辛 virtual 局部化的一个应用

作者使用辛virtual 局部化公式来计算一类特殊的 Calabi-Yau 流形Wk的 Gromov-Witten 不变量.在对 Gromov-Witten 不变量进行局部化处理之后,作者计算出了不动点轨迹的 virtual 法丛的等变欧拉类和障碍丛的等变欧拉类.最后作者枚举了模空间在S1作用下的不动点对应的所有可能的图,给出了当d＜5时亏格为0的 Gromov-Witten 不变量.     

关于方程x~2 y~2=2z~2的正整数解

方程x~2 y~2=2z~2 (1)的正整解为 i 当其正整解相等时,有x=y=z=t,其中t∈N={1,2,3,…}; ii 当其正整数解互不相等且同为奇数时,有x=m~2 2mn-n~2,y=|-m～2 2mn N~2|,z=m~2 n~2,其中m,n∈N,m>n,(m,n)=1,m、n为一奇一偶。证明 i 显然。今证ii。由方程 (1) 知,它的正整数解x,y,z同为奇数或同为偶数,否则方程 (1) 是不成立的。特x,y为奇数,z为偶数,令x=2p 1,y=2q 1,z=2u,其中p,q,u∈N。将x,y之值代入 (1) 并将其两边同除以2,则其左边等于2(p~2 q~2 p q) 1为奇数,而右边等于4u~2为偶数,引出矛盾,方程 (1) 不成立。故方程 (1) 不存在x,y为奇数而z为偶数的解。同理可证方程 (1) 不存在x,y为偶数而z为奇数,或x,y一奇一偶而z为奇数,或x,y一奇一偶而z为偶数的正整数解。所以方程 (1) 的互不相等的正整数解x,y,z同为奇数或同为偶数。而要求方程 (1) 的同为偶数的解x,y,z,这可将方程 (1) 的同为奇数的解x,y,z     

关于一类特殊的指数不定方程

利用同余式证明了不定方程px+(p2-1/2)y=(p2+1/2)z在p为奇素数,且p≡3(mod 4)的条件下,仅有正整数解x=y=z=2.     

关于丢番图方程ax~2 by~2 cz~2=dw~2的整数解

当丢番图方程ax2 by2 cz2 =dw2 有整数解x0 ,y0 ,z0 ,w0 (w0 ≠ 1) ,(x0 ,y0 ,z0 ,w0 ) =1时 ,给出了它满足 (x ,y ,z,w) =1的全部整数解的公式 :x =(an2 bm2 cp2 )x0 - 2n(anx0 bmy0 cpz0 )t ,　y =(an2 bm2 cp2 )y0 - 2m(anx0 bmy0 cpz0 )t ,z =(an2 bm2 cp2 )z0 - 2p(anx0 bmy0 cpz0 )t ,　w =(an2 bm2 cp2 )w0t .     

关于丢番图方程px~4-（p-1）y~2=z~4

对任意的奇素数p,还没有找到给出丢番图方程px4-（p-1）y2=z4的全部正整数解的统一的初等方法,目前只解决了某类特殊的奇素数p的求解问题,例如王洪昌等人完全解决了p-1=Q2;或2Q2;或qQ2,2｜Q,q≡3（mod4）为奇素数,Q为正整数的情形.认为对某类特殊的奇素数p求解丢番图方程px4-（p-1）y2=z4,目的是对任意的奇素数p,寻找给出丢番图方程px4-（p-1）y2=z4的全部正整数解的统一解法.当p=2q＋1,q≡5（mod8）,p,q为奇素数时,利用初等方法把方程px4-（p-1）y2=z4化为方程x2＋my2=z2,从而给出方程px4-（p-1）y2=z4的全部正整数解;当q为任意正整数时,上述解法仍然适用,因此对任意给定的奇素数p,实际上已经给出了丢番图方程px4-（p-1）y2=z4的全部正整数解的统一解法.     

关于丢番图方程x4+py4=z2

利用初等方法给出了丢番图方程x4+py4=z2(2z,(x,y)=1,p为奇素数)当2(×)Q,p=2Q2+1时的全部正整数解,从而改进了Mordell、佟瑞洲关于x4+py4=z2的结果.     

非退化平面系统在平衡曲线附近的轨道结构

讨论平面系统.x=A（x,y）y,·↑y=B（x,y）y在满足非退化条件A^2（0,0）＋B^2（0,0）≠0时,在平衡流形y=0附近轨线的拓扑结构,并对平衡流形y=0上的点附近的一类向量场进行局部分类.     

一类广义的带参数的Hilbert型奇异积分算子的范数

Hilbert型奇异积分算子在分析学中有重要的作用.本文通过引入参数λ和两个实数A1,A2,在广义区间(0,b)上定义了一个带参数的核为1/xλ+yλ的Hilbert型奇异积分算子T:(Tf)(y)=∫bc f(x)/xλ+yλdx,利用权函数方法和算子理论,研究了T的有界性问题,在条件A2 p+A1q=2-λ下,得到了算子T的范数‖ T ‖=B(1-A2p/λ,1-A1q/λ)/λ.作为应用,还考虑其涉及内积的等价形式(Tf,g)≤[B(1-A2p/λ,λ-1+A2q/λ)/λ]1/p[B(1-A1q/λ,λ-1+A1q/λ)/λ]1/q‖f‖p,ω'‖g‖q,w".     

关于丢番图方程x8+py2=4z4与x4+16py8=z2

设p为奇数，证明了丢番图方程x^8＋py^2=4z^4（x，y）；1除开p=3时仅有正整数解（z，y，z）=（1，1，1）和p=7时仅有正整数解（x，y，z）=（1，3，2）之外，无其它正整数解。证明了方程x^4＋16py^8=z^2，p≡3（mod 4），2/z，（x，y）=1，无正整数解。证明了P≡3（mod 4），方程x^4＋16py^8=z^2，（x，y）=1当2/x时，除开p=3时仅有正整数解（x，y，z）-（1，1，7）外，无其它正整数解；当2｜x时，有解x^2=2｜pr^8-s^8｜，y=rs，z=2（pr^8＋s^8），2/rs，（r，s）=1。从而推广了文[4]的结果。由此可知（x，y，z）=（2，1，8）是方程x^4＋48y^8=z^2的一个本原解，文[4]漏掉了此解，这说明文[4]引理2不是完全正确的，依据引理2证明的结论也是不可靠的。     

方程xp±y2p=z2与广义费尔马猜想

设p为奇素数,证明了丢番图方程x4 -y4 =zp 与x2p±y2p=z2 均无正整数解;方程xp y2p=z2 仅有整数解 16 2 3 =32 ;方程x2p 2 kyp =z2 (k≥ 1)仅有整数解 12p 2 3 · 1p =32 ;同时还获得了方程x2 ±y4 =zp与x2 ±y4 =±z2p 的深刻结果,从而很大程度地支持广义Fermat猜想.     

Orbifold嵌入定理

证明了orbifold嵌入定理在高维的orbifold上成立，即对于一紧致复orbifold M，若其上有一个正定的线丛，则存在正整数N使得M可以拓扑嵌入到CPＮ.     

局部 Calabi-Yau 三维轨形上的2点 Gromov-Witten 不变量的计算

在本文中,作者研究了一类源自特定 terminal 奇点的小解消的Zr 商的 Gorenstein 轨形,并且计算了该模型2点轨形 Gromov-Witten 不变量.     

Orbifold上的积分

Orbifold的研究源于SATAKE对V-manifold的讨论．作者通过orbifold在一点附近的性质导出了带边区域的定义，还具体的构造出orbifold上的外微分形式丛，最后证明了对orbifold上的紧支集外微分形式Stokes公式成立。     

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.     

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.     

A computer generator for randomly layered structures

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

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。     

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     

《Chinese Science Bulletin》SUBJECT INDEX TO VOLUME 59(2014)

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