一种改进的小波域图像修复算法

针对全变分小波图像修复算法在平滑区易产生阶梯效应并且噪声抑制不充分的缺陷,提出一种新颖的小波域图像修复模型。通过优化一个全变分和图像梯度的二范数的能量泛函来实现小波域的图像修复,使得在去除噪声的同时较好地保留了图像的边缘,在平滑区域削弱了阶梯效应,并利用有限差分法对所建立的扩散方程进行数值求解。实验结果表明:所提方法对于不同丢失比例的图像以及噪声图像都取得了较好的修复效果,尤其当小波系数丢失率较高时更为明显。     

基于互补变分原理的恒定磁场后验误差估计(Ⅰ)

互补变分原理用于有限元近似解的后验误差估计,从原理本身看是整体误差估计,将其用于局部误差估计是否可行,仍需研究。为此,本文对恒定磁场的拉普拉斯方程非齐次混合边值模型题进行了研究,给出了互补泛函的有限元离散格式,提出了对补泛函中强加二类边界条件的处理方法,解决了互补问题中标量位和向量位的匹配问题;通过逐步加密网格和逐个单元的计算,并与解析解对比,验证了互补变分原理对局部误差估计的可行性。     

参数型非空交定理及其在变分不等式理论中的应用

在已经证明的广义区间空间中几个参数型非空交定理的基础上，利用这些结果得到了广义区间空间中变分不等式解的存在性定理。这一研究成果推广了ＹｅｎＣＬ１９８１年所发表的“极大极小定理及其在变分不等式中的应用”一文中的定理３。     

Duality for nondifferentiable static multiobjective variational problems involving generalized (F, ?)-Convex functions

Using the generalized Schwarz inequality, we establish some weak duality theorems for nondifferentiable static multiobjective variational problems involving generalized (F, )-convex functions. Later in the sequel, we introduce three dual models for the nondifferentiable static multiobjective fractional variational problems and derive weak duality results for such programs.     

Investigation of the Temperature and Density Dependences of the Effective Pair Potential Parameters Using Variational Theory

A variational theory (VT), in which the potential energy of a real system is evaluated relative to the hard-sphere system, has been used to investigate the medium's effects on the pair potential parameters. By adding the medium's effects to the isolated pair potential, the concept of an effective pair potential (EPP) has been introduced. The advantage of such a potential (EPP) over the isolated pair potential is that the configurational energy can exactly be written as the sum of all EPP of all pairs available in the system. The parameters of such a pair potential will then show state dependence. The EPP parameters for different dense fluids at various temperatures have been obtained via the VT, and they have been shown to be density independent for densities greater than the Boyle density, _B 1.8 _c , (where _c is the critical density), while at lower densities the parameters depend on density as well as temperature. For any dense fluid, the depth of the EPP, , is found to be larger than its corresponding isolated pair. When the EPP parameters are used to reduce temperature and density, the cut-off parameter, C=d/ depends only on the reduced density, and this parameter shows a strong principle of corresponding states for different fluids. The resulting expression for the cut-off parameter has then been used to accurately predict the internal energy. Finally, the EPP parameters are compared with those of the average effective pair potential (AEPP) for Ar, to show the importance of the medium effects and the long-range interactions of the AEPP in dense fluids, individually. This comparison shows that the depth parameter of the AEPP is much larger than that of the EPP. Since the long-range interactions are mainly attractive, such a conclusion is reasonable.     

泛函建立方法的研究──变积方法

在变分学中，存在两类互道的问题，一类是将泛函的驻（极）值问题化为微分方程的边（初）值问题（正问题），一类是将微分方程的边（初）值问题化为泛函的驻（极）值问题（逆问题）．本文研究变分学中的逆问题．首先建立了变分的逆运算—变积的概念，然后应用变积运算顺利地将数理方法中的三类典型方程的边（初）值问题化为泛函的驻（极）值问题．     

大位移非线性弹性理论的广义变分原理

应用半反推法（凑合反推法）推导了大位移非线性弹性理论中的二类及三类独立变量的广义变分原理,由于半反推法不用拉氏乘子,所以可以避免由于拉氏乘子引起的临界变分现象,结果证明Ｈｕ－Ｗａｓｈｉｚｕ为分原理只是二类独立变量的变发原理。     

求解伪单调变分不等式的新的自适应投影算法

考虑求解一类变分不等式问题的新的自适应投影算法，该算法改进了搜索的方向和步长，改进的方向、步长在解点附近均不趋于0，保证算法的快速收敛性。并在伪单调的条件下证明了算法是全局收敛的，使得该算法的适用性更广。数值实验表明算法是有效的。     

小孔的偶极子模型

分析了小孔的偶极子模型，给出了小孔等效磁荷和位函数的积分方程以及电极化率和磁化率的变分公式．     

应用Gurtin变分原理求解板动力问题的样条有限元法

以Ｇｕｒｔｉｎ变分原理为基础,空间上应用样条有限元法,时间域上采用逐步代换的方法,建立了计算板动力问题的样条有限元法,算例表明,与现有板动力分析方法相比本中的方法具有更高的精度。