For a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-Armendariz ring, that is a generalization of both $pi$-Armendariz rings, and $(alpha,delta)$-compatible skew Armendariz rings. We first observe the basic properties of skew $pi$-Armendariz rings, and extend the class of skew $pi$-Armendariz rings through various ring extensions. We nex...

Phosphorus (P), in the form of phosphate ion (Pi), is a vital element contributing in biomolecule structures, metabolic reactions, signaling pathways and energy transfer within the living cells. The objective of the present study was to assess the influence of fungal infection on Pi metabolism in compare to the effects of phosphate stress in Arabidopsis. Quantification of total P contents showe...

Phosphorus (P), in the form of phosphate ion (Pi), is a vital element contributing in biomolecule structures, metabolic reactions, signaling pathways and energy transfer within the living cells. The objective of the present study was to assess the influence of fungal infection on Pi metabolism in compare to the effects of phosphate stress in Arabidopsis. Quantification of total P contents showe...

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 ...