The mass spectrum of hidden charm pentaquark states composed two diquarks and an antiquark are calculated by use effective Hamiltonian which includes explicitly the spin, color, flavor dependent interactions. results show that $$P_c(4312)^+$$ $$P_c(4440)^+$$ could be explained as with isospin spin-parity $$IJ^P=1/2\left( 3/2^-\right) $$ , $$P_c(4457)^+$$ state a 5/2^-\right) $$P_{cs}(4459)^+$$ ...

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}^{(\...