In this work, we study the renormalization group invariance (RGI) of recently proposed covariant power counting (PC) scheme in case nucleon-nucleon scattering [Chin.Phys. C42 (2018) 014103] at leading order (LO). We show that unlike LO Weinberg case, RGI is satisfied $^3P_{0}$ channel, because a term $pp'$ appears naturally PC LO. Another interesting feature $^1S_{0}$ and $^3P_{1}$ channels are...

Abstract Let $$ (P_n)_{n\ge 0}$$ ( P n ) ? 0 be the sequence of Perrin numbers defined by ternary relation P_0=3 = 3 , P_1=0 1 P...

In this paper, we prove that the weighted BMO space $${\rm{BM}}{{\rm{O}}^p}(\omega ) = \left\{ {f \in L_{{\rm{loc}}}^1:\mathop {\sup }\limits_Q \left\| {{\chi _Q}} \right\|_{{L^p}(\omega )}^{ - 1}{{\left\| {(f {f_Q}){\omega ^{ 1}}{\chi \right\|}_{{L^p}(\omega )}} < \infty } \right\}$$ is independent of scale p ∈ (0, ∞) in sense norm when ω A1. Moreover, can replace Lp(ω) by Lp,∞(ω). As an appli...

A path in an edge-colored graph is called a monochromatic if all edges of the have same color. We call k paths \(P_1,\ldots ,P_k\) rainbow every \(P_i\) and for any two \(i\ne j\), \(P_j\) different colors. An edge-coloring G said to be k-edge-connection coloring (or \(RMC_k\)-coloring short) distinct vertices are connected by at least paths. use \(rmc_k(G)\) denote maximum number colors that e...

Pigou's problem has many applications in real life scenarios like traffic networks, graph theory, data transfer internet etc. The two player classical network an unique Nash equilibrium with the Price of Stability and Anarchy agreeing each other. situation changes for $k-$person $n$ being total number people. If we fix behaviour $(n-2)$ people assume that $k-$persons take path $P_2$ where $k<(n...

We propose a new formula for the nonlinear viscous numerical flux and extend direct discontinuous Galerkin method with interface correction (DDGIC) of Liu Yan (H. Liu, J. Yan, The (DDG) diffusion corrections, Communications in Computational Physics 8 (3) (2010) 541) to compressible Navier-Stokes equations. DDGIC framework is based on observation that can be represented as sum multiple individua...

&lt;p style='text-indent:20px;'&gt;A recent result of Frantzikinakis in [&lt;xref ref-type="bibr" rid="b17"&gt;17&lt;/xref&gt;] establishes sufficient conditions for joint ergodicity the setting &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ \mathbb{Z} $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-actions. We generalize this actions second-countable locally compact ab...

The radiative transfer equation (RTE) models the transport of light inside photonic scattering samples such as paint, foam and tissue. Analytic approximations to solve RTE fail for with strong absorption dominant anisotropic predict unphysical negative energy densities diffuse flux in wrong direction. Here we fully characterize regions three popular a slab, namely $P_1$ approximation (or diffus...

We are grateful to Peter Thompson for pointing out an error in [1, Lemma 3.5, p. 1848]. The original proof worked only under the assumption that θ ̂ $\hat{\theta }$ is a vector of constants. However, some components $\hat{\bm{\theta }}$ could be states dynamic consideration, and lemma was used such setup (i.e., with involving states) later Proposition 3.4]. give more explicit version statement p...