希尔伯特:引领20世纪数学发展的大师

正除希尔伯特之外,还没有一个人能够像他那样提出23个重要的数学问题,对未来一个世纪的数学发展产生如此广泛与深远的影响。1895年,33岁的大卫·希尔伯特(David Hilbert,1862~1943)来到了德国哥廷根大学,这个时间正好是在数学家高斯到哥廷根100年之后。希尔伯特是注入哥廷根学派的新鲜血液与活力因子,是被特地选中请来振兴哥廷根、再创哥廷根学派辉煌的。他在这里工作了48年。著名的演讲,不朽的篇章1900年,第二届国际数学家大会在巴黎召开,希尔伯特在一个分组会上发     

今日的数学

二十世纪的数学多才多艺的伟大德国数学家希尔伯特向国际数学家1960年代表大会提出由23个数学上主要面对的问题组成挑战性征答,从而使数学进入了二十世纪。这个23个问题在前半个二十世纪对于数学发展的方向是有特殊影响的。解答成功的人立刻名噪一时。但是比具体问题更为重要的也许还是希尔伯特公开表示他对数学上没有“不可知”的信心。希尔伯特的观点——确实在他一生中的实践都是如此——是数学的实质就是提出问题和解答问题;在希尔伯特看     

十九世纪晚期统一几何学的两种途径

十九世纪几何学呈现出分支林立、支离破碎的局面,由此,用统一的观点解释几何学便成为数学家的重要任务.克莱因以变换群的思想统一几何学,希尔伯特提出了另一条对现代数学影响深远的途径——公理化方法,这两种思路已经远远超出几何学的范围而成为现代数学统一化趋势的重要推手.然而,这种统一化、标准化的数学思维和数学"生产方式"只是基础主义者一厢情愿的幻想.     

大卫·希尔伯特简介

今年是希尔伯特诞辰125周年纪念。希尔伯特是19世纪末和20世纪初与克莱茵,闵可夫斯基,庞加莱等同时代的德国伟大数学家之一。今天世界上难得有一位数学家的工作不是以某种途径导源于希尔伯特的工作的。他在整个数学版图上留下了他那巨大显赫的名字。那里有希尔伯特空间,希尔伯特不等式,希尔伯特变换,希尔伯特不变积分,希尔伯特不可约性定理,希尔伯特基定理,希尔伯特子群,希尔伯特类域。他在解决果尔丹问题时的那些思想,无论是方法还是重要性方面都已远超出了代数不变量的范围。那本有关几何基础的小册子,它对数学的发展产生了最深刻的影响,它把公理化方法深刻地扎根于一切数学领域中。19世纪和20世纪前半叶,好几个数学分支趋于严格化的发展都极大地受惠于希尔伯特的成就。在     

“我们必须知道,我们必将知道!”——对希尔伯特的评述

希尔伯特作为数学领域的领头人以他卓越的数学成就闻名于世,而且他追求真理、无私无畏的精神更是人类社会的一笔宝贵财富.本文先对希尔伯特的生平经历进行介绍,然后主要从希尔伯特对数学、哥廷根大学以及他的学生三个方面论述希尔伯特产生的影响.他的工作和他所从事科学事业的那种精神和态度,一直深深影响着数学科学的发展.     

试析希尔伯特的问题观

希尔伯特不仅以他卓著的数学成就闻名于世，而且提出了对20世纪数学发生重大影响的23个问题．本文分析了希尔伯特独到的问题观，即他根据数学发展历史和他的数学研究实践，明确了问题的价值、一个好问题的标准和问题的来源．希尔伯特关于问题的精辟论述，对我们今天从事科学研究，更好地发现问题、分析问题、研究问题具有广泛的指导意义．     

关于希尔伯特第十问题

希尔伯特第十问题的解决,是本世纪七十年代数学领域中一个重大突破。正因为如此,近年来国内外写了关于它的很多评论文章。然而,由于这个问题的解决及其评论文章、深奥难解。因此,本文试图从另一个角度对希尔伯特第十问题地解决在方法论上的重要意义及其对数学发展的深远影响作以全面论述(为了在很短篇幅内达到本文的目的,有些概念和定理采取了直观的说明)。不妥之处请批评指正。一、问题的提出及其演变希尔伯特第十问题。是希尔伯特1900年在巴黎举行的一次国际数学会议上提出的著名23个问题中的第十问题。其内容是:找一个“能行”(机械)的方法来判定整系数多项式(刁     

高斯巧算数列的传说是真是假?

正德国数学家高斯被称为"数学王子",他对数学做出的贡献一般人并不了解,但是人们都知道他是一个数学天才,在学习数列时,老师或课本都会讲高斯小时候发现计算等差数列的和的快速方法的故事。这个故事的常见版本是这样的:高斯上小学时,其数学老师布置了一道从1加到100的习题,想让学生们算上一整节课,没想到题目刚刚布置下来,高斯就报出了答案"5050"。原来高斯     

20世纪初期德国某些数学学说在中国的传播

介绍德国数学学说在20世纪初期传人中国的简要情况,包括高斯的代数基本定理、正17边形尺规作图和正多边形尺规作图的判另4方法以及对数表;戴德金和康脱的实数理论及康脱的集合论;克莱因的变换群下几何学的分类、古代几何三大尺规作图问题(倍方问题,又称Delian problem、三等分角、圆积问题,即几何的作图问题)和数学教育问题;希尔伯特的几何学基础、代数数域和理想数以及其他数学学说．     

希尔伯特的数学教育思想对我国高师数学教育改革的启示

对希尔伯特的数学教育思想进行评述 ,并从教育观念、课程体系及教学方法等方面 ,探讨了它对我国高师数学教育改革的启示     

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