In this paper, first we introduce the notions of an $(m,n)$-hyperideal and a generalized $(m,n)$-hyperideal in an ordered semihypergroup, and then, some properties of these hyperideals are studied. Thereafter, we characterize $(m,n)$-regularity, $(m,0)$-regularity, and $(0,n)$-regularity of an ordered semihypergroup in terms of its $(m,n)$-hyperideals, $(m,0)$-hyperideals and $(0,n)$-hyperideal...

Let $mathbf{c}_0$ be the real vector space of all real sequences which converge to zero. For every $x,yin mathbf{c}_0$, it is said that $y$ is block diagonal majorized by $x$ (written $yprec_b x$) if there exists a block diagonal row stochastic matrix $R$ such that $y=Rx$. In this paper we find the possible structure of linear functions $T:mathbf{c}_0rightarrow mathbf{c}_0$ preserving $prec_b$.

Inspired by the recent measurement of $CP$ asymmetry in individual mode on LHCb, we study $D\to \pi\pi$ system isospin and topological analysis. The ratio between penguin tree amplitudes $P/(T+C)$ is found to be greater than two most values relative strong phase. And $D^0\to \pi^0\pi^0$ a potential reveal order $10^{-3}$, which would observed Belle II future. large might understood $t$-channel ...