求解丢番图方程1/x~2+1/y~2=1/z~2+1/w~2

利用高斯二平方和定理求解一个特殊的丢番图方程1/x~2+1/y~2=1/z~2+1/w~2,将其转化为a~2+b~2=c~2+d~2.经讨论得知,a~2+b~2≡c~2+d~2≡1,2(mod 4),当(k_1-k_3)(k_1+k_3-1)≡(k_4+k_2)(k_4-k_2)时,a~2+b~2≡c~2+d~2≡1(mod4);当(k_1-k_3)(k_1+k_3-1)≡(k_4-k_2)(k_4+k_2-1)≡0.2(mod 4)时,a~2+b~2≡c~2+d~2≡2(mod 4).     

Euler方程φ(xy)=k_1φ(x)+k_2φ(y)(k_1≠k_2)的正整数解

讨论了一个形如φ(xy)=k_1φ(x)+k_2φ(y)(k_1≠k_2)的具体方程φ(xy)=5φ(x)+7φ(y)的可解性,给出了其一切整数解.并根据这一方程的解的情况,给出了(x,y)=(k_1+k_2,k_1+k_2)是方程φ(xy)=k_1φ(x)+k_2φ(y)(k_1≠k_2)的1组整数解的结论,这里的k_1,k_2都是正整数.     

半素环的交换性

讨论元素满足两个以上多项式关系之一的半素环的交换性,证明了:定理1 R为半素环,(?)x,y∈R,若x,y满足如下3个关系式之一,则R为交换环:(i)(xy)~m-(xy)~(m_1)(yx)~(m_2)∈Z(R);(ii)(xy)~5-(yx)~1∈Z(R);(iii)(xy)~(k_1)(yx)~(k_2)-(yx)~(k_2)(xy)~(k_1)∈Z(R).其中m,m_i,k_i,s及t与x,y有关且m_1+m_2,t,k_1+k_2为有界自然数.定理2 R为半素环,若R满足下述四个条件之一,则R可换:(1)(?)x,y∈R,x~(2m)y~(2n)-x~my~(2n)x~m∈Z(R)或x~sy~t-y~tx~s∈Z(R);(2)(?)x,y∈R,x~(2m)y~(2n)-y~nx~(2m)y~n∈Z(R)或x~sy~t-y~tx~s∈Z(R);(3)(?)x,y∈R,(yx)~n-yx~ny~(n-1)∈Z(R)或(xy)~n-x~ny~n∈Z(R);(4)(?)x,y∈R,(yx)~n-x~(n-1)y~nx∈Z(R)或(xy)~n-x~ny~n∈Z(R).其中m,n,s,t为自然数,而(1)及(2)中的m,n,s,t与x,y相关,(3)及(4)中n(>1)只与x(或y)有关.     

Vertex disjoint cycles in intersection graphs of bases of matroids

The intersection graph of bases of a matroid M=(E, B) is a graph G=G~I(M) with vertex set V(G) and edge set E(G) such that V(G)=B(M) and E(G)={BB′:|B∩B′|≠0, B, B′∈B(M), where the same notation is used for the vertices of G and the bases of M. Suppose that|V(G~I(M))| =n and k_1+k_2+…+k_p=n, where k_i is an integer, i=1, 2,…, p. In this paper, we prove that there is a partition of V(G~I(M)) into p parts V_1 , V_2,…, V_p such that |V_i| =k_i and the subgraph H_i induced by V_i contains a k_i-cycle when k_i ≥3, H_i is isomorphic to K_2 when k_i =2 and H_i is a single point when k_i =1.     

关于方程x~(n/(n 1)) y~(n/(n 1)) z~(n/(n 1))=a~(n/(n 1))的图形特征

本文给出形如方程n/x~(n 1) n/y~(n 1) n/z~(n 1)=n/a~(n 1)(a>0)的图形的一个共同特征,并得到一个逆定理和一些应用.     

任意矩阵特征值的秩1修正扰动界

设A是一个n阶的任意复矩阵且E是A的Hermite秩1扰动,即E=xx',其中x是n维的复列向量,x'是x的共轭转置向量.则A+E为矩阵A的Hermite秩1修正矩阵.基于矩阵分析理论中Hermite矩阵特征值分布的性质,研究得到了矩阵A特征值的任意Hermite秩1修正扰动的上下界限,即给出了矩阵A+E特征值的上下界限:λ_i(H(A))+l_i(x)+δ_i≤R(λ_i(A+xx'))≤λ_i(H(A))+u_i(x)+δ'_i(i=1,n),λ_i(H(A))+l_i(x)+δ_i≤R(λ_i(A+xx'))≤min{λ_i(H(A))+u_i(x),λ_(i-1)(H(A))}+δ'_i(2≤i≤n-1),且λ_(min)(-SH(A)τ)≤S(λ_i(A+xx'))≤λ_(max)(-SH(A)τ)(1≤i≤n),其中δ_i=sgn(‖SH(A)‖_2)[λ_(min)(H(A))-λ_(i-1)(H(A))-u_i(x)],δ'_i=sgn(‖SH(A)‖_2)[λ_(max)(H(A))-λ_i(H(A))-l_i(x)+‖x‖_2~2],gap_i=λ_(i-1)(A)-λ_i(A),i=2,…,n,H(A)和SH(A)分别代表矩阵A的Hermite部分和反Hermite部分,τ=(-1)~(1/2),sgn(·)代表符号函数.当A为Hermite矩阵时,上述结果退化为已有的结果λ_i(A)-‖x‖_2~2≤R(λ_i(A+xx'))≤λ_i(A)+‖x‖_2~2.     

关于递推关系ααi-1,j-1+βαi-1,j=αi,j

研究了满足ααi-1,j-1+βαi-1,j=αi,j的序列{αi,j}.用发生函数法得到了n+1阶矩阵A=(αi,j)(n+1)×(n +1)的精确表达式.用数学归纳法证明(1-βx-αxy)-n中一般项xiyj(i≥j)的系数为αjβi-j(i+n-1/n-1)(i j).导出了一些有关二项式系数(n k)的新的组合恒等式.     

关于递推关系aai-1,j-1＋βai-1,j=ai,j

研究了满足ααi-1,j-1+βαi-1,j=αi,j的序列{αi,j}.用发生函数法得到了n+1阶矩阵A=(αi,j)(n+1)×(n +1)的精确表达式.用数学归纳法证明(1-βx-αxy)-n中一般项xiyj(i≥j)的系数为αjβi-j(i+n-1/n-1)(i j).导出了一些有关二项式系数(n k)的新的组合恒等式.     

方程y+Tx=x有解的一个充要条件

本文研究了映射T_1+T_2的不动点存在性,其中Ti:(?)是k_i集压缩(i=1,2),k_1+k_2≤1.由此引出方程y+Tx=x的可解性和I—T的满值性结果。还得到方程y+Tx=x有解的一(?)充要条件.     

三次样条函数拟合在光度分析中的作用

1三次样条插值的基本原理本文采用以下的三次样条函数的插值公式:q_i(x)=ty_i+■y_(i-1)+△x_i[(k_(i=1)-d)t■~2-(k_i-d_i)t~2■],i=1,2,3,…,m(1)式中,△x_i=x_i-x_(i-1),t=(x-x_(i-1)j)/△x_i,■=1-t,△y_i=y_i-y_(i-1),△y_i/△x_i=d_i.x_i,y_i为已知的实验数据.三次样条函数是由(1)式所示的m个三次多项式组合而成的分段表示的函数.它适合于处理多个数据点且多弯曲的曲线问题,由(1)式可知,每一q_i(x)方程只有两个待定常教K_(i-1)和K_i.     

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.     

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.     

A computer generator for randomly layered structures

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

Perspherical Approaches for Electrons in Atoms and Charged Excitons in Quantum Wells

Instead of following Fock’s expansion,we solve the Schrodinger equation for some quantum mechanical manybody systems such as electrons in atoms and charged excitons in quantum wells in a similar way in hyperspherical coordinates by expanding the wave functions into orthonormal complete basis sets of the hyperspherical hannonics(HHs)of hyperangles and generalized Laguerre polynomials(GLPs)of the hyperradius.This leads the equation to     

Advances in broadband wireless communications under high-mobility scenarios

Future mobile communication systems aim at providing very high data transmission rates, even in high-mobility scenarios such as high-speed wheel-track trains, maglev trains, highway vehicles, airplanes, guided missiles or spacecraft. A particularly important commercial application is the strong and increasing worldwide demand for high- speed broadband wireless communications （up to 574.8 km/ h test speeds or 380 km/h commercial speeds） in railways, providing data, voice and video services for applications such as onboard entertainment services to passengers, train control, train dispatch, train sensor status handling and sur- veillance. In such high-mobility scenarios, there are a number of communication challenges, including fast hand- over, location updating, high-speed channel modeling, estimation and equalization, anti-Doppler spreading tech- niques, fast power control, and dedicated network architec- ture. Because signal transmission in very high-speed scenarios will inevitably experience serious deterioration, it is imperative to develop key broadband mobile communi- cation techniques for such high-speed vehicles.     

Wuhan University Journal of Natural Sciences TOTAL CONTENTS

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海南岛地体及其毗邻陆缘晚中生代—新生代古地磁研究和构造演化

本文叙述了对海南岛及其毗邻大陆边缘白垩纪到第四纪地层岩石进行古地磁研究的全部工作过程。通过分析岩石中剩余磁矢量的磁偏角及磁倾角的变化,提出海南岛白垩纪以来经历的构造演化模式如下:早期伴随顺时针旋转而向南迁移,后期伴随逆时针转动并向北运移。联系该地区及邻区的地质、地球物理资料,对海南岛上述的构造地体运动提出以下认识:北部湾内早期有一拉张作用,主要是该作用使湾内地壳显著伸长减薄,形成北部湾盆地。从而导致了海南岛的早期构造运动,而海南岛后期的构造运动则主要是受南海海底扩张的影响。海南地体运动规律的阐明对于了解北部湾油气盆地的形成演化有重要的理论和实际意义。     

Scale-based spatial data model for GIS

Being the primary media of geographical information and the elementary objects manipulated, almost all of maps adopt the layer-based model to represent geographic information in the existent GIS. However, it is difficult to extend the map represented in layer-based model. Furthermore, in Web-Based GIS, It is slow to transmit the spatial data for map viewing. In this paper, for solving the questions above, we have proposed a new method for representing the spatial data. That is scale-based model. In this model we represent maps in three levels: scale-view, block, and spatial object, and organize the maps in a set of map layers, named Scale-View, which associates some given scales.Lastly, a prototype Web-Based GIS using the proposed spatial data representation is described briefly.     

Exciton Seebeck in Molecular Systems

Various applications relevant to the exciton dynamics,such as the organic solar cell,the large-area organic light-emitting diodes and the thermoelectricity,are operating under temperature gradient.The potential abnormal behavior of the exicton dynamics driven by the temperature difference may affect the efficiency and performance of the corresponding devices.In the above situations,the exciton dynamics under temperature difference is mixed with     

Achieving Unusual States of Matter Under High Pressure

The elongation method,originally proposed by Imamura was further developed for many years in our group.As a method towards O(N)with high efficiency and high accuracy for any dimensional systems.This treatment designed for one-dimensional(ID)polymers is now available for three-dimensional(3D)systems,but geometry optimization is now possible only for 1D-systems.As an approach toward post-Hartree-Fock,it was also extended to