The sampling theorem on the real axis R was disscussed by many mathematician, a survey paper was given by P. L. Butzer (see[1]). The same kind theorem for Walsh transform was proved by Cheng Mingde. Shen Xiechang and ...The sampling theorem on the real axis R was disscussed by many mathematician, a survey paper was given by P. L. Butzer (see[1]). The same kind theorem for Walsh transform was proved by Cheng Mingde. Shen Xiechang and Zhou Mingqian in [4]. In [5], Li Shi-Xun established the sampling theorem on a kind of locally compact abelian groups, so extanded the two cases mentioned before. But the dual groups of the LCA groups which Li discussed was required to be compactly generated groups. In this paper, we proved the sampling theorem on the addition groups of p-series fields which do not have compactly generated dual groups.展开更多
On the basis of a unified definition of the dual operation and the (anti )self dual operation, the connections of the su(2,2｜1) main cluster was used as the fundamental field variables to construct the self dual L...On the basis of a unified definition of the dual operation and the (anti )self dual operation, the connections of the su(2,2｜1) main cluster was used as the fundamental field variables to construct the self dual Lagrangian of conformal supergravity. A Yang Mill like Lagrangian is obtained and a new gauge theory of supergravity is put forward. The spatial projects of its spin connection are Ashtekar variables.展开更多
Let H be an extension of a finite group Q by a finite group G. Inspired by the results of duality theorems for etale gerbes on orbifolds, the authors describe the number of conjugacy classes of H that map to the same ...Let H be an extension of a finite group Q by a finite group G. Inspired by the results of duality theorems for etale gerbes on orbifolds, the authors describe the number of conjugacy classes of H that map to the same conjugacy class of Q. Furthermore, a generalization of the orthogonality relation between characters of G is proved.展开更多
Monomorphism categories of the symmetric and alternating groups are studied via Cayley's Em-bedding Theorem. It is shown that the parity is well defined in such categories. As an application, the parity in a finit...Monomorphism categories of the symmetric and alternating groups are studied via Cayley's Em-bedding Theorem. It is shown that the parity is well defined in such categories. As an application, the parity in a finite group G is classified. It is proved that any element in a group of odd order is always even and such a group can be embedded into some alternating group instead of some symmetric group in the Cayley's theorem. It is also proved that the parity in an abelian group of even order is always balanced and the parity in an nonabelian group is independent of its order.展开更多
This paper deals with homology groups induced by the exterior algebra generated by the simplicial compliment of a simplicial complex K. By using ech homology and Alexander duality, the authors prove that there is a du...This paper deals with homology groups induced by the exterior algebra generated by the simplicial compliment of a simplicial complex K. By using ech homology and Alexander duality, the authors prove that there is a duality between these homology groups and the simplicial homology groups of K.展开更多
基金Supported by NSFC (Nos.11701254,12061030)Education and Teaching Reform Project of Lingnan Normal University (No.LSJGYB1922)Key Subject Program of Lingnan Normal University (No.1171518004)。
文摘The sampling theorem on the real axis R was disscussed by many mathematician, a survey paper was given by P. L. Butzer (see[1]). The same kind theorem for Walsh transform was proved by Cheng Mingde. Shen Xiechang and Zhou Mingqian in [4]. In [5], Li Shi-Xun established the sampling theorem on a kind of locally compact abelian groups, so extanded the two cases mentioned before. But the dual groups of the LCA groups which Li discussed was required to be compactly generated groups. In this paper, we proved the sampling theorem on the addition groups of p-series fields which do not have compactly generated dual groups.
文摘On the basis of a unified definition of the dual operation and the (anti )self dual operation, the connections of the su(2,2｜1) main cluster was used as the fundamental field variables to construct the self dual Lagrangian of conformal supergravity. A Yang Mill like Lagrangian is obtained and a new gauge theory of supergravity is put forward. The spatial projects of its spin connection are Ashtekar variables.
基金supported by the National Science Foundation(No.0900985)the National Security Agency(No.H98230-13-1-0209)+1 种基金the National Science Foundation(No.DMS-0757722)the Simons Foundation collaboration grant
文摘Let H be an extension of a finite group Q by a finite group G. Inspired by the results of duality theorems for etale gerbes on orbifolds, the authors describe the number of conjugacy classes of H that map to the same conjugacy class of Q. Furthermore, a generalization of the orthogonality relation between characters of G is proved.
文摘Monomorphism categories of the symmetric and alternating groups are studied via Cayley's Em-bedding Theorem. It is shown that the parity is well defined in such categories. As an application, the parity in a finite group G is classified. It is proved that any element in a group of odd order is always even and such a group can be embedded into some alternating group instead of some symmetric group in the Cayley's theorem. It is also proved that the parity in an abelian group of even order is always balanced and the parity in an nonabelian group is independent of its order.
基金supported by the National Natural Science Foundation of China(Nos.11371093,11261062,11471167)
文摘This paper deals with homology groups induced by the exterior algebra generated by the simplicial compliment of a simplicial complex K. By using ech homology and Alexander duality, the authors prove that there is a duality between these homology groups and the simplicial homology groups of K.
