Interaction of mixed convection in two-sided lid driven differentially heated square enclosure with radiation in presence of participating medium

The current study addresses the mathematical modeling aspects of transport phenomena in steady, two-dimensional, laminar flow accompanied by heat transfer in a lid-driven differentially heated cavity in presence of radiatively absorbing, emitting and scattering gray medium. The walls of the enclosure are considered to be opaque, diffusive and gray. Mixed convection is the outcome of the interaction of forced convection induced by the moving vertical hot and cold wall with the natural convection induced due to the differentially heated enclosure. Two different orientations of the wall movement have been considered to simulate opposing and aiding mixed convection phenomenon and to study its interaction with radiation. Vorticity-stream function formulation of N–S equation has been employed. The discrete ordinate method has been used in modeling the radiative transport equation followed with finite volume method as discretisation technique. The effect of influencing parameters on fluid flow and heat transfer has been studied.     

基于声粒子分布积分的无网格声场计算方法

小尺度封闭空间内部声场的数值计算是声学设计、噪声控制等领域的关键技术。由于波动声学及几何声学方法计算频率上的限制,中频段声场计算问题一直是个难点。本文以声学无网格法为基础,提出了一种基于声粒子分布积分的无网格声场数值计算方法。文中利用声线跟踪理论计算声场中的声粒子分布,并以某个时间点上的声粒子作为蒙特卡罗法中的积分点,将其应用于无网格法中,从而获得声场中的节点声压。利用该方法对一个矩形封闭空间的中低频声场进行了计算,并与模态叠加法、商用声场计算软件、经典无网格法的结果进行了对比,证明基于声粒子分布积分的无网格声场数值计算方法在中低频段相较于传统基于网格的方法具有更高的精度。     

阶数不超过4的交叉超立方体是点可迁的

P Kulasinghe and S Bettayeb showed that any multiply-twisted hypercube with five or more dimensions is not vertex-transitive. This note shows that any multiply-twisted hypercube with four or less dimensions is vertex-transitive, and that any multiply-twisted hypercube with three or larger dimensions is not edge-transitive.     

The Median Stabilization Degree of a Median Algebra

The median stabilization degree (msd, for short) of a median algebra measures the largest possible number of steps needed to generate a subalgebra with an arbitrary set of generators. We determine the value of msd of a graphic n-cube Qn and we derive an estimation of msd for the natural median operator of Rn which is sharp up to one or two units. Interestingly, msd of Qn and of Rn grows like log1.5n. Finally, we characterize median algebras and median graphs of msd 1 in terms of forbidden subspaces.     

On translation invariant operators which preserve the B-spline recurrence

It was observed in [4] that the Hilbert transform of the univariate B-spline preserves the B-spline recurrence. Motivated by this observation, we characterize translation invariant operators that preserve the multivariate B-spline recurrence and analogous results are also provided for the multivariate cube spline. Charles A. Micchelli was supported in part by the US National Science of Foundation under grant CCR-0407476. Yuesheng Xu was supported in part by the US National Science Foundation under grant CCR-0407476, by the Natural Science Foundation of China under grant 10371122, by the Chinese Academy of Sciences under the program “One Hundred Distinguished Chinese Scientists” and by Ministry of Education, People’s Republic of China, under the Changjian Scholarship through Zhongshan University.     

A Geometric Proof of Stallings' Theorem on Groups with More than One End

Stallings showed that a finitely generated group which has more than one end splits as an amalgamated free product or an HNN extension over a finite subgroup. Dunwoody gave a new geometric proof of the theorem for the class of almost finitely presented groups, and separately, using somewhat different methods, generalised it to a larger class of splittings. Here we adapt the geometric method to the class of finitely generated groups using Sageev's generalisation of Bass Serre theory concerning group pairs with more than one end, and show that this new proof simultaneously establishes Dunwoody's generalisation.     

The hyperspace of the regions below continuous maps with the fell topology

For a Tychonoff space X,we use ↓USC F(X) and ↓C F(X) to denote the families of the hypographs of all semi-continuous maps and of all continuous maps from X to I = [0,1] with the subspace topologies of the hyperspace Cld F(X × I) consisting of all non-empty closed sets in X × I endowed with the Fell topology.In this paper,we shall show that there exists a homeomorphism h:↓USC F(X) → Q = [1,1] ω such that h(↓CF(X))=c0 = {(xn)∈Q| lim n→∞ x n = 0} if and only if X is a locally compact separable metrizable space and the set of isolated points is not dense in X.