Interpolation of positive operators

We study problems of interpolation of positive linear operators in couples of ordered Banach spaces. From this viewpoint, we study couples of noncommutative spaces L ₁, L _∞ associated with weights and traces on von Neumann algebras.     

基于二次插值的非饱和土壤水流问题的特征差分方法及数值模拟

本文针对一类非饱和土壤水流问题,提出了基于二次插值的特征差分格式,得到了严谨的L2模误差估计.并作了数值试验,指明方法的有效性.     

Evaluation formulas for Tornheim's type of alternating double series

In this paper, we give some evaluation formulas for Tornheim's type of alternating series by an elementary and combinatorial calculation of the uniformly convergent series. Indeed, we list several formulas for them by means of Riemann's zeta values at positive integers.

     

Modified Householder iterative method free from second derivatives for nonlinear equations

In this paper, we suggest and analyze a new two-step predictor–corrector type iterative method free from second derivatives for solving nonlinear equations of the type f(x)=0. This new method includes the two-step Newton method as a special case. We prove that the new iterative method is of fourth-order. Several examples are given to illustrate the efficiency of this new method and its comparison with other iterative methods. This method can be considered as a significant improvement of the Newton method and its variant forms.     

(Mn1−xPbx)Pb10+ySb12−yS26−yCl4+yO, a new oxy-chloro-sulfide with ∼2 nm-spaced (Mn,Pb)Cl4 single chains within a waffle-type crystal structure

The new oxy-chloro-sulfide (Mn_1−xPb_x)Pb_10+ySb_12−yS_26−yCl_4+yO (x ∈ [0.2-0.3]; y ∈ [0.3-1.6]) was synthesized by dry way at 500-600 °C. A single crystal ∼Mn_0.7Pb_11.0Sb_11.3S_25.3Cl_4.7O indicates a monoclinic symmetry, space group C2/m, with a = 37.480(8), b = 4.1178(8), c = 18.167(4) Å, β = 106.37(3)°, V = 2690.2(9) Å³, Z = 2. Its crystal structure was determined by X-ray single crystal diffraction, with a final R = 5.11%. Modular analysis of the crystal structure reveals a “waffle” architecture, where complex rods with lozenge section delimitate an internal channel filled by a single chain of (Mn_0.7Pb_0.3)Cl₆ octahedra connected by opposite edges. Minimal inter-chain distances are close to 18 Å. The rod wall, two-atom thick, presents, in alternation with S atoms, Pb or (Pb,Sb) cations with prismatic coordination in the internal atom layer, while the external atom layer is constituted exclusively by Sb cations with dissymmetric square pyramidal coordination. A (Pb,Sb)₂S₂ fragment connects two successive rods along (2 0 1) to form a waffle-type palissadic layer. The unique O position, half filled, presents the same environment than the isolated O positions in the oxy-sulfide Pb₁₄Sb₃₀S₅₄O₅, or oxy-chloro-sulfides Pb₁₈Sb₂₀S₄₆Cl₂O and (Cu,Ag)₂Pb₂₁Sb₂₃S₅₅ClO. This compound belongs to a pseudo-homologous series of chalcogenides with waffle structure, ordered according to the size of their lozenge shape channel. Such a complex senary compound of the oxy-chloro-sulfide type illustrates the structural competition between three cations, on one hand, and, on the other hand, three anions. This compound is of special interest regarding the 1D distribution of magnetic Mn²⁺ atoms at the ∼2 nm scale.     

Asymptotic Distribution of Nodes for Near-Optimal Polynomial Interpolation on Certain Curves in R 2

Let E\subset \Bbb R ^s be compact and let d _n ^E denote the dimension of the space of polynomials of degree at most n in s variables restricted to E . We introduce the notion of an asymptotic interpolation measure (AIM). Such a measure, if it exists , describes the asymptotic behavior of any scheme τ _n ={ \bf x _k,n } _k=1 ^dnE , n=1,2,\ldots , of nodes for multivariate polynomial interpolation for which the norms of the corresponding interpolation operators do not grow geometrically large with n . We demonstrate the existence of AIMs for the finite union of compact subsets of certain algebraic curves in R ² . It turns out that the theory of logarithmic potentials with external fields plays a useful role in the investigation. Furthermore, for the sets mentioned above, we give a computationally simple construction for ``good' interpolation schemes. November 9, 2000. Date revised: August 4, 2001. Date accepted: September 14, 2001.     

串联系统可靠性虚拟系统法置信下限的小样本性质

本文讨论了具有r个成败型元件串联系统可靠性的置信下限问题。研究了虚拟系统法置信下限的小样本性质,证明了,在通常情况下虚拟系统法置信下限要大于常见的L-M法置信下限.更一般地,本文证明了在成败型试验中,当成功数与试验数之比保持不变时,试验次数的增加将直接缩小成功率置信区间的长度。     

纯量反馈系统同时强镇定的充分条件

一个稳定的补偿器可同时镇定n个对象(同时强镇定)等价于一个补偿器(不一定稳定)同时镇定n 1个对象(同时镇定)．两个以上对象的同时强镇定和三个以上对象的伺时镇定是线性系统中一个急待解决的公开问题．文中所作的基本假定是所有的对象具有相同的简单不稳定零点，在此条件下给出了n个对象同时强镇定的一个充分条件．当仅有一个不稳定零点时．容易检验是否同时强镇定，否则仅需确定n个对象的不稳定零点并且判定由不稳定零点导出一个相应矩阵是正定的，就能判定n个对象同时强镇定．因此是一个易于检验的充分条件．文章同时给出了n个对象同时强镇定的算法，丰富了同时强镇定的充分条件．     

Strong asymptotics in Lagrange interpolation with equidistant nodes

In this paper we prove three conjectures of Revers on Lagrange interpolation for f_λ(t)=|t|^λ,λ>0, at equidistant nodes. In particular, we describe the rate of divergence of the Lagrange interpolants L_N( f_λ,t) for 0<|t|<1, and discuss their convergence at t=0. We also establish an asymptotic relation for max_|t|1| |t|^λ−L_N( f_λ,t)|. The proofs are based on strong asymptotics for |t|^λ−L_N( f_λ,t), 0|t|<1.     

The application of spectral distribution of product of two random matrices in the factor analysis

In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted.