m（n）相依样本回归函数改良核估计的强相合性

ｍ（ｎ）相依样本回归函数改良核估计的强相合性杜斌秦更生（数学系）１引言设（Ｘ，Ｙ），（Ｘ１，Ｙ１）……是Ｒｄ×Ｒ１上的同分布随机向量序列，Ｅ｜Ｙ｜＜∞．回归函数ｍ（ｘ）＝Ｅ（Ｙ｜Ｘ＝ｘ）为未知实函数．Ｗａｔｓｏｎ［１］和Ｎａｄａｒａｙａ［２］首先建议...     

一类约束下的参数估计问题

考虑线性模型ｙｎ×１＝Ｘｍ×ｐβｐ×１＋εｎ×１，（１）其中ｙｎ×１为样本观测值，Ｘ为ｎ×ｐ阶的设计阵，β为ｐ维参数向量，εｎ×１为ｎ维随机向量，ε为随机误差．Ｅε＝０，Ｄε＝σ２Ｖ这里σ２已知或未知皆可，Ｖ为ｎ×ｎ阶非负定阵．对于线性模型（１），...     

三星体R_（n－p，n，n＋p）（P＝1，2）是强优美树

引入强优美树概念，证明了三星体Ｒ＿［（ｎ－ｐ），ｎ，ｎ＋ｐ］（ｎ为自然数；ｐ＝１．２）是强优美树，从而得到四星体Ｒ＿［（ｎ－ｐ），ｎ，ｎ＋ｐ，ｍ］（ｍ，ｎ为自然数；ｐ＝１，２）是优美树的结果。     

方差分量生长曲线模型中回归系数线性估计的泛容许性

讨论了方差分量生长曲线模型： Ｙ＝ Ｘ１ Ｂ Ｘ２′＋ ε Ｅ（ε） ＝ ０ Ｖａｒ（ Ｖｅｃ（ε）） ＝ ＷθΣ＝ ∑ｍｉ＝ １ θｉ Ｖｉ Σ其中 Ｙ、ε为ｎ ×ｐ 的随机矩阵; Ｘ１、 Ｘ２ 分别为ｎ ×ｋ、ｐ ×ｑ 的设计矩阵; Ｖｉ ≥０, ｉ＝１,２,…,ｍ ; Σ≥０已知; Ｂ、θｉ ≥０（或＞ ０）, ｉ＝ １,２,…,ｍ 都是参数。在损失函数（ｄ － Ｋ Ｂ Ｌ）（ｄ － Ｋ Ｂ Ｌ）′下我们给出了可估函数 Ｋ Ｂ Ｌ的线性估计的泛（Φ） 容许性定义, 得到了 Ｍ Ｙ Ｎ（ Ｍ Ｙ Ｎ ＋ Ｃ） Ｋ Ｂ Ｌ的泛容许性估计的充要和充分条件     

较弱条件下线性回归系统回归系数协方差改进估计的弱相合性

对于由ｍ个相依的线性回归方程组成的线性回归系统：其中Ｙｉ为ｎ×１观测向量，Ｘｉ为ｎ×Ｐｉ列满秩矩阵，βｉ为Ｐｉ×１的未知回归系数，ｅｉ为ｎ×１随机误差向量，且σｉｊ≠０．［１］的作者分别在已知及未知的情况下给出了β１的协方差改进估计和两步改进估计β１，并在ε＝（ｅ１，…，ｅｍ）的各行相互独立同分布的情况下讨论了β１的弱相合性．本文在较弱条件下讨论β１及Ｂ１的弱相合性，从而推广了［１］中相应的结果．     

分布自由的密度核估计的强收敛

设（Ｘｎ，ｎ≥１）是Ｒ＾１中的平稳过程，具有公共的未知概率密度函数ｆ（ｘ），本文考察基于前ｎ个观测值Ｘ１，．．．Ｘｎ的ｆ（ｘ）的核估计ｆｎ（ｘ）的核估计ｆｎ（ｘ），在过程是ψ－混合或强混合的情形下，我们证明了ｆｎ（ｘ）的逐点强相合性和一致强相合性，并得到了ｆｎ（ｘ）的强相合性的收敛速度。     

多元相依线性模型的M－估计

讨论多元线性模型Ｙ＿ｉ＝ｘ＇＿ｉβ＋Ｅ＿ｉ，ｉ＝１，２，…中凸偏差函数最小问题的解定义的多元线性回归系数β的Ｍ－估计的相合性及渐近分布，其中｛Ｅ＿ｉ，ｉ≥１｝为严平稳α－混合ｐ维随机误差序列，在十分一般的条件下，建立了β的Ｍ－估计的相合性，并基于过程收敛得到了Ｍ－估计的渐近分布。     

线性模型中误差分布的基于L1估计的相合核估计

线性模型ｙｉ＝ｘｉ＇β＋ｅｉ，ｉ＝１，…，ｎ，的误差序列｛ｅｉ｝ｉ＾ｎ＝１有未知密度ｆ（ｘ）。本文在一定条件下证明了ｆ（ｘ）的核估计ｆｎ（ｘ）＝１／ｎａｎ∑＾ｎｉ＝１ｋ（ｅｎｉ－ｘ／ａｎ）的弱相合性，逐点强相合性，一致强相合性，其中ｅｎｉ为Ｌ１估计的残差。     

环的交换性的两点注记

讨论半素环和有单位元环的交换性，用较初等的方法证明如下两个定理，并利用这两个定理对近期的一些结果作了推广。定理１．１环Ｒ为无零因子环，ｍ和ｎ为给定自然数且ｍ＞ｎ．若有ｘ￣ｍ－ｘ￣ｎ∈Ｚ（Ｒ），则Ｒ可换。定理２．２环Ｒ有单位元，ｍ，ｎ为正整数。设（Ⅰ）设ｍ＿ｉ，ｎ＿ｉ（ｉ＝１，２…，ｋ）为非负整数，满足：且存在ｉ，ｊ使ｉ＞ｊ而ｍ＿ｉｎ＿ｊ≠０．若Ｒ为ｌ－扭自由的，且都有：则Ｒ可换。（Ⅱ）若有，其中ｍ＿１＋ｍ＿２＝ｍ，ｎ＿１＋ｎ＿２＝ｎ，ｍ＿１，ｍ＿２，ｎ＿１，ｎ＿２为自然数，且Ｒ为ｈ－扭自由的，则Ｒ可换。     

最大似然估计的相合性、渐近正态性及重对数律

设有样本｛Ｙｉ，Ｚｉ｝，ｉ＝１，２，…，ｎ，其中：Ｙｉ＝ｍｉｎ（Ｘｉ，Ｔｉ），Ｚｉ＝Ｉ（ＸＩ≤Ｔｉ）．假定Ｘ１，Ｘ２，…，Ｘｎ相互独立，有共同的分布函数ＦＸ（ｘ）＝１－ｅ－αＱ（βｘ），Ｔ１，Ｔ２，…，Ｔｎ相互独立，分布函数分别为Ｇ１（ｔ），Ｇ２（ｔ），…，Ｇｎ（ｔ）本文给出参数（α，β）的最大似然估计具有相合性、渐近正态性及重对数律的一个充分条件，然后验证Ｌｏｍａｘ分布满足该条件     

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.     

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     

An affordable accurate evaluation of the binding conformations predicted by molecular docking studies in bio-system

Franck-Condon factors bridge the gap between theoretical modeling and experimental observations for molecular electronic spectroscopy and electron transfer.Under the displaced harmonic oscillator approximation,multidimensional Franck-Condon factors are decomposed into a product of many one-dimensional(1D)Franck-Condon(FC)factors,and each 1D-FC factor is associated with one Huang-Rhys factor that determines the leading contribution of     

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