In this paper, the mutual information between clock-controlled input and output sequences is discussed. It is proved that the mutual information is a strictly monotone increasing function of the length of output seque...In this paper, the mutual information between clock-controlled input and output sequences is discussed. It is proved that the mutual information is a strictly monotone increasing function of the length of output sequence, and its divergent rate is gaven.展开更多
Let G be a finite group with order g and S be a subring of the algebraic number field which contains the integral extension over Z generated by a g-th primitive root co of unity, and R（G） be the character ring of G....Let G be a finite group with order g and S be a subring of the algebraic number field which contains the integral extension over Z generated by a g-th primitive root co of unity, and R（G） be the character ring of G. The prime spectrum of the commutative ring S×Z R（G） iv denoted by Spec（S×Z R（G）） and set π={p｜p is a rational prime number such that p^-1 S}. We prove that when G is a regroup, a π＇-group, or a finite Abelian group, the number of the connetted components of Spec（ S×Z R （G） ） coincides with the number of the π-regular classes in G,展开更多
Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts f...Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs' work, Slattery has developed some Brauer's ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer's three main theorems to the π-blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the first main theorem for π-blocks.展开更多
文摘In this paper, the mutual information between clock-controlled input and output sequences is discussed. It is proved that the mutual information is a strictly monotone increasing function of the length of output sequence, and its divergent rate is gaven.
文摘Let G be a finite group with order g and S be a subring of the algebraic number field which contains the integral extension over Z generated by a g-th primitive root co of unity, and R（G） be the character ring of G. The prime spectrum of the commutative ring S×Z R（G） iv denoted by Spec（S×Z R（G）） and set π={p｜p is a rational prime number such that p^-1 S}. We prove that when G is a regroup, a π＇-group, or a finite Abelian group, the number of the connetted components of Spec（ S×Z R （G） ） coincides with the number of the π-regular classes in G,
基金supported by the National Natural Science Foundation of China(Grant No.10471085)the BS Foundation of Shandong Province,China(Grant No.03bs006).
文摘Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs' work, Slattery has developed some Brauer's ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer's three main theorems to the π-blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the first main theorem for π-blocks.
