A reduced-order extrapolated approach to solution coefficient vectors in the Crank-Nicolson finite element method for the uniform transmission line equation

This work is concerned mainly with developing and testing the reduced-order extrapolated approach to the unknown coefficient vectors in the Crank-Nicolson finite element (CNFE) solutions for the uniform transmission line equation. For this objective, the CNFE functional and matrix models and the existence, stability, and errors of the CNFE solutions of the uniform transmission line equation are first derived. Then a reduced-order extrapolated CNFE (ROECNFE) matrix model is established by means of a proper orthogonal decomposition technique, and the existence, stability, and error estimates of the ROECNFE solutions are demonstrated by matrix analysis, leading to an elegant theoretical development. Especially, our work shows that the basis functions and accuracy of the ROECNFE matrix model are the same as those of the CNFE matrix model. Finally, some numerical tests are illustrated to computationally experimentally confirm the validity and sharpness of the ROECNFE method.     

A stabilized Crank-Nicolson mixed finite element method for non-stationary parabolized Navier-Stokes equations

In this study, a time semi-discrete Crank-Nicolson (CN) formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite element (SCNMFE) formulation based on two local Gauss integrals and parameterfree with the second-order time accuracy is established directly from the time semi-discrete CN formulation. Thus, it could avoid the discussion for semi-discrete SCNMFE formulation with respect to spatial variables and its theoretical analysis becomes very simple. Finaly, the error estimates of SCNMFE solutions are provided.     

Characterizations of Weighted BMO Space and Its Application

In this paper, we prove that the weighted BMO space■is independent of the scale p ∈(0, ∞) in sense of norm when ω∈ A_1. Moreover, we can replace L~p(ω) by L~(p,∞)(ω). As an application, we characterize this space by the boundedness of the bilinear commutators [b, T ]_j(j = 1, 2), generated by the bilinear convolution type Calderón–Zygmund operators and the symbol b, from L~(p1)(ω) × L~(p2)(ω) to L~p(ω~(1-p)) with 1 p_1, p_2 ∞ and 1/p = 1/p_1 + 1/p_2.Thus we answer the open problem proposed by Chaffee affirmatively.     

Smoothed analysis of condition numbers and complexity implications for linear programming

We perform a smoothed analysis of Renegar’s condition number for linear programming by analyzing the distribution of the distance to ill-posedness of a linear program subject to a slight Gaussian perturbation. In particular, we show that for every n-by-d matrix Ā, n-vector [`(\varvec b)]{\bar{\varvec b}}, and d-vector [`(\varvec c)]{\bar{\varvec c}} satisfying ||[`(A)], [`(\varvec b)], [`(\varvec c)]||_F ￡ 1{{||\bar{\bf A}, \bar{\varvec b}, \bar{\varvec c}||_F \leq 1}} and every σ ≤ 1,

Primitive non-powerful symmetric loop-free signed digraphs with given base and minimum number of arcs

In [B.M. Kim, B.C. Song, W. Hwang, Primitive graphs with given exponents and minimum number of edges, Linear Algebra Appl. 420 (2007) 648-662], the minimum number of edges of a simple graph on n vertices with exponent k was determined. In this paper, we completely determine the minimum number, H(n,k), of arcs of primitive non-powerful symmetric loop-free signed digraphs on n vertices with base k, characterize the underlying digraphs which have H(n,k) arcs when k is 2, nearly characterize the case when k is 3 and propose an open problem.     

具有非线性边界条件的奇摄动微分系统边值问题

研究了一类具有非线性边界条件的奇摄动半线性微分系统边值问题．利用边界层校正法构造了形式渐近解．并且在适当的假设下,用微分不等式理论,证明了解的存在性及其一致有效性．     

Permanence and global attractivity for discrete nonautonomous two-species Lotka-Volterra competitive system with delays and feedback controls

A discrete nonautonomous two-species Lotka-Volterra competitive system with delays and feedback controls is proposed and investigated. By using the method of discrete Lyapunov functionals, new sufficient conditions on the permanence of species and global attractivity of the system are established. Particularly, an interesting fact is found in our results, that is, the feedback controls are harmless to the permanence of species for the considered system.     

三角帆蚌钩介幼虫体外培养及变态稚贝的形态变化

以超纯水为对照,利用普通温控培养箱,在(24.0±1.0)℃条件下对三角帆蚌钩介幼虫进行了15d的体外培养实验.结果显示:钩介幼虫排出体外24h内存活率显著下降为50.7%(p=0.006);A组(MEM高糖)、B组(RPMI1640)、C组(MEM 199)幼虫变态率分别为(7.5±3.9)%、(13.3±12.0)%、(42.1±10.0)%;D组(L-15)的幼虫变态率最高,为(66.1±3.8)%,极显著高于C组(p=0.007).相关分析表明,培养液中葡萄糖含量与钩介幼虫变态率存在显著负相关(r=-0.886).利用光镜和扫描电镜对体外培养变态发育的稚贝形态观察发现:稚贝双壳表面圆形凹陷数量和深度比幼虫显著减少,双壳边缘外套膜增厚,在外套膜、斧足表面分布有大量乳状突起,但形态不同.体外培养稚贝的外部形态和内部器官均发生了显著改变,完成了变态发育过程.     

Filtering partially observable diffusions up to the exit time from a domain

We consider a two-component diffusion process with the second component treated as the observations of the first one. The observations are available only until the first exit time of the first component from a fixed domain. We derive filtering equations for an unnormalized conditional distribution of the first component before it hits the boundary and give a formula for the conditional distribution of the first component at the first time it hits the boundary.