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.     

几何位置对封闭方腔内水平孤立平板自然对流换热的影响

本文以冰箱蒸发器等实际问题为背景，以空气为介质用数值模拟方法研究了封闭方腔内水平孤立平板层流自然对流时Ｒａ数及平板位置变化对Ｎｕｍ的影响，得出了可供工程应用参考的结论。同时用烟可视化的实验验证了计算结果的正确性。     

无陀螺仪惯性系统构型中安装误差分析与标定

针对一种立方构型的无陀螺仪惯性系统，分析了构型安装误差对惯性系统测量精度的影响及构型误差的标定方法。首先分析了立方构型下载体姿态与加速度的解算方法，然后给出了安装误差对于系统输出的影响，最后通过分析安装误差的敏感性因子给出了一种有针对性的标定方法。理论分析与仿真计算表明，惯性系统角速度与线速度输出是加速度计输出的线性组合，构型安装误差对无陀螺仪惯性系统测量精度的影响非常明显，在给出的标定方案中，方向安装误差标定精度较位置安装误差要高，而且转台角速度对位置安装误差的标定精度影响很大，对方向安装误差影响较小；无陀螺仪惯性系统中安装误差不可忽略，必须进行标定，据此提出的一种标定方案简单、切实可行。     

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.     

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.     

Homology representations arising from the half cube, II

In a previous work, we defined a family of subcomplexes of the n-dimensional half cube by removing the interiors of all half cube shaped faces of dimension at least k, and we proved that the reduced homology of such a subcomplex is concentrated in degree k−1. This homology module supports a natural action of the Coxeter group W(Dn) of type D. In this paper, we explicitly determine the characters (over C) of these homology representations, which turn out to be multiplicity free. Regarded as representations of the symmetric group Sn by restriction, the homology representations turn out to be direct sums of certain representations induced from parabolic subgroups. The latter representations of Sn agree (over C) with the representations of Sn on the (k−2)-nd homology of the complement of the k-equal real hyperplane arrangement.     

方腔尺寸对封闭方腔内多块孤立平板自然对流换热影响的数值分析

１引言封闭方腔内多块孤立平板自然对流换热是许多电子设备散热的近似模拟，因此，了解封闭方腔内多块孤立平板的自然对流换热规律，对于电子设备的热设计具有重要的意义。国内外许多学者针对这方面的问题进行了较为广泛的研究［１－５］，许多学者研究了封闭方腔内一块或...