Comparison Results Between Preconditioned Jacobi and the AOR Iterative Method

The large scale linear systems with M-matrices often appear in a wide variety of areas of physical,fluid dynamics and economic sciences.It is reported in[1]that the convergence rate of the IMGS method,with the preconditioner I S_α,is superior to that of the basic SOR iterative method for the M-matrix.This paper considers the preconditioned Jacobi(PJ)method with the preconditioner P=I S_α S_β,and proves theoretically that the convergence rate of the PJ method is better than that of the basic AOR method.Numerical examples are provided to illustrate the main results obtained.     

A Model for Fractal Dimension of Rough Surfaces

We report a model for the fractal dimension D8 of rough surfaces based on the fractal distribution of roughness elements on surfaces and the fractal character of surface profiles. The proposed model for the fractal dimension Ds is expressed as a function of the fractaJ dimensions D for conic roughness diameter/height and Dp for surface profile, maximum roughness base diameter λmax, the ratio β of conic roughness height to its base radius as well as the ratio λmin/λmasx of the minimum to the maximal base diameter.     

绳系小球上升最高点速度参数的设置

在高中阶段学生所学习的曲线运动中,竖直面内的圆周运动比较典型、综合的运动,其运动过程存在较多变数和不确定性.绳系小球或者单轨光滑内侧的物体在竖直面内的圆周运动,是学习圆周运动知识过程中一个难点.其中的变数和不确定性是由设置竖直面内最低点的速度大小不同所决定的.不同的速度大小就会有不同的运动过程,比如是一般的摆动、完整的圆周运动还是圆周运动与斜上抛运动结合,求解最大高度时的方法大不相同.下面通过分析例题,总结求最大高度的方法,讨论不同难易度的题目应如何设置最低点的速度大小.     

A narrow-linewidth continuous wave Ho：YAL03 laser with Fabry-Perot etalons

A narrow linewidth continuous wave Ho：YAP laser with two Fabry-Perot etalons pumped by a Tm：YLF laser is reported. The maximum output power reaches 8.3 W when the incident pump power is 15.8 W, with 52.5% optical-to- optical conversion efficiency and 62.6% slope efficiency. A stable laser output at 2118.1 nm is achieved, with a linewidth less than 0.4 nm （full width at half maximum）. The beam quality factor is M2- 1.25, measured by the traveling knife-edge method.     

阵列天线最大输出信干噪比下最优权重降维算法

本文研究阵列天线系统最大输出信干噪比准则下最优权重的降维算法。在求最优权重的过程中，计算复杂度是我们要关心的重要的问题，而计算复杂度与权重矢量的维数成正比。权重矢量的维数和天线阵的阵元个数相同。在期望方向和干扰方向小于天线阵元个数的情况下，完全可以通过某种变换，降低计算最优权重的实际维数，从而降低计算复杂度。     

环境因子对东湖几种沉水植物生理的影响研究

报道了光照强度、水体温度及水体ｐＨ值对东湖５种沉水植物生理的影响．实验结果表明，在一定温度范围内，５种植物的光补偿点均随温度的升高而上升，且种间有较大的差异．各植物光合色素的含量，受生态因子的影响，表现出一定的适应性．５种植物对水体高ｐＨ值耐受能力有明显的差异．探讨了富营养化湖泊沉水植物消亡的原因及生态分布的规律，提出了富营养化湖泊水生植被的恢复及水生生态系统重建中的植物选种原则．     

A Result On the Probability Measures Dominated by g-Expectation

It is proved that a probability measure is dominated by g-expectation ε_μ[·] if and only if it can begenerated by Girsanov transformation via a process which is uniformly bounded by μ.     

Upper Bounds for the Laplacian Graph Eigenvalues

We first apply non-negative matrix theory to the matrix K = D A, where D and A are the degree-diagonal and adjacency matrices of a graph G, respectively, to establish a relation on the largest Laplacian eigenvalue λ1 (G) of G and the spectral radius p(K) of K. And then by using this relation we present two upper bounds for λ1(G) and determine the extremal graphs which achieve the upper bounds.     

资源约束下的投资优化模型

资源约束下的投资问题在决策中很常见.本文提出运用边际净现值比较的思想来解决资源约束下多项目多地区投资决策问题的观点,并且尝试用"区域影响力系数"来衡量区域经济规模对投资项目的影响.在此基础上建立了资源约束下的投资优化模型,并给出解决此类问题的方法.     

单部件可修系统的一个几何过程维修模型

本文研究了单部件、一个修理工组成的可修系统的最优更换问题,假定系统不能修复如新,以系统年龄T为策略,利用几何过程求出了最优的策略T^*,使得系统经长期运行单位时间内期望效益达到最大,并求出了系统经长期运行单位时间内期望效益的显式表达式。在一定条件下证明了T^*的唯一存在性。最后还证明了策略T^*比文献[6]中的策略T^*优。