关于分块矩阵的g—逆的反问题

考虑如下的问题:给定Ａ∈Ｃｍ×ｎ,Ｂ∈Ｃｍ×ｐ,Ｃ∈Ｃｎ×ｍ,求Ｘ∈Ｃｐ×ｍ,使得(Ａ,Ｂ)-=ＣＸ.(1)　　文[1]中给出了分块矩阵(Ａ,Ｂ)的ｇ＿逆公式,很有意义的一个问题就是:如果(Ａ,Ｂ)的ｇ＿逆中有一块是指定的,那么另一块是否存在?本文对此问题给出了较全面的解答.引理1[1]　设Ａ∈Ｃｍ×ｎ,Ｂ∈Ｃｍ×ｐ,则(Ａ,Ｂ)-=Ａ--Ａ-Ｂ(ＥＡＢ)-ＥＡ　　　(ＥＡＢ)-ＥＡ,其中ＥＡ=Ｉ-ＡＡ-.引理2[2]　矩阵方程ＡＸＢ=Ｄ可解的充要条件是ＡＡ-ＤＢ-Ｂ=Ｄ.(2)当(2)成立时,此方程的一般解为Ｘ=Ａ-ＤＢ-+Ｚ-Ａ-ＡＺＢＢ-,或等价地Ｘ=Ａ-ＤＢ-+ＦＡ…     

超立方体上的奇异值分解

本给出了在超立方体连接的单指令流多数据流（ＳＩＭＤ）机器上进行矩阵奇异值分解（ＳＶＤ）的算法，对ｍ×ｎ／２个处理单元的ＳＩＭＤ机器上进行ＳＶＤ，时间复杂度为Ｏ（ｌｏｇｍ．ｎ．ｌｏｇｎ）。本还给出了大型矩阵在固定大小的ＳＩＭＤ机器上求解ＳＶＤ的行压缩与列分割方法。     

关于正视规矩阵的谱变分

本文对正规矩阵Ａ，Ｂ的谱变分给出一些新的估计，证明了对于任何单调酉不变范数‖．‖，ｖ（Ａ，Ｂ）≤‖Ａ－Ｂ‖。设Ａ＝ＵΣ１Ｕ＾Ｈ和Ｂ＝ＶΣ２Ｖ＾Ｈ是谱分解，则Ｖ（Ａ，Ｂ）≤‖｜Ｕ＾Ｈ（Ａ－Ｂ）Ｖ｜‖。一个推论部分地改进了已知的结果。     

广义四元数代数上伴随λ—矩阵及应用

设ＨＦ（ａ，ｂ）是域Ｆ上广义四元数代数，本文定义了ＨＦ（ａ，ｂ）上ｎ阶λ－矩阵的伴随矩阵，作为伴随矩阵的应用，得到了义四元数方阵可逆的充要条件与逆矩阵计算公式，给出了ＨＦ９ａ，ｂ）上矩阵Σ（Ｋｉ＝０）Ａｉ×Ｂｉ＝Ｃ有唯一解的充分条件以及唯一解的显式解公式。     

拟正态分布均值矩阵的容许线性估计(Ⅰ

考虑了以下问题：设ｎ×ｍ随机矩阵Ｙ有分布Ｎ（Θｎ×ｍ,Ｖｍ×ｍΣｎ×ｎ）,即Ｙ服从均值向量为Θ协方差矩阵为Ｖｍ×ｍΣｎ×ｎ的多元正态分布,其中Θ为未知矩阵．讨论了当Ｖｍ×ｍΣｎ×ｎ已知时,均值矩阵Θ在３种比较标准下的容许线性估计．并称以上分布为拟正态分布．     

分块矩阵[ABCD]的奇异性

设Ｍ＝ＡＢＣＤ为复数域上的矩阵,其中Ａ为ｍ×ｎ矩阵,ｒａｎｋＡ＝ｒ≤ｍｉｎ（ｍ,ｎ）,Ｂ为ｍ×ｒ１矩阵,ｒａｎｋＢ＝ｒ１,Ｃ为ｒ２×ｎ矩阵,ｒａｎｋＣ＝ｒ２,ｍ＋ｒ２＝ｎ＋ｒ１．本文研究了矩阵Ｍ的奇异性,给出了Ｍ为非奇异矩阵的充分必要条件,也给出了Ｍ－１＝Ａ＋Ｃ＋Ｂ＋Ｄ＋的充分必要条件．     

Lanczos算法误差估计的若干问题

设Ａ为ｎＸｎ实对称矩阵，对于给定的ｊ个线性无关列向量组成的ｎ×ｊ实矩阵Ｑ，对任意ｊ×ｊ实矩阵Ｔ，记Ｒ（Ｔ）＝ＡＱ－ＱＴ。本文给出ｊ×ｊ实矩陈Ｈ，使｜｜Ｒ（Ｈ），并证明当Ｔ取矩阵Ｈ时，文献［１］中Ｐ．１２２定理４．１０的“”可以改变成“１”。     

环上矩阵的Moore－Penrose逆

环上矩阵的Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ逆周建华（东南大学数学力学系．南京２１００１８）本文中的环Ｒ均指含单位元的结合环，Ｒ￣（ｍ×ｎ）表示Ｒ上地（ｍ×ｎ）矩阵全体。若σ是Ｒ上的对合反自同构，Ａ∈Ｒ￣（ｍ×ｎ），Ａ＝（ａ＿（ｉｊ）），则以Ａ＊表示（ａ＿（...     

自回归模型的极限定理

考虑如下自回归模型 :ｙｔ=ＺｔＣｏ ｃ1 ｙｔ- 1 ｃ2 ｙｔ- 2 … ｃＨｙｔ-Ｈ εｔ. (1 )这里Ｃ0 为ｋ× 1常向量 ,Ｚｔ 为 1×ｋ非随机向量 ,Ｚｔ=(ｚｔ1 ,ｚｔ2 ,… ,ｚｔｋ) ,ｃｈ(ｈ =1 ,2 ,… ,Ｈ)为常数 ,εｔ 为扰动项[1 ,2 ] 令ｘｔ=(Ｚｔ,ｙｔ- 1 ,ｙｔ- 2 ,… ,ｙｔ-Ｈ) ,β′=(Ｃ′0 ,ｃ1 ,ｃ2 ,… ,ｃＨ) ,则式 (1 )化为ｙｔ=ｘｔβ εｔ. (2 )令Ｙ =(ｙ1 ,ｙ2 ,… ,ｙＴ)′,Ｘ =(ｘ′1 ,ｘ′2 ,… ,ｘ′Ｔ)′,ε=(ε1 ,ε2 ,… ,εＴ)′,则式 (2 )化为Ｙ =Ｘβ ε. (3)定理 1　假设式 (3)满足(Ａ)　εｔｉ.ｉ.ｄ且四阶矩…     

二阶矩阵线性微分方程的振动性定理

考虑二阶线性微分系统Ｙ″ Ｑ(ｔ)Ｙ=0,ｔ∈[ｔ0,∞).　　　　　(1)其中Ｑ(ｔ),Ｙ(ｔ)为ｎ×ｎ实连续矩阵函数,且Ｑ(ｔ)是对称的.系统(1)的解Ｙ(ｔ)称为非平凡解,如果至少存在一个ｔ∈[ｔ0,∞)使ｄｅｔＹ(ｔ)≠0;系统(1)的平凡解称为预备解,若Ｙ(ｔ)Ｙ′(ｔ)-(Ｙ(ｔ))′Ｙ(ｔ)≡0,ｔ∈[ｔ0,∞).(其中对任意矩阵Ａ,Ａ表示Ａ的转置).系统(1)称为振动的,若对任何Ｔ>ｔ0,系统(1)的每一个非平凡预备解Ｙ(ｔ)的行列式在[Ｔ,∞)上有零点,否则称(1)为非振动的.对任何矩阵Ａ,用λ1[Ａ]表示Ａ的最大特征根,用ｔｒＡ表示Ａ的迹.本文建立了两个振动新定…     

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.     

An Analysis of Catherine＇s Character——Wuthering Heights

Wuthering Heights, Emily Bronte＇s only novel, was published in December of 1847 under the pseudonym Ellis Bell. The book did not gain immediate success, but it is now thought one of the finest novels in the English language. Catherine is the key character of this masterpiece, because everybody and everything center on her though she had a short life. We can understand this masterpiece better if we know Catherine well.     

Lower Paleozoic oil relationships within Williston Basin, Canada

The Williston Basin is a significant petroleum province, containing oil production zones that include the Middle Cambrian to Lower Ordovician, Upper Ordovician, Middle Devonian, Upper Devonian and Mississippian and within the Jurassic and Cretaceous. The oils of the Williston Basin exhibit a wide range of geochemical characteristics defined as "oil families", although the geochemical signature of the Cambrian Deadwood Formation and Lower Ordovician Winnipeg reservoired oils does not match any "oil family". Despite their close stratigraphic proximity, it is evident that the oils of the Lower Palaeozoic within the Williston Basin are distinct. This suggests the presence of a new "oil family" within the Williston Basin. Diagnostic geochemical signatures occur in the gasoline range chromatograms, within saturate fraction gas chromatograms and biomarker fingerprints. However, some of the established criteria and cross-plots that are currently used to segregate oils into distinct genetic families within the basin do not always meet with success, particularly when applied to the Lower Palaeozoic oils of the Deadwood and Winnipeg Formation.     

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.     

Design and analysis of generic LBS application developing platform

Location based services is promising due to its novel working style and contents.A software platform is proposed to provide application programs of typical location based services and support new applications developing efficiently. The analysis shows that this scheme is easy implemented, low cost and adapt to all kinds of mobile nework system.     

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