Expression for the Number of Spanning Trees of Line Graphs of Arbitrary Connected Graphs

For any graph G, let be the number of spanning trees of G, be the line graph of G, and for any nonnegative integer r, be the graph obtained from G by replacing each edge e by a path of length connecting the two ends of e. In this article, we obtain an expression for in terms of spanning trees of G by a combinatorial approach. This result generalizes some known results on the relation between and and gives an explicit expression if G is of order and size in which s vertices are of degree 1 and the others are of degree k. Thus we prove a conjecture on for such a graph G.     

Statistical and Geometrical Way of Model Selection for a Family of Subdivision Schemes

The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes(for any integer m, n ≥ 2). The proposed algorithm has been derived from uniform B-spline blending functions. In particular, we study statistical and geometrical/traditional methods for the model selection and assessment for selecting a subdivision curve from the proposed family of schemes to model noisy and noisy free data. Moreover, we also discuss the deviation of subdivision curves generated by proposed family of schemes from convex polygonal curve. Furthermore, visual performances of the schemes have been presented to compare numerically the Gibbs oscillations with the existing family of schemes.     

胜利断块油藏细分注水技术界限研究

老油田进入特高含水期后,剩余油分布更加零散,各种地质因素也因长期注水开发而发生了一定的改变.此时稳油控水难度进一步加大,为了进一步挖掘剩余油,控制含水上升速度、减缓产量递减,必须对注水井采取进一步的细分调整.基于水湿油藏注水井注水层段吸水效果,从注入水受力分析入手,运用达西定律推导出了水驱油藏水驱油全过程中的单位体积注入水沿竖直、地层两个方向运移的渗流速度公式,明晰了水驱油藏注水层段不同开发阶段砂岩吸水机理.研究结果表明,水驱油藏细分注水效果与岩石绝对渗透率、水相相对渗透率、注入水黏度、水动力压力梯度、注水井启动压力梯度、含水饱和度、地层倾角、油水密度差等参数有关.结合胜利油田断块油藏地质特征及细分注水工艺要求,制定了一套适合胜利油田不同断块区的细分注水技术政策界限:层段内渗透率变异系数小于0.3,砂岩条带宽度极比小于2.5,且东辛油区断块油藏层段内砂岩厚度小于6m,小层数小于4个;现河油区断块油藏层段内砂岩厚度小于5m,小层数小于5个;临盘油区断块油藏层段内砂岩厚度小于6m,小层数小于6个.矿场试验证实,该细分注水技术政策界限是合理、实用的,其为胜利断块油藏注上水、注够水、注好水,实现多层断块油藏的高效开发提供了技术保障,对类似油藏细分注水技术界限研究具有一定的借鉴意义.     

一类新的(2n-1)点二重动态逼近细分

利用正弦函数构造了一类新的带有形状参数ω的(2n-1)点二重动态逼近细分格式.从理论上分析了随n值变化时这类细分格式的C~k连续性和支集长度;算法的一个特色是随着细分格式中参数ω的取值不同,相应生成的极限曲线的表现张力也有所不同,而且这一类算法所对应的静态算法涵盖了Chaikin,Hormann,Dyn,Daniel和Hassan的算法.文末附出大量数值实例,在给定相同的初始控制顶点,且极限曲线达到同一连续性的前提下和现有几种算法做了比较,数值实例表明这类算法生成的极限曲线更加饱满,表现力更强.     

Effect of the subdivision strategy on convergence and efficiency of some global optimization algorithms

We investigate subdivision strategies that can improve the convergence and efficiency of some branch and bound algorithms of global optimization. In particular, a general class of so called weakly exhaustive simplicial subdivision processes is introduced that subsumes all previously known radial exhaustive processes. This result provides the basis for constructing flexible subdivision strategies that can be adapted to take advantage of various problem conditions.     

关于图的若干介值问题

对连通图G,以C_i(G),■(G)分别表G的有i条边的连通支撑子图之集与连通子图之集,以C~i(G),(?)(G)分别表G的顶点数为i的子树集与连通子图之集.本文讨论了这四类子图簇对若干基本参数及端点数的介值性,从而对已有的一些结果作了若干有意义的拓广.     

双圈拟阵

Sim■es Pereira于1992年提出双圈拟阵.本文讨论了(i)双圈拟阵及其秩函数;(ii)次模函数在双圈拟阵中的应用;(iii)双圈拟阵B(G)的横贯拟阵.主要结果:1°由圈矩阵Bf=[I,Bf12]和圈秩的概念,推出M(f0)为双圈拟阵;2°证明了双圈拟阵B(G)等于由子集族{Av∶v∈V(G)},e与v在G中相关联}所确定的横贯拟阵;3°用不同于Matthews(1977)的方法证明了(iii).     

On polynomial symbols for subdivision schemes

Given a dilation matrix A :ℤ^d→ℤ^d, and G a complete set of coset representatives of 2π(A ^−Tℤ^d/ℤ^d), we consider polynomial solutions M to the equation ∑ _g∈G M(ξ+g)=1 with the constraints that M≥0 and M(0)=1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric polynomials of this type play an important role as symbols for interpolatory subdivision schemes. For isotropic dilation matrices, we use the method introduced to construct symbols for interpolatory subdivision schemes satisfying Strang–Fix conditions of arbitrary order. Research partially supported by the Danish Technical Science Foundation, Grant No. 9701481, and by the Danish SNF-PDE network.     

基于线阵探测器的单圈绝对轴角编码器

为了解决轴角编码器尺寸与角度分辨率之间的矛盾,同时提高编码器的响应频率,提出了一种基于线阵探测器的单圈绝对式光电轴角编码器.该编码器使用了一种新型单圈绝对式编码盘,整个码盘只有一个码道,粗码被直接刻在这个单圈的码道上,码盘图像经光学放大后被线阵探测器接收.利用FPGA控制电路将数据传送至计算机,并对数据进行译码处理,分别利用图像处理技术读取粗码和利用像素细分技术获得细码,两者相结合得到角度信息.通过该技术设计一个码盘直径为40 mm的绝对式轴角编码器,其分辨率为15位.