空间l∞(Xn)中的弱紧性

本文首先得到了以l_∞(X_n)为值域的有界线性算子为弱紧算子的一个充要条件和一个充分条件，讨论了l_∞(X_n)中的弱收敛，然后给出了l_∞(X_n)中弱紧性的几种等价刻画．     

性质（U）及其在lp（Xn）上的提升

首先讨论了具有性质（ｕ）的Ｂａｎｃｈ空间的若干性质，然后证明了性质（ｕ）在某条件下可以提升到空间l_p（X_n）(1≤p < ∞)上去．     

退化弱拟正则映射的正则性

本文考虑退化弱拟正则映射.利用Hodge分解、逆Holder不等式等工具,证明了其正则性结果:存在指数q₁=q₁（n,l,K）1,q_1loc(Ω,Rⁿ)，都有f∈W^1,l_loc(Ω,Rⁿ) ，即f为退化拟正则映射.     

最近邻密度估计的一致收敛速度

设X₁,…X_n是从具密度函数f的一维总体中抽出的iid。样本。1965年,Loftsgarden等在[1]中提出了如下的估计f(x)的方法:选择最小的a_n(x)=a_n(x;X₁,…,X_n),使区间[x-a_n(x),x+a_n(x)]中至少包含X₁,…,X_n中的K_n个样本     

空间的几种超投影性质及其局部化

讨论Banach空间几种超投影性质(及其相应的局部化性质)之间的关系,证明了在Banach空间X自反的条件下,X是l_p-次投影空间的充要条件是X^*是l_p-超投影空间,X是局部l_p-次投影空间的充要条件是X^*是局部l_p-超投影空间,以及X是局部次投影空间的充要条件是X^*是局部超投影的。其中1/p+1/q=1(p>1,q>1)。     

On Cramer Approximations under Violation of Cramer's Condition

Let X ₁, X ₂,... be independent identically distributed random variables with distribution function F, S ₀ = 0, S _n = X ₁ + ⋯ + X _n , and Sˉ _n = max_1⩽k⩽n S _k . We obtain large-deviation theorems for S _n and Sˉ _n under the condition 1 − F(x) = P{X ₁ ⩾ x} = e^−l(x), l(x) = x ^α L(x), α ∈ (0, 1), where L(x) is a slowly varying function as x → ∞. __________ Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 447–456, October–December, 2005.     

关于CW复形的同伦群的挠

本文讨论了CW复形X的同伦群π_nX的p挠群的性质.利用X的Z_p系数同调群H_*(X;Z_p)以及基本群π₁X的性质,给出了对无穷多个n,Tor(π_n,X,Z_p)≠0的充分条件.     

矩阵方程A1X1B1 + A2X2B2 + · · · + AlXlBl = C的中心对称解及其最佳逼近

设矩阵X=(x_ij) ∈^Rn×n, 如果xi_j=x_{n+1-i, n+1-j} (i,j=1,2, …,n), 则称X是中心对称矩阵. 该文构造了一种迭代法求矩阵方程A₁X₁B₁+A₂X₂B₂+…+A_lX_lB_l=C的中心对称解组(其中[X₁, X₂, …, X_l]是实矩阵组). 当矩阵方程相容时, 对任意初始的中心对称矩阵组[X₁⁽⁰⁾, X₂⁽⁰⁾, …, X_l⁽⁰⁾], 在没有舍入误差的情况下,经过有限步迭代,得到它的一个中心对称解组, 并且, 通过选择一种特殊的中心对称矩阵组, 得到它的最小范数中心对称解组. 另外, 给定中心对称矩阵组[X₁, X₂, …, X_l], 通过求矩阵方程A₁X₁B₁+A₂X₂B₂+…+A_lX_lB_l=C(其中C=C-A₁X₁B₁-A₂X₂B₂－…－A_lX_lB_l)的中心对称解组, 得到它的最佳逼近中心对称解组. 实例表明这种方法是有效的.     

辛流形M×R2n中的Hofer-Zehnder辛容量及应用

本文讨论辛流形(M×R²ⁿ,ωσ)中的 Hofer-Zehnder辛容量,定义 l₁(M,ω)=:inf{〈ω,α〉|〈ω,α〉>0,α∈π₂(M)}.证明若l₁(M,ω)>0,πr²<1/2l₁(M,ω),则C_HZ(M×B(r))=C_HZ(M×Z(r))=πr².当M等于点{P}时,就得到目前已知的结论.设CPⁿ是复投影空间,ω是CPⁿ上的辛形式,满足∫_cp¹ω=n+1,那么当πr²<1/2(n+1)时,C_HZ(CPⁿ×B(r))=C_HZ(M×Z(r))=πr².作为应用,还将证明M×Z((l₁(M,ω)/2π)^1/2)中的 Weinstein猜想成立.     

纳米复合材料Fex(SiO2)1-x中的界面相互作用和渗透效应对磁性的影响

采用机械合金法制备了纳米复合材料Fe_x(SiO₂)_1-x系列样品 .用X射线粉末衍射 (XRD)、透射电子显微镜 (TEM )、M ssbauer谱和Faraday磁天平系统地研究了该系列样品不同Fe合量和不同球磨时间的微结构和磁性 .实验表明样品的微结构和磁性与球磨时间和Fe含量密切相关 .当样品的Fe含量少于 2 0wt% ,并球磨了 80h后呈现出非常复杂的微观结构 :α -Fe纳米晶粒和Fe团簇镶嵌在SiO₂ 基质中 ,形成α -Fe纳米岛状和纳米尺度的类三明治结构 .Fe-SiO₂ 界面的相互作用和渗透效应、纳米晶的尺寸效应和类三明治的特殊微观结构导致了纳米复合材料Fe_x(SiO₂)_1-x的物理性能的变化     

F_2+vF_2上的循环码

本文研究了环F_2+vF_2上的循环码.利用标准形生成元集刻画了环F_2+vF_2上的循环码的代数结构,证明了环F_2+vF_2上的每一个非零的循环码均有唯一的标准形生成元集,进而得到了每一个循环码均是由一个多项式生成的.     

The decomposition of Kv into K2×K5''''s

The decomposition of the complete graph Kv into Kr×Kc's, the products of Kr and Kc,is originated from the use of DNA library screening. In this paper, we consider the case where r=2 and c = 5, and show that such a decomposition exists if and only if v ≡ 1 (mod 25).     

Laser molecular-beam epitaxy and second-order optical nonlinearity of BaTiO3/SrTiO3 superlattices

A series of c-axis oriented BaTiO₃/SrTiO₃ superlattices with the atomic-scale precision were epitaxially grown on single-crystal SrTiO₃(l00) substrates using laser molecular-beam epitaxy (LMBE). A periodic modulation of the intensity of reflection high-energy electron diffraction (RHEED) in BaTiO₃ and SrTiO₃ layers was observed and attributed to the lattice-misfit-induced periodic variation of the terrace density in film surface. The relationship between the second-order nonlinear optical susceptibilities and the superlattice structure was systematically studied. The experimental and theoretical fitting results indicate that the second-order nonlinear optical susceptibilities of BaTiO₃/SrTiO₃ superlattices were greatly enhanced with the maximum value being more than one order of magnitude larger than that of bulk BaTiO₃ crystal. The mechanism of the enhancement of the second-order optical nonlinearity was discussed by taking into account the stress-induced lattice distortion and polarization enhancement.     

具有广义可行性余弦序列的E1?Ed型距离正则图

给出了具有广义可行性余弦序列的E₁?E_d型距离正则图的特征,并计算了这类图的交叉数.     

Differential-geometric Newton method for the best rank-(R1, R2, R3) approximation of tensors

An increasing number of applications are based on the manipulation of higher-order tensors. In this paper, we derive a differential-geometric Newton method for computing the best rank-(R ₁, R ₂, R ₃) approximation of a third-order tensor. The generalization to tensors of order higher than three is straightforward. We illustrate the fast quadratic convergence of the algorithm in a neighborhood of the solution and compare it with the known higher-order orthogonal iteration (De Lathauwer et al., SIAM J Matrix Anal Appl 21(4):1324–1342, 2000). This kind of algorithms are useful for many problems. This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with its authors. Research supported by: (1) Research Council K.U.Leuven: GOA-Ambiorics, CoE EF/05/006 Optimization in Engineering (OPTEC), (2) F.W.O.: (a) project G.0321.06, (b) Research Communities ICCoS, ANMMM and MLDM, (3) the Belgian Federal Science Policy Office: IUAP P6/04 (DYSCO, “Dynamical systems, control and optimization”, 2007–2011), (4) EU: ERNSI. M. Ishteva is supported by a K.U.Leuven doctoral scholarship (OE/06/25, OE/07/17, OE/08/007), L. De Lathauwer is supported by “Impulsfinanciering Campus Kortrijk (2007–2012)(CIF1)” and STRT1/08/023.     

Microstructure of a-SiOx:H

A set of a-SiO_x:H (0.52 <x< 1.58) films are fabricated by plasma-enhanced-chemical-vapor-deposition (PECVD) method at the substrate temperature of 250°C. The microstructure and local bonding configurations of the films are investigated in detail using micro-Raman scattering, X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared spectroscopy (FTIR). It is found that the films are structural inhomogeneous, with five phases of Si, Si₂O:H, SiO:H, Si₂O₃:H and SiO₂ that coexist. The phase of Si is composed of nonhydrogenated amorphous silicon (a-Si) clusters that are spatially isolated. The average size of the clusters decreases with the increasing oxygen concentration x in the films. The results indicate that the structure of the present films can be described by a multi-shell model, which suggests that a-Si cluster is surrounded in turn by the subshells of Si₂O:H, SiO:H, Si₂O₃:H, and SiO₂.     

Phase transition in layered perovskite-like manganate Ca3Mn2O7 under high pressure

In situ high pressure energy dispersive X-ray diffraction measurements on the layered perovskite-like manganate Ca₃Mn₂O₇ powder under pressures were performed by using the diamond anvil cell with synchrotron radiation. The results show that the structure of layered perovskite-like manganate Ca₃Mn₂O₇ is unstable under pressure due to the easy compression of NaCl-type blocks. The structure of Ca₃Mn₂O₇ underwent two phase transitions under pressures in the range of 0–35 GPa. One was at about 1.3 GPa with the crystal structure changing from tetragonal to orthorhombic. The other was at about 9.5 GPa with the crystal structure changing from orthorhombic back to another tetragonal.     

Liquid structure of undercooled Cu70Ni30 alloy

Experiments of X-ray diffraction for liquid Cu₇₀Ni₃₀ alloy above and below its liquidus (l 230°C) have been carried out. By the analysis of experimental results, it is discovered that difference between structures of liquid and undercooled Cu₇₀Ni₃₀ alloy is their cluster sizes. The correlation radius of cluster is 1.125 nm and the atom number of cluster is 403 at l 250—l 400°C, and they are 1.3 nm and 704 respectively at the undercooled liquid state (1 200°C). The structure of liquid Cu₇₀Ni₃₀ alloy is fcc short order and its solid structure, fcc, is kept from liquid fcc short order.     

Cut elimination for S4n and K4n with the central agent axiom

We analyze the multimodal logic S4 _n with the central agent axiom. We present a Hilbert-type calculus, then derive a Gentzen-type calculus with cut, and prove a cut-elimination theorem. The work shows that it is possible to construct a cut-free Gentzen-type calculus for this logic. Moreover, it also provides analogous results for the multimodal logic K4 _n with the central agent axiom.     

Synthesis and characterization of C3N4 hard films

C₃N₄ films have been synthesized on both Si and Ft substrates by microwave plasma chemical vapor deposition (MPCVD) method. X-ray spectra were calculated for single phase α-C₃N₄ and β-C₃N₄ respectively. The experimental X-ray spectra of films deposited on both Si and Pt substrates showed all the strong peaks of α-C₃N₄ and β-C₃N₄ so the films are mixtures of α-C₃N₄ and β-C₃N₄. The N/C atomic ratio is in the range of 1.0–2.0. X-ray photoelectron spectroscopy (XPS) analysis indicated that the binding energy of Is and N ls are 286.2 eV and 399.5 eV respectively, corresponding to polarized C-N bond. Fourier transform infrared absorption (FT-IR) and Raman spectra support the existence of C-N covalent bond in the films. Nano-indentation hardness tests showed that the bulk modulus of a film deposited on Pt is up to 349 GPa