黎曼——斯蒂阶积分存在的一个充要条件

实函中证明了[a b]上的有界函数f(x)黎曼可积的充要条件是f(x)不连续点所成之集的勒贝格测度为零。关于黎曼——斯蒂阶积分也有类似定理:f(x)在[a,b]上有界,α(x)为[a,b]上的有界变差函数,则f(x)在[a,b]上关于a(x)黎曼——斯蒂阶可积的充要条件是α(x)在f(x)不连续点所成之集上的全变差为零。本文就是给出这个定理的一个证明。     

关于δ样条函数逼近δ函数的定理

本文得到了以δ-样条逼近δ-函数的普遍结果。它阐明在[1]文意义下的逼近与节点和f(x)的间断点的相对位置有关。其主要结果如下。设函数f(x)连续于[a,b]或只有第一类间断点。若把f(x)以b-a为周期延拓到(-∞,∞)则其中,当x_0→x,…,x_0→x时 a_i→0 (i=1,2,3)     

用导数判别函数的一致连续性

一、引理引理1 若函数f(x)在闭区间[a,b]连续,则f(x)在[a,b]上一致连续.引理2 若函数f(x)在[a,b]及[b,c]都一致连续,则f(x)在[a,c]上一致连续.注改[b,c]为[b, ∞)时,结论也成立.引理3 设函数f(x)在开区间(a,b)连续,则f(x)在(a,b)一致连续的充分必要条件是f(a 0)、f(b-0)都存在且为有限值.证明见[1]之正文及相应习题.二、主要结论定理1 若函数f(x)在区间I(I可开、半开、有限或无限,下同)可导,且f’(x)在I有界,则函数f(x)在I一致连续.     

积分第二中值公式补註

定积分的第二中值公式有下列三个定理给出的三种形式。定理1 假设函数f(x)在闭区间[a,b]上单调减小(包括广义的)且非负,又函数g(x)在[a,b]上可积,则在闭区间[a,b]上至少有一点ζ,使得定理2 假设函数f(x)在闭区间[a,b]上单调增加(包括广义的)且非负,又函数g(x)在[a,b]上可积,则在闭区间[a,b]上至少有一点ζ,使得     

牛顿—莱布尼兹公式的一个推广

本文将证明牛顿—莱布尼兹公式对于 schwarz 导数亦成立。设函数 f(x)定义在[a,b]上,若对于 x∈(a、b)(?)(f(x+h)-f(x-h))/(2h)存在,则该极限值为 f(x)在点 x 的 schwarz 导数。记作 f~s(x)引理1 设 f(x)是[a,b]上的连续函数,f~s(x)在(a、b)上存在,若 f(b)>(<)f(a),则存在点,c∈(a,b),使得:f~s(c)≥0(≤0)引理2 设 f(x)在[a,b]上连续,f~s(x)在(a,b)上存在,f(a)=f(b)=0,则存在点 x_1,a相似文献   

函数列一致收敛性定理

1 函数列一致收敛性定理定理1 若函数列f_n(x)在[a,b]上同等连续,且对于任一x∈[a,b],有f_n(x)→f(x)(n→∞),则f_n(x)在[a,b]一致收敛于f(x)。     

积分中值定理的证明与应用

本文在分析教材中第一积分中值定理的条件下，证明了介值点ξ必可在开区间（a，b）内取得，进一步将这个结论推广到被积函数f以区间端点a和b为第一类间断点或瑕点以及在（a，b）内有间断点的情形，并且给出了一些应用。     

R_ρ积分与Riemann积分

引言本文引入了函数f(x)在[a,b]上R_φ积分概念,研究R_φ积分的性质以及R_φ积分与Riemann积分的关系,并得出函数f(x)在[a,b]上Riemann积分的几个等价定义。在本文中,[a,b]是实数轴上的有界闭区间;f(x)是定义在[a,b]上的实值函数;I是实常数,[a,b]上的分法T是有限点集T={x_0,x_1,…,x_n:a=x_0相似文献   

哥西定理之推廣

本文主要系构造一辅助函数,从而将哥西中值定理推广到n个函数。茲先讨论三个函数的情形。定理1 设函数f(x),φ(x),ψ(x)在闭区间[a,b]上连续,在开区间[a,b]上可微,则一定有这样—点c(a相似文献   

积分学基本定理

这文章证明了如下的积分基本定理: 假定f(x)是定义在区间[a,b]上的实函数,同时, (ⅰ) 它的右上导数D~+f(x)>-∝,右下导数D_+f(x)<∝,在(a,b)上至多除掉一个可列集Γ以外处处成立, (ⅱ) f(x)在(a,b]上处处在半连续, (ⅲ) 对所有的x∈Γ成立, (ⅳ) 存在一个L可测的实函数ψ(x),使D~+f(x)≥ψ(x)≥D_+f(x)在[a,b)上几乎处处成立,而且max{ψ(x),0}(或min(ψ(x),0})在[a,b]上可积,那末ψ(x)在[a,b]上可积;而且 这里,有关的积分概念可以是Lebesgue的,也可以是Perron的。定理关于ψ(x)这种函数可积分的判断有它独立的意义。证明中吸收了I.S.Gal的方法,同时弥补了原作者忽略的部份。 文章最后举例说明定理的几个条件的相互独立性和对于定理的成立的必要性。     

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.     

Characterization of Ordovician carbonate reservoirs, southeastern Saskatchewan, Canada

The discovery of the prolific Ordovician Red River reservoirs in 1995 in southeastern Saskatchewan was the catalyst for extensive exploration activity which resulted in the discovery of more than 15 new Red River pools. The best yields of Red River production to date have been from dolomite reservoirs. Understanding the processes of dolomitization is, therefore, crucial for the prediction of the connectivity, spatial distribution and heterogeneity of dolomite reservoirs.The Red River reservoirs in the Midale area consist of 3～4 thin dolomitized zones, with a total thickness of about 20 m, which occur at the top of the Yeoman Formation. Two types of replacement dolomite were recognized in the Red River reservoir: dolomitized burrow infills and dolomitized host matrix. The spatial distribution of dolomite suggests that burrowing organisms played an important role in facilitating the fluid flow in the backfilled sediments. This resulted in penecontemporaneous dolomitization of burrow infills by normal seawater. The dolomite in the host matrix is interpreted as having occurred at shallow burial by evaporitic seawater during precipitation of Lake Almar anhydrite that immediately overlies the Yeoman Formation. However, the low δ18O values of dolomited burrow infills (-5.9‰～ -7.8‰, PDB) and matrix dolomites (-6.6‰～ -8.1‰, avg. -7.4‰ PDB) compared to the estimated values for the late Ordovician marine dolomite could be attributed to modification and alteration of dolomite at higher temperatures during deeper burial, which could also be responsible for its 87Sr/86Sr ratios (0.7084～0.7088) that are higher than suggested for the late Ordovician seawaters (0.7078～0.7080). The trace amounts of saddle dolomite cement in the Red River carbonates are probably related to "cannibalization" of earlier replacement dolomite during the chemical compaction.     

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.     

A computer generator for randomly layered structures

AcomputergeneratorforrandomlylayeredstructuresYUJia shun1,2,HEZhen hua2(1.TheInstituteofGeologicalandNuclearSciences,NewZealand;2.StateKeyLaboratoryofOilandGasReservoirGeologyandExploitation,ChengduUniversityofTechnology,China)Abstract:Analgorithmisintrod…     

An Index mechanism for multi-scale view in spatial databases

There are numerous geometric objects stored in the spatial databases. An importance function in a spatial database is that users can browse the geometric objects as a map efficiently. Thus the spatial database should display the geometric objects users concern about swiftly onto the display window. This process includes two operations:retrieve data from database and then draw them onto screen. Accordingly, to improve the efficiency, we should try to reduce time of both retrieving object and displaying them. The former can be achieved with the aid of spatial index such as R-tree, the latter require to simplify the objects. Simplification means that objects are shown with sufficient but not with unnecessary detail which depend on the scale of browse. So the major problem is how to retrieve data at different detail level efficiently. This paper introduces the implementation of a multi-scale index in the spatial database SISP (Spatial Information Shared Platform) which is generalized from R-tree. The difference between the generalization and the R-tree lies on two facets: One is that every node and geometric object in the generalization is assigned with a importance value which denote the importance of them, and every vertex in the objects are assigned with a importance value,too. The importance value can be use to decide which data should be retrieve from disk in a query. The other difference is that geometric objects in the generalization are divided into one or more sub-blocks, and vertexes are total ordered by their importance value. With the help of the generalized R-tree, one can easily retrieve data at different detail levels.Some experiments are performed on real-life data to evaluate the performance of solutions that separately use normal spatial index and multi-scale spatial index. The results show that the solution using multi-scale index in SISP is satisfying.     

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