The main objective of this paper is to use the newly proposed $(p,q;l)$-extended beta function introduce $τ$-Gauss hypergeometric and $τ$-confluent functions with some their properties, such as Laplace-type Euler-type integral formulas. Another apply them fractional kinetic equations that appear in astrophysics physics using Laplace transform method.

Thermal nucleation of two-dimensional charges is studied. It is argued that the probability of N charge pairs to appear has a simple asymptotics for large N: p(N)=[q(c,beta,micro)](N)/Z(beta,micro), where q(c,beta,micro) is a function of charge concentration c, inverse temperature beta, and chemical potential micro, and Z(beta,micro) is the partition function. We present q(c,beta,micro) as a li...

We study the cyclic vectors and spanning set of circle for $\ell^p\_\beta(\mathbb{Z})$ spaces all sequences $u= (u\_n ){n\in \mathbb{Z}}$ such that $(u\_n (1+|n|)^{\beta} \mathbb{Z}} \in \ell^p(\mathbb{Z})$ , with $p>1$ $\beta>0$. The uniqueness distribution on whose Fourier coefficients are in $\ell^q\_{-\beta}(\mathbb{Z})$ is spaces, where $q$ conjugate $p$. Our characterizations given terms ...

This paper deals with the quasilinear attraction-repulsion chemotaxis system \begin{align*} \begin{cases} u_t=\nabla\cdot \big((u+1)^{m-1}\nabla u -\chi u(u+1)^{p-2}\nabla v +\xi u(u+1)^{q-2}\nabla w\big) +f(u), \\[1.05mm] 0=\Delta v+\alpha u-\beta v, w+\gamma u-\delta w \end{cases} \end{align*} in a bounded domain $\Omega \subset \mathbb{R}^n$ ($n \in \mathbb{N}$) smooth boundary $\partial\Ome...

Any oligo- or polynucleotide able to offer a C-C-C-sequence at the 3'-terminus and a second C-C-C-sequence in a defined steric position to Qbeta replicase is an efficient template. Corresponding chemical modifications convert non-template RNAs to template RNAs.

Abstract In this study, we conduct an analysis of traversable wormhole solutions within the framework linear gravity, ensuring that all energy conditions hold for entire spacetime. The presented in paper are derived through a comprehensive analytical examination parameter space associated with model. This involves considering exponents governing redshi...

let $p$ be a prime number greater than three. in this paper, we prove the existence of a new family of homotopy elements in the stable homotopy groups of spheres $pi_{ast}(s)$ which is represented by $h_nh_mtilde{beta}_{s+2}in {rm ext}_a^{s+4, q[p^n+p^m+(s+2)p+(s+1)]+s}(mathbb{z}_p,mathbb{z}_p)$ up to nonzero scalar in the adams spectral sequence, where $ngeq m+2>5$, $0leq sext}_a^{s+2,q[(s+2)p...

Logistic and Gompertz growth equations are the usual choice to model sustainable immoderate causing depletion of resources, respectively. Observing that logistic distribution is geo-max-stable function proportional Gumbel max-stable distribution, we investigate other models either distributions (log-logistic backward log-logistic) or (Fréchet max-Weibull). We show former arise when in hyper-log...