Stieltjes积分的产生和发展

在1884年,当斯蒂尔杰斯研究高斯关于某种定积分的近似计算公式时,惊讶地发现连分数与定积分之间的某种奇妙关系.他花费10年时间终于探明这一事实的一般性:他把力学中矩问题与源于积分的“自然”连分数联系起来,建立了一种新的积分———Stieltjes-积分(以下简称为S-积分),完成了对R-积分的第一次推广.几乎同时,匈牙利数学家柯尼克在研究R-积分第二中值定理时,在不经意之中推广了S-积分.又过了大约10年,匈牙利数学家里斯利用S-积分提供了有限区间上的连续函数空间中的线性泛函的一般表示形式.在20世纪第2个10年中,许多数学家都在推广并应用这种积分.人们发现,S-积分与许多数学分支都有着非常广泛的联系,对许多理论和实际问题的解决都是十分有效的.这里作者主要讨论S-积分的产生、发展和应用,努力遵循理论发展与应用需要这两条线索,尝试从数学思想史的角度来展开讨论.     

Polya计数定理及其若干性质

G·Polya是美籍匈牙利数学家、教育家。他在数学的广泛领域里都有许多发现,又热心于教育,1980年被邀请担任第四次国际数学教育会议的名誉主席。他一生中发表过二百多篇论文和许多专著,其作品清晰优美,方法灵巧独特。被人们誉为“Polya的风格”、“Polya的方法”……。Polya早在1937年就对树的计数和化合物的同分异构体的枚举问题进行研究,他巧     

S-系的余直积

在模范畴中一簇左R-模的余直积即是它们直和，而在中心S-范畴中，余直各表现为零直并．考虑到模范畴与S-系范畴之间的联系，本章首先给出了中心S-系范畴中余直积的一个充要条件，进而利用一般S-系范畴和一元S-系的不交并含零元这一性质。将该充要条件推广到了一般S-系范畴中（定理2．5），成功的给出余直积的一个具体刻画．     

函数单向S-粗集对偶生成的F-粗积分

单向函数S-粗集对偶中的上近似与下近似均可以看作是一个R-函数等价类,他们生成的函数如果在一闭区间上连续,则在该区间存在积分,这样就得到一个积分对,称这个积分对是单向函数S-粗集对偶生成的F-粗积分．F-粗积分是普通积分的推广,而且它具有动态特性和良好的性质,为解决实际问题提供了一个方便有效的工具．     

Г函数、β函数的应用

Г函数、β函数是由世界著名数学家欧拉(Euler，瑞士，1707～1783)最先用积分定义的函数，又叫欧拉积分，在数学、物理和工程技术等方面都有广泛的应用．下面给出Г函数、β函数在数学方面的应用．     

Fuzzy测度与积分理论

自1965年美国数学家L.A.Zadeh教授提出Fuzzy集合论以来,这个理论在国际上已引起极大的注意,并已渗透到许多重要的数学领域,形成诸如模糊拓朴、模糊积分、模糊逻辑、模糊系统、模糊图论、模糊语言、模糊程序……新的数学分枝,特别是在许多应用数学领域,为我们处理人类行为的许多复杂问题提供了一个有力的工具.1972年,日本应用数学家M.Sugeno首创了一种集合函数(Fuzzy测度)和一种泛函(Fuzzy积分)的理论,并将此理论应用于具有Fuzzy判据的某些Fuzzy现象的宏     

数学家的使命

世界上有三种不同的数学家．第一类是有构思，能够建立理论并致力于发展数学理论的数学家．数学理论的研究有很多不同的方法，第一个就是从现象界出发到发现理论，我们发展了一套系统化理论解释很多相类似的问题．就好像连续变换群的发现，它是从不同现象里面得出对称观念，并作系统化的研究．第二个方法是将本来既有的理论推广或搬移到类似的学科上．如有人将微积分从有限维空间推广到无限维空间，有限维推广到曲面理论．第三个方法是比较方法．Weil用整数方程与代数几何比较得出来一个伟大的发展，叫做算术几何．第四个方法，为了解释新的数学产生现象，而发展     

从微积分发展史试论数学的发展规律

<正>微积分是由牛顿与莱布尼兹在研究物理与几何问题时创立的,但数学家们的兴趣不在于作为实际问题的原型,N—L创立的微积分在数学上还缺乏理论,直到十九世纪,法国数学家柯西给出了连续函数积分的明确定     

函数单向S-粗集生成的F-粗积分

函数单向S-粗集中的上近似与下近似均可看作是一个R-函数等价类,他们生成的函数如果在一闭区间上连续,则在该区间存在积分,这样就得到一个积分对,称这个积分对是函数单向S-粗集生成的F-粗积分。F-粗积分是普通积分的推广,而且它具有动态特性,也有一些良好的性质,为解决实际问题提供了一个方便有效的工具。     

留数概念的起源

采用历史分析和文献考证的方法,探讨和分析了柯西定义留数概念的原因及背景指明柯西从一些数学家的相关工作出发,在对C—R方程进行了讨论和分析之后,产生了他关于复积分问题的讨论．在处理了连续函数的复积分问题后,为了使复积分理论更加完善,他又开始讨论不连续函数的复积分,进而提出了留数概念．结论指出柯西的留数定义是他追求数学理论完美化的一种体现和产物．     

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