With the discovery of some hidden-charm pentaquark resonances by LHCb Collaboration, investigations states containing heavy quarks have aroused interest theorists. We study herein $qqq\bar{q}Q$ ($q = u$ or $d$, $Q=c$ $b$) system, in framework chiral quark model. In consequence, charmed and bottomed pentaquarks are considered to exist five-body dynamical calculations. charm sector, $\Sigma_c\pi(...

Let $E/\mathbb{Q}$ be an elliptic curve that has complex multiplication (CM) by imaginary quadratic field $K$. For a prime $p$, there exists $\theta_p \in [0, \pi]$ such $p+1-\#E(\mathbb{F}_p) = 2\sqrt{p} \cos \theta_p$. $x>0$ large, and let $I\subseteq[0,\pi]$ subinterval. We prove if $\delta>0$ $\theta>0$ are fixed numbers $\delta+\theta<\frac{5}{24}$, $x^{1-\delta}\leq h\leq x$, $|I|\geq x^{...

In osteoblasts only the type III Na(+)-dependent phosphate (NaPi) transporter isoforms Pit-1 and Pit-2 have been identified. We tested the effects of extracellular Pi, Ca(2+) and IGF-I on Na(d)Pi transport and Pit-1 or Pit-2 mRNA expression in rat osteoblastic (PyMS) cells. The v(max) of Na(d)Pi transport was higher in cells kept in Pi-free, serum-free medium for 24 h than in controls at 1 mM P...

Despite the central bioenergetic importance of inorganic phosphate (Pi), little is known about the control of Pi metabolism in skeletal muscle, where resting [Pi] is maintained at 2-4 mM despite a highly unfavourable electrochemical gradient, and is partially regulated against changes in extracellular [Pi] [ I ,2]. We have discussed elsewhere how cellular [Pi] can be controlled by active transm...

The nonleptonic weak decay processes ${\mathrm{\ensuremath{\Omega}}}_{c}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Omega}}{\ensuremath{\pi}}^{+}/\mathrm{\ensuremath{\Omega}}(1P){\ensuremath{\pi}}^{+}/\mathrm{\ensuremath{\Omega}}(1D){\ensuremath{\pi}}^{+}/\mathrm{\ensuremath{\Omega}}(2S){\ensuremath{\pi}}^{+}$ are studied using the constituent quark model. branching fraction of ${\mathrm{\ensu...

Let q be a prime with primitive root 2. We show that (a) if (pi) q−2 i=0 is a sequence of primes such that pi = 2pi−1 + 1 for all 1 ≤ i ≤ q − 2, then q divides p0 + 1 or p0 ∈ {2, 3, 5} and (b) if (pi) q−2 i=0 is a sequence of primes such that pi = 2pi−1 − 1 for all 1 ≤ i ≤ q − 2, then q divides p0 − 1 or p0 ∈ {2, 3}.

let $g$ be a connected graph. the multiplicative zagreb eccentricity indices of $g$ are defined respectively as ${bf pi}_1^*(g)=prod_{vin v(g)}varepsilon_g^2(v)$ and ${bf pi}_2^*(g)=prod_{uvin e(g)}varepsilon_g(u)varepsilon_g(v)$, where $varepsilon_g(v)$ is the eccentricity of vertex $v$ in graph $g$ and $varepsilon_g^2(v)=(varepsilon_g(v))^2$. in this paper, we present some bounds of the multi...