RS码时域编码算法及其计算机模拟

RS码被广泛应用于数据通信和存储系统的差错控制中。从RS码的结构出发,给出了RS码时域编码的基本过程,并对影响RS码编码器设计复杂度的因素进行了分析讨论;采用基于有限域中多项式乘法理论的快速有限域乘法器的设计,得到了简单的有限域上乘积运算算法。该算法中乘数与被乘数都采用标准基来表示,而不需基与基的转换;最后对RS(255,223)码编码器的设计过程进行了计算机模拟。     

Efficiently counting affine roots of mixed trigonometric polynomial systems

Estimating the number of isolated roots of a polynomial system is not only a fundamental study theme in algebraic geometry but also an important subproblem of homotopy methods for solving polynomial systems. For the mixed trigonometric polynomial systems, which are more general than polynomial systems and rather frequently occur in many applications, the classical B′ezout number and the multihomogeneous B′ezout number are the best known upper bounds on the number of isolated roots. However, for the deficient mixed trigonometric polynomial systems, these two upper bounds are far greater than the actual number of isolated roots. The BKK bound is known as the most accurate upper bound on the number of isolated roots of a polynomial system. However, the extension of the definition of the BKK bound allowing it to treat mixed trigonometric polynomial systems is very difficult due to the existence of sine and cosine functions. In this paper, two new upper bounds on the number of isolated roots of a mixed trigonometric polynomial system are defined and the corresponding efficient algorithms for calculating them are presented. Numerical tests are also given to show the accuracy of these two definitions, and numerically prove they can provide tighter upper bounds on the number of isolated roots of a mixed trigonometric polynomial system than the existing upper bounds, and also the authors compare the computational time for calculating these two upper bounds.     

考虑相关性的串联系统动态机会成组维修优化

多部件串联系统存在复杂的相关性,制定最优的维修策略以保持最低的维护成本是设备科学管理的关键之一。本文提出多部件串联系统动态成组机会维修策略。该策略在考虑部件间的经济相关性和结构相关性的基础上,以节省的总维修成本最大为目标,构建了有限时间内系统维修优化模型;应用了遗传算法对系统各部件进行分组优化,解决了NP难问题;应用滚动计划,将长期计划与短期计划相结合,实现对维修计划的动态实时更新。案例分析表明,该方法能够有效地降低维修成本,值得在工程实践中借鉴。     

电磁跟踪系统磁场畸变规律数值模拟及校正方法

电磁跟踪系统参数定位精度易受工作环境中金属物体的影响。为了研究由于金属干扰导致电磁跟踪系统空间磁场的畸变规律,采用基于消息传递模式的网络并行计算系统和区域分割技术实现了并行时域有限差分算法。引入快速傅里叶变换算法,克服了系统激励源频率较低难以模拟的困难。通过对磁场畸变规律的研究,引入误差校正矩阵,通过修正发射矩阵进而校正磁场畸变引起的目标参数定位误差。采用正交多项式拟合的算法求解误差校正矩阵,数值模拟结果验证了校正方法的正确性,可以明显提高磁场畸变时系统参数的定位精度。磁场畸变规律的数值模拟,降低了系统实时数据采集的工作量,提高了系统校正方法检验的快速性。     

Application of Sturm Theorem in the Global Controllability of a Class of High Dimensional Polynomial Systems

In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress.Finally, the authors will give some examples to show the application of our results.     

Characteristic polynomial assignment in F-M model Ⅱ of 2-D systems

The problems of characteristic polynomial assignment in Fornasini-Marchesini (F-M) model Ⅱ of 2-D systems are investigated. The corresponding closed-loop systems described by F-M model Ⅱ are obtained via the state feedback.Using the algebraic geometry method, the characteristic polynomial assignment in the closed-loop systems is discussed. In terms of the theory of algebraic geometry, the problem of characteristic polynomial assignment is transferred to the one whether a rational mapping is onto. Sufficient conditions for almost arbitrary assignment coefficients of characteristic polynomial in F-M model Ⅱ of 2-D systems via state feedback are derived, and they are available for multi-input cases. It also has been shown that this method can be applied to assign the characteristic polynomial with output feedback. The sufficient conditions for almost arbitrary assignment coefficients of characteristic polynomial of multi-input 2-D systems described by F-M model Ⅱ with output feedback are established.     

折扣加权总完工时间的调整时间可分离无等待Flow Shop排序问题

研究3台机器调整时间可分离的无等待F1ow Shop排序问题，目标函数为极小化折扣加权总完工时间。对某些特殊情况，给出问题存在多项式最优算法的充分条件。在此条件下得到求解调整时间可分离的无等待F1ow Shop排序问题的分派规则。     

Finite time stability and stabilization of hybrid dynamic systems

Finite time stability and stabilization are studied for hybrid dynamic systems. By combining multiple Lyapunov function and finite time Lyapunov function, a sufficient condition of finite time stability is given for the system. Compared with the previous works, our results have less conservativeness. Furthermore, based on the state partition of continuous and resetting parts of system, a hybrid feedback controller is constructed, which stabilizes the closed-loop systems in finite time. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

线性系统有限时间函数观测器设计的参数化方法

研究了线性系统有限时间函数观测器的参数化设计问题,其目的是通过设计参数化形式的函数观测器,使其在给定有限时间内能够直接估计关于线性系统状态的线性函数。基于一类Sylvester矩阵方程的参数化解,给出了该有限时间函数观测器所有增益矩阵的参数化表达式,其所含的自由参数为控制系统设计提供了全部的自由度,可通过适当选择这些自由参数使其满足某些系统性能指标。最后,数值例子及其仿真结果验证了所提线性系统有限时间函数观测器参数化设计方法的简单性和有效性。     

一类不确定离散切换广义系统的一致有限时间稳定准则

利用Lyapunov like函数方法和线性矩阵不等式（linear matrix inequality, LMI）技术研究了一类不确定离散时间切换广义系统的一致有限时间稳定和状态反馈镇定问题。首先,在任意给定的切换规则且假定不确定参数项范数有界的情况下,给出了保证不确定离散切换广义系统一致有限时间有界和有限时间稳定的充分条件和状态反馈控制器的设计方法,然后利用Matlab中的LMI工具箱对建立的LMI问题进行求解。最后的仿真算例验证了所提方法的有效性。     

THE MATRIX ITERATION ALGORITHM SOLVING AN ENUMERATION PROBLEM ON BACTERIAL COMPLETE GENOMES

Given an alphabet E and a finite minimal set B of forbidden words, a combinatorial enumeration problem on bacterial complete genomes is transformed to enumerating strings of a given length which do not, contain any string in B as their substrings. Prom the fact that a string in the language is equivalent to a path in the corresponding graph, we have obtained a polynomial time algorithm by modifying the power of the adjacency matrix in the graph.     

一类索赔时间相依的离散时间的二元风险模型的破产概率

研究一类索赔时间相依的离散时间的二元风险模型，模型中假设每次主索赔可能引起一次副索赔，而每次副索赔有可能推迟发生。通过引入辅助模型得到有限时间生存概率的递推公式，并在某些特殊情形下得到有限时间生存概率和最终破产概率的明确表达式。     

MPS上作业的分配和调度问题

多处理机系统MPS(MultiprocessorSystem)上作业的分配和调度问题是其运行效率的关键.本文讨论的是具有不相容性作业集的作业分配和调度问题,提出了一种启发式方法及其定量分析技术,并证明了相关定理和若干推论.     

STABILITY OF SWITCHED POLYNOMIAL SYSTEMS

This paper investigates the stability of （switched） polynomial systems. Using semi-tensor product of matrices, the paper develops two tools for testing the stability of a （switched） polynomial system. One is to convert a product of multi-variable polynomials into a canonical form, and the other is an easily verifiable sufficient condition to justify whether a multi-variable polynomial is positive definite. Using these two tools, the authors construct a polynomial function as a candidate Lyapunov function and via testing its derivative the authors provide some sufficient conditions for the global stability of polynomial systems.     

严格第k最小支撑树问题

提出了严格第 k最小树的概念 .利用定长支撑树问题的复杂性 ,证明了求支撑树的长度分布L( G)问题是 NP-C的 ,从而证明了严格第 k最小支撑树问题也是 NP-C的 .对于 k=2的情况 ,给出了一个多项式时间算法 ,其时间复杂性为 $O( | EX| n^2 )$ ,其中 EX是正交换的集合 ,n是顶点数.     

最优箭线图的判定与唯一性

统筹图又叫计划网络图或箭线（工程）图．任给一个有限偏序集（简称序集,其元素叫做工序或作业）,要绘制它的一个最优统筹图（含虚工序数最少者）是一个尚未解决的困难问题．本文给出了一个判定一序集存在唯一最优箭线图的充分条件以及绘制这类序集的最优箭线图的方法;并指出：若Ｐ一个序集满足Ｗ－ｆｒｅｅ和Ｍ－ｆｒｅｅ,则Ｐ的最优箭线图唯一且可在多项式时间内作出．     

ON FIRST INTEGRALS OF POLYNOMIAL AUTONOMOUS SYSTEMS

Using Carleman linearization procedure, this paper investigates the problem of first integrals of polynomial autonomous systems and proposes a procedure to find the first integrals of polynomial family for the systems. A generalized eigenequation is obtained and then the problem is reduced to the solvability of the eigenequation. The result is a generalization of some known results.     

COHERENT, REGULAR AND SIMPLE SYSTEMS IN ZERO DECOMPOSITIONS OF PARTIAL DIFFERENTIAL SYSTEMS

1.IntroductionWeareconcernedwithalgebraicdifferentialpolynomials(abbreviatedas'd-pcis)inafinitenumberofdifferentialindeterminatesoveradifferentialfieldofcharacteristic0.Givenafinitesetofsuchd-pcis,wewouldliketostudyd-Zero(),thedifferentialalgebraicsetdefinedbyPoverauniversaldifferentialfield.Wemayaskwhetherd-Zero()isempty,whetherad-pcivanishesond-Zero()(differentialradicalidealmembershipproblem),whatthedimensionofd-Zero()is,howtodecomposed-Zero()intoirreduciblealgebraicdifferentialsets,andso…     

有限需求量的网络路径优选研究

“有限需求量的网络路径优选”是一种比较特殊的费用流问题。本文描述并分析有限需求量的网络路径优选问题,建立路径优选的最短时间非线性模型,该模型考虑把物资发送到相应路径的时间。在有限需求条件下,给出n条独立路径的优选定理。借助于该定理和最小费用最大流算法,提出有限需求量的网络路径优选算法,并用示例作算法验证。     

ON THE CONSTRUCTION OF GROEBNER BASIS OF A POLYNOMIAL IDEAL BASED ON RIQUIER-JANET THEORY

As a consequence of a previons study of algebraic differential geometry(see [WU1]) theremay be associated to certain special kinds of differential ideals some well-behaved basis enjoyingsome well-behaved properties.If the differential ideals are further specialized so that theycorrespond to ordinary polynomial ideals then such a well-behaved basis will become the usualGroebner basis of the polynomial ideals while the latter is not known for differential ideals.