关于矩阵方程AXB-C=0的最佳逼近解的一个注记

举反例说明：对于矩阵的2-范数，存在矩阵A，B和C，使得A^†CB^†不是矩阵方程AXB-C=0的最佳逼近解，其中A^†和B^†分别是A和B的Moore-Penrose逆.     

相对论性量子场反常维度与动量空间维度——纪念爱因斯坦《相对论》诞生百周年

 量子场中的奇异性(发散困难)被量子场反常维度C_B(g_R,e_R)与D=D₀-ε(D₀=4)中ε参数所控制,C_B(g_R,e_R)与ε可以相互替换.C_B(g_R)(QCD)的渐进自由被实验√S=30~1 800 GeV所证实.强相互作用的电荷依赖为C_B(g_R,±)=C_B(g_R,0)[1+be_R/g_R]²(b≤1).非线性相互作用改变了量子场的维度与量子场的拓扑不变性.     

GL2(C)的一些不可约表示

设G=GL₂(C), 并且B是G的标准Borel子群, 并且CG, CB分别是群G和群B的在复数域C上的群代数.对于任意B的特征标θ, 定义G的离散诱导模M(θ) = CG×_CBθ. 证明了当θ是反支配权时,M(θ)是个不可约表示.由此给出了一类GL₂(C)全新的、无限维的不可约表示.     

GH105合金元素含量对析出相的影响

采用Thermo-Calc及JMatPro软件,对GH105合金在600～1 600℃的相图进行计算,并对C,Cr,Co,Mo,Zr,Ti,Al以及微量B对GH105合金主要析出相MC,M₂₃C₆,M₃B₂,μ,σ和γ''的影响进行探究。结果表明：C的增加提高了M₂₃C₆和MC相的析出量和M₂₃C₆相的析出温度,降低了σ相的析出量和析出温度,同时μ相的析出温度明显下降;Cr的增加显著提高了σ相的析出量和析出温度;Co的增加提高了μ相和σ相的析出量和析出温度,降低了M₂₃C₆相的析出量和析出温度;Mo的增加显著提高了μ相和σ相的析出量和析出温度;Zr的增加提高了σ相的析出量和析出温度,提高了MC相的析出量,降低了M₂₃C₆相的析出量和析出温度;B的增加显著提高了M₃B₂相的析出量;Al,Ti和m（Al）：m（Ti）的增加,提高了γ''相的析出量,其中Al和m（Al）：m（Ti）相的增加还提高了γ''相的析出温度。     

CH2(X3B1)分子的结构与解析势能函数

 运用密度泛函理论(DFT)的B3LYP方法在6-311++G^**水平上,对基态CH₂分子的结构进行了优化计算,得到CH₂分子的稳定结构为C_2v构型,电子态为X³B₁,平衡核间距R_CH=0.1072nm、离解能D_e=8.034eV,用多体项展式理论推导了基态CH₂分子的解析势能函数,其等值势能图准确再现了基态CH₂分子的结构特征及其势阱深度与位置.     

含频率噪声信号对单模激光损失模型随机共振的影响

 采用抽运噪声和实虚部关联的量子噪声驱动的单模激光损失模型,运用线性化近似方法计算了频率有涨落的周期信号输入时激光系统的输出光强的相关函数、功率谱及信噪比.研究了信号的频率噪声强度D、振幅B和频率Ω对信噪比与噪声关联系数共振曲线的影响,结果发现:频率的强度D会减小输出光强的信噪比,使共振现象减弱.     

N,N′-双水杨醛缩二氨基乙醚的合成和晶体结构

合成了一种新的西佛碱配体N,N''双水杨醛缩二氨基乙醚,并采用x射线单晶衍射法测定了它的晶体结构。该晶体属正交晶系空间群P_bcn,a=5.667(2)Å,b=9.192(3)Å,c=31.829(11)Å,v=1658.2(7)ų,分子式为C₁₈H₂₀N₂O₃,Mr=312.36,Z=4,D_C=1.251g·cm^-3,晶体结构测定和UV,IR谱均表明分子内形成氢键。在甲醇溶液中有一个荧光发射带,λ_max=443nm。     

四元数张量方程A*NX=B超对称极小范数最小二乘解

本文研究一种实张量和向量的乘积，并讨论四元数张量方程A*_NX=B的最小二乘超对称问题，其中*_N为张量A与X的Einstein积。我们的主要研究是求出此张量方程的超对称极小范数最小二乘解，并提供求解的数值算法和数值例子。     

钠基蒙脱土对水分子吸附机理的第一性原理计算

钠基蒙脱土吸水膨胀是造成深部巷道中软岩膨胀的主要原因。为了解决钠基蒙脱土吸水膨胀带来的工程安全问题，本文基于量子力学的第一性原理，利用材料模拟软件VASP计算模拟钠基蒙脱土对水分子吸附的机理，并研究吸附能、弹性常数与吸附量之间的关系。计算结果表明：钠基蒙脱土层间吸附水分子之后，体积主要是沿着c轴方向膨胀，体系吸附能与吸水量总体成线性正相关的关系。随着钠基蒙脱土层间水分子吸附量的增多，弹性常数C₁₁、C₂₂、C₃₃大于其他弹性常数，且C₃₃明显大于C₁₁、C₂₂。此外，钠基蒙脱土的体积模量B、剪切模量G、杨氏模量E都随吸水量的增加而减小。该计算结果为解决钠基蒙脱土相关的工程安全问题提供了理论指导。     

总目次

对于两个非负矩阵A和B的Hadamard积,利用特征值包含域定理给出谱半径的新上界估计式.数值例子表明新估计式在某些情况下比现有的估计式更为精确,并且这些估计式只依赖于两个非负矩阵的元素,更容易计算.     

A categorical interpretation of Yetter-Drinfel’d modules

It is known that any strict tensor category (C,⊗,I) can determine a strict braided tensor categoryZ(C), the centre ofC. WhenA is a finite Hopf algebra, Drinfel’d has proved thatZ( _AM) is equivalent to_D(A)M as a braided tensor category, where_AM is the left A-module category, andD(A) is the Drinfel’d double ofA. This is the categorical interpretation ofD(A). Z( _AM) is proved to be equivalent to the Yetter-Drinfel’d module category,_AYD ^A as a braided tensor category for any Hopf algebraA. Furthermore, for right A-comodule categoryM ^A, Z(M^A) is proved to be equivalent to the Yetter-Drinfel’d module category_AY D^A as a braided tensor category. But,in the two cases, the Yetter-Drinfel’d module category_AY D^A has different braided tensor structures.     

应用正交试验法的RHT模型参数敏感性研究

基于RHT模型的理论分析,选出A、N、B、M、B_Q、f_s/f_c、T_ten、D₁和E_f,min 9个参数作为正交试验分析参数,研究RHT模型中参数的敏感性.运用Autodyn程序对弹丸侵彻混凝土过程进行数值分析,确定了不同参数、不同水平值下弹丸的侵彻深度.采用极差分析法对参数的敏感程度进行量化分析,得出9个参数的敏感性排序为B > E_f,min > T_ten > f_s/f_c > N > M > D₁ > B_Q > A.结合3组典型数值试验损伤云图和侵彻深度的对比分析,认为参数B、E_f,min和T_ten对数值模拟试验结果的影响极大,应采取可靠的技术手段准确确定其取值.      

Composition operators with linear fractional symbols on vector-valued Bergman spaces

0　IntroductionLetDdenotetheopenunitdiskinthecomplexplaneC , DitsboundaryanddAtheLebesguemeasureonD ,normal izedsothatA(D) =1.ForaBanachspace (X ,‖·‖X) ,wewriteH(D ,X)fortheclassofallX valuedanalyticfunctionsonD .Let1≤ p<∞ ,theX valuedBergmanspaceBp(X)istheclassofallf∈H(D ,X) forwhich‖f‖Bp(X) =∫D‖f(z)‖pXdA(z) 1 /p <∞ (1)IfX =C,thenwewriteBp =Bp(C) fortheclassicalBergmanspaces.Letφ∶D→Dbeananalyticself mapofD .Thenthee quation Cφf=f φdefinesacompositionoperator…     

Orientational domains at room temperature in La0.33Ca0.67MnO3 perovskite

Orientational domains at room temperature in orthorhombic perovskite La_0.33Ca_0.67MnO₃ were studied by group-theory and observed systematically using transmission electron microscopy. There are six orientational variants (A, A′, B, B′, C andC′) in orthorhombic perovskite La_0.33Ca_0.67MnO₃. Their orthorhombicb _o directions are parallel to thea _p,b _p andc _p directions of the cubic prototypic perovskite, respectively. In each case there are two orientational variants (e.g.,A andA′) with theira _o andc _o axes interchanged. Among the possible 15 boundaries between these 6 variants there are only two types of domain boundaries: (1) m<100>boundariesC′/C, A′/A, andB′/B. (2) m<110>boundaryiesC′/A, C′/A′, C′/B, C′/B′, C/A, C/A′, C/B, C/B′, B′/A, B′/A′, B/A, andB/A′. Foundation item: Supported by the National Natural Science Foundation of China (19974031) and US DOE(DE-AC02-98CH10886) Biography: WANG Ren-hui (1937-), male, Professor.     

New classes of interconnection topology structures and their properties

In the first part of this paper, three generalizations of arrangement graphA _n,k of [1], namelyB _{n, k},C _{n, k} andD _{n, k}, are introduced. We prove that all the three classes of graphs are vertex symmetric, two of them are edge symmetric. They have great faulty tolerance and high connectivity. We give the diameters ofB _{n, k}andC _n,k, the Hamiltonian cycle ofC _{n, k} and Hamiltonian path ofB _n,k. We list several open problems, one of them related to the complexity of sorting algorithm on the arrangement graphs. All these graphs can be thought as generalizations of star graph but are more flexible so that they can be considered as new interconnection network topologies. In the second part of this paper, we provide other four classes of combinatorial graphes,Ch _n, Cy_n, Zh_n, andZy _n. Many good properties of them, such as high node-connectivity, node symmetry, edge symmetry, diameter, ets., are shown in this paper.     

DNA modular subtraction algorithm based on linear self-assembly

This paper presents a DNA algorithm based on linear self-assembly which gives the result of the modular subtraction operation of two nonnegative integers. For two n-bit nonnegative integers A and B, the algorithm gives the result of A-B mod 2 ⁿ . An extended borrow tag which indicates the relation of the minuend and the subtrahend is included in the resulting strand so that the pre-classification based on A>B or B>A is not required before the experiment. From the resulting strand, we can draw the information of operation result, operands, borrow, and the tag of the relation between the minuend and the subtrahend. The algorithm takes advantage of the parallelism characteristic of DNA computing: while given two sets of operands (one the minuend set and the other subtrahend set), the modular subtraction operation of these two sets can be achieved by a parallel processing procedure. The feasibility of the algorithm is based on a known experiment. The algorithm is of spontaneous characteristic which prevents the scale of the experimental procedures from growing with the length of the operands. As for the length of the operands n, there are O(n) kinds of strands required in the experiment, and the biochemical experimental procedures can be accomplished in constant number of steps.