设A=(a<sub>jk</sub><sub>)</sub>（n×n）为n阶复矩阵(本文记为A∈C<sup>n×n</sup>,记o<sub>j</sub>=sum from k=1 k≠j to n |a<sub>jk</sub>|,j=1,...,n若|a&...设A=(a<sub>jk</sub><sub>)</sub>（n×n）为n阶复矩阵(本文记为A∈C<sup>n×n</sup>,记o<sub>j</sub>=sum from k=1 k≠j to n |a<sub>jk</sub>|,j=1,...,n若|a<sub>jj</sub>|】a<sub>j</sub>,j=1,…,n,则称a为（按行）严格对角占优矩阵.若（?）=1/2（A+A<sup>x</sup>）为严格对角占优矩阵,则称A为共轭（严格）对角占优矩阵.关于各类对角占优矩阵特征值的分布。展开更多
To improve the treatment efficiency of essential boundary condition in mesh-less methods, a simple and robust method is proposed in this paper. Rising weight of nodes in the construction of trail function, specified f...To improve the treatment efficiency of essential boundary condition in mesh-less methods, a simple and robust method is proposed in this paper. Rising weight of nodes in the construction of trail function, specified for essential boundary condition, can make the trail function pass through these nodes. And then, the trail function can satisfy the essential boundary condition previously by setting diagonal element to 1 or multiplying diagonal element by a big number in FEM. The MLS method is adopted to validate this method, and it is proved that this method is eostless and robust in most of mesh-less methods.展开更多
If a semicircular element and the diagonal subalgebra of a matrix algebra are free in a finite von Neumann algebra （with respect to a normal trace）, then, up to the conjugation by a diagonal unitary element, all ent...If a semicircular element and the diagonal subalgebra of a matrix algebra are free in a finite von Neumann algebra （with respect to a normal trace）, then, up to the conjugation by a diagonal unitary element, all entries of the semicircular element are uniquely determined in the sense of （joint） distribution. Suppose a selfadjoint element is free with the diagonal subalgebra. Then, in the matrix decomposition of the selfa^tjoint element, any two entries cannot be free with each other unless the selfadjoint element is semicircular. We also define a ＂matricial distance＂ between two elements and show that such distance for two free semicircular elements in a finite von Neumann algebra is nonzero and independent of the properties of the von Neumann algebra.展开更多
文摘设A=(a<sub>jk</sub><sub>)</sub>（n×n）为n阶复矩阵(本文记为A∈C<sup>n×n</sup>,记o<sub>j</sub>=sum from k=1 k≠j to n |a<sub>jk</sub>|,j=1,...,n若|a<sub>jj</sub>|】a<sub>j</sub>,j=1,…,n,则称a为（按行）严格对角占优矩阵.若（?）=1/2（A+A<sup>x</sup>）为严格对角占优矩阵,则称A为共轭（严格）对角占优矩阵.关于各类对角占优矩阵特征值的分布。
文摘To improve the treatment efficiency of essential boundary condition in mesh-less methods, a simple and robust method is proposed in this paper. Rising weight of nodes in the construction of trail function, specified for essential boundary condition, can make the trail function pass through these nodes. And then, the trail function can satisfy the essential boundary condition previously by setting diagonal element to 1 or multiplying diagonal element by a big number in FEM. The MLS method is adopted to validate this method, and it is proved that this method is eostless and robust in most of mesh-less methods.
文摘If a semicircular element and the diagonal subalgebra of a matrix algebra are free in a finite von Neumann algebra （with respect to a normal trace）, then, up to the conjugation by a diagonal unitary element, all entries of the semicircular element are uniquely determined in the sense of （joint） distribution. Suppose a selfadjoint element is free with the diagonal subalgebra. Then, in the matrix decomposition of the selfa^tjoint element, any two entries cannot be free with each other unless the selfadjoint element is semicircular. We also define a ＂matricial distance＂ between two elements and show that such distance for two free semicircular elements in a finite von Neumann algebra is nonzero and independent of the properties of the von Neumann algebra.
