Little’s law when the average waiting time is infinite

One version of Little’s law, written as $L = \lambda w$ , is a relation between averages along a sample path. There are two others in a stochastic setting; they readily extend to the case where the average waiting time $w$ is infinite. We investigate conditions for the sample-path version of this case to hold. Published proofs assume (our) Eq. (3) holds. It is only sufficient. We present examples of what may happen when (3) does not hold, including one that may be new where $w$ is infinite and $L$ is finite. We obtain a sufficient condition called “weakly FIFO” that is weaker than (3), and through truncation, a necessary and sufficient condition. We show that (3) is sufficient but not necessary for the departure rate to be equal to the arrival rate.     

A cell functional minimization scheme for domain decomposition method on non-orthogonal and non-matching meshes

We are interested in a robust and accurate domain decomposition algorithm with interface conditions of Robin type on non-matching multiblock grids using a cell functional minimization scheme, which has a good performance on non-orthogonal meshes. In order to treat the non-matching grids at the interface, we introduce the \(L^2\) projection operator to ensure weak continuity of the primary unknown and of the normal flux across the non-matching interface. Furthermore, we prove the wellposedness of local and global problems and obtain as well an error estimate of first order in a discrete \(H^{1}\) -norm only using the \(L^{2}\) projection operator on the non-matching interface, as done in the matching case. Numerical results are presented in confirmation of the theoretical results.     

Schur定理的推广

通过计算及归纳的方法,得到了n×n矩阵代数中极大线性无关的反交换2-幂零矩阵的个数,推广了相关文献中的一般线性李代数gl(n)的交换子代数的最大维数这一结论.     

Characterizations of Strength Extremal Graphs

With graphs considered as natural models for many network design problems, edge connectivity κ′(G) and maximum number of edge-disjoint spanning trees τ(G) of a graph G have been used as measures for reliability and strength in communication networks modeled as graph G (see Cunningham, in J ACM 32:549–561, 1985; Matula, in Proceedings of 28th Symposium Foundations of Computer Science, pp 249–251, 1987, among others). Mader (Math Ann 191:21–28, 1971) and Matula (J Appl Math 22:459–480, 1972) introduced the maximum subgraph edge connectivity \({\overline{\kappa'}(G) = {\rm max} \{\kappa'(H) : H {\rm is} \, {\rm a} \, {\rm subgraph} \, {\rm of} G \}}\) . Motivated by their applications in network design and by the established inequalities $$\overline{\kappa'}(G) \ge \kappa'(G) \ge \tau(G),$$ we present the following in this paper:

1. For each integer k > 0, a characterization for graphs G with the property that \({\overline{\kappa'}(G) \le k}\) but for any edge e not in G, \({\overline{\kappa'}(G + e) \ge k+1}\) .
2. For any integer n > 0, a characterization for graphs G with |V(G)| = n such that κ′(G) = τ(G) with |E(G)| minimized.

     

扩散模型中扩散系数的非参数组合估计

为了提高扩散系数估计的准确度, 我们利用动态组合时间域与状态域信息提出一个新的组合估计量. 我们发现所提组合估计量能有效估计扩散模型的扩散系数, 正如在本文中模拟所示. 在一定的条件下, 建立了估计量的渐进正态性, 并证明了时间域估计量与状态域估计量是渐进独立的. 大量的模拟展示了所提组合估计量优于单域估计量, 也优于本文所提估计量.     

伊犁河、额尔齐斯河两水域中东方欧鳊的几个生化指标的比较研究

东方欧鳊(Abramis brama orientalis Berg)源于苏联咸海,我区伊犁河和额尔齐斯河均有分布,由于地理隔离的结果,两水系的东方真鳊已在形态学上出现了某些差异,为进一步探明二者间的亲缘关系,我们进行了鱼肉蛋白质含量、鱼肉氨基酸组成,LDH同工酶、血清蛋白等生化指标的比较研究,结果表明除了氨基酸组成及含量基本未发生变化外,其余三项指标均有显著不同,即说明两水系的东方欧鳊已出现种群间差异,至于是否已分化成两个不同的亚种,尚待进一步研究.     

平行六边形区域上的快速离散傅立叶变换

In this paper, we propose a fast algorithm for computing the DGFT (Discrete Generalized Fourier Transforms) on hexagon domains [6], based on the geometric properties of the domain. Our fast algorithm (FDGFT) reduces the computation complexity of DGFT from O(N4) to O(N2 log N). In particulary, for N =2^P23^P34^P45^P56^P6, the floating point computation working amount equals to(17/2P2 16p3 135/8p4 2424/25p5 201/2P6)3N^2. Numerical examples are given to access our analysis.     

Acyclic edge coloring of triangle-free 1-planar graphs

A proper edge coloring of a graph G is acyclic if there is no 2-colored cycle in G. The acyclic chromatic index of G, denoted by χ a(G), is the least number of colors such that G has an acyclic edge coloring. A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that χ a(G) ≤Δ(G) + 22, if G is a triangle-free 1-planar graph.     

细胞神经网络的指数稳定性

该文研究了具有可变时滞的随机细胞神经网络的指数 稳定性,应用Razumikhin定理与Lyapunov函数,建立了这种细胞神经网络均方指数稳定与几乎必然指数稳定的两类判据,一类是时滞无关而另一类是时滞相关.     

Fabrication of a freestanding GaN layer by direct growth on a ZnO template using hydride vapor phase epitaxy

A new hydride vapor phase epitaxy (HVPE)-based approach for the fabrication of freestanding GaN (FS-GaN) substrates was investigated. For the direct formation of low-temperature GaN (LT-GaN) layers, the growth parameters were optimized: the polarity of ZnO, the growth temperature, and the V/III ratio. The FS-GaN layer was achieved by gas etching in an HVPE reactor. A fingerprint of Zn out-diffusion was detected in the photoluminescence measurements, especially for the thin (80 μm) FS-GaN film; however, a thicker film (400 μm) was effectively reduced by optimization of GaN growth.