Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero 3-flow. In this paper, we show that this conjecture is true for Cayley graph on generalized dihedral groups and generalized quaternion groups, ...Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero 3-flow. In this paper, we show that this conjecture is true for Cayley graph on generalized dihedral groups and generalized quaternion groups, which generalizes the result of F. Yang and X. Li [Inform. Process. Lett., 2011, 111： 416-419]. We also generalizes an early result of M. Nanasiova and M. Skoviera [J. Algebraic Combin., 2009, 30： 103-110].展开更多
Let H_F be the generalized quaternion division algebra over a field F with charF≠2. In this paper, the ad joint matrix of any n×n matrix over H_F[λ] is defined and its properties is discussed. By using the adjo...Let H_F be the generalized quaternion division algebra over a field F with charF≠2. In this paper, the ad joint matrix of any n×n matrix over H_F[λ] is defined and its properties is discussed. By using the adjoint matrix and the method of representation matrix, this paper obtains several necessary and sufficieut conditions for the existence of a solution or a unique solution to the matrix equation sum from n=i to k A^iXB_i=E over H_F, and gives some explicit formulas of solutions.展开更多
The main purpose of this paper is to study different types of sampling formulas of quaternionic functions,which are bandlimited under various quaternion Fourier and linear canonical transforms.We show that the quatern...The main purpose of this paper is to study different types of sampling formulas of quaternionic functions,which are bandlimited under various quaternion Fourier and linear canonical transforms.We show that the quaternionic bandlimited functions can be reconstructed from their samples as well as the samples of their derivatives and Hilbert transforms.In addition,the relationships among different types of sampling formulas under various transforms are discussed.First,if the quaternionic function is bandlimited to a rectangle that is symmetric about the origin,then the sampling formulas under various quaternion Fourier transforms are identical.If this rectangle is not symmetric about the origin,then the sampling formulas under various quaternion Fourier transforms are different from each other.Second,using the relationship between the two-sided quaternion Fourier transform and the linear canonical transform,we derive sampling formulas under various quaternion linear canonical transforms.Third,truncation errors of these sampling formulas are estimated.Finally,some simulations are provided to show how the sampling formulas can be used in applications.展开更多
基金Acknowledgements The first author was supported by the Natural Science Foundation of China （Grant No. 11301254）, the Natural Science Foundation of Henan Province （Grant No. 132300410313）, and the Natural Science Foundation of Education Bureau of Henan Province （Grant No. 13A110800）. The second author was supported by the National Natural Science Foundation of China （Grant No. 11171129） and the Doctoral Fund of Ministry of Education of China （Grant No. 20130144110001）.
文摘Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero 3-flow. In this paper, we show that this conjecture is true for Cayley graph on generalized dihedral groups and generalized quaternion groups, which generalizes the result of F. Yang and X. Li [Inform. Process. Lett., 2011, 111： 416-419]. We also generalizes an early result of M. Nanasiova and M. Skoviera [J. Algebraic Combin., 2009, 30： 103-110].
基金the National Natural Science Foundation of China and Hunan
文摘Let H_F be the generalized quaternion division algebra over a field F with charF≠2. In this paper, the ad joint matrix of any n×n matrix over H_F[λ] is defined and its properties is discussed. By using the adjoint matrix and the method of representation matrix, this paper obtains several necessary and sufficieut conditions for the existence of a solution or a unique solution to the matrix equation sum from n=i to k A^iXB_i=E over H_F, and gives some explicit formulas of solutions.
基金the Research Development Foundation of Wenzhou Medical UniversityChina(No.QTJ18012)+6 种基金the Wenzhou Science and Technology Bureau of China(No.G2020031)the Guangdong Basic and Applied Basic Research Foundation of China(No.2019A1515111185)the Science and Technology Development FundMacao Special Administrative RegionChina(No.FDCT/085/2018/A2)the University of MacaoChina(No.MYRG2019-00039-FST)。
文摘The main purpose of this paper is to study different types of sampling formulas of quaternionic functions,which are bandlimited under various quaternion Fourier and linear canonical transforms.We show that the quaternionic bandlimited functions can be reconstructed from their samples as well as the samples of their derivatives and Hilbert transforms.In addition,the relationships among different types of sampling formulas under various transforms are discussed.First,if the quaternionic function is bandlimited to a rectangle that is symmetric about the origin,then the sampling formulas under various quaternion Fourier transforms are identical.If this rectangle is not symmetric about the origin,then the sampling formulas under various quaternion Fourier transforms are different from each other.Second,using the relationship between the two-sided quaternion Fourier transform and the linear canonical transform,we derive sampling formulas under various quaternion linear canonical transforms.Third,truncation errors of these sampling formulas are estimated.Finally,some simulations are provided to show how the sampling formulas can be used in applications.
