For any minimal system(X,T)and d≥1,there is an associated minimal system(N_(d)(X),G_(d)(T)),where G_(d)(T)is the group generated by T x…x T andT xT^(2)x.…x T^(d),and N_(d)(X)is the orbit closure of the diagonal und...For any minimal system(X,T)and d≥1,there is an associated minimal system(N_(d)(X),G_(d)(T)),where G_(d)(T)is the group generated by T x…x T andT xT^(2)x.…x T^(d),and N_(d)(X)is the orbit closure of the diagonal under G_(d)(T).It is known that the maximal d-step pro-nilfactor of N_(d)(X)is N_(d)(Xa),where X_(d)is the maximal d-step pro-nilfactor of X.In this paper,we further study the structure of N_(d)(X).We show that the maximal distal factor of N_(d)(X)is N_(d)(X_(dis))with X_(dis)being the maximal distal factor of X,and prove that as minimal system(N_(d)(X),G_(d)(T))has the same structure theorem as(X,T).In addition,a non-saturated metric example(X,T)is constructed,which is not T x T^(2)-saturated and is a Toeplitz minimal system.展开更多
Fifth-order isotropic descartes tensor and its existence theorem and representation problems are researched, then a general representation formula of fifth-order isotropic descartes tensor is got.
As the Welch-Berlekamp (W-B) theorem accurately predicts structure of error locator polynomials of the error patterns, it results in the Welch-Berlekamp algorithm of decoding cyclic codes. However, it is only valid wi...As the Welch-Berlekamp (W-B) theorem accurately predicts structure of error locator polynomials of the error patterns, it results in the Welch-Berlekamp algorithm of decoding cyclic codes. However, it is only valid within the BCH bound. Now, a prediction formula for error locator determination is presented based on the study of theory of minimal homogeneous interpolation problem, which extends the Welch-Berlekamp theorem and expands the Welch-Berlekamp algorithm so that the constraint from the BCH展开更多
A finite group G is called PN-group if G is not nilpotent and for every p-subgroup P of G, there holds that either P is normal in G or P lohtain in Z∞（G） or NG（P） is nilpotent, arbitary p ∈ π（G）. In this pap...A finite group G is called PN-group if G is not nilpotent and for every p-subgroup P of G, there holds that either P is normal in G or P lohtain in Z∞（G） or NG（P） is nilpotent, arbitary p ∈ π（G）. In this paper, we prove that PN-group is meta-nilpotent, especially, PN-group is solvable. In addition, we give an elementary, intuitionistic, compact proof of the structure theorem of PN- group.展开更多
文摘For any minimal system(X,T)and d≥1,there is an associated minimal system(N_(d)(X),G_(d)(T)),where G_(d)(T)is the group generated by T x…x T andT xT^(2)x.…x T^(d),and N_(d)(X)is the orbit closure of the diagonal under G_(d)(T).It is known that the maximal d-step pro-nilfactor of N_(d)(X)is N_(d)(Xa),where X_(d)is the maximal d-step pro-nilfactor of X.In this paper,we further study the structure of N_(d)(X).We show that the maximal distal factor of N_(d)(X)is N_(d)(X_(dis))with X_(dis)being the maximal distal factor of X,and prove that as minimal system(N_(d)(X),G_(d)(T))has the same structure theorem as(X,T).In addition,a non-saturated metric example(X,T)is constructed,which is not T x T^(2)-saturated and is a Toeplitz minimal system.
文摘Fifth-order isotropic descartes tensor and its existence theorem and representation problems are researched, then a general representation formula of fifth-order isotropic descartes tensor is got.
基金the National Natural Science Foundation of China and the Military Science Foundation in Ministry of Electronic Industry of China.
文摘As the Welch-Berlekamp (W-B) theorem accurately predicts structure of error locator polynomials of the error patterns, it results in the Welch-Berlekamp algorithm of decoding cyclic codes. However, it is only valid within the BCH bound. Now, a prediction formula for error locator determination is presented based on the study of theory of minimal homogeneous interpolation problem, which extends the Welch-Berlekamp theorem and expands the Welch-Berlekamp algorithm so that the constraint from the BCH
基金the National Natural Science Foundation of China （No. 10571181） the Natural Science Foundation of Guangdong Province （No. 06023728）.Acknowledgement The author wishes to thank Prof. Guo Wenbin for his help. The author also thanks the referees for their helpful comments.
文摘A finite group G is called PN-group if G is not nilpotent and for every p-subgroup P of G, there holds that either P is normal in G or P lohtain in Z∞（G） or NG（P） is nilpotent, arbitary p ∈ π（G）. In this paper, we prove that PN-group is meta-nilpotent, especially, PN-group is solvable. In addition, we give an elementary, intuitionistic, compact proof of the structure theorem of PN- group.
