利用有限域上非零向量的道路图结构与内积构作结合方案

Um（n,R）表示域F上n元非零向量之集．本文先确定了有限域上n≥5维非零向量的道路图结构,然后利用有限域Fq上Um（n,R）／EnR中具有相同范数的向量的道路图结构与内积构作了具有多个结合的结合方案,并计算出相应的参数．     

捷联惯导系统静基座解析粗对准的误差研究

本文讨论了两种陆用捷联惯导系统（ＳＤＩＮＳ） 在静基座情况下解析粗对准的计算方法,求解载体到导航坐标系的变换矩阵时,选择不同的参考矢量将导致失准角不同。计算和仿真结果对比给出了形象的说明。     

求解大规模非对称矩阵特征问题的精化双正交Lanczos算法

We combine Lanczos algorithm with the thought of the refined projection method using QR factorization and propose the refined biothogonalization Lanczos method for computing the desired eigenvalues of large unsymmetric matrix. With low cost of work space and flops the algorithm cures the disease that the Ritz vectors may not converge when the Ritz values converge usingthe Lanczos method. Numerical experiments show our algorithm is considerably more stable and efficient than its counterpart.     

各向同性弹性力学求解新体系正交关系的研究

在弹性力学求解新体系中,将文献[3]对偶向量进行重新排序后,提出了一种新的对偶微分矩阵L,对于各向同性3维弹性力学问题发现了一种新的正交关系,文中证明了这种正交关系的成立,对于各向同性问题,新的正交关系包含文献[3]的正交关系。     

On the Fiedler vectors of graphs that arise from trees by Schur complementation of the Laplacian

The utility of Fiedler vectors in interrogating the structure of graphs has generated intense interest and motivated the pursuit of further theoretical results. This paper focuses on how the Fiedler vectors of one graph reveal structure in a second graph that is related to the first. Specifically, we consider a point of articulation r in the graph G whose Laplacian matrix is L and derive a related graph G_{r} whose Laplacian is the matrix obtained by taking the Schur complement with respect to r in L. We show how Fiedler vectors of G_{r} relate to the structure of G and we provide bounds for the algebraic connectivity of G_{r} in terms of the connected components at r in G. In the case where G is a tree with points of articulation rR, we further consider the graph G_R derived from G by taking the Schur complement with respect to R in L. We show that Fiedler vectors of G_R valuate the pendent vertices of G in a manner consistent with the structure of the tree.     

Decay properties of Markovian bulk-arrival and bulk-service queues with state-independent control

We consider decay properties regarding decay parameter and invariant measures of Markovian bulk-arrival and bulk-service queues with state-independent control. The exact value of the decay parameter, denoted by λz, is firstly revealed. A criterion regarding ）λz-recurrence and λz-positive is obtained. The corresponding λz-subinvariant/invariant measures and λz-subinvariant/invariant vectors are then presented.     

H+CH→H2+C（1D）反应的立体动力学研究

利用从头计算的对称性为1A′的势能面,用准经典轨线（QCT）方法在不同的碰撞能下研究了反应H+CH→H₂+C（¹D）的产物和反应物的矢量相关性质.在质心系下计算了四个极化微分反应截面.计算并讨论了描述k和j′夹角分布关系的P（θ_r）和描述k-k′-j′三者的二面角分布关系的P（（?）_r）.计算结果表明势能面上的深势阱和不同的碰撞能对产物分子H₂有重要影响.     

Avoiding abelian squares in partial words

Erd?s raised the question whether there exist infinite abelian square-free words over a given alphabet, that is, words in which no two adjacent subwords are permutations of each other. It can easily be checked that no such word exists over a three-letter alphabet. However, infinite abelian square-free words have been constructed over alphabets of sizes as small as four. In this paper, we investigate the problem of avoiding abelian squares in partial words, or sequences that may contain some holes. In particular, we give lower and upper bounds for the number of letters needed to construct infinite abelian square-free partial words with finitely or infinitely many holes. Several of our constructions are based on iterating morphisms. In the case of one hole, we prove that the minimal alphabet size is four, while in the case of more than one hole, we prove that it is five. We also investigate the number of partial words of length n with a fixed number of holes over a five-letter alphabet that avoid abelian squares and show that this number grows exponentially with n.     

多小波采样定理的拓展

采样定理在数字信号通讯中发挥了十分重要的作用,因为信号通常由它的离散采样数据来恢复.Han Bin等人在[J.Comput.Appl.Math.,2009,227:254-270]中构造了广义插值加细函数向量.本文研究与广义插值加细函数向量有关的采样定理的拓展问题.具体而言,对于已知的广义插值d-加细函数向量φ=(φ_1,…,φ_r)~T,即φe(m/r+k)=δ_kδ_(e-1-m),k∈Z,m=0,1,…,r-1,e=1,…,r我们将构造一组函数{φ_(r+1),…,φ_(dr)},使得φ~ロ=(φ~T,φ_(r+1),…,φ_(dr))~T也是d-加细的,而且满足φ_e(m/(dr)+k)=δ_kδ_(θ_(d,r(e)-m))k∈Z,m=0,1,…,dr-1,e=r+1,…,dr,其中θ_(d,r(e))=e-r+R_(e-1-r,d-1),R_(e-1-r,d-1)=「(e-1-r)/(d-1)」.我们建立与φ~■有关的采样定理.显然,φ的多小波子空间采样定理的适用范围得到了拓展.给出φ~■的多小波子空间采样级数的截断误差估计.