@1 Definition 1 Let A=(α<sub>ij</sub>)∈C<sup>n×n</sup>,B=(b<sub>ij</sub>)∈C<sup>n×n</sup>,is nonsingular.The generalizedsingular values of A（relative to B...@1 Definition 1 Let A=(α<sub>ij</sub>)∈C<sup>n×n</sup>,B=(b<sub>ij</sub>)∈C<sup>n×n</sup>,is nonsingular.The generalizedsingular values of A（relative to B）are following determinate nonnegative real numberswhen ||·||<sub>2</sub> denotes the Euclid vector norm,〈n〉={1,2,…,n}.Definition 2 Let A,B∈C<sup>n×n</sup>,if there exist λ∈C and x∈C<sup>n</sup>\{0}。展开更多
In this paper,we describe multiplicative derivations on the set of all rank-s matrices of Mn(K)over a field K with a relatively small integer s.Concretely,for fixed integers n,s satisfying 1≤s≤n/2 and n≥2,we prove ...In this paper,we describe multiplicative derivations on the set of all rank-s matrices of Mn(K)over a field K with a relatively small integer s.Concretely,for fixed integers n,s satisfying 1≤s≤n/2 and n≥2,we prove that if a map d:Mn(K)→Mn(K)satisfiesδ(xy)=δ(x)y+xδ(y)for any two rank-s matrices,y∈Mn(K),then there exists a derivation D of Mn(K)such thatδ(x)=D(x)for each rank-k matrix a E Mn(K)with 0≤k≤s.As an application,we prove that a multiplicative derivation on a special subset of Mn(K)must be a derivation.展开更多
Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, no...Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets enjoy many desirable theoretical properties and are often intrinsically linked to the refinable structure and multiresolution analysis. In this paper, we provide a comprehensive study on connecting homogeneous wavelets and framelets to nonhomogeneous ones with the refinable structure. This allows us to understand better the structure of homogeneous wavelets and framelets as well as their connections to the refinable structure and multiresolution analysis.展开更多
文摘@1 Definition 1 Let A=(α<sub>ij</sub>)∈C<sup>n×n</sup>,B=(b<sub>ij</sub>)∈C<sup>n×n</sup>,is nonsingular.The generalizedsingular values of A（relative to B）are following determinate nonnegative real numberswhen ||·||<sub>2</sub> denotes the Euclid vector norm,〈n〉={1,2,…,n}.Definition 2 Let A,B∈C<sup>n×n</sup>,if there exist λ∈C and x∈C<sup>n</sup>\{0}。
基金supported by the NSF of China(grants No.11971289,No.11771176)Wang Yanhua was supported by the NSF of China(grant No.11971289)+1 种基金Zhao Zhibing was supported by the NSF of China(grant No.11571329)the Project of University Natural Science Research of Anhui Province(grant No.KJ2019A0007).
文摘In this paper,we describe multiplicative derivations on the set of all rank-s matrices of Mn(K)over a field K with a relatively small integer s.Concretely,for fixed integers n,s satisfying 1≤s≤n/2 and n≥2,we prove that if a map d:Mn(K)→Mn(K)satisfiesδ(xy)=δ(x)y+xδ(y)for any two rank-s matrices,y∈Mn(K),then there exists a derivation D of Mn(K)such thatδ(x)=D(x)for each rank-k matrix a E Mn(K)with 0≤k≤s.As an application,we prove that a multiplicative derivation on a special subset of Mn(K)must be a derivation.
基金supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Canada) (Grant No. RGP 228051)
文摘Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets enjoy many desirable theoretical properties and are often intrinsically linked to the refinable structure and multiresolution analysis. In this paper, we provide a comprehensive study on connecting homogeneous wavelets and framelets to nonhomogeneous ones with the refinable structure. This allows us to understand better the structure of homogeneous wavelets and framelets as well as their connections to the refinable structure and multiresolution analysis.
