非均质地层中自然电位测井的数学模型和数值方法

针对非均质地层中电阻率非分块常数,提出一个新的自然电位测井模型.自然电位满足具有交界面跳跃的椭圆边值问题.证明了该椭圆边值问题弱解的存在唯一性;提出一种捕捉交界面电位跳跃的有限差分方法求解此类问题,数值例子验证了该方法的可靠性和有效性.     

X射线CT成像的数学模型及其有关问题

介绍了X射线CT系统和有关物理基础,综述了理想假设下的CT成像的连续数学模型和离散数学模型,以及相应的图像反演公式（重建算法）,并对其基本思想及优缺点进行了分析。最后,分类阐述了实际X射线CT系统研制和应用需要研究的若干问题。 关键词：计算机断层成像;数学模型;Radon变换;投影变换;图像重建算法     

放缩,反演和障碍问题

代替移动平面法和滑动区域法，作者利用放缩和反演变换研究某些半线性椭圆型分分下等方程解的单调性和对称性，这些变换依赖某一参数，在关于数据的单调性的适当假定下，当参数近某一初始值最大值时，解和其变换的差在某一“窄区域”满足一个椭圆型不等式，利用Ｖａｒａｄｈａｎ的极值原理，即得这个差是正的并得到解的单调性。     

混凝土重力坝多参数弹性位移反演分析不唯一性理论探讨

反演分析是现场监测⁃反演分析⁃工程实践检验⁃正演分析及预测的闭环系统的重要环节,而参数反分析是工程实践中研究最多的反分析问题.针对混凝土重力坝多参数反演分析是否具有唯一性,基于均质地基上重力坝在水压力作用下的位移解析解建立目标函数,进而以目标函数和非空凸集构建一个凸规划问题,然后通过分析目标函数的Hesse矩阵是否是正定矩阵,验证目标函数是否是严格凸函数,从而辨识构建的凸规划问题是否具有唯一全局极小点.对坝体和岩基弹性参数的不同组合方案分析表明,当采用理论值与实测值的差值的l1范数作为目标函数时,目标函数的Hesse矩阵均不能保证为正定矩阵,即混凝土重力坝多参数弹性位移反演分析凸规划问题不具有唯一全局极小点,反演分析不唯一.     

一个追逐问题的数学模型和matlab仿真

就两人绕正三角形的追逐问题建立起了两个数学模型:一个充分应用运动的周期性首先给出了两人共边的充要条件,然后直接给出在一个周期内两人共边的次数及起止时刻;另一个则利用初等数论的方法给出了两人共边的另一个充要条件.利用matlab长于计算和强大的绘图功能,分别给出了求解两个模型的matlab程序,通过动画仿真演示两个绕正三角形的追逐模型,并给出了二者同边的时间起止点和同边的次数.     

椭圆问题的非线性边界条件均匀化

在本文我们讨论了在等值面边值问题中的非线性边界条件的均匀化,推广了相应的边界条件均匀化结果,而且可应用到用于处理热敏电阻问题中的一类非线性非局部边值问题的边界条件均匀化问题。     

一类渗透率反演问题解的存在性与唯一性

本根据Thierry Bourbie et al建立的测定致密岩心的渗透率的装置，交换相应的数学模型中的边界条件和附加条件位置，得到了相应正问题的解析解．尔后，运用偏微分方程反问题中的系数反演方法，构造出了反演渗透率的关系式，在此基础上，运用不动点定理讨论了解析反演解的存在性与唯一性．反演的结果表明：只要在L端持续测量t1时间间隔，则所给的附加条件可以唯一确定渗透率．     

核磁共振弛豫信号的多指数反演

从第一类积分方程的反演求解入手,推导出适合于岩石核磁共振弛豫时间多指数反演的两种算法：奇异值分解（singular value decomposition）方法和变换反演算法.对算法的具体实现过程进行了详细的论述,从理论和实例处理两方面分析讨论了两种算法的优缺点.从解的自由度的角度,讨论解的分辨率及最优反演模型的选取原则：SVD算法适合于信噪比较高的数据反演,变换反演算法适应于较低信噪比的数据反演.在进行岩石核磁共振信号的多指数反演处理时,应优先选用变换反演算法,只有当原始数据的信噪比SNR≥80时,可选用SVD反演算法.为保证T₂反演结果的真实性,T₂布点数应在30～50个之间.[KG*2]研究内容对核磁共振岩心分析和核磁共振测井工作具有重要参考价值.     

卡车调度系统多目标最优控制的数学模型

应用最优控制的理论建立了多目标的卡车调度系统的数学模型。     

AN ADAPTIVE INVERSE ITERATION FEM FOR THE INHOMOGENEOUS DIELECTRIC WAVEGUIDES

We introduce an adaptive finite element method for computing electromagnetic guided waves in a closed, inhomogeneous, pillared three-dimensional waveguide at a given frequency based on the inverse iteration method. The problem is formulated as a generalized eigenvalue problems. By modifying the exact inverse iteration algorithm for the eigenvalue problem, we design a new adaptive inverse iteration finite element algorithm. Adaptive finite element methods based on a posteriori error estimate are known to be successful in resolving singularities of eigenfunctions which deteriorate the finite element convergence. We construct a posteriori error estimator for the electromagnetic guided waves problem. Numerical results are reported to illustrate the quasi-optimal performance of our adaptive inverse iteration finite element method.     

微分连续正则化方法与一维声波方程系数反演问题求解

本文将求解非线性方程组的微分连续法与求解不问题的Ｔｉｋｈｏｎｏｖ正则化方法结合起来，形成了兼有大范围收性与稳定性的“微分连续正则化方法”，给出了方法的收敛性分析，文中最后给出的关于一维波动方程反问题的计算实例表明了方法的有效性。     

THE DUAL MIXED METHOD FOR AN UNILATERAL PROBLEM

In this paper, the dual mixed method for an unilateral problem, which is the simplified modelling of scalar function for the friction-free contact problem, is considered. The dual mixed problem is introduced, the existence and uniqeness of the solution of the problem are presented, and error bounds O(h^3/4 ) and O(h^3/2 ) are obtained for the dual mixed finite element approximations of Raviart-Thomas elements for k= 0 and k= 1 respectively.     

拉单晶问题差分解的收敛性

本文考虑一源于拉单晶热传导数学模型的三角形区域上的自由边界问题的数值解,给出差分格式,并证明其数值解的收敛性。     

均匀材料导温系数的一种测定方法

§1.引言 本文将讨论测定一般均匀材料导温系数的一个新模型。在该模型中我们所需数据(?)仅是温度,而且在我们导出的可用于数值求解的方程(1.5)中只用所测温度本身而不是像[1][2]中所使用的它们的导函数,因而它不仅将会大大减小实验难度而且能提高测试精     

鞍点问题迭代解法收敛因子估计

分析Ｂａｎｋ（１９９０年）的论文中的求解鞍点问题的迭代解法,得到一个改进的收敛因子估计。     

Proximal interior point approach in convex programming (ill-posed problems) * †

The paper deals with the theoretical analysis of a regularized logarithmic barrier method for solving ill-posed convex programming problems. In this method a multi-step proximal regularization of the auxiliary problems is performed in the framework of the interior point approach. The termination of the proximal terations for each auxiliary problem is controlled by means of estimates, characterizing the efficiency of the iterations. A special deleting rule permits to use only a part of the constraints of the original problem for constructing the auxiliary Problems.

Convergence and rate of convergence of the method suggested are studied as well as its stability with respect to data perturbations. An example is given showing the behavior of the classical barrier method in the case of ill-posed convex programming problems.     

一类强非线性二阶椭圆问题混合元方法的最大模误差估计

本文利用正规格林函数及对偶论证技术证明了一类强非线性二阶椭圆问题混合方法对函数的Ｌ＾２投影具有几乎超收敛一阶的最大模误差估计,对伴随向量函数具有拟最优最大模误差估计。     

An Approach to the Subproblem of the Cutting Angle Method of Global Optimization

The solution of the Subproblem of the Cutting Angle Method of Global Optimization for problems of minimizing increasing positively homogeneous of degree one functions is proved to be NP-Complete. For the proof of this fact we formulate another problem which we call “Dominating Subset with Minimal Weight”. This problem is also NP-Complete. An O(n²)-time algorithm is presented for approximate solution of Dominant Subset with Minimal Weight Problem. This problem can be expressed as a kind of Assignment Problem in which it is allowed to assign multiple tasks to a single processor. Experimental analysis of the algorithm is performed using the program implemented in ANSI-C. The results of the analysis show the efficiency of the proposed algorithm.Mathematics Subject Classification (2000): 65K05, 90C27, 68Q25     

A METHOD FOR SOLVING THE INVERSE SCATTERING PROBLEM FOR SHAPE AND IMPEDANCE

The inverse problem considered in this paper is to determine the shape and the impedance of an obstacle from a knowledge of the time-harmonic incident field and the phase and amplitude of the far field pattern of the scattered wave in two-dimension. Single-layer potential is used to approach the scattered waves. An approximation method is presented and the convergence of the proposed method is established. Numerical examples are given to show that this method is both accurate and easy to use.