In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind...In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level k (r 1,r 2,…,r k) circulant matrices are derived,and it is also proved that the sort of matrices are diagonalizable.展开更多
In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of th...In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.展开更多
In this pape,we give four methods of discriminations its nonsingularity by utilizing only parametr r1,r2 and elements of the first row of level-2 (r1, r2)-circulant matrices of type (m,n).
In this paper,it is given that the new equivalent definition of level-k (r1,r2, …,rk)-cir culant matrices of type (n1,n2,…,nk) in [1] and we give the explicit expression of its the eigenval ues and four methods of d...In this paper,it is given that the new equivalent definition of level-k (r1,r2, …,rk)-cir culant matrices of type (n1,n2,…,nk) in [1] and we give the explicit expression of its the eigenval ues and four methods of discriminations its nonsingularity by utilizing only parameter r1,r2, …,rk and elements of the first row of the sorts matrices.展开更多
The title compound has been synthesized by the reaction of 3,3-dimethyl-1-（1H-1,2,4-triazol-1-yl）butan-2-one oxime with 2-chlorobenzyl chloride, and then treated with 65～68% HNO3. Its crystal structure was determin...The title compound has been synthesized by the reaction of 3,3-dimethyl-1-（1H-1,2,4-triazol-1-yl）butan-2-one oxime with 2-chlorobenzyl chloride, and then treated with 65～68% HNO3. Its crystal structure was determined by single-crystal X-ray diffraction. The crystal belongs to the monoclinic system, space group P21/c with a = 14.5481（8）, b = 9.3351（5）, c = 13.1911（7） , β = 98.9450（10）°, Z = 4, V = 1769.67（17） 3, Mr = 369.81, Dc = 1.388 g/cm3, S = 1.06, μ = 0.247 mm-1, F（000） = 776, the final R = 0.0352 and wR = 0.0960 for 3069 observed reflections （I 2σ（I））. X-ray crystal structure presents the intramolecular N–H…O hydrogen bond. The packing is nearly parallel without π-π stacking interactions between two adjacent phenyl rings and stabilized by Van der Waals force. The preliminary bioassay shows that the title compound possesses fungicidal activity against Gibberella zeae at the dosage of 25 mg/L.展开更多
文摘In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level k (r 1,r 2,…,r k) circulant matrices are derived,and it is also proved that the sort of matrices are diagonalizable.
文摘In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.
文摘In this pape,we give four methods of discriminations its nonsingularity by utilizing only parametr r1,r2 and elements of the first row of level-2 (r1, r2)-circulant matrices of type (m,n).
文摘In this paper,it is given that the new equivalent definition of level-k (r1,r2, …,rk)-cir culant matrices of type (n1,n2,…,nk) in [1] and we give the explicit expression of its the eigenval ues and four methods of discriminations its nonsingularity by utilizing only parameter r1,r2, …,rk and elements of the first row of the sorts matrices.
基金Supported by the Central University Basic Scientific Research Fund of Hunan University (2009)the Key Scientific and Technological Project of Changsha, Hunan Province (No. 0901077-31)
文摘The title compound has been synthesized by the reaction of 3,3-dimethyl-1-（1H-1,2,4-triazol-1-yl）butan-2-one oxime with 2-chlorobenzyl chloride, and then treated with 65～68% HNO3. Its crystal structure was determined by single-crystal X-ray diffraction. The crystal belongs to the monoclinic system, space group P21/c with a = 14.5481（8）, b = 9.3351（5）, c = 13.1911（7） , β = 98.9450（10）°, Z = 4, V = 1769.67（17） 3, Mr = 369.81, Dc = 1.388 g/cm3, S = 1.06, μ = 0.247 mm-1, F（000） = 776, the final R = 0.0352 and wR = 0.0960 for 3069 observed reflections （I 2σ（I））. X-ray crystal structure presents the intramolecular N–H…O hydrogen bond. The packing is nearly parallel without π-π stacking interactions between two adjacent phenyl rings and stabilized by Van der Waals force. The preliminary bioassay shows that the title compound possesses fungicidal activity against Gibberella zeae at the dosage of 25 mg/L.
