let $g$ be a simple graph of order $n$ and size $m$.the edge covering of $g$ is a set of edges such that every vertex of $g$ is incident to at least one edge of the set. the edge cover polynomial of $g$ is the polynomial$e(g,x)=sum_{i=rho(g)}^{m} e(g,i) x^{i}$,where $e(g,i)$ is the number of edge coverings of $g$ of size $i$, and$rho(g)$ is the edge covering number of $g$. in this paper we stud...

In this paper, we considerably extend the results on global existence of entropy-weak solutions to compressible Navier–Stokes system with density dependent viscosities obtained, independently (using different strategies) by Vasseur–Yu \[Invent. Math. 206 (2016) and arXiv:1501.06803 (2015)] Li–Xin \[arXiv:1504.06826 (2015)]. More precisely, are able consider a physical symmetric viscous stress t...

Recently, the BESIII Collaboration reported a resonance $Y(2040)$ with $M=2034\pm13\pm9$ MeV and $\Gamma=234\pm30\pm25$ in process of $e^+e^-\rightarrow\omega\pi^0$. In addition, new measurements much higher precision for $\rho(1900)$ $\rho(2150)$ states are obtained by BABAR Collaborations. this work, we perform systematic study on mass spectrum excited $\rho$ resonances using modified Godfrey...

Based on the Hugenholtz–Van Hove theorem, six basic quantities of EoS in isospin asymmetric nuclear matter are expressed terms nucleon kinetic energy t(k), symmetric and parts single-nucleon potentials $$U_0(\rho ,k)$$ $$U_{\text {sym},i}(\rho . The include quadratic symmetry $$E_{\text {sym,2}}(\rho )$$ , quartic {sym,4}}(\rho their corresponding density slopes $$L_2(\rho $$L_4(\rho incompress...

This paper is concerned with a one-dimensional isentropic compressible Navier-Stokes-Allen-Cahn system density-dependent viscosity, which models the motion of mixture two viscous fluids. The case when pressure $ p(\rho) = \rho^\gamma $, viscosity \nu(\rho, \chi) \rho^\alpha interface thickness \delta(\rho) \rho^\beta and relaxation time function a(\rho, \chi, \chi_y) \rho^\lambda considered, wh...

In the budding yeast Saccharomyces cerevisiae, loss of mitochondrial DNA (rho(0)) can induce the retrograde response under appropriate conditions, resulting in increased replicative lifespan (RLS). Although the retrograde pathway has been extensively elaborated, the nature of the mitochondrial signal triggering this response has not been clear. Mitochondrial membrane potential (MMP) was severel...