规划模型等效转化为二阶锥规划模型。二阶锥规划模型将更加简单而且计算复杂度获得很大的改善。借助优化软件SeDuMi的计算机仿真表明:设计的收发器比现存收发     

二维双曲型方程初边值问题的块三对角并行求解算法

讨论用块三对角线性方程组的可扩展并行算法,求解带Dirichlet边界条件的一阶二维双曲型方程初边值问题。用本文方法在上海大学超级计算机"自强3000"上进行数值实验,实验结果与理论分析一致。在保证精度的前提下,得到线性加速比,并行效率达到90%以上。     

The Bott-Borel-Weil Theorem for direct limit groups

We show how highest weight representations of certain infinite dimensional Lie groups can be realized on cohomology spaces of holomorphic vector bundles. This extends the classical Bott-Borel-Weil Theorem for finite-dimensional compact and complex Lie groups. Our approach is geometric in nature, in the spirit of Bott's original generalization of the Borel-Weil Theorem. The groups for which we prove this theorem are strict direct limits of compact Lie groups, or their complexifications. We previously proved that such groups have an analytic structure. Our result applies to most of the familiar examples of direct limits of classical groups. We also introduce new examples involving iterated embeddings of the classical groups and see exactly how our results hold in those cases. One of the technical problems here is that, in general, the limit Lie algebras will have root systems but need not have root spaces, so we need to develop machinery to handle this somewhat delicate situation.

     

一类大系统目标规划问题分解算法中最优解之间的关系

将一类大系统目标规划问题分解为若干个子问题,研究了原问题的最优解和各个子问题最优解之间的关系,并讨论了原问题最优解的判别条件。     

Existence, uniqueness and stability of C m solutions of iterative functional equations

In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f ⁿ (x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ℝ,G∈C ^m (J ⁿ⁺¹, ℝ) andn ≥ 2. Using the method of approximating fixed points by small shift of maps, choosing suitable metrics on functional spaces and finding a relation between uniqueness and stability of fixed points of maps of general spaces, we prove the existence, uniqueness and stability ofCm solutions of the above equation for any integer m ≥ 0 under relatively weak conditions, and generalize related results in reference in different aspects.     

A Counterexample to 0-Diagonal Quasiconcavity in a Minimax Inequality

In this paper, a very simple example shows that, in a n- person nonzero-sum game, the quasiconvexity of the payoff functions is not sufficient to establish the 0-diagonal quasiconcavity in the Fan minimax inequality.     

The Effects of Charged Amino Acid Side-Chain Length on Diagonal Cross-Strand Interactions between Carboxylate- and Ammonium-Containing Residues in a β-Hairpin

The β-sheet is one of the common protein secondary structures, and the aberrant aggregation of β-sheets is implicated in various neurodegenerative diseases. Cross-strand interactions are an important determinant of β-sheet stability. Accordingly, both diagonal and lateral cross-strand interactions have been studied. Surprisingly, diagonal cross-strand ion-pairing interactions have yet to be investigated. Herein, we present a systematic study on the effects of charged amino acid side-chain length on a diagonal ion-pairing interaction between carboxylate- and ammonium-containing residues in a β-hairpin. To this end, 2D-NMR was used to investigate the conformation of the peptides. The fraction folded population and the folding free energy were derived from the chemical shift data. The fraction folded population for these peptides with potential diagonal ion pairs was mostly lower compared to the corresponding peptide with a potential lateral ion pair. The diagonal ion-pairing interaction energy was derived using double mutant cycle analysis. The Asp2-Dab9 (Asp: one methylene; Dab: two methylenes) interaction was the most stabilizing (−0.79 ± 0.14 kcal/mol), most likely representing an optimal balance between the entropic penalty to enable the ion-pairing interaction and the number of side-chain conformations that can accommodate the interaction. These results should be useful for designing β-sheet containing molecular entities for various applications.     

非均匀对角减载最小方差无失真响应多目标分辨

针对最小方差无失真响应(Minimum Variance Distortionless Response,MVDR)方法在起伏非相关噪声环境下多目标分辨性能严重下降的问题,提出一种非均匀对角减载MVDR (Inhomogeneous Diagonal Unloading MVDR,IDU-MVDR)方法。该方法首先对协方差矩阵进行非均匀对角减载,然后实施MVDR方法。各阵元上的对角减载量通过求解半正定优化问题获得,优化问题中最大化减载量之和,但约束减载后协方差矩阵的最小特征值是一个较小的正值。数值仿真表明,IDUMVDR方法可通过非均匀对角减载消除大部分非相关噪声,但保留小部分噪声分量.因此IDU-MVDR方法较MVDR方法分辨力更高,空间谱中背景级更低、弱目标谱峰更加明显,并且具备一定的稳健性.海上实验结果与数值仿真相一致,验证了IDU-MVDR方法的有效性.