Sobolev空间的a尺度紧支撑小波基

在条件很弱的情况下,对给定的一对属于L2(R)的紧支撑加细函数φ和,构造了一个a尺度小波ψ,且使得小波ψjk=a(j)/(2)ψ(aj·-k)(j,k∈Z)构成L2(R)的Riesz基,当φ属于Sobolev空间Hm(R)的时,导数a(j)/(2)ψ(m)(aj·-k)(j,k∈Z)也构成L2(R)的Riesz基,相应地,{ψjk:j,k∈Z}便成为Sobolev空间H(m)(R)的小波基.     

L^2（R）的a尺度紧支撑小波基的构造

给定一对属于L2(R)的紧支撑加细函数和~,当它们满足适度的条件时,构造了一个a尺度小波ψ并且使得小波jψk=aj/2ψ(aj.-k)(j,kZ)构成L2(R)的R iesz基,相应地,{jψk:j,kZ}成为L2(R)的小波基.     

具有矩阵伸缩的正交双向小波包

为了将正交双向小波包推广到高维情形φan+λ(t)=∑〖DD(X〗k∈Zdp+k,λφn(At－k)+p－k,λφn(k－At),构造了伸缩因子为矩阵A的正交双向小波包{φan+λ(t),λ=0,1,…,a－1}n∈Z+,分别从时频域角度通过小波包基函数的正交性研究了高维正交双向小波包的性质,得到了小波包子空间的分解算法、重构算法及频域表示为∏ SymboleB@ j=1P λjωajΦ^0(0)。
     

高斯基插值算子的Lebesgue常数的强渐近估计

设λ>0,考虑从lp(Z)到Lp(R)(p=1)的算子Lλ:(Lλy)=∑k∈ZykLλ(x-k),y=(yk)k∈Z,x∈R,其中Lλ(x)=∑k∈Zcke-λ(x-k)2,x∈R,满足插值条件Lλ(j)=δ0j,j∈Z,且δ0j是Kronecher常数.在此研究的‖Lλ‖p(λ→0)渐近行为是基于‖Lλ‖p的积分表达式进行的.得到了一个强渐近估计:‖Lλ‖p=π42logπλ2 π42(log2λ γ) π2A o(1)(λ→0)其中A是一绝对常数并且γ是欧拉常数.     

二维正交小波变换的向量空间算法研究

小波 {ψej,k,m(x ,y) |e=1,2 ,3,j,k,m∈Z}不仅可以构成L2 (R2 )空间的正交基 ,通过小波分解与重构 ,以及对Hj,Gj,H j ,G j 的行向量修改等 ,还可以产生N×N空间的正交基 .同时 ,N×N点阵信号 {Sl,r}( 0≤l,r,≤N - 1)的小波变换等价N×N于空间的正交变换 ,用我们的方法进行信号或图像压缩 ,不涉及对信号或图象进行周期延拓 ,可严格在N×N空间中进行 .首先研究了二维信号的小波分解与重构 ,给出了适用的二维张量积小波的分解与重构公式 .其次 ,给出了信号用分解公式进行小波分解与重构公式进行小波重构后完全恢复原信号的充要条件 ,并对完全重构充要条件的实现作了处理 .最后得到了N×N空间中由小波分解与重构滤波产生的正交基 .这样就推导出对N2 个数据进行小波分解后可精确重构的算法 ,该算法可避免信号做小波分解后在边界处不能精确重构 .     

关于多分辨分析的定义

总结多分辨分析的性质和多分辨分析的最本质特征,然后给出多分辨分析的最简洁的定义.即若{Vj}j∈z是L2(R)的一串闭子空间序列,满足条件:(1)单调性:…V-1 V0 V1 V2…;(2)稠密性: ∪∞j=-∞Vj=L2(R);(3)伸缩性:若f(x)∈Vj f(2x)∈Vj 1,j∈Z;(4)R iesz基的存在性:存在(x)∈V0使{(x-k)¨k∈Z}是V0的R iesz基.则称{Vj}j∈z为L2(R)的一个多分辨分析.     

具有矩阵伸缩的正交双向小波包

为了将正交双向小波包推广到高维情形φan+λ(t)=∑k∈Zdp+k,λφn(At-k)+p-k,λφn(k-At),构造了伸缩因子为矩阵A的正交双向小波包{φan+λ(t),λ=0,1,…,a-1}n∈Z+,分别从时频域角度通过小波包基函数的正交性研究了高维正交双向小波包的性质,得到了小波包子空间的分解算法、重构算法及频域表示为∏∞j=1Pλjωa()jΦ0(0)。     

一类向量不规则小波标架

研究了一类向量小波系统{tl,j1/2Ψl(tlj·-kbl):1≤l≤r,j,k∈Z}.对{Ψl}1≤l≤r, {tl,j}1≤l≤r,j∈Z及{bl}1≤l≤r施加一定的条件,这类小波系统生成L2(R)的标架.     

高阶色散方程的柯西问题

主要研究了高阶色散方程ut+2j+1xu=j+1x(u2)+j-1x(ux2),j≥2,j∈N,x,t∈R的柯西问题.使用修正傅里叶限制范数方法和Strichartz估计以及修正Bourgain空间,证明了这个问题在修正的Sobolev空间H(s,1/2j)(s-j/2+3/4)上是局部适定的.使用迭代技巧,也证明了这个问题在H(s,w)(0w1/2j)中,对于任意的s∈R,流映射不是C2的.     

缓增样条在非正规样本上对Bπ,p类函数的恢复

证明了当f∈PWπ时,‖ s2m^(k)f-f^(k)‖Lp(R)→0(m→∞,2≤p≤∞,k=0,1,2,…）其中PWπ是经典的Paley-Wiener类,s2mf是在实Riesz基序列上对f插值的唯一确定2m-1次缓增样条,同时还证明了当｛f(ti)｝∈ι2,f∈Lp(R)(p≥2）,‖s2mf‖2≤A一致成立时,若lin/m→∞‖f-s2mf‖p=0,则f∈Bπ,p,其中Bπ,p为指数π型整函数R上的限制与 Lp(R)的交。     

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-