Abstract Using new experimental data on photoproduction and $$\Lambda _b^0$$ Λ b 0 decays, we derive constraints the properties of LHCb $$P_c$$ P c states. We conclude that $$P_c(4312)$$ <mm...

We consider the frog model with geometric lifetime (parameter $1-p$) on homogeneous trees of dimension $d$. In 2002, \cite{alves2002-2} proved that there exists a critical parameter $p_c\in(0,1)$ above which infinitely many frogs are activated positive probability, and they gave lower upper bounds for $p_c$. Since then, literature this focussed refinements bound. present paper we improve $p_c$ ...

Let $mathcal {A}$ be an abelian category with enough projective objects and $mathcal {X}$ be a full subcategory of $mathcal {A}$. We define Gorenstein projective objects with respect to $mathcal {X}$ and $mathcal{Y}_{mathcal{X}}$, respectively, where $mathcal{Y}_{mathcal{X}}$=${ Yin Ch(mathcal {A})| Y$ is acyclic and $Z_{n}Yinmathcal{X}}$. We point out that under certain hypotheses, these two G...

‎Let $mathcal{A}$ be a commutative Banach algebra and $mathscr{X}$ be a left Banach $mathcal{A}$-module‎. ‎We study the set‎ ‎${rm Dec}_{mathcal{A}}(mathscr{X})$ of all elements in $mathcal{A}$ which induce a decomposable multiplication operator on $mathscr{X}$‎. ‎In the case $mathscr{X}=mathcal{A}$‎, ‎${rm Dec}_{mathcal{A}}(mathcal{A})$ is the well-known Apostol algebra of $mathcal{A}$‎. ‎We s...

We give a new derivation of mean-field percolation critical behaviour from the triangle condition that is quantitatively much better than previous proofs when diagram $\nabla_{p_c}$ large. In contrast to earlier methods, our approach continues yield bounds reasonable order $\nabla_p$ unbounded but diverges slowly as $p \uparrow p_c$, expected occur in on $\mathbb{Z}^d$ at upper-critical dimensi...

The pentaquark states, $P_{c}(4312)$, $P_{c}(4440)$ and $P_{c}(4457)$, could be nicely arranged into a multiplet of seven molecules $\bar{D}^{(\ast)}\Sigma_{c}^{(\ast)}$ dictated by heavy quark spin symmetry. However, the spins $P_c(4440)$ $P_c(4457)$ are not yet fully determined. In this work we employ contact-range effective field theory to investigate $SU(3)$-flavor counterparts $\bar{D}^{(\...

The observation of the $P_{cs}(4459)$ by LHCb collaboration adds a new member to set known hidden-charm pentaquarks, which includes $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$. is expected have light-quark content $\Lambda$ baryon ($I=0$, $S=-1$), but its spin unknown. Its closeness $\bar{D}^* \Xi_c$ threshold -- $4478\,{\rm MeV}$ in isospin-symmetric limit suggests molecular hypothesis as plausib...

‎let $g$ be a graph without an isolated vertex‎, ‎the normalized laplacian matrix $tilde{mathcal{l}}(g)$‎‎is defined as $tilde{mathcal{l}}(g)=mathcal{d}^{-frac{1}{2}}mathcal{l}(g) mathcal{d}^{-frac{1}{2}}$‎, where ‎$‎mathcal{‎d}‎$ ‎is a‎ diagonal matrix whose entries are degree of ‎vertices ‎‎of ‎$‎g‎$‎‎. ‎the eigenvalues of‎‎$tilde{mathcal{l}}(g)$ are ‎called ‎ ‎ as ‎the ‎normalized laplacian ...