关于n维半线性反应扩散系统

本文利用单调方法、极位原理、Schauder不动点定理、以及常微系统整体稳定的結论,给出一类带Neumann边值条件的半线性反应扩散系统整体正解的存在唯一性及渐近性.     

基础科学

一类独立的动态投入产出模型；模糊命题演算系统L^＊的简化与独立性；代数教学中的模式直观；Banach空间中非线性奇异两点边值问题的多重正解；迭代函数系统的吸引子和OSC集；战斗对策：有约束极小极大途径（Ⅰ）；具有三个年龄阶段的单种群自食模型。[编者按]     

一种挖掘加权最大频繁序列的新算法

由于其内在的计算复杂性,在密集型数据序列数据库中挖掘全部频繁项集往往非常困难,解决方案之一是挖掘最大频繁序列。传统的序列模式方法对满足最小支持度阈值的序列同等对待,但在真实数据库中不同的序列往往具有不同的重要程度。为解决上述问题,提出了一种挖掘加权最大频繁序列的新算法。该算法利用频繁项目出现的频率来计算频繁序列的权重,给出了频繁加权序列的定义,该定义的引入不仅可以找出较为重要的最大频繁序列,而且可以使挖掘结果同样具有反单调性,从能够加速剪枝,提高算法效率。实验结果表明,加权最大频繁序列算法是有效的。     

关于L1逼近的某些结果

假如存在α>0使得n~(-α)q_n↓0,则称{q_n}为拟单调序列,简记为{q_n}∈QM,假如正数序列{l_n}满足l_(n+1)/l_n→1(n→∞),则称它为慢变化序列,若对上述l_n及某一α>0有q_n/n~αl_n↓0,则称{q_n}为正则拟单调序列,简记为{q_n}RQM,如果其中{l_n}满足条件n+1/l_n=1+O(1/n),则称q_n∈RQM,易见QM(?)RQM(?)RQM.     

灰色Verhulst模型在火灾事故中的应用

Verhulst模型适用于非单调的摆动发展序列或具有饱和状态的S形序列。火灾事故中的火灾死亡人数具有饱和状态S形过程的特性,采用Verhulst预测模型对我国近年发生的火灾统计数据进行分析预测。预测结果表明,该模型简单实用,精度较高,具有实用价值。     

扩展L-系统树木多态模拟研究

L-系统是树木模拟的重要方法之一,实现了风吹树动、自然生长等自然现象的模拟,但缺憾是少了诸如修剪、折枝现象的模拟。通过在L-系统中加入扩展参数,并且对L-系统中的字符序列进行新的龟解释,实现了树枝断裂现象的模拟。同时,将字符统计迭代算法的三元素集应用于字符序列中,通过有限次迭代替换,实现了花草树木修剪过程的模拟。实验结果表明,通过调整L-系统中的扩展参数,可以得到拓扑结构相同但形态差异较大的模拟结果。     

中国二氧化碳排放的环境库兹涅茨曲线——基于时间序列与面板数据的经验估计

本文利用时间序列数据和省际面板数据,选取排放总量、人均排放量、排放强度作为二氧化碳排放指标对中国二氧化碳排放的环境库兹涅茨曲线进行了经验估计.1952-2007年的时间序列协整检验表明,排放总量、人均排放量与人均收入之间存在单调递增的关系,而单位GDP排放量与人均收入之间支持倒U型的环境库兹涅茨曲线,拐点位于1319元.1995-2007年省际面板数据协整检验表明,排放总量与人均收入呈单调递增关系,单位GDP排放量与人均收入之间呈单调递减关系.而人均排放量与人均收入之间存在倒N型关系,两个拐点分别位于3304元和44049元.目前除北京、上海、天津外,其他各省的人均二氧化碳排放量仍位于上升阶段.     

科技杂志要览 大学学报

集值微分方程初值问题的拟线性化方法 摘要 利用拟线性化方法研究了一阶集值微分方程初值问题,构造了2个单调序列．获得了解的一致收敛性和平方收敛性结果．     

极大极小问题的模松弛拟强次可行方向算法

结合模松弛SQP算法和强次可行方向算法思想,给出了初始点任意选取的新的拟强次可行方向算法。每步迭代,只需求解一个总有最优解的二次规划子问题来产生主搜索方向,引入一种新的非单调曲线搜索来产生步长,在较弱的条件下,可以得到算法的全局收敛性。     

二次非线性项复差分方程正解的存在性分析

在动力系统理论中,二次非线性项复差分方程的正解存在性问题,在解决动力系统的稳定性控制方面具有重要意义。在相空间的一个子集上构建二次非线性项复差分方程,采用Lyapunov-Kraso-vskii泛函进行交叉项干扰的临界阈值确定,对方程正解的收敛性问题看作是时频对偶问题,通过多迹B?cklund变换,分析接收数据矩阵与阵列流型张成的空间之间的时频耦合性,得到方程的所有正解向量的递归计算式,构建差分方程的正解约束模型,进行二次非线性项复差分方程正解的稳定性证明,保证了非线性动力系统的稳定性和有界性,推导结论真实有效。     

几类混合单调算子方程解存在的唯一性定理

本文利用锥理论和半序方法在Banach空间研究了一类混合单调算子方程解的存在唯一性,把压缩映射推广到了函数及算子的形式,得到一些新的定理,所获结果推广了已知的结论。     

一种新的椭球算法

基于更动约束的思想[1 ] 与方法 ,提出了求解线性规划问题的新椭球算法 .它与L .G .Khachian的椭球算法[2 ] 不同 ,在新算法的椭球迭代过程中 ,不仅用约束不等式割掉不含约束集的半个椭球 (椭球中心不在约束集内时 ) ,称之为约束割 ;而且在椭球中心落在约束集内时 ,它用目标不等式割掉含约束集的半个椭球 ,称之为目标割 .新算法的不等式系统是由原规划 (或对偶规划 )的约束不等式与目标不等式组成的 (规模小 ) ,而不是由原椭球算法的K K T条件[5] 组成的不等式系统 (规模大 ) .这种新椭球算法即有多项式计算复杂性的特性 ,又在迭代过程中得到一系列单调趋向最优解的可行解 (在解存在时 ) .如果认为已得满意解 ,可随时停机 .对于实际问题 ,大多数是变量有界的 ,初始椭球不大 ,因此新算法更为实际 ,有效 .     

Global behavior of a two-stage contact process on complex networks

Masuda and Konno [14] first formulated a two-stage contact process on complex networks with heterogeneous degree distribution, and they derived a critical birth or infection rate β_c, above which there exists a unique positive equilibrium. The global behavior of this model is not well understood, and the authors have not given a rigorous mathematical analysis of their model. In this paper, we investigate the global behavior in detail and show that the global behavior is completely determined by a threshold R₀. In particular, by comparison arguments, we establish the global asymptotic stability of the trivial equilibrium E₀ for R₀?<?1; by constructing a bounded function, we show that the system is uniformly persistent for R₀?>?1. Furthermore, by means of a monotone iterative approach, we obtain a sufficient condition for the global asymptotic stability of the positive equilibrium E*.     

Global smooth stabilization of a class of feedforward systems under the framework of generalized homogeneity with monotone degrees

In this paper, based on the concept of generalized homogeneity with monotone degrees (HWMD), we develop a new design procedure to explicitly construct global stabilizers for a class of feedforward systems. The proposed controller design strategy has several new features. First, a series of positive constant gains instead of function gains are employed for a simpler controller construction. Second, the flexibility of HWMD provides a general framework to unify several existing results. Third, it is now possible to design continuously differentiable stabilizers for some feedforward systems, for which only continuous stabilizers were previously designed. Moreover, for feedforward systems with decreasing powers, the proposed approach will enable us to design a locally linear saturation control law which is easier to be implemented in practical applications.     

Finding exact periodic solutions in Lure systems through periodic signal mapping

A solution of the periodic problem in a nonlinear system comprising a single-valued symmetric nonlinearity (Lure system) and linear dynamics is presented. The solution is designed as an iterative application of Periodic Signal Mapping to refine the approximate solution obtained through the describing function method. The algorithm is based upon the transformation of the original nonlinear system into an equivalent nonlinear system for which the filtering hypothesis is satisfied exactly, and for that reason the latter being suitable for application of the developed algorithm. The solution sought for is a fixed point of the periodic signal mapping. Conditions of asymptotic convergence of the proposed algorithm are given. The proposed approach is illustrated by two examples of analysis of periodic motions in a relay feedback system and chattering in a terminal sliding mode.     

A property of the eigenvalues of the symmetric positive definite matrix and the iterative algorithm for coupled Sylvester matrix equations

In this paper, we discuss the properties of the eigenvalues related to the symmetric positive definite matrices. Several new results are established to express the structures and bounds of the eigenvalues. Using these results, a family of iterative algorithms are presented for the matrix equation AX=F and the coupled Sylvester matrix equations. The analysis shows that the iterative solutions given by the least squares based iterative algorithms converge to their true values for any initial conditions. The effectiveness of the proposed iterative algorithm is illustrated by a numerical example.     

Robust identification of nonlinear time-delay system in state-space form

This paper puts forward a robust identification solution for nonlinear time-delay state-space model (NDSSM) with contaminated measurements. To enhance the robustness of the developed method for outliers, the heavy-tailed Laplace distribution is employed to describe and protect the output measurement process. The undetermined time-delay is considered to be uniformly distributed and the boundary of it is known as a priori. In the developed solution, the uncertain time-delay is treated as a latent process variable and it is iteratively calculated with the expectation–maximization (EM) algorithm. The EM algorithm is actually an iterative optimization algorithm and it is effective for the hidden variable problems. The particle filter is introduced to numerically approximate the cost function (Q-function) in the EM algorithm since it is difficult to calculate directly. The efficacy of the developed solution is evaluated via a numerical test and a two-link robotic manipulator.     

The relaxed gradient-based iterative algorithms for a class of generalized coupled Sylvester-conjugate matrix equations

In this paper, two relaxed gradient-based iterative algorithms for solving a class of generalized coupled Sylvester-conjugate matrix equations are proposed. The proposed algorithm is different from the gradient-based iterative algorithm and the modified gradient-based iterative algorithm that are recently available in the literature. With the real representation of a complex matrix as a tool, the sufficient and necessary condition for the convergence factor is determined to guarantee that the iterative solution given by the proposed algorithms converge to the exact solution for any initial matrices. Moreover, some sufficient convergence conditions for the suggested algorithms are presented. Finally, numerical example is provided to illustrate the effectiveness of the proposed algorithms and testify the conclusions suggested in this paper.     

K—S函数的一致不变凸性

对求争最优化问题的极大熵方法中的关键函数－K－S函数的一致不变凸性作了讨论得出“K－S函数是一致不变凸的，则一定是不变凸的”结论，其于K－S函数的特殊熵参数，在证明K－S函数的一致不变凸性中，引入了一个很小的正数ε，以说明只要熵足够大，K－S函数就是一致不变凸的。     

Finite-time general function consensus for multi-agent systems over signed digraphs

This paper solves the finite-time consensus problem for discrete time multi-agent systems (MASs) where agents update their values via linear iteration and the interactions between them are described by signed digraphs. A sufficient condition is presented that the agents can reach consensus on any given linear function of multiple initial signals in finite time, i.e., there exists an eventually positive Laplacian-based matrix associated with the underlying graph. We prove that the linear iterative framework “ratio consensus” developed for unsigned graphs in the literature can be extended to the computation for signed graphs with appropriate modifications. Our method weakens the limitation of the iterative framework on the “marginal Schur stability” of the weight matrix without increasing the computational complexity. Reaching average consensus on unsigned graphs as in the literature is regarded as a special case of our algorithm. Two illustrative examples are presented to demonstrate the correctness of the proposed results.