离散问题

Although, there has a progress in employing the lattice Boltzmann equation for fluid dynamics and modeling complex physics in fluids recently, there are some problems to be solved, such as the negativity of discrete local equilibrium or evolutionary distribution and the limitation of low Mach number.

尽管近年来在应用格子Boltzmann 方程对流体模拟和建模方面取得了重要进展，格子Boltzmann 方法仍有很多问题需要解决，例如离散的平衡态分布函数及分布函数的非负性问题、低Mach 数的限制问题。

First, we discuss the noncharacteristic Cauchy problem for 1-D heat equation.

首先，对一维的热传导方程的非特征Cauchy问题，我们利用边界积分方法将问题的求解转化成解积分方程组的问题，再对积分方程组进行离散化来数值求解，最后的数值结果表明我们的算法是有效的。

The combinatorial and delimitative algorithm can be used to solve the problem. A software called "Power Discrete" to implement this algorithm is developed by using Microsoft Visual6.0. It is a useful tool for linear programming problem with discrete variables and for discrete optimum design of structures, and in addition, the software also includes other algorithms such as genetic algorithm.

在国际上， 20世纪 60年代末期和 70年代初期，研究人员已开始对工程离散变量优化设计问题进行研究，但由于当时对于连续变量的非线性规划问题的研究还不够深入，所以在 70年代和80年代，研究的重点集中于连续变量的非线性规划问题。

In chapter 4 and chapter 5, the Dirichlet transmission conditions for overlapping Schwarz methods will be replaced by Robin transmission conditions when applied to general linear elliptic partial differential equations.

为了能够直接应用于某些实际问题，本文第六章把最优Robin参数的确定方法推广到由椭圆型问题离散化得到的稀疏矩阵问题。

This problem is defined as: Given points X, Y on the elliptic curve, find z such that: X = zY The discrete logarithm problem over this group in a finite field is a good one way function because there are currently no known polynomial time attacks forsolving the problem.

这个问题是指：鉴于点X和Y的椭圆曲线，找到这样： X =模糊离散对数问题，这个集团在有限的领域是一个很好的方法之一的功能，因为目前没有任何已知的攻击forsolving多项式时间的问题。

This paper is devoted to solving linear saddle point problems, Specifically, We consider nonsymmetric systems, written as usual in block form, where the upper left block is an invertible linear operator with positive definite symmetric part. Such saddle point problems arise, for example, in certain finite element and finite difference discretizations of NavierStokes equations, Oseen equations, and mixed finite element discretization of second order convection-diffusion problems.

中文题名求解鞍点问题的迭代方法副题名外文题名论文作者冯丽红导师曹志浩教授学科专业计算数学研究领域\研究方向学位级别博士学位授予单位复旦大学学位授予日期2002 论文页码总数87页关键词鞍点问题迭代方法网格离散线性方程组馆藏号BSLW /2003 /O241 /15 论文针对鞍点问题的求解分析了一些典型的快速算法。

The security of the dynamic group signature is based on the fact that the gap Diffie Hellman problem and discrete logarithm problem are hard problems.

该方案的安全性是建立在间隙群上计算Diffie-Hellaman问题和离散对数问题均是困难问题的基础上。

To price the continuously sampled arithmetic average Asian option, an implicit upwind difference scheme is constructed based on the final boundary value problem of partial differential equation, which is satifiable to the option pricing problem. Then the unique existence and unconditional stability of the difference solution are demonstrated and the error estimate is given under the discrete L2 norm.

研究连续取样的算术平均亚式期权定价问题的差分方法，根据问题所满足的偏微分方程终边值问题，构造出一种隐式的迎风差分格式，论证了差分解的惟一存在性和绝对稳定性，并给出差分解在离散L2范数下的误差估计。

Further, in order to reconstruct flow real-time image, inverse problem is transferred to a linear system of equations by simplification based on reasonable suppose, which solves the technical problem of data processing and flow image reconstruction.

再之，根据图像重建实时性要求，通过简化反问题并将之转化为离散化线性问题，解决了测量数据处理和流动图像重建的方法技术问题。

For the original infinite dimensional problem, if the inexact quasi-newton method with Broyden updating can not converge quickly , for example, it can not attain super linear convergence rate , then when the discretization is becoming finer and finer , we can not get fast convergence rate for the corresponding finite dimensional problem.

对于原来的无限维问题，如果使用不精确Broyden方法不能得到较快的收敛速度，比如超线性收敛性，那么当离散化逐渐加细的时候，对于所得的有限维问题使用不精确Broyden方法也不可能得到较快的收敛速度，所以有必要在无穷维空间上对收敛性问题加以分析，从而为不精确拟牛顿法结合投影法求解算子方程做好准备。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。