This paper investigated Hirano inverse of anti-triangular operator matrix in Banach algebra.Let a∈AH,b∈AsD.Assuming that bDa=0,babπ=0,it was proven that [ab10] had Hirano inverse.Moreover,Hirano inverse of anti-triangular operator matrix under certain weak commutative conditions was studied.These results provided a new kind of operator matrix with tripotent and nilpotent decompositions.
If $w=u\alpha$ for $\alpha\in \Sigma=\{1,2\}$ and $u\in \Sigma^*$, then $w$ is said to be a \textit{simple right extension}of $u$ and denoted by $u\prec w$. Let $k$ be a positive integer and $P^k(\epsilon)$ denote the set of all $C^\infty$-words of height $k$. Set $u_{1},\,u_{2},..., u_{m}\in P^{k}(\epsilon)$, if $u_{1}\prec u_{2}\prec ...\prec u_{m}$ and there is no element $v$ of $P^{k}(\epsilon)$ such that $v\prec u_{1}\text{or} u_{m}\prec v$, then $u_{1}\prec u_{2}\prec...\prec u_{m}$ is said to be a \textit{maximal right smooth extension (MRSE) chains}of height $k$. In this paper, we show that \textit{MRSE} chains of height $k$ constitutes a partition of smooth words of height $k$ and give the formula of the number of \textit{MRSE} chains of height $k$ for each positive integer $k$. Moreover, since there exist the minimal height $h_1$ and maximal height $h_2$ of smooth words of length $n$ for each positive integer $n$, we find that \textit{MRSE} chains of heights $h_1-1$ and $h_2+1$ are good candidates to be used to establish the lower and upper bounds of the number of smooth words of length $n$ respectively, which is simpler and more intuitionistic than the previous methods.
稻瘟病菌是危害水稻种植的重要病害,也是研究丝状真菌的重要模式菌.从细胞层面揭示稻瘟病菌的抑菌机制,可以为水稻病害防治和新药开发提供靶点.文章总结了近年来稻瘟病菌防控3种常用方法的优劣,并从细胞膜结构损伤、氧化损伤、膜相关酶活性变化和基因表达等方面对基于细胞膜损伤的抑菌活性研究进行了详细阐述,为高效绿色防控稻瘟病、开展基于细胞膜损伤的抑菌机制研究提供参考.
文章研究基于第四类切比雪夫节点的重心拉格朗日插值及其相关性质,讨论了重心拉格朗日插值公式的具体构造及其计算速度,推导其在加权Lp范数意义下的逼近阶,选取采样函数利用Matlab绘图并比较插值误差.由图示及数据表可知,误差随采样函数光滑性的增强或插值节点个数的增加而变小.
金属介导或催化的Si—C键断裂构建硅环骨架是目前被广泛关注的课题之一.文章从C(sp3)—Si、C(sp2)—Si和C(sp)—Si键活化3个方面对近20年来Si—C键断裂的转化反应研究进行了综述.结果发现Si—C键的活化主要局限于环张力高的小硅碳环或CH3—Si键,对Si—C键和底物的更大范围的适用性需要更多的研究.另外,开发一些新的催化剂类型以获得更高的对映选择性,构建更多的以碳或硅为中心的手性有机硅烷也是需要关注的课题.
