A second-order nonlinear neutral delay differential equation was studied, and some sufficient conditions for existence of positive solutions for this equation were established. The advantage of the results is omitting the restriction condition of for any， must be negative. Furthermore, some examples were presented to illustrated that the results is more effective.

The higher-order moment of sum of independent and identically distributed exponential random variables was investigated. The higher-moment of exponential random variable was computed by mathematical induction method. Base on this result, combining the multinomial theorem and the knowledge about the partition of integer in combinatorics, the higher-order moment of sum of independent and identically distributed exponential random variables was computed and the computation formula was got. At last, the conclusion was illustrated by numerical example.

Let A=(a _ij)∈C ^{n ×n}, if there existsα∈(0,1) [WTBZ]which can make |a _ii|≥R ^α _iS ^{1- α} _i be right for i∈N={1,2,…,n},then  is called anα-chain diagonally dominant matrix.It gave an equivalent condition for chain strictly diagonally dominant matrices，and obtains a necessary condition for a matrix to be a nonsingular H-matrix indirectly. The result obtained improves the known corresponding results．At last, some numerical examples are given for illustrating advantages of the result.

 

Some iteration methods for solving linear system were studied，when coefficient matrix is α-diagonal strictly dominance or doubly diagonal strictly dominance, and some convergence theorems were given. Results obtained were applicable to α-diagonal strictly dominance matrix or doubly diagonal strictly dominance matrix, and improved the known results and were suited to extended matrices. Finally, an numerical examples were given for illustrating advantage of results．