An elliptic problem with integral constraints with application to large-scale geophysical flows

We present a weak formulation of a non-standard elliptic equation whose boundary values are determined in part by integral relations. Existence and uniqueness of its solution are proved, and a finite element discretization is described, analyzed, and implemented on a test problem. The equation is a generalization of one that is solved during integration of the three-dimensional Quasigeostrophic equations, which model large-scale rotating stratified flows, where the integral constraints represent conservation of physical properties.     

Control-Volume Discretization Method for Quadrilateral Grids with Faults and Local Refinements

This paper extends the multipoint flux-approximation (MPFA) control-volume method to quadrilateral grids for which the adjacent cells do not necessarily share corners. Examples are grids with faults and locally refined grids. This paper gives a derivation of the method for such grids. The difference between two-point flux-approximation (TPFA) results and MPFA results for faults and local grid refinements is demonstrated for synthetic problems. Further, the results are compared with results from uniform fine-grid simulations. The effect of repeated fault patterns as well as anisotropy is investigated. Large errors may be found for the TPFA method for flow through a series of faults in an anisotropic medium. Finally, a comparison is done for a reservoir field application.     

塑料排水板处理地基非线性固结计算研究

针对目前国内外竖井地基非线性固结计算大多均采用近似等效法求解的不足,根据软土固结理论及数学理论推导,基于塑料排水板椭圆柱假定,推导了考虑地基土水平渗透系数、压缩模量随固结过程非线性变化影响下的排水板处理地基非线性固结控制方程,并利用数学中非线性微分方程理论,给出了非线性固结解析解。通过与Indraratna等非线性固结近似解对比分析,认为理想井下预压荷载越大（Nu越大）,则Indraratna等近似法成果误差越大;且在Cc/Ck = 1.8、Nu = 5时Indraratna等近似解与该理想井非线性固结精确解析解误差高达16%,而解析解与精确数值解基本一致。最后通过Indraratna等典型工程案例验证分析,认为所得理论更符合工程实际,具有较好的工程应用价值。     

A fair E-cash scheme based on elliptic curve cryptography

A new fair off-line electronic cash scheme on elliptic curve cryptography was presented. The new scheme is more efficient than those by extending fair off-line electronic cash scheme from finite field into elliptic curve cryptography and introducing a new elliptic curve discrete logarithm assumption. The expiry date and denomination are embedded into the blindly signed coin by integrating partially blind signature with restrictive blind signature. A bank need not use different public keys for different coin values, shops and users need not carry a list of bank‘s public keys to verify in their electronic wallet. At the same time, the bank just needs to keep undue electronic coins for double spending check in his database, thus bank‘s database can be dramatically reduced.     

基于第二类椭圆积分的子午线弧长公式变换及解算

通过推导,将子午线弧长公式变换为基于第二类椭圆积分的两种形式：“形式Ⅰ”将子午线弧长公式表达为一个有理函数和第二类椭圆积分之和,建立了以大地纬度B为自变量的子午线弧长公式与第二类椭圆积分之间的关系;“形式Ⅱ”给出了以归化纬度μ为自变量、直接利用第二类椭圆积分计算子午线弧长的公式。利用此两种形式的子午线弧长公式,在Matlab中编写程序,调用第二类椭圆积分函数Elliptic E(x, k)计算子午线弧长,精度和计算效率均优于经典算法。对CGCS2000所采用的地球椭球子午线弧长的计算表明,此两种形式的子午线弧长公式建立了子午线弧长公式与第二类椭圆积分的关系,结构简洁,易于展开,一定程度上完善了子午线弧长理论,且便于手工计算及计算机程序实现。     

Vertical image waves in elliptically anisotropic media

By reparameterization of the kinematic expressions for remigration in elliptically anisotropic media using a new ellipticity parameter, we derive a new image-wave equation in elliptically anisotropic media describing the position of the reflector as a function of the medium ellipticity. This image wave equation, which is a kind of medium-dependent one-way wave equation, can be used for automatically stretching a time-migrated image in depth until wells are tied or other given geologic criteria are met. In this way, it provides a useful means to use a priori depth information for finding an estimate of the vertical velocity, which cannot be detected from time processing only. Simple numerical examples confirm the validity of the image-wave equation even for nonconstant velocity.     

一类退化椭圆型方程的边值问题解的存在性及唯一性

运用逼近理论及矩阵理论证明 :如果一类退化椭圆型方程在非退化边界上满足第三边界条件 ,在退化边界上满足给定微商值 ,那么它的解是存在且唯一的。     

带梯度项的半线性椭圆型方程正径向整大解的存在性

本文研究带梯度项的半线性椭圆型方程正径向整大解的存在性.先利用Banach不动点定理和反证法得出正径向解的局部及整体存在性,进而得到正径向整大解的存在性结论.结果发现,正径向整大解的存在性依赖于梯度项的系数符号和指数的范围.     

Periodic orbits accumulating onto elliptic tori for the (<Emphasis Type="Italic">N</Emphasis> + 1)-body problem

We prove the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori for (an “outer solar-system” model of) the planar (N + 1)-body problem.      

产生安全椭圆曲线的MPI并行实现

快速产生安全的椭圆曲线是椭圆曲线密码体制(ECC)理论研究和实际应用的前提和基础，构造给定阶的椭圆曲线的复乘(CM)方法，是实践中构造安全椭圆曲线最常用的方法。基于消息传递接VI(MPI)的并行实现了复乘方法，实验表明，在两台主机上加速比达到了1．38。