正负相间齐次式之和

设A_(t9)B_t为m阶矩阵或复数,d_t为复数(1≤y≤s)r,s为正整数,本文讨论如下形式的齐次式之和 sum from k=0 to n(-1)~k sum from t=1 to 5 [A_t Kd_t B_t]~r得到了此和的计算公式     

曲面片角点扭矢的相容

本文根据Gregory修正曲面片的方法,利用双三次Coons曲面片与双三次Bezier曲面片之间的相互关系,提出了扭矢相容性修正的双三次Bezier曲面的构造方法,从而避免了曲面片连接或插值时由于扭夫相容带来的局限性,使得复杂曲面的造型设计成为可能。     

Non-minimal sums of disjoint products

We refine a conjecture of M.O. Locks and J.M. Wilson [Reliab Eng Syst Saf 1994;46:283–286] regarding disjoint forms of the Abraham reliability problem. We also present other examples of reliability problems with the interesting property that their minimal disjoint forms do not arise from the familiar tautology .     

Sum Coloring of Bipartite Graphs with Bounded Degree

We consider the Chromatic Sum Problem on bipartite graphs which appears to be much harder than the classical Chromatic Number Problem. We prove that the Chromatic Sum Problem is NP-complete on planar bipartite graphs with $\Delta \leq 5$, but polynomial on bipartite graphs with $\Delta \leq 3$, for which we construct an $O(n^{2})$-time algorithm. Hence, we tighten the borderline of intractability for this problem on bipartite graphs with bounded degree, namely: the case $\Delta =3$ is easy, $% \Delta =5$ is hard. Moreover, we construct a $27/26$-approximation algorithm for this problem thus improving the best known approximation ratio of $10/9$.     

一种精确而快速的块匹配算法

为提高基于块的运动预测的搜索精度,该文基于块匹配准则,提出最小绝对差分误差和(SADD)算法。SADD以SAD为基础,利用块匹配中相邻像素点误差之间相关性,将块内各像素误差按一定顺序进行差分,消除了相邻点误差之间的冗余。该算法更精确地表达了块与快之间的相似程度。实验结果表明,该算法可有效降低码率,提高PSNR值,而且其鲁棒性好,可适用于各种序列。     

多元物系中的虚拟溶解度和迭加原理

通过对酮麝香多元物系溶液结晶的研究,首次提出了多元物系中关于“虚拟溶解度”和“迭加原理”的概念。经实验验证,理论预测与试验相符;提出了可以利用某物质真实溶解度来推算它的虚拟溶解度的计算公式,并指出虚拟溶解度和溶剂化条件近似无关;给出了计算多元物系中某一组分总溶解度的关联式;迭加原理用于工程计算可使计算大大简化。     

N-甲酰吗啉芳烃萃取塔等温流率加和法模拟计算

Ｎ－甲酰吗啉是新一代芳烃萃取溶剂。以平衡级的概念为基础,应用等温流率加和法,建立了包括相平衡、物料平衡、分子分数加和式在内的多元体系液－液萃取过程的通用模拟计算程序,在不同的理论板数、溶剂比和回流比下,对以Ｎ－甲酰吗啉为溶剂从重整脱戊烷油中分离芳烃的萃取塔进行了模拟计算。在给定的条件下,得出了一组较适宜的操作参数。当操作温度为６０℃、理论塔板数为６、进料板为５、溶剂比为２．５、溶剂回收率为１．０和塔底萃取相回流比为０．７时,苯的收率可达９９．９９％,甲苯收率可达９９．９７％。     

LMI-based model predictive control for switched nonlinear systems

This paper proposes an LMI approach to model predictive control of nonlinear systems with switching between multiple modes. In this approach, at each mode, the nonlinear system is divided to a linearized model in addition to a nonlinear term. A sum of squares (SOS) optimization problem is presented to find a quadratic bound for the nonlinear part. The stability condition of the switching system is obtained by using a discrete Lyapunov function and then the sufficient state feedback control law is achieved so that guarantees the stability of the system and also minimizes an infinite prediction horizon performance index. Moreover, two other LMI optimization problems are solved at each mode in order to find the maximum area region of convergence of the nonlinear system inscribed in the region of stability. The performance and effectiveness of the proposed MPC approach are illustrated by two case studies.     

Krein-space approach to robust filtering for uncertain systems with time-varying bias

In this paper, a novel Krein space approach to robust estimation for uncertain systems with accumulated bias is proposed. The bias is impacted by system uncertainties and exists in both state transition and observer matrices. Initial conditions and cross-correlated uncertainty inputs are described by the sum quadratic constraint （SQC）. Without modifying the SQC, the minimal state of the SQC is obtained through Krein space method. The inertia condition for a minimum of a deterministic quadratic form is derived when the coefficient of observer uncertainty input is non-unit matrix. Recursions of Krein space state filtering and bias filtering are developed respectively. Since the cross correlation between uncertainties is considered, a cross correlation gain is introduced into the posteriori estimator. Finally, a numerical example illustrates the performance of the proposed filter.     

A linear algebra method to decompose forms whose length is lower than the number of variables into weighted sum of squares

In this paper, an algorithm based on linear algebra tools is proposed to compute a weighted sum of squares decomposition of a given form whose length is lower than the number of variables. Such an objective is pursued by using linear algebra techniques to perform tasks that are usually carried out through computational algebraic geometry tools. Several examples are reported to show that the use of linear algebra rather than algebraic geometry leads to a reduction of the execution times, without affecting the effectiveness of the algorithm. Applications of the given procedure to system analysis and to control design problems are reported as well as a detailed complexity analysis.