In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
Let DD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(jj)|≥A_iA_j,i≠j,i,j∈N}.PD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(kk)|≥A_iA_jA_k,i≠j≠k,i,j,k∈N}. In this paper,we show DD_0(R)PD_0(R),and the conditions under which the nu...Let DD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(jj)|≥A_iA_j,i≠j,i,j∈N}.PD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(kk)|≥A_iA_jA_k,i≠j≠k,i,j,k∈N}. In this paper,we show DD_0(R)PD_0(R),and the conditions under which the numbers of eigen vance of A∈PD_0(R)\DD_0(R)are equal to the numbers of a_(ii),i∈N in positive and negative real part respectively.Some couter examples are given which present the condnions can not be omitted.展开更多
In the paper,a necessary and sufficeent condition for generalized diagonal domiance matrices is given.Further, the relations among all generalized positive definite matrices are shown, also,some flaws and mistakes in...In the paper,a necessary and sufficeent condition for generalized diagonal domiance matrices is given.Further, the relations among all generalized positive definite matrices are shown, also,some flaws and mistakes in the references are corrected.展开更多
In this paper, we provide some new criteria conditions for generalized strictly diagonally dominant matrices, such that the corresponding results in [1] are generalized and improved.
This essay poses Walras＇s theory of price mechanism in its merits and limitations. Walras proposed two laws as conditions for general equilibrium, namely： （1） the law of the variation of equilibrium prices, a subj...This essay poses Walras＇s theory of price mechanism in its merits and limitations. Walras proposed two laws as conditions for general equilibrium, namely： （1） the law of the variation of equilibrium prices, a subjective condition; and （2） the law of the establishment of equilibrium prices, an objective condition. Walras jointed both laws in order to develop his law of supply and demand. This paper offers a formal Walrasian approximation in terms of the Lyapounov＇s function, taking the diagonal dominant hypothesis as departure point, rediscovered almost a century after it was originally proposed by Walras. The paper concludes with critical reflection concerning the idea of equilibrium economics as medium of social cohesion.展开更多
文摘In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
文摘Let DD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(jj)|≥A_iA_j,i≠j,i,j∈N}.PD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(kk)|≥A_iA_jA_k,i≠j≠k,i,j,k∈N}. In this paper,we show DD_0(R)PD_0(R),and the conditions under which the numbers of eigen vance of A∈PD_0(R)\DD_0(R)are equal to the numbers of a_(ii),i∈N in positive and negative real part respectively.Some couter examples are given which present the condnions can not be omitted.
文摘In the paper,a necessary and sufficeent condition for generalized diagonal domiance matrices is given.Further, the relations among all generalized positive definite matrices are shown, also,some flaws and mistakes in the references are corrected.
基金Supported by the Nature Science Foundation of Henan Province（2003110010）
文摘In this paper, we provide some new criteria conditions for generalized strictly diagonally dominant matrices, such that the corresponding results in [1] are generalized and improved.
文摘This essay poses Walras＇s theory of price mechanism in its merits and limitations. Walras proposed two laws as conditions for general equilibrium, namely： （1） the law of the variation of equilibrium prices, a subjective condition; and （2） the law of the establishment of equilibrium prices, an objective condition. Walras jointed both laws in order to develop his law of supply and demand. This paper offers a formal Walrasian approximation in terms of the Lyapounov＇s function, taking the diagonal dominant hypothesis as departure point, rediscovered almost a century after it was originally proposed by Walras. The paper concludes with critical reflection concerning the idea of equilibrium economics as medium of social cohesion.
