二维Abel积分方程的解

此处求二维Abel积分方程[1]的一特殊形式的方程的解。其中r~=x~2 y~2,ρ~2=(ξ-x)~2 (η-y)~2,f(x,y)为已知函数,υ(ξ-η)为未知函数。     

另一類型的序数方程

§1.根据序数正常表示的唯一性,M.Sierpi ski证明了方程ξ~2=η~3+1没有超限序数解;王戍堂和王克显拓广了这一结果证明了更广一类的序数方程ξ~n=η~(n+1)+1没有超限序数解,此处n>1是自然数.本文目的在于研究另一类型的序数方程ξ~2=η~ +1和ξ~n=η~( n)+1之求解问题. §2.首先证明     

奇型偏微分方程

§1.前言考虑一类含奇线的偏微分方程:(()~2υ)/(()ξ()η)-a/(ξ-η)()υ/()ξ+b/ξ-η()υ/()η-c/(ξ-η)~2υ=0,其中 a,b,c 均系常数。它称为 Euler-Poisson-Darboux 方程;或简写为 EPD 方程。因为最早是 Euler,以后是 Poisson 对它的特殊情形进行过研究,Darboux在它的名著“曲面论”一书中作了系统的结总。其实历史上研究过方程(1.1)的著名     

迭代微分方程x〃(t)=∑ai(t)fi(x(t))解的存在性

首先通过构造一个连续函数集合上的连续自映射的方法,利用Schuder不动点定理,证明了一类二阶自迭代泛函微分方程x＇(t)=∑ai(t)fi(x相似文献   

FUCHS型奇异积分方程Fouier解

本文利用希尔伯特空间完备组Fourier展开理论,给出FUCHS型奇异积分方程级数解.首先把奇异性转化为解析函数论中的围道积分,再根据残数理论求出其解,最后把这种方法推广到Foppd奇异型积分方程,并证明在希尔伯特空间中它们的解的结构的一致性.方程:1/2π- sum form (-a) to a (g(ξ))/(ξ-x)dξ=f(x) -a≤x≤a (1)工程上称之谓弗奇(FUCHS)型积分方程.其中未知函数g(ξ)在[-a,a]上按段光滑;f(x)在[-a,a]上连续可导,奇点在x=ξ之处,因此是一奇异积分方程.该方程最初出现在FUCHS-Hops-Seewalp合著的《气体动力学》一书中,但其解很不理想.由于理论物理中的势论进展,1/(ξ-x)作为牛顿势,把g(ξ)看作源密度分布函数,FUCHS型积分方程的重要性日益突出.例如在J·D杰克逊著的《经典电动力学》中便是主要工具.从另一角度来看,势函数作为积分方程的核,其本质就是格林(Green)函数,其重要性不必待言.     

迭代微分方程x"(t)=sum(ai(t)fi(x~()(t))) from i=1 to n解的存在性

首先通过构造一个连续函数集合上的连续自映射的方法 ,利用 Schauder不动点定理 ,证明了一类二阶自迭代泛函微分方程 x" ( t) = ni=1 ai( t) fi( x( t) )满足初始条件 x(ξ) =η,x′(ξ) =0 ,ξ,η∈ R的周期解的存在性 .其次将该解 x( t)延拓至 ( -∞ ,∞ ) ,从而证明了所给方程在所给条件下具有满足初始条件 x( ξ) =η,x′(ξ) =0 ,ξ,η∈ R的周期解 x( t) ,t∈ ( -∞ ,∞ )     

用双线性算子推导Bcklund变换

本文用Hirota双线性算子推导了双线性Boussinesq方程(D_t~2-D_x~2-D_x~4)f·f=0的一个含参数B(?)cklund变换,这个结果与文献[1]的结果一致.文中还讨论了双参数B(?)cklund变换与复合scale变换的关系,得到了有关分解等式B_(ξ,η)=S~(-1)(ξ,η)B_(0,1)S(ξ,η).这一工作改进了文献[3]中的结果.     

二阶无穷多点半正边值问题正解的存在性问题

研究二阶无穷多点半正边值问题:x″(t)+λf(t,x(t))=0,0ξ1>ξ2>…>ξn>…>0,0<η1<η2<…<ηn<…<1,αi,βi∈(0,∞),0<∑∞i=1αi(1-ξi)<1,0<∑∞i=1βiηi<1且ρ∞=∑∞i=1αiξi1-∑∞i=1(β)i+1-∑∞i=1(βiη)i1-∑∞i=1α()i>0.给正参数λ和函数f(t,x(t))赋予一定的条件,使得上述问题至少存在一个正解.该文应用锥上不动点定理证明了主要定理.     

关于一类非线性演化方程的求解

D.J.Kaup,A.C.Newell用反散射变换解决了一个与(1.1)相联系的非线性发展方程——带导数的非线性Schr(?)dinger方程(这时r=±q~*) iq_t=-q_(xx)±i(q~*q~2)x (1.5)的求解。但[2]对位势q需加紧支的条件,本文对q,r在无穷远处加较弱的条件,用反散射变换的方法,解决了方程(1.3)的求解,且对ξ_t=k_oξ的情形,也给出了方程(1.2)的求解。而对方程(1.2)的求解将在另外一篇文章中发表。     

EPD方程边值问题

在角形区域{ξ=η,η≥0}中研究EPD方程奇性第三问题已有结果。1981年,有人研究了{ξ=η,ξ=-η,ξ≥0}区域第三问题,采用了分解函数为奇、偶部分,化为两     

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.     

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.     

Jane Eyre——A Feminist In The 19th Century

In the 19th century the society was controlled by men, and women were just appendants of them, they had not any rights and freedom. But Jane was an exception, she showed some characteristics of early feminist. Jane showed her characteristics of feminism in three aspects: rebellion, equality, and independence. These characteristics were helpful to her success, and feminism is the only way out for women of that time.     

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-