线性方程神经网络—Minimax准则的光滑法方法

将神经网络用于线性系统方程的求解问题,但所用的准则函数不是通常的最小二乘函数而是ｌ∞范数准则函数,即Ｅ∞（ｘ）＝ｍａｘ／ｘ∈Ｒ＾ｎ｛｜ｒｉ（ｘ）｜｝或Ｅ∞（ｘ）＝ｍａｘ／ｘ∈Ｒ＾ｎ｛１／２ｒ＾２ｉ（ｘ）｝。先将Ｅ∞（ｘ）光滑化,再利用神经网络来求解无约束光滑优化问题。并讨论了网络的收敛性和稳定性。     

余维≤5的光滑函数在C^∞（R^n,R）中的稠密性

证明了在函数空间Ｃ＾∞（Ｒ＾ｎ，Ｎ）中，适合条件“在每一点ｘ，函数ｆ作为ｘ点的芽，余维≤５”的光滑函数全体是Ｃ＾∞（Ｒ＾ｎ，Ｒ）中的稠密子集，从而使“几乎所有”的光滑函数能够选用Ｔｈｏｍ的７种突变模型。     

帐蓬空间的一点注记

设ｆ（ｘ）是Ｒ＾ｎ上的可测函数，ｕ（ｘ，ｔ）＝ｆ＊ｐｔ（ｘ）为ｆ的Ｐｏｉｓｓｏｎ积分，定义算子Ｆ（ｆ）（ｘ，ｔ）＝ｔ（θｕ（ｘ，ｔ）／θｔ）。在本注记中我们首先给出一则反例以说明Ｆ不是Ｌ＾∞（Ｒ＾ｎ）到帐蓬空间Ｔ＾∞的有界算子，然后证明了Ｆ却是ＢＭＯ（Ｒ＾ｎ）到Ｔ＾∞的有界算子。它补充、完善了Ｃｏｉｆｍａｎ－Ｍｅｙｅｒ－Ｓｔｅｉｎ的结果。     

偏微分方程中的Fourier变换及其应用

Ｆｏｕｒｉｅｒ变换在偏微分方程理论中占有相当重要的地位。本文通过经典的Ｆｏｕｒｉｅｒ变换求解一维、二维热传导方程Ｃａｕｃｈｙ问题的方法，推广Ｆｏｕｒｉｅｒ变换到速降函数空间ψ（Ｒ＾ｎ）和ψ（Ｒ＾ｎ）上的线性连续泛函ψ＇（Ｒ＾ｎ）广义函数空间上，求出了Ｃａｕｃｈｙ－Ｒｉｅｍａｎｎ方程、热传导方程、常系数椭圆算子方程以及形如δｕ／δｔ＝ｐ（δ／δｘ）ｕ的方程的Ｃａｕｃｈｙ问题的基本解。最后引入了Ｆｏｕ     

一类特殊Lagrange多项式逼近光滑函数

证明了当函数ｆ（ｓ）在［－１，１］上有二阶连续导数时，用以ｎ阶Ｃｈｅｂｙｓｈｅｖ多项式的零点为节点所确定的Ｌａｇｒａｎｇｅ多项式Ｐｎ－１（ｘ）来逼近ｆ（ｘ），其收敛速度不只为Ｏｎ＾－ｄ１／２），ｆ（ｘ）－Ｐｎ－ｄ１（ｘ）＝ｏ（ｎ＾－ｄ１）也成立。     

B值鞅差阵列强大数定律的收敛速度

设Ｂ是ｐ阶一致光滑空间，１〈ｐ≤２，Ｘ＝｛Ｘｎｋ，Ｆｎｋ，１≤ｋ≤ｎ，ｎ≥１｝是Ｂ值鞅差阵列且对非负实值随机为量Ｙ尾概率一致有界，若存在α≥１，δ〉０，α〈ｐ＋δ（ｐ－１），使（Ｙ〉ｘ）－１／ｘ＾ａ＋δ（ｘ→∞），则对任意的ε〉０，都有＾∞∑ｎ＝１ ｎ＾ａ－２Ｐ（‖Ｓｎｎ／ｎ‖≥ε）〈∞。其中Ｓｎｎ＝＾ｎ∑Ｋ＝１ Ｘｎｋ（ｎ≥１）。     

C^n空间中具有逐块光滑边界的有界域上光滑函数的一种积分表示

本文得到了Ｃ＾ｎ中具有逐块Ｃ＾（１）光滑边界的有界域上光滑函数的一种积分表示，这种积分表示的特点是积分核中含有向量函数Ｗ。由这个公式，通过适当选择其中的向量函数Ｗ，可以得到许多具有逐块光滑边界的区域上光滑函数相应的积分表示式。     

随机右删失下核光滑乘积限估计的大样本性质

讨论了随机右删失下乘积限估计Ｆｎ（ｔ）与核光滑乘积限估计Ｆｎ（ｔ）之差（Ｆｎ－Ｆｎ）（ｔ）的大样本性质，得出了Ｆｎ（ｔ）的一般大样本性质，特别是ｎ＾１／２（Ｆ（ｔ）－Ｆ（ｔ）＝γｎ（ｔ）→Ｇｐ（ｔ）的充分与必要条件。     

C^n空间中具逐块光滑边界的有界域上光滑函数的Norguet—Ono公式

得到Ｃ＾ｎ空间中具有逐块Ｃ＾（１）光滑边界的界域上光滑函数一个Ｎｏｒｇｕｅｔ－Ｏｎｏ公式，它是有界域上光滑函数的Ｂｏｃｈｎｎｅｒ－Ｏｎｏ公式的一种拓广，这个公式的显特点是其中三个积分核关于变量ｚ都是全纯的，而已有的具这种逐块Ｃ光滑边界的有界域上光滑函数的种种积分表示，其积分核关于ｚ都不是全纯的。     

等度变换微分方程的解的唯一性

给定欧氏空间Ｒ＾ｎ上正定矩阵（ａｉｊ）ｎ×ｎ：Ｒ＾ｎ→ＧＬ（ｎ，Ｒ），本文借助测地理论获得了非线性椭圆型微分方程组解的唯一性定理。其中ｙ＾ｉ＝ｙ＾ｉ（ｘ），ｘ∈Ｒ＾ｎ为未知函数。     

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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