The Theory of Operators with Dominant Main Diagonal. I.

In this paper a characterization of the symmetric operators on a finite dimensional Hilbert space which have a matrix representation with a dominant diagonal with respect to any orthonormal basis are obtained. The set of such operators is a solid, reproducing, normal and acute cone in the space of symmetric operators. These results are applied to localizing the spectrum of operators pencils.     

对角占优矩阵奇异-非奇异的充分必要判据

本文研究对角占优矩阵奇异-非奇异的充分必要条件.基于Taussky定理,本文得出,可约对角占优矩阵的奇异性由其独立Frobenius块的奇异性决定,从而将这一问题化为不可约对角占优矩阵的奇异-非奇异性问题;运用Taussky定理研究奇异不可约对角占优矩阵的相似性和酉相似性,获得这类矩阵元素辐角间的关系;并与Taussky定理给出的这类矩阵元素模之间的关系结合在一起,研究不可约对角占优矩阵奇异的充分必要条件;最后给出不可约对角占优矩阵奇异-非奇异性的判定方法.     

一类预条件AOR迭代法的比较定理(英文)

本文研究了当线性方程组的系数矩阵是严格对角占优L-矩阵时带有预条件子P1→kα的预条件AOR迭代方法.利用矩阵分裂的相关理论,获得了预条件AOR迭代法的收敛性结论以及参数α和k对收敛速度影响的比较定理.结果表明当α和k取值较大时这类预条件方法更加有效.文中的结论推广了Li等人关于预条件Gauss-Seidel迭代法的相关结论.最后,用数值例子进一步验证了这些结果.     

Combined higher order finite volume and finite element scheme for double porosity and non-linear adsorption of transport problem in porous media

In this work, a dual porosity model of reactive solute transport in porous media is presented. This model consists of a nonlinear-degenerate advection-diffusion equation including equilibrium adsorption to the reaction combined with a first-order equation for the non-equilibrium adsorption interaction processes. The numerical scheme for solving this model involves a combined high order finite volume and finite element scheme for approximation of the advection-diffusion part and relaxation-regularized algorithm for nonlinearity-degeneracy. The combined finite volume-finite element scheme is based on a new formulation developed by Eymard et al. (2010) [10]. This formulation treats the advection and diffusion separately. The advection is approximated by a second-order local maximum principle preserving cell-vertex finite volume scheme that has been recently proposed whereas the diffusion is approximated by a finite element method. The result is a conservative, accurate and very flexible algorithm which allows the use of different mesh types such as unstructured meshes and is able to solve difficult problems. Robustness and accuracy of the method have been evaluated, particularly error analysis and the rate of convergence, by comparing the analytical and numerical solutions for first and second order upwind approaches. We also illustrate the performance of the discretization scheme through a variety of practical numerical examples. The discrete maximum principle has been proved.     

Assignment markets that are uniquely determined by their core

A matrix A defines an assignment market, where each row represents a buyer and each column a seller. If buyer i is matched with seller j, the market produces a_ij units of utility. Quint (1991) points out that usually many different assignment matrices exist that define markets with the same core and poses the question of when the matrix is uniquely determined by the core of the related market. We characterize these matrices in terms of a strong form of the doubly dominant diagonal property. A matching between buyers and sellers is optimal if it produces the maximum units of utility. Our characterization allows us to show that the number of optimal matchings in markets uniquely characterized by their core is a power of two.     

广义对角占优矩阵的判定

利用α-对角占优矩阵的性质,给出了判定广义对角占优矩阵的几个充分条件,改进了近期的一些结果,并用相应的数值实例说明了这些结果的有效性.     

对角占优矩阵直积的注记

将对角占优矩阵的性质与矩阵的直积结合起来,给出了两矩阵的直积是对角占优矩阵的一些充分和必要条件,推广了近期的一些结果.最后用相应的数值例子说明了所得结果的有效性.     

一类算子的凸性条件(英文)

In this paper,we find a subclass of starlike functions on the unit disk,which are mapped by a operator,given by F（z）=1＋u/zu∫z0 f（t）tu-1dt（Re u≥0）,onto convex functions.The main results extend some known results.     

非奇H-矩阵的实用判别准则

非奇H-矩阵在科学和工程实际中有着广泛地应用,但在实际中判定一个矩阵是否为非奇H-矩阵是比较困难的.通过构造不同的正对角阵,结合不等式的放缩技巧,给出了一些比较实用的新条件,改进和推广了现有的一些结论,并给出相应的一些数值算例来说明结果的有效性.