Let $$F_1$$ and $$F_2$$ be two disjoint graphs. The union $$F_1\cup F_2$$ is a graph with vertex set $$V(F_1)\cup V(F_2)$$ edge $$E(F_1)\cup E(F_2)$$ , the join $$F_1+F_2$$ E(F_2)\cup \{xy\;|\; x\in V(F_1)\hbox { } y\in V(F_2)\}$$ . In this paper, we present characterization to $$(P_5, K_1\cup K_3)$$ -free graphs, prove that $$\chi (G)\le 2\omega (G)-1$$ if G -free. Based on result, further $$ ...

In recent times, several discrepancies at the level of $(2-3)\sigma$ have been observed in decay processes mediated by flavour changing neutral current (FCNC) transitions $b \to s \ell^+ \ell^-$, which may be considered as smoking-gun signal New Physics (NP). These intriguing hints NP attracted a lot attention and many attempts are made to look for possible signature other related processes, th...

In order to characterize the dissociation of receptor-bound prolactin (PRL) by mammary cells, cells were prepared from lactating mice by collagenase digestion and loaded with PRL. The dissociation reaction was performed in the presence of PRL. In the concentration range 1 ng/ml-1 μg/ml examined, PRL at higher than 10 ng/ml accelerated the dissociation of PRL in a concentration-dependent manner....

Using the helicity amplitude technique, we derive differential decay widths and angular distributions for cascade $D\to K_{1}(1270,1400)\ell^+\nu_{\ell}\to (K\pi\pi)\ell^+\nu_{\ell} (\ell=e,\mu)$, in which electron muon mass is explicitly included. a set of phenomenological results K_1$ form factors, calculate partial branching fractions $D^0\to K_1^-\ell^+\nu_{\ell}$ $D^+\to K_1^0\ell^+\nu_{\e...

Let G = (V,E) be a nontrivial, finite, and connected graph. A function c from E to {1,2,...,k},k ∈ N, can considered as rainbow k-coloring if every two vertices x y in has an x- path. Therefore, no path's edges receive the same color; this condition is called “rainbow path”. The smallest positive integer k, designated by rc(G), connection number. Thus, k-coloring. Meanwhile, strong within for h...

Let $\mathbf L_k$ be the holomorphic line bundle of degree $k \in \mathbb Z$ on projective line. Here, tuples $(k_1 k_2 k_3 k_4)$ for which there does not exists homogeneous non-split supermanifolds $CP^{1|4}_{k_1 k_4}$ associated with vector L_{−k_1} \oplus \mathbf L _{−k_2} L_{−k_3} L_{−k_4}$ are classified. \\For many types remaining tuples, listed cocycles that determine supermanifolds. \\P...