We show that the series expansions of certain $q$-products have \textit{matching coefficients} with their reciprocals. Several results are associated to Ramanujan's continued fractions. For example, let $R(q)$ denote Rogers-Ramanujan fraction having well-known $q$-product repesentation $$R(q)=\dfrac{(q;q^5)_\infty(q^4;q^5)_\infty}{(q^2;q^5)_\infty(q^3;q^5)_\infty}.$$ If \begin{align*} \sum_{n=0...

In this paper, we focus on the parametrization of effective equation state (EoS) parameter within framework $f(Q)$ symmetric teleparallel gravity. Here, gravitational action is represented by an arbitrary function non-metricity scalar $Q$. By utilizing a specific EoS and power-law model theory, namely $f(Q)=\beta Q^{\left( m+1\right) }$ (where $\beta$ $m$ are constants), derive cosmological sol...

We consider modified symmetric teleparallel gravity (STG), in which gravitational Lagrangian is given by the arbitrary function of non-metricity scalar $Q$ to study static and spherically charged traversable wormhole solutions with non-commutative background geometry. The matter source at throat acknowledged be anisotropic, redshift has a constant value (thus, our solution non-tidal). obtained ...

We explore connections between the phenomenon of correlation decay (more precisely, strong spatial mixing) and location Lee--Yang Fisher zeros for various spin systems. In particular we show that, in many instances, proofs showing that weak mixing on Bethe lattice (infinite $\Delta$-regular tree) implies all graphs maximum degree $\Delta$ can be lifted to complex plane, establishing absence ass...

In this study, the beta function that is encountered in computational mathematics and physics analyzed. The correct evaluation of also affects accuracy other mathematical functions quantum mechanical calculations. Especially recent years, there an interest studies related to for zero negative p q integers. This considering neutrix limits function, presents new relations numerical computation es...

Qbeta replicase, in the presence of Mn(++), can use various RNAs as templates for synthesis of full-length RNA products and can also use Qbeta plus-strand RNA as template in the absence of host factors.

Let $$u(\cdot ,\cdot )$$ be the Caffarelli–Silvestre extension of f. The first goal this article is to establish fractional trace-type inequalities involving In doing so, firstly, we Sobolev/logarithmic Sobolev/Hardy trace in terms $$\nabla _{(x,t)}u(x,t).$$ Then, prove anisotropic $$ {\partial _{t} u(x,t)}$$ or $$(-\varDelta )^{-\gamma /2}u(x,t)$$ only. Moreover, based on an estimate Fourier t...

We investigate the nonnegative solutions to nonlinear integral inequality $u \ge I_{\alpha}\ast\big((I_\beta \ast u^p)u^q\big)$ a.e. in $\mathbb{R}^N$, where $\alpha, \beta\in (0,N)$, $p, q>0$ and $I_\alpha$, $I_\beta$ denote Riesz potentials of order $\alpha$ $\beta$ respectively. Our approach relies on a nonlocal positivity principle which allows us derive optimal ranges for parameters $\alph...