Identification of a dissipation coefficient by a variational method

A generalized inverse problem for the identification of the absorption coefficient for a hyperbolic system is considered. The well-posedness of the problem is examined. It is proved that the regular part of the solution is an L ₂ function, which reduces the inverse problem to minimizing the error functional. The gradient of the functional is determined in explicit form from the adjoint problem, and approximate formulas for its calculation are derived. A regularization algorithm for the solution of the inverse problem is considered. Numerical results obtained for various excitation sources are displayed.     

Numerical solution of the linear inverse problem for the Euler-Darboux equation

An inverse problem of the reconstruction of the right-hand side of the Euler-Darboux equation is studied. This problem is equivalent to the Volterra integral equation of the third kind with the operator of multiplication by a smooth nonincreasing function. Numerical solution of this problem is constructed using an integral representation of the solution of the inverse problem, the regularization method, and the method of quadratures. The convergence and stability of the numerical method is proved.     

对称矩阵与反对称矩阵广义特征值反问题的拓广

定义了上三角等次对角线矩阵和上三角交错次对角线矩阵;讨论了矩阵方程AX-XA=0的对称解与AX XA=0的反对称解.在此基础上考虑了以下问题的可解性:给定A∈Rn×m,D∈Rm×m,分别求X,Y∈SRn×n和X,Y∈ASRn×n,使得XA=YDA.     

EACVD中用氢原子谱线测定电子平均能量

采用蒙特卡罗方法，对EACVD中氢原子的发射过程进行了模拟。给出了由氢原子谱线测定电子平均能量的方法，结果对EACVD生长金刚石薄膜过程中实时监测电子平均能量，进而可以有效地控制工艺条件，生长出高质量的金刚石薄膜具有重要意义。     

阻尼落体运动的分析力学研究

应用分析力学理论和方法,研究了两种情况下的阻尼落体运动:1)阻力大小与速度成正比;2)阻力大小与速度平方成正比.对两种运动分别给出了等效的Lagrange函数和Hamilton函数,并应用第一积分法、点变换法、正则变换法和Ham-ilton-Jacobi方程法等不同的求解方法进行了求解.     

基于队列式缓存结构的视频图像存储算法

针对视频图像数据实时存储过程中普遍存在的丢帧问题，通过深入分析典型的存储算法，找出实时存储过程中视频图像数据丢失的原因：计算机在连续存储相同大小的文件时，存储速度在一定的范围内波动.本文采用队列式缓存结构有效地消除了存储速度波动所带来的影响，保证了在数据流速小于磁盘平均存储速度的前提下,高速视频图像数据的实时存储，解决了丢帧问题.实践验证了该算法的可行性与可靠性.     

Shadowing and Inverse Shadowing for C^1 Endomorphisms

In this paper, we consider the shadowing and the inverse shadowing properties for C^1 endomorphisms. We show that near a hyperbolic set a C^1 endomorphism has the shadowing property, and a hyperbolic endomorphism has the inverse shadowing property with respect to a class of continuous methods. Moreover, each of these shadowing properties is also ＂uniform＂ with respect to C^1 perturbation.     

On Numerical Solution of Shape Inverse Problems

The new method is proposed for the numerical solution of a class of shape inverse problems. The size and the location of a small opening in the domain of integration of an elliptic equation is identified on the basis of an observation. The observation includes the finite number of shape functionals. The approximation of the shape functionals by using the so-called topological derivatives is used to perform the learning process of an artificial neural network. The results of computations for 2D examples show, that the method allows to determine an approximation of the global solution to the inverse problem, sufficiently closed to the exact solution. The proposed method can be extended to the problems with an opening of general shape and to the identification problems of small inclusions. However, the mathematical theory of the proposed approach still requires futher research. In particular, the proof of global convergence of the method is an open problem.     

银盐干板的皱缩控制及其在彩色反射全息上的应用

分析了影响全息干板银盐乳胶在处理过程中收缩的几个因素，并通过实验，找出了在拍摄及处理体积反射全息图过程中，曝光量、漂白液温度及脱水的方式对乳胶收缩影响的规律.在此基础上提出控制乳胶的收缩，即控制反射全息图衍射波长的方法，从而达到彩色反射全息图的实现.实验结果表明该方法做出的全息图效果良好.     

对称正交反对称矩阵反问题解存在的条件

矩阵反问题和矩阵特征值反问题在科学和工程技术中具有广泛的应用,有关它们的研究已取得了许多进展[1,2].[3]和[4]分别研究了反对称矩阵反问题和双反对称矩阵特征值反问题等.本文研究一类更广泛的对称正交反对称矩阵反问题.用Rn×m（Cn×m）表示n×m实（复）矩阵的全体,ASRn×n表示n阶反对称矩阵的全体,ABSRn×n表示n阶双反对称矩阵的全体,ORn×n表示n阶正交矩阵的全体.A+表示矩阵A的Moore-Penrose广义逆.In表示n阶单位矩阵.ei表示n阶单位矩阵的第i列,Sn=[en,en-1,