与算术函数相关联的广义GCD矩阵的行列式（英文）

设S={x_1,…,x_n}是由n个元素组成的正整数集合,f是一个算术函数.用(f(S))表示一个n×n的矩阵,其(i,j)项为∑d|x_i d∈S f(d)-∑d|(x_i,x_j)d∈S f(d),用(f(S))表示另一个n×n的矩阵,其(i,j)项为∑x∈S f(x)-∑d|x_i d∈S f(d)-∑d|x_j d∈S f(d)+∑d|(x_i,x_j)d∈S f(d).首先研究了矩阵(f(S))和(f(S))的结构,然后给出了这2个矩阵的行列式计算公式,这推广了Bege在2010年所得到的结果.     

一类行列式的计算

本文的目的是给出n阶行列式det(a_ij)的计算公式,其中a_ij=f[(i,j)],f为任意一个数论函数,(i,j)表示i和f的最大公因子.为了利用初等变换将行列式化为三角形,我们首先证明了一个恒等式.引理.对任意正整数i 和m,如果i相似文献   

关于一个相关函数行列式的计算

用两种方法计算了下列行列式:F_(z)=(?)其中(?)为正定阵。这行列式来源自平稳随机序列的相关函数。在计算过程中还证明了一个有趣的行列式等式:任给矩阵 A=(a_(ij))_(i,i=1,…,n 和两个列向量 b1=(?)及 b_2=(?)以 A_(i,0) 记把矩阵 A 的第 i 列换成 b_1所得之矩阵,以 A_(0,j)记把矩阵 A 的第 j 列换成 b_2所得之矩阵,以 A_(i,j)(i≠j)记把矩阵 A 的第 i 列及第 j 列分别换成 b_1及 b_2所得之矩阵,则(i≠j)|A||A_(i,j)|=|A_(i,0) ||A_(0,j)|-|A_(j,0) ||A_(0,i)|     

导函数具有最大亏量和的亚纯函数

设 f(z)是一下级μ有穷的亚纯函数。如对一正整数k则这里是的非零有穷亏值数,f~((0))=f 当 j 为负整数时,f~((f))是 f 的|j|次原函数(若存在)。     

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)。     

k-集合上与算术函数关联矩阵的行列式

设S={x1,…,xn}是由n个不同元素组成的正整数集合,f是一个算术函数.用(f(S))=(f(xi,xj))表示一个n×n的矩阵,其(i,j)项为f在xi与xj的最大公因子(xi,xj)处的取值,用(f[S])=(f[xi,xj])表示另一个n×n的矩阵,其(i,j)项为f在xi与xj的最小公倍数[xi,xj]处的取值.若xi与xj的最大公因子(xi,xj)=k,1≤i≠j≤n,则称S是k-集合.本文主要给出了定义在k-集合上的矩阵(f(S))和(f[S])的行列式的计算公式.进而作为推论给出了det(f(S))|det(f[S])的条件.     

具有非零元素链的对角占优矩阵为非奇异的定理的一个简短证明

设 A=(a_(ij))是 n 阶对角占优矩阵,即若记 N={1,2,…,n},则对任意 i∈N 都有|a_n|≥sum from j=1 j≠i to n |a_(ij)|.本文所涉及的矩阵总假定是对角占优的。记 J(A)={i∈N||a_(ii)|>sum from j=1 j≠i to n |a_(ij)|}.当 J(A)=N 时,A 为严格对角占优矩阵,当 J(A)≠Φ,且 A 不可约时,A 是不可约对角占优矩阵,这两种矩阵都是非奇异的。当 J(A)≠Φ,A 为可约矩阵时,一九七四年 P.N.shivakumar 和 kim Ho Chew 给出了它为非奇异的一个充分条件:定理.设 A 为可约矩阵,J(A)≠Φ,若对每个 (?)J(A),都存在由 A 中非零元素构成的序列(也叫非零元素链):a_(ii_1),a_(i_1i_2),…,a_(i_(s-1))i_s,i_s∈J(A),那末 A 是非奇异的.P.N Shivakumar 和 kim Ho Chew 在证明此定理时,引用了 M—矩阵的性质,篇幅     

多元正态参数估计极大似然估计的注记

(一)设X′=(ξ_1~(?),ξ_2~(?),…,ξ_m)～N(0,R),其中R为m×m非负定矩阵,它的元素为α_(ij),α_(ij)=E(ξ_iξ_j),已知X的n个独立样本X′_i=(x_(i1),…,x_(in))i=1,2,…,n,用其估计α_(ij),i,j=1,2,…,m。本文讨论α_(ij)满足一定约束,比如α_(ij)=α_(|i-j|),即ξ_1,…ξ_m是平稳序列的一段时,α_(ij)的极大似然估计。 (二)下面列举一些求导公式。设M为m×m的矩阵,|M|表M的行列式,M′表M之转     

关于具有泛分解态射f=pgq的加权(i,…,j)逆

研究预加法范畴中具有泛分解态射f=pgq关于h,k的加权(i,…,j)逆,给出其存在的新的充要条件及其新的表达式,推广了具有泛分解态射的广义(i,…,j)逆的相应结果.     

线性泛函的广义Sard逼近

本文利用具有重结点的自然样条函数,讨论了线性泛函Ff=sum from i=0 to n-1[integral from a to b a_i(x)D~i f(x)dx+sum from j=0 to L~1 b_(ij)D~i f(x_(ij))]的广义Sard逼近问题。文中给出了线性泛函Lf=sum from i=0 to k sum from j=0 to k_1-1 a_(ij)D~j f(x_i)逼近F为n-1阶准确的存在定理与唯一性定理;给出了L做为F的广义Sard逼近的充分必要条件。     

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.     

橡胶颗粒沥青混合料低温抗裂性试验研究

以AC-13级配为基础,将橡胶颗粒代替部分集料掺入混合料中,以低温弯曲试验为评价方法对不同橡胶颗粒掺量下沥青混合料的低温抗裂性进行研究,并引入应变能密度值对混合料的低温抗裂性进行综合评价.试验结果表明:橡胶颗粒沥青混合料试件的破坏微应变均超过2 300,满足冬寒区的技术指标;无论是否掺加橡胶颗粒,随着温度的下降,沥青混合料破坏时的最大弯拉强度增大,弯拉应变降低,劲度模量增大;弯曲应变能密度在胶粒掺量为1%左右时具有较大的弯曲应变能密度值,此时橡胶颗粒沥青混合料具有较好的低温抗裂性.     

Jane Eyre——A Feminist In The 19th Century

In the 19th century the society was controlled by men, and women were just appendants of them, they had not any rights and freedom. But Jane was an exception, she showed some characteristics of early feminist. Jane showed her characteristics of feminism in three aspects: rebellion, equality, and independence. These characteristics were helpful to her success, and feminism is the only way out for women of that time.     

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-