退化(K_1,K_2)拟正则映射的充分条件

研究了退化弱(k1,k2)拟正则映射的正则性.利用H lder不等式、Sobolev空间的空间分析方法,以及内插定理等工具,给出了退化弱(k1,k2)拟正则映射事实上为退化(k1,k2)拟正则映射的一个充分条件,其结果对非退化情形也成立.     

群J~(6,k_1,…,k_l)的决定

设 ｋ１＜ｋ２＜…＜ ｋｌ， ｋｉ；为正整数，我们已决定群Ｊ６，ｋ２，…，ｋｌ（ｋｉ为偶数， ｋ２＞ １２），本文决定了群Ｊ６，１０，ｋ３…，ｋｌ，Ｊ６，８，ｋ３，…，ｋ１（ｋ３＞ １０），Ｊ６，８，１０，ｋ４，…，ｋｌ（ｋｉ为偶数）     

Bounds on the maximum numbers of clear two-factor interactions for 2^{(n_1 + n_2 ) - (k_1 + k_2 )} fractional factorial split-plot designs

Fractional factorial split-plot (FFSP) designs have an important value of investigation for their special structures. There are two types of factors in an FFSP design: the whole-plot (WP) factors and sub-plot (SP) factors, which can form three types of two-factor interactions: WP2fi, WS2fi and SP2fi. This paper considers FFSP designs with resolution III or IV under the clear effects criterion. It derives the upper and lower bounds on the maximum numbers of clear WP2fis and WS2fis for FFSP designs, and gives some methods for constructing the desired FFSP designs. It further examines the performance of the construction methods.     

双圆盘加权Hardy空间上$T_{z_1^{k_1}z_2^{k_2}+\bar{z}_1^{l_1}\bar{z}_2^{l_2}}$的约化子空间

本文中, 我们主要刻画了Toeplitz算子$T=M_{z^k}+M^*_{z^l}$的约化子空间, 其中 $k_i, l_i$ ($i=1,2$) 均是正整数, $k=(k_1,k_2), l=(l_1,l_2)$ 且 $k\neq l$, $M_{z^k}$, $M_{z^l}$ 是双圆盘加权Hardy空间$\mathcal{H}_\omega^2(\mathbb{D}^2)$上的乘法算子. 对权系数 $\omega$ 适当限制, 我们证明了由 $z^m$ 生成的 $T$ 的约化子空间均是极小的. 特别地, Bergman 空间和加权 Dirichlet 空间 $\mathcal{D}_\delta(\mathbb{D}^2)(\delta>0)$ 均是满足该限制条件的加权Hardy空间. 作为应用, 我们刻画了 $\mathcal{D}_\delta(\mathbb{D}^2)(\delta>0)$ 上 Toeplitz 算子 $T_{z^k+\bar{z}^l}$ 的约化子空间, 该结论是对双圆盘Bergman 空间上相关结论的推广.