全正矩阵的逆阵的P—范数的一个性质

首先引进必要的定义和記号。定义.n×n的方陣是全正的,是指它的任何子陣的行列式。A_r~(-1):=(α_(ij)~((r)))_(i,j)~r表示A_r的逆陣,r=1,2,…,n。向量x∈R~n的p范数定义为‖x‖_p:=(sum from i=1 to n(|x_i|~p))~(1/r),相应的矩阵,A_n的p范数定义为‖A_n‖_p:=(?)(‖A_nx‖_p)/(‖x‖_p)。     

近于凸函数相邻系数的一点注记

成立的最佳值A,B是很有趣的,此问题与著名的Littlewood问题紧密相连,有很多数学家进行过研究,目前最好结果为胡克教授所得-2.793<|a_(n+1)|-|a_n|<3.26对于f(z)∈Sc,Hamilton已得||a_(n+1)-|a_n||<3,并且对f∈Sc,在解决Robertson猜测的同时,他也提出了似乎有||a_(n+1)|-|a_n||≤1成立,Koepf得到||a_3|-|a_2||≤1成立.本文对f(z)∈Sc∩S(a)时,得到||a_(n+1)|-|a_n|≤1 设函数f(z)在单位圆△:|z|<1内解析单叶,且有展开式     

单叶函数相邻两系数模之差

设 f_p(z)=∑~∞_(n=0)C~(P)_n(P+1)z~(n(P+1))εSp 在|z|<1内的 p 次对称单叶函数,(p=1时 f_1(z)=f(z),C~(1)_n=C_n)Γ.М.Γалуэин曾得到:||C_(n+1)|-|C_n||≤A_n~(1/4)log n n=2,3,…… (1)||C~(2)_(2n+1)|-|G~(2)_(2(n-1)+1))|≤B_n~(-(1/4))log n n=2,3,…… (2)其中 A 和 B 都是常数。М.Бернацкий改进(1)为:||C_(n+1)|—|C_n||≤C(log n) n=2,3,…… (3)其中是 C 常教。对于 p=1,2,3对,张玉麟及龚升都已得到:     

矩阵求逆条件数在误差估计中的最优性

本文给出了矩阵求逆条件数K(A)=||A| ||A~(-1)||在矩阵求逆的误差估计以及在线性方程组求解的误差估计中的最优性。这里||·||是由任意向量范数,利用等式||A||=max||Ax|| 所定义的矩阵范数。     

关于矩阵的积和式

基于对方阵积和式性质的讨论和积和式概念的推广,运用极限的思想给出了一个逐步降阶而计算积和式的思路.通过引入复杂积的概念,给出了积和式与行列式之间的关系.得出:若A为n阶方阵,P和Q均为n阶对角阵,则Per(PAQ)=Per(P)·Per(A)·Per(Q);若n阶方阵A有形式1ααTB,其中α=(1,…,1)为n-1维行向量,则PerA=PerB+σn-2(B);若A为方阵,则(PerA)2=|A|2+4ComA.     

矩阵特征值的分布及其在数值分析中的应用

对于n阶复方阵A,其所有特征值都位于如下的单一圆盘中：D：{z:|z-trA/n|≤R1=√n-1/2n-1√n-1/nq √q^2-2n-1/n^2△A},且这些特征值的实部和虚部分别位于如下的区间:[trReA/n-√n-1/nqRe,trReA/n √n-1/nqRe],[trImA/n-√n-1/nqIm,trImA/n √n-1/nqIm],其中,q=||A||F^2-1/n|trA|^2,△A=1/2||AA*-A*A||F^2,qRe=||ReA||F^2-1/n(trReA)^2,qIm=||ImA||F^2-1/n(trImA)^2同时,利用上述结果得到了对Jacobi迭代矩阵的谱半径以及对线方程组的条件数和最优松弛因子的某种估计.     

关于正定矩阵的一个行列式不等式

本文讨论正定的厄米特(Hermite)矩阵的一个行列式不等式,即定理设■是n阶正定的厄米特矩阵(简称正定阵),n—r>1,则|H|≤|A|·|C|—|A|·|B·A~(-1)B|,(1)且等式成立的充要条件是B=0。     

关于T—矩阵特征值的分布

本文讨论了一类矩阵(T—矩阵) 的特征值的公布,并且获得了下列结果:设A=(ajk)nxn 为非负既约T—矩阵,则有(1)ajj=tja, j=1,2,…n其中o≤tj<1, j=1,2…n;α为A的模为模为ρ(A)的特征值.(2)其中(3)其中设A=(ajk)为nxn复矩阵(本文记为A∈C~(mkn)).称Rj(A)=sum from k=1 to n|ajk|,R(A)=(?) Rj(A)分别为A的第j个(模)行和与最大(模)行和,同样可定义A的n个(模)列和Cj(A)与最大(模)列和C_A.众所周知,ρ(A)≤min(R(A).C(A))=||A||RC其中ρ(A)为A的谱半径.定义 设A∈C~(mkn),若ρ(A)=||A||RC.则称A为T—矩阵,则称A为T—矩阵,记为A∈(?);若ρ(A)<||A||RC,则称A为非T—矩阵,记为(?).在本文中,记|A|=(|ajk|)axm.     

L~p范数的极限性质

研究了函数的Lp范数的极限性质.给出了f的Lp范数||f||p的若干性质,在此基础上,证明了Lp范数关于p的连续性以及极限limp→a||f||p=||f||s,同时证明了在μ(X)=1时,limp→0||f||p=exp{∫xln│f│d│μ.}.     

F空间C~∞[a,b]上的线性连续泛函

设C~∞[d,b]是[a,b]上无穷次可微的函数全体组成的线性空间,其上定义F-范数: |u|=sum from K=0 to ∞(1/2~k(?) |u|_k/(1+|u|_k),这里。本文给出上述空间上线性连续泛函的一般形式。首先建立一延拓定理。定理1.设A。A_n(n=0,1,2,…)是线性空间,A(?)A.|·|,|·|_n,分别是A上F-范数及A。上B-范数,满足: 1) |x_m|→0(m→+∞)(=)对k=0,1,…,|x_m|_k→0(m→+∞); 2) 对n=1,2,…则对A上任一线性连续泛函T(指|x_n|→0),存在n及T_n∈A_n~+,使得T=T_n|A。     

Markedness and its Interpretation in Language Use

Language markedness is a common phenomenon in languages, and is reflected from hearing, vision and sense, i.e. the variation in the three aspects such as phonology, morphology and semantics. This paper focuses on the interpretation of markedness in language use following the three perspectives, i.e. pragmatic interpretation, psychological interpretation and cognitive interpretation, with an aim to define the function of markedness.     

Features of Women's language

Language is a means of verbal communication. People use language to communicate with each other. In the society, no two speakers are exactly alike in the way of speaking. Some differences are due to age, gender, statue and personality. Above all, gender is one of the obvious reasons. The writer of this paper tries to describe the features of women＇s language from these perspectives： pronunciation, intonation, diction, subjects, grammar and discourse. From the discussion of the features of women＇s language, more attention should be paid to language use in social context. What＇s more, the linguistic phenomena in a speaking community can be understood more thoroughly.     

低渗透非均质砂岩油藏启动压力梯度研究

理论推导与室内实验相结合,建立了低渗透非均质砂岩油藏启动压力梯度确定方法。首先借助油藏流场与电场相似的原理,推导了非均质砂岩油藏启动压力梯度计算公式。其次基于稳定流实验方法,建立了非均质砂岩油藏启动压力梯度测试方法。结果表明:低渗透非均质砂岩油藏的启动压力梯度确定遵循两个等效原则。平面非均质油藏的启动压力梯度等于各级渗透率段的启动压力梯度关于长度的加权平均;纵向非均质油藏的启动压力梯度等于各渗透率层的启动压力梯度关于渗透率与渗流面积乘积的加权平均。研究成果可用于有效指导低渗透非均质砂岩油藏的合理井距确定,促进该类油藏的高效开发。     

On Tragic Consciousness In The Works By Ernest Hemingway

As an American modern novelist who were famous in the literary world, Hemingway was not a person who always followed the trend but a sharp observer. At the same time, he was a tragedy maestro, he paid great attention on existence, fate and end-result. The dramatis personae's tragedy of his works was an extreme limit by all means tragedy on the meaning of fearless challenge that failed. The beauty of tragedy was not produced on the destruction of life, but now this kind of value was in the impact activity. They performed for the reader about the tragedy on challenging for the limit and the death.     

Achieving Unusual States of Matter Under High Pressure

正The periodicity of the elements and the non-reactivity of the inner-shell electrons are two related principles of chemistry,rooted in the atomic shell structure.Within compounds,Group I elements,for example,invariably assume the+1 oxidation state,and their chemical properties differ completely from those of the p-block elements.These general rules govern our understanding of chemical structures and reactions.Using first principles calcula-     

Exchange-Correlation and Electronic Excitation Energies from Pairing Matrix Fluctuations

We have developed an adiabatic connection to formulate the ground-state exchange-correlation energy in terms of pairing matrix linear fluctuations.This formulation of the exchange-correlation energy opens a new channel for density functional approximations based on the many-body perturbation theory.We illustrate the potential of such approaches with an approximation based on the particle-particle Random Phase Approximation(pp-RPA).This re-     

Density Functional Theory for the Response of Periodic Systems to Electric Fields Based on the Vector Potential Approach

正The electronic and nuclear(structural/vibrational)response of 1D-3D nanoscale systems to electric fields gives rise to a host of optical,mechanical,spectral,etc.properties that are of high theoretical and applied interest.Due to the computational difficulty of treating such large systems it is convenient to model them as infinite and periodic(at least,in first approximation).The fundamental theoretical/computational problem in doing so is that     

On the Thermodynamic Limit for Responses to Static Electromagnetic Fields

For molecular systems,the quantum-mechanical treatment of their responses to static electromagnetic fields usually employs a scalar-potential treatment of the electric field and a vector-potential treatment of the magnetic field.Although the potential for each field separately is associated with the choice of an(unphysical)origin,the precise choice of the origin for the electrostatic field has little consequences for the results.This is different for the     

Call for Papers

<正>"The Journal of Shanghai Normal University:Mathematics"is published by Shanghai Normal University as regular issues of The Journal of Shanghai Normal University each year from 2014 in English.The editors-in-chief of the issues are professors Yuhao Cong and Maoan Han.The Journal of Shanghai Normal University was started in 1958 with     

Journal of Donghua University ( English Edition) Contents of Volume 31

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