Multivariate Gini Indices

Two extensions of the univariate Gini index are considered:R_D, based on expected distance between two independent vectors from the same distribution with finite meanμ ^d; andR_V, related to the expected volume of the simplex formed fromd+1 independent such vectors. A new characterization ofR_Das proportional to a univariate Gini index for a particular linear combination of attributes relates it to the Lorenz zonoid. TheLorenz zonoidwas suggested as a multivariate generalization of the Lorenz curve.R_Vis, up to scaling, the volume of the Lorenz zonoid plus a unit cube of full dimension. Whend=1, bothR_DandR_Vequal twice the area between the usual Lorenz curve and the line of zero disparity. Whend>1, they are different, but inherit properties of the univariate Gini index and are related via the Lorenz zonoid:R_Dis proportional to the average of the areas of some two-dimensioned projections of the lift zonoid, whileR_Vis the average of the volumes of projections of the Lorenz zonoid over all coordinate subspaces.     

三维Minkowski空间中的曲面及其可积性

利用可积系统的思想,借助三维Minkowski空间L3的矩阵模型,研究了L3中具有调和逆平均曲率的类空曲面和洛伦兹调和逆平均曲率类时曲面的可积性及其形变.     

关于三次高斯和的均值

主要研究三次高斯和的均值性质，并给出一个较强的渐近公式。     

Oscillations of the Solutions of Nonlinear Delay Hyperbolic Partial Differential Equations

In this paper, oscillatory properties of solutions of certain hyperbolic partial differential equations with multi-delays are investigated and a series of sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by delays.     

北京自由电子激光最近进展──实现饱和振荡

北京自由电子激光(BFEL)装置于1993年底在10.68μm处实现了饱和振荡.输出激光能量为3mJ,饱和平顶宽度2μs.对应饱和振荡平均功率为210kW(宏脉冲),峰值功率约为20MW,比自发辐射高8个量级,单程小讯号净增益为24%,转换效率为0.45%,与理论预期结果相符.光束质量接近衍射极限.目前装置可工作于9-11μm.     

沉浮,俯仰及控制面振动引起的跨音速非定常气动载荷计算

本文将文献[9]提出改进的通量分裂方法,应用于随时间变化的贴体网格中,建立了可用于求解非定常Euler方程的通量分裂方法.该方法是以连续的特征值分离为基础,它具有方法简单,便于推广使用的特点.同时克服了Steger-Warming通量分裂方法存在的问题.对通量分裂后的Euler方程.利用MUSCL型迎风差分建立了具有二阶精度的有限体积方程.文中以NACA64A—10翼型为例,对其在跨音速流场中进行沉浮、俯仰及带有振动控制面引起的非定常气动载荷进行了计算.部分计算结果与相应的实验结果进行了比较,吻合良好     

局部对称共形平坦黎曼流形中具有平行平均曲率向量的子流形

本文把[1]的结论推广到了环绕空间是局部对称共形平坦的情形,即获得了:设M~是局部对称共形平坦黎曼流形N~+p(p>1)中具有平行平均曲率向量的紧致子流形,如果则M~位于N~+p的全测地子流形N~+1中。其中S,H分别是M~的第二基本形式长度的平方和M~的平均曲率,T_C、t_c分别是N~+p的Ricci曲率的上、下确界,K是N~+p的数量曲率。     

Studies on the properties of flow-induced oscillation and sound radiation in streamlined protuberant special cavities

I.IntroductionAsanuidpassingthroughthecavityatcertainflowrate,themediuminthemouthandthccavityisoscillatingandsoundisradiated.Noton1ystochasticturbu1encenoiscispossi-blyproducedbutsinglefrequencysoundofspecia1lydesignatedpitchisalsoproduced.Andthusthespcctrumofthcradiatedsoundisshownascontinuousspectrumandcharacteristiclinespcctrum.Inthiscascwcmaycallitflow-inducedosci1lation.Flow-inducedoscillationandsoundradiationcanbeproducedasafluid(waterorgas)passingthroughthecavitybysinkingcavityunderint…     

On the absolute matrix summability of Fourier series and some associated series

The object of the paper is to study the absolute matrix summability problem of Fourier series, conjugate series and some associated series under a new set of conditions on matrix methods, generalising many known results in the literature.     

OSCILLATION FOR SOLUTIONS OF SYSTEMS OF N-TH ORDER PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, some sufficient conditions for the oscillation for solutions to systems of n-th order partial functional differential equations are obtained.