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.     

天然树脂局部结构的径向分布函数研究

本工作用x射线衍射技术分析计算了二种天然树脂的局部结构参数,由测得的衍射强度数据求出了它们的结构因子I(r)和径向分布函数RDF(r),并由此得到了分子链内临近原子和次临近原子平均间距、配位数和短程有序畴。     

On CCE graphs of doubly partial orders

Let D be a digraph. The competition-common enemy graph (CCE graph) of D has the same set of vertices as D and an edge between vertices u and v if and only if there are vertices w and x in D such that (w,u), (w,v), (u,x), and (v,x) are arcs of D. We call a graph a CCE graph if it is the CCE graph of some digraph. In this paper, we show that if the CCE graph of a doubly partial order does not contain C₄ as an induced subgraph, it is an interval graph. We also show that any interval graph together with enough isolated vertices is the CCE graph of some doubly partial order.     

HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

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Thermal stability of poly(mono-n-alkylitaconates) and mono-n-alkylitaconate-co-vinylpyrrolidone copolymers I

Poly(monoitaconates) containing octyl, decyl and dodecyl groups and random monoalkylitaconate-co-vinylpyrrolidone copolymers were studied by thermogravimetric analysis. Copolymers of mono-n-octylitaconate (MOI), mono-n-decylitaconate (MDI), and mono-n-dodecylitaconate (MDoI), respectively, with N-vinyl-2-pyrrolidone (VP) of different compositions were studied by dynamic thermogravimetric analysis. The thermal stability of the copolymers depends on the structure of the monoitaconate comonomer and on the composition of the copolymer The kinetic analysis of the degradation data shows that the thermal decomposition of these copolymers can be described by several kinetic orders depending on the copolymer and on the composition. The relative thermal stability of the copolymers increases as the VP content increases and as the length of the side chain of the itaconate increases, following the same trend as the flexibility of the copolymers in solution.     

Higher-order implicit strong numerical schemes for stochastic differential equations

Higher-order implicit numerical methods which are suitable for stiff stochastic differential equations are proposed. These are based on a stochastic Taylor expansion and converge strongly to the corresponding solution of the stochastic differential equation as the time step size converges to zero. The regions of absolute stability of these implicit and related explicit methods are also examined.     

关于Fejer点上的一种复有理型插值的一致逼近阶

设D是一个Jordan,Г为其边界，并设Г满足Aльпер条件。本文得到了一种基于Fejer点的有理型插值算子对于f(z)∈C（Г）的一致逼近阶。     

二阶椭圆型微分方程解的振动定理

考虑二阶非线性椭圆型微分方程∑^n_{i,j}∂/∂x_i{A_{i,j}(x,y)∂/∂x_j}+q(x)f(y)=0 (E)，其中q(x)在外区域 Ω∈R\+n上变号. 利用偏Riccati变换和积分平均技巧, 建立了方程(E)所有解振动的充分准则.     

Lehmer序列中的平方数

设V_n(R,Q)表示参数为R和Q的Lehmer伴随序列,如果R和Q为互素奇数且D=R-4Q>0,我们找出了满足Q_n(R,Q)或nQ_n(R,Q)是平方数的所有奇数n,这里Q_n(R,Q)R~(1/2)=V_n(R,Q)。     

The optical near-field speckles and their first order statistics on the basis of the integral equations of electromagnetic field

Speckle fields are the random light wave distributions produced when the light fields are scattered from random surfaces or a random medium. They appear in many optical phenomena that are related to light propagations[1,2] and have found wide appli-cations in a variety of scientific and technical fields. The examples of the recent impor-tant applications of speckles include the analysis of the movement of the granules[3], the three-dimensional imaging for the microstructures of metal nanocryst…