Generalized strictly diagonally dominant matrices play a wide and important role in computational mathematics, mathematical physics, theory of dynamical systems, etc.But it is difficult to judge a matrix is or not gen...Generalized strictly diagonally dominant matrices play a wide and important role in computational mathematics, mathematical physics, theory of dynamical systems, etc.But it is difficult to judge a matrix is or not generalized strictly diagonally dominant matrix.In this paper, by using the properties of α-chain diagonally dominant matrix, we obtain new criteria for judging generalized strictly diagonally dominant matrix, which enlarge the identification range.展开更多
In this paper,the solution of a parallel redundant repairable system is investigated.by using the method of functional analysis.Especially,the linear semigroups of operator theory on Banach space,we prove the existenc...In this paper,the solution of a parallel redundant repairable system is investigated.by using the method of functional analysis.Especially,the linear semigroups of operator theory on Banach space,we prove the existence of the strictly dominant eigenvalue,and show the linear stability of solution.展开更多
In this paper,the time-dependent neutron transport integro-differential equationin a nonuniform slab with generalized boundary conditions and initial value is considered forgeneral cases concerned with an arbitrary no...In this paper,the time-dependent neutron transport integro-differential equationin a nonuniform slab with generalized boundary conditions and initial value is considered forgeneral cases concerned with an arbitrary nonhomogeneous medium possibly with cavity,withthe anisotropic scattering and fission,and with continuous energy varying from null to any finiteconstant or from one positive constant to another positive constant.We prove that the correspon-ding neutron transport operator A has finite Spectrum points in any strip {λ|β<sub>1</sub>≤R（?）λ≤β<sub>2</sub>}whereβ<sub>2</sub>】β1】-λ<sup>*</sup>（λ<sup>*</sup> is the essential infimum of v∑（x,v））,and obtain the asymptotic expansion ofthe time-dependent solution which exists and is unique.Furthermore,we give the existence ofthe dominant eigenvalue and indicate the asymptotic behavior of the neutron density as t→+∞.展开更多
基金Supported by the National Natural Science Foundation of China（71261010）
文摘Generalized strictly diagonally dominant matrices play a wide and important role in computational mathematics, mathematical physics, theory of dynamical systems, etc.But it is difficult to judge a matrix is or not generalized strictly diagonally dominant matrix.In this paper, by using the properties of α-chain diagonally dominant matrix, we obtain new criteria for judging generalized strictly diagonally dominant matrix, which enlarge the identification range.
基金Supported by the Nature Science Foundation of Henan Education Committee(2008A110022)
文摘In this paper,the solution of a parallel redundant repairable system is investigated.by using the method of functional analysis.Especially,the linear semigroups of operator theory on Banach space,we prove the existence of the strictly dominant eigenvalue,and show the linear stability of solution.
基金This work is supported by the National Natural Science Foundation of China
文摘In this paper,the time-dependent neutron transport integro-differential equationin a nonuniform slab with generalized boundary conditions and initial value is considered forgeneral cases concerned with an arbitrary nonhomogeneous medium possibly with cavity,withthe anisotropic scattering and fission,and with continuous energy varying from null to any finiteconstant or from one positive constant to another positive constant.We prove that the correspon-ding neutron transport operator A has finite Spectrum points in any strip {λ|β<sub>1</sub>≤R（?）λ≤β<sub>2</sub>}whereβ<sub>2</sub>】β1】-λ<sup>*</sup>（λ<sup>*</sup> is the essential infimum of v∑（x,v））,and obtain the asymptotic expansion ofthe time-dependent solution which exists and is unique.Furthermore,we give the existence ofthe dominant eigenvalue and indicate the asymptotic behavior of the neutron density as t→+∞.
