离散算子的本征投影与本征幂零

本文给出例子，说明离散算子本征投影一致有界推不出其本征幂零一致，有界幂零一致有界也推不出本征幂零的幂一致有界。     

Large eddy simulation of turbulent premixed piloted flame using artificial thickened flame model coupled with tabulated chemistry

A sub-grid scale (SGS) combustion model, which combines the artificial thickened flame (ATF) model with the flamelet generated manifold (FGM) tabulation method, is proposed. Based on the analysis of laminar flame structures, two self-contained flame sensors are used to track the diffusion and reaction processes with different spatial scales in the flame front, respectively. The dynamic formulation for the proposed SGS combustion model is also performed. Large eddy simulations (LESs) of Bunsen flame F3 are used to evaluate the different SGS combustion models. The results show that the proposed SGS model has the ability in predicting the distributions of temperature and velocity reasonably, while the predictions for the distributions of some species need further improvement. The snapshots of instantaneous normalized progress variables reveal that the flame is more remarkably and severely wrinkled at the flame tip for flame F3. More satisfactory results obtained by the dynamic model indicate that it can preserve the premixed flame propagation characteristics better.     

矩阵核心逆在0点特征投影的刻画

研究了矩阵核心逆在0点特征投影的刻画,并利用特征投影的性质给出了核心逆的扰动界.     

THE EXPLICIT SOLUTION OF THE MATRIX EQUATION AX-XB=C——To the memory of Prof. Guo Zhongheng

Almost all of the existing results on the explicit solutions of the matrix equation AX−XB=C are obtained under the condition that A and B have no eigenvalues in common. For both symmetric or skewsymmetric matrices A and B, we shall give out the explicit general solutions of this equation by using the notions of eigenprojections. The results we obtained are applicable not only to any cases of eigenvalues regardless of their multiplicities, but also to the discussion of the general case of this equation. To the memory of Prof. Guo Zhongheng Project Supported by the National Natural Science Foundation of China     

矩阵方程AX－XB＝C的显式解──纪念导师郭仲衡教授

现有关于矩阵方程ＡＸ－ＸＢ＝Ｃ的显式解的几乎所有结论都是在Ａ与Ｂ无公共特征值的条件下获得的。本文利用特征投影给出了方程在Ａ与Ｂ均对称或反对称时一般解的显式形式。我们所得到的结果不仅适用于任何特征值重数情形，而且可以用来讨论该方程的一般情形。     

The Explicit Solution of the Matrix Equation AX-XB=C

ＴＨＥＥＸＰＬＩＣＩＴＳＯＬＵＴＩＯＮＯＦＴＨＥＭＡＴＲＩＸＥＱＵＡＴＩＯＮＡＸ－ＸＢ＝Ｃ──ＴｏｔｈｅｍｅｍｏｒｙｏｆＰｒｏｆ．ＧｕｏＺｈｏｎｇｈｅｎｇＣｈｅｎＹｕｍｉｎｇ（陈玉明）ＸｉａｏＨｅｎｇ（肖衡）（ＲｅｃｅｉｖｅｄＦｅｂ．．２８．１９９５...