An applied cell mapping method for optimal control problems

From the application point of view, a series of modifications are proposed for the cell mapping method discussed in Ref. 1 for the optimal control analysis of dynamical systems. The cell order around the target set is rearranged. A set of common discriminate principles is used for the selection of the optimal one among competing control strategies of the same cost. Inequality constraints of the system are taken into account. The number of elements in the set of allowable time intervals is not prescribed, but left open. These modifications seem to make the cell mapping method more efficient for analyzing feedback systems and for obtaining their global optimal control information. The algorithms presented in this paper could broaden the application of the cell mapping approach of Ref. 1 to a wider class of engineering problems.     

Stress concentration and effective stiffness of aligned fiber reinforced composite with anisotropic constituents

The paper addresses the problem of calculation of the local stress field and effective elastic properties of a unidirectional fiber reinforced composite with anisotropic constituents. For this aim, the representative unit cell approach has been utilized. The micro geometry of the composite is modeled by a periodic structure with a unit cell containing multiple circular fibers. The number of fibers is sufficient to account for the micro structure statistics of composite. A new method based on the multipole expansion technique is developed to obtain the exact series solution for the micro stress field. The method combines the principle of superposition, technique of complex potentials and some new results in the theory of special functions. A proper choice of potentials and new results for their series expansions allow one to reduce the boundary-value problem for the multiple-connected domain to an ordinary, well-posed set of linear algebraic equations. This reduction provides high numerical efficiency of the developed method. Exact expressions for the components of the effective stiffness tensor have been obtained by analytical averaging of the strain and stress fields.     

Local approximations for maximum partial subgraph problem

We deal with MAXH₀-FREE PARTIAL SUBGRAPH. We mainly prove that 3-locally optimum solutions achieve approximation ratio (δ₀+1)/(B+2+ν₀), where B=max_v∈Vd_G(v), δ₀=min_v∈V(H0)d_H0(v) and ν₀=(|V(H₀)|+1)/δ₀. Next, we show that this ratio rises up to 3/(B+1) when H₀=K₃. Finally, we provide hardness results for MAXK₃-FREE PARTIAL SUBGRAPH.     

在几何和参数上表示同一条曲线的两条有理NURBS曲线的权与控制顶点之间的关系

The paper discusses the relationship between weights and control vertices of two rational NURBS curves of degree two or three with all weights larger than zero when they represent the same curve parametrically and geometrically, and gives sufficient and necessary conditions for coincidence of two rational NURBS curves in non-degeneracy case.     

Optimal algebraic multilevel preconditioning for local refinement along a line

The application of some recently proposed algebraic multilevel methods for the solution of two-dimensional finite element problems on nonuniform meshes is studied. The locally refined meshes are created by the newest vertex mesh refinement method. After the introduction of this refinement technique it is shown that, by combining levels of refinement, a preconditioner of optimal order can be constructed for the case of local refinement along a line. Its relative condition number is accurately estimated. Numerical tests demonstrating the performance of the proposed preconditioners will be reported in a forthcoming paper.     

Halin-图的点强全染色

图G(V,E)的一个k-正常全染色f叫做一个k-点强全染色当且仅当对任意v∈V(G), N[v]中的元素被染不同色,其中N[v]={u|uv∈V(G)}∪{v}．χTvs(G)=min{k|存在图G的k- 点强全染色}叫做图G的点强全色数．对3-连通平面图G(V,E),如果删去面fo边界上的所有点后的图为一个树图,则G(V,E)叫做一个Halin-图．本文确定了最大度不小于6的Halin- 图和一些特殊图的的点强全色数XTvs(G),并提出了如下猜想:设G(V,E)为每一连通分支的阶不小于6的图,则χTvs(G)≤△(G) 2,其中△(G)为图G(V,E)的最大度．     

On the chromatic polynomial of a graph

Let P(G,λ) be the chromatic polynomial of a graph G with n vertices, independence number α and clique number ω. We show that for every λ≥n, ()^α≤≤ () ^{n −ω}. We characterize the graphs that yield the lower bound or the upper bound.?These results give new bounds on the mean colour number μ(G) of G: n− (n−ω)() ^{n −ω}≤μ(G)≤n−α() ^α. Received: December 12, 2000 / Accepted: October 18, 2001?Published online February 14, 2002     

On-line arbitrarily vertex decomposable trees

A tree T is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to the order of T there is a sequence of vertex-disjoint subtrees of T whose orders are given by τ. An on-line version of the problem of characterizing arbitrarily vertex decomposable trees is completely solved here.     

Co@SiO2核壳式纳米磁性粒子的合成、性质表征及在细胞分离和细胞芯片上的应用

合成了Co@SiO2核壳式纳米粒子,并采用透射电镜(TEM)、X射线衍射(XRD)、扫描电镜(SEM)和振动样品磁强计(VSM)对其形状、尺寸、荧光及磁特性进行了表征,探讨了其在细胞分离和细胞芯片上的应用和原理.     

关于半无爪图点泛圈性的两个结果

给出了半无爪图(quasi-claw-freegraph)点泛圈性方面的两个结果,作为推论,可得到D.Oberly,D.Sumner,L.Clark等人的相关结果.