In this work, we provide estimates of the branching ratios, direct $CP$ asymmetries and triple product in $B_{(s)} \to (\pi\pi)(K\pi)$ decays perturbative QCD approach, where $\pi\pi$ $K\pi$ invariant mass spectra are dominated by vector resonances $\rho(770)$ $K^*(892)$, respectively. Some scalar backgrounds, such as $f_0(500,980) \pi\pi$ $K^*_0(1430) K\pi$ also accounted for. The $\rho(700)$ ...

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...

In this paper, at first we mention to some results related to PI and vertex Co-PI indices and then we introduce the edge versions of Co-PI indices. Then, we obtain some properties about these new indices.

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...