中立抛物型时滞偏微分方程解振动的充要条件

本丈讨论一类多滞量中立抛物型时滞偏微分方程解的振动性质。获得了其一切解振动的充要条件；所得充要条件将时滞偏微分方程解的振动判别问题转化为时滞微分方程解的振动判别问题；指出了其与普通抛物型偏微分方程解的质的差异．  

基于ARMA模型和自由振动提取技术的海洋平台结构参数识别

用随机减量方法提取海洋平台结构在随机环境荷载非白噪声输入下的自由振动信号和用ARMA（Auto Regressive Moving Average)模型对自由振动数据建模。为了消除平台输出信号中有色噪声的影响。在随机减量系统中加入了一个虚拟系统。并采用导通条件和前导点技术使自由振动提取过程仍在有色输入的状态下进行。同时为了消除参数识别的多值性，提出了采用MA系数修正技术识别海洋平台结构的频率和阻尼动力参数的方法，最后用该套技术对海洋平台结构试验模型进行了参数识别。结果表明该方法具有较好的效果和在线识别使用价值。  

非线性中立双曲型时滞偏微分方程解的振动性质

讨论一类多滞量非线性中立双曲型时滞偏微分方程解的振动性质，应用积分不等式和泛函微分方程的某些结果，获得了其一切解振动的一系列充分条件。结论充分表明了时滞量的决定性作用，指出了其与普通双曲型偏微分方程质的差异。  

THE PREDICTION-CORRECTION LEGENDRE COLLOCATION METHOD FOR NONLINEAR EVOLUTIONARY PROBLEMS

The initial-boundary value problem of Burgers equation is considered. A prediction-correction Legendre collocation scheme is presented, which is easy to be performed. Its numerical solution possesses the accuracy of second-order in time and higher order in space. Numerical results are reported, which show the high accuracy of this approach. The techniques used in this paper are also applicable to other nonlinear evolutionary problems.  

广义半无限规划问题的一种可行方向算法

基于Zoutendijk可行方向算法,本文提出了一种求解广义半无限规划问题的可行方向算法,在保证算法收敛的情况下,此算法比以往的算法在假设条件的要求上有着一定的优势,且数值试验表明此法是可行的.  

Algebraic Structure on Dirichlet Spaces

In this short note, we shall give a few equivalent conditions for a closed form to be Markovian, and prove that the closure of a sub-algebra of bounded functions in a Dirichlet space must be Markovian. We also study the regular representation of Dirichlet spaces and the classification of Dirichlet subspaces.  

Parallel algorithms for large-scale linearly constrained minimization problem

In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construct the PVD directions in parallel computation, which can greatly reduce the computation amount each iteration and is closer to practical applications for solve large-scale nonlinear programming. Moreover, based on an active set computed by the coordinate rotation at each iteration, a feasible descent direction can be easily obtained by the extended reduced gradient method. The direction is then used as the PVD direction and a new PVD algorithm is proposed for the general linearly constrained optimization. And the global convergence is also proved.  

A remark on Kac’s scattering length formula

The scattering length formula was formulated and proved in special cases by Kac in 1974 and 1975.It was discussed by a series of authors,including Taylor 1976,Tamura 1992 and Takahashi 1990.The formula was proved by Takeda 2010 in symmetric case and by He 2011 assuming weak duality.In this article,we shall use the powerful tool of Kutznetsov measures to prove this formula in the general framework of right Markov processes without further assumptions.  

控制数固定的树的谱半径(英文)

阶数为n,控制数为γ的树的集合记为T_n,γ（其中n≥max{12,2γ+1},γ≥3）。本文给出了T_n,γ中前三大的邻接谱半径以及它们对应的图。  

图P_m□K_n的邻点可区别Ⅰ-全染色

应用构造具体染色的方法给出了m阶路和n阶完全图K_n的Cartesian积图的令β点可区别I-全染色得到了图P_m囗K_n的邻点可区别I-全色数.