基于凸多面体方法的时滞和连续系统稳定性分析

针对一类状态向量中含有时滞和的连续系统,研究其时滞相关稳定性问题。利用凸组合方法和积分不等式并构造合适的李雅普诺夫泛函,以线性矩阵不等式形式给出了保证系统稳定的时滞相关充分条件,该线性矩阵不等式形式的系统稳定条件易于验证。由于在对李雅普诺夫泛函求导过程中使用了凸多面体方法,使得所得到的结论具有更小的保守性,仿真算例验证了结论的有效性。     

线性控制系统的无界多面体不变集

本文利用非光滑分析方法,讨论了线性控制系统的无界多面体不变集问题.当无界多面体的极方向满足一定条件时,得到了该无界多面体为一类线性控制系统弱不变集的判别方法.然后在更一般的线性控制系统下给出了无界多面体为强不变集的充分条件.最后给出两个应用实例.     

Solvent-controlled synthesis of mesoporous CoO with different morphologies as binder-free anodes for lithium-ion batteries

The solvent-controlled synthesis of mesoporous CoO with different morphologies was investigated through a facile route including hydrothermal reaction and subsequent calcination. By altering the solvent of reaction, CoO nanowires (CoO-NWs) and CoO polyhedron (CoO-PHn) were favorably loaded on nickel foam with robust adhesion. Compared with CoO-PHn, CoO-NWs for lithium storage has enhanced electrochemical performance in term of high reversible capacity and extraordinary rate capability. After 80 cycles, an outstanding reversible specific capacity for CoO-NWs was 1398?mA?h/g at a current density of 200?mA/g. Furthermore, a reversible specific capacity was up to 1175?mA?h/g even at a current density of 1000?mA/g. The extraordinary electrochemical property was owing to the presence of free voids, which significantly buffered the mechanical stress during the insertion/de-insertion process. In addition, one-dimensional (1D) morphology ensured a relatively short transmission route to accelerate electron transport.     

PID Stabilization of Retarded‐Type Time‐Delay System

An analytical method is proposed to construct the stabilizing PID region of a retarded‐type time‐delay system, based on Pontryagin's results and a generalization of the Hermite‐Biehler theorem. It is shown that the stable region in the (k_i, k_d)‐plane is made up of some convex polygons for a fixed k_p, and the whole region in the (k_p, k_i, k_d)‐space is comprised of some polyhedrons, each of which is mapped onto a real used string. Additionally, a method for determining the feasible k_p‐intervals is given in this paper. Two examples are employed to illustrate and verify the construction procedure of the stabilizing PID region in detail.     

一组广义余弦定理探究

在引入边矢量及面矢量概念的基础上 ,以类比作为手段 ,对余弦定理进行由平面三角形到空间多边形乃至任意多面体的一系列推广 ,得出了形式对称一致的一组广义余弦定理 ,并给出了其简捷严谨的证明。     

Method of ordering the values of a linear function on a set of permutations

The paper deals with a new method of solving a combinatorial problem with account for the properties of the set of permutations and its structure. Using this method, the values of the linear objective function are sequenced and the set of permutations is decomposed over hyperplanes, with account of element recurrences. This makes it possible to develop an algorithm of finding the point (an element of the set of permutations) at which the objective function attains a given value. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 50–61, March–April 2009.     

基于面向对象八叉树的虚拟漫游碰撞检测

借助面向对象概念,根据层数和叶结点链表个数上限来构建存储场景物体信息的高效八叉树。每个叶结点指向记录对应空间区域内物体信息的链表,每个空间物体信息链表按照其对象大小降序排列。在逐步求精阶段用降序包围球遍历链表进行检测,然后根据凸多面体剖分算法,使用主从MPI模式并行处理以实现精确碰撞检测。该方法利用物体空间位置关系进行碰撞检测,毋需存储大量空间物体三角面片。在基于粒子系统的土壤可视化漫游中的运行结果表明,该方法精度高、实时性好,具有一定的研究和应用价值。     

采用单幅草图的正交多面体模型生成方法

为便于用户在工程设计时使用草图进行三维模型设计,提出一种从单幅草图生成正交多面体模型的方法.根据正交多面体模型的结构特点定义了建模过程中的特征层次体系及其转换规则,通过规则推理实现各层次特征的转换,以支持用户使用简图方式快速地生成多面体模型;同时,使用决策树管理转换规则集合实现对规则的训练和更新,以保证规则集的可拓展性和鲁棒性.实验结果表明:该方法能生成多种复杂的正交多面体模型,且决策树方法能有效地支持对规则集合的训练和更新.     

任意多面体的四面体剖分算法

该文提出一种将任意多面体剖分为四面体的算法,该算法首先依据顶点凸凹性算法判定多面体顶点的凸凹性性质,再寻找符合剖分条件的凸顶点,将该凸顶点的凸空间从原多面体中剖分出去,得到一个新的多面体,剖分出来的凸空间再分为多个四面体;再重复对新的多面体进行剖分,直到剖分完毕。该算法的平均时间复杂度为O(N+M),其中N为多面体的凸顶点数目,M为多面体的凹顶点数目。