Amissibility of linear model with linear quality constraints under matrix loss function;

The seemingly unrelated regression model(1) converting into(2) is studied,under matrix loss,it is given a unique linear Minimax estimator of a linear estimable function SXβ,for Cov(Y)=σ2(∑In) when σ2>0 is unknown while ∑>0 is know.

For the admissibility of linear estimator LY+D of parameters SYΘ in multivariate linear model Y～N(XΘ,σ 2ΣV), where Σ≥0 and V≥0 are known, when Σ=I m, V≥0, Deng Qirong and Chen Jianbao obtained the necessary and sufficient conditions for the estimator LY+D, which is to be admissible under matrix loss.

A useful way of quantitative analysis and a method to determine loss matrix of underway ships in heavy sea has been put forward.

In this paper,we consider the Minimax admissible estimates of the multivariate regression coefficient in the constraint growth curve model under a matrix loss function.

Based on the matrix loss function,it was compared with least square estimator(LSE).

We give a unique linear Mihanax estimator of linear estimator of SXβ in the class ofhomogeneous (non homogenous) linear chimator under matrix loss function.

Study on the improved topological index of distance matrix and its application;

The element of matrix in the distance matrix S*_~ij is defined and the topological index W* based on the distance matrix is defined as well.

According to the adjacency matrix and distance matrix of the two units, the sequential formulas to calculate Wiener topological indices or molecular topological indices have been given.

Based on the minimum matrix distance criterion, the method equals to aggregating individual pairwise judgment matrices to find a matrix, the sum of whose distances to the individual matrices is minimized, and then the latter reduces to a goal programming model.