一般矩阵函数的不等式

本文研究一般矩阵函数不等式.运用一般矩阵函数的两个公式和lp-范数的性质,结出了两个矩阵运算的一般矩阵函数不等式.     

Post's Problem for Reducibilities of Bounded Complexity

In this paper we consider the we known method by E. Post of solving the problem of construction of recursively enumerable sets that have a degree intermediate between the degrees of recursive and complete sets with respect to a given reducibility. Post considered reducibilities ≤_m, ≤_btt, ≤_tt and ≤_T and solved the problem for al of them except ≤_T. Here we extend Post's original method of construction of incomplete sets onto two wide classes of sub‐Turing reducibilities what were studying in [1, 2].     

New methods for calculating the dew/bubble curves of classical model fluids

We describe two new methods for locating the dew/bubble curves of fluids. One is a numerical method and the other an analytical method based on the use of series expansions. The utility of these two methods is illustrated by application to a simple one-component fluid model and to several model polydisperse fluids. The numerical method is based on a new geometric representation of the equilibrium conditions-similar in spirit to the geometric representations often used for solving the equilibrium conditions of pure fluids. Our calculations show that the series-expansion technique can be quite effective at producing accurate representations of the phase boundaries.     

谱半径前六位的n阶单圈图

恰含一个圈的简单连通图称为单圈图。Cn记n个顶点的圈。△（i,j,κ）记C3的三个顶点上分别接出i,j,κ条悬挂边所得的图，其中i≥j≥κ≥0.Sl^n-l记Cl的某一顶点上接出n-l条悬挂边所得到的图。△（n-4 1,0,0)记△（n-4,0,0)的某个悬挂点上接出一条悬挂边所得到的图。本文证明了：若把所有n(n≥12）阶单圈图按其最大特征值从大到小的顺序排列，则排在前六位的依次是S3^n-3，△（n-4,1,0),△（n-4 1,0,0),S4^n-4,△（n-5,2,0),△（n-5,1,1)。     

The algebra of harmonic functions for a matrix-valued transfer operator

We analyze matrix-valued transfer operators. We prove that the fixed points of transfer operators form a finite-dimensional C^∗-algebra. For matrix weights satisfying a low-pass condition we identify the minimal projections in this algebra as correlations of scaling functions, i.e., limits of cascade algorithms.     

激光能量叠加过程中对准精度对焦斑的影响

利用多光束激光输出耦合叠加是一种提高激光器输出功率的有效方法。采用两束矩形激光对准系统,分析两光束不同对准情况下的焦斑特性。完全对准的情况下,两束光的远场焦斑重合在一起,焦斑能量是两光束能量之和。在实际光束对准系统中,讨论了三种常见的对准误差,并比较了这些误差对焦斑特性的影响。利用ZEMAX软件对设计系统进行了模拟分析,并进行了实验验证。结果表明,元件的位置误差会使远场焦斑能量集中度降低,焦斑半径增大。     

Eigenvalues of the k‐th power of a graph

The k‐th power of a graph G, denoted by , is a graph with the same set of vertices as G such that two vertices are adjacent in if and only if their distance in G is at most k. In this paper, we give the bounds on the spectral radius of and . The Nordhaus–Gaddum‐type inequality for the spectral radius of the graph is also presented. Moreover, we obtain an upper bound on the energy of the second power of graphs.     

Smooth diameter and eigenvalue rigidity in positive Ricci curvature

A recent injectivity radius estimate and previous sphere theorems yield the following smooth diameter sphere theorem for manifolds of positive Ricci curvature: For any given and there exists a positive constant 0$">such that any -dimensional complete Riemannian manifold with Ricci curvature , sectional curvature and diameter is Lipschitz close and diffeomorphic to the standard unit -sphere. A similar statement holds when the diameter is replaced by the first eigenvalue of the Laplacian.

     

水中上浮气泡动态特性研究

针对水中的上浮气泡,计入表面张力的作用,然后将气泡边界层内黏性效应分为法向和切向两部分,其中附加法向黏性应力通过Young-Laplace关系考虑;附加切向黏性力是基于黏性耗散能量等效原理,引入黏性修正压力代替.首先建立了轴对称和三维上浮气泡边界元模型,将数值结果与理论值和实验值进行对比分析,有良好的符合度,验证了数值模型的有效性;然后针对毫米量级上浮气泡的平衡速度与形态,讨论了气泡初始条件、表面张力和黏性对气泡上浮过程中动力学行为的影响;最后,提出了一种处理三维上浮气泡融合的数值方法,计算结果与实验现象符合良好,并且能够反映气泡融合后的复杂现象细节.     

相同尺度下气泡与复杂壁面的耦合特性研究

采用格子Boltzmann方法(LBM)建立了气液固三相耦合的动力学模型,研究了相同尺度下上浮气泡与复杂壁面的相互耦合作用.首先,基于黏性流体理论,通过构建一组格子Boltzmann(LB)方程来描述气液两相的运动,并以LB离散体积力的形式计入了黏性力、表面张力和重力.同时,采用LBM中的Half-way反弹模型与有限差分格式相结合的方式进行固壁边界的处理.然后,利用本文建立的模型,对不同特征尺寸比条件下,气泡与考虑边缘效应的平面固壁和曲面固壁的耦合特性进行了研究.研究发现固壁边界条件以及特征尺寸比对气泡的运动和拓扑结构的变化都具有明显的非线性影响.最后,研究了流体属性对气泡与复杂壁面耦合规律的影响.