In this paper, we investigate the exact solution of an anisotropic space-time in context $f(Q)$ gravity, where $f\left( Q\right) $ is arbitrary function non-metricity scalar $Q$. Here, consider a specific power-law form as =\alpha Q^{n+1}+\beta $, $\alpha $\beta and $n$ are free model parameters. Using cosmology ($a\left( t\right) \propto t^{m}$), analyze physical behavior cosmological paramete...

The main goal of the present paper is to construct some families of the Carlitz's $q$-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz's $q$-Bernoulli polynomials and numbers with weight ($_{p}$. We then define the modified degenerate Carlitz's $q$-Bernoulli polynomials and numbers with weight ($alpha ,beta $) and obtain some recurrence relations and other identities...

The presence of exotic matter for the existence wormhole geometry has been an unavoidable problem in GR. In recent studies researchers have tried to deal with this issue using modified gravity theories where WH is explained by extra curvature terms and NEC's are not violated signifying standard geometry. present article we trying find solutions traversable wormholes normal throat within framewo...

The aim of this paper is to construct generating functions for q-beta polynomials. By using these generating functions, we define the q -beta polynomials and also derive some fundamental properties of these polynomials. We give some functional equations and partial differential equations (PDEs) related to these generating functions. By using these equations, we find some identities related to t...

For real $\xi$ we consider the irrationality measure function $\psi_\xi(t) = \min_{1\leqslant q \leqslant t, q\in\mathbb{Z}} || q\xi ||$, where $||\cdot||$ - distance to nearest integer. We prove that in case $\alpha\pm\beta\notin\mathbb{Z}$ there exist arbitrary large values of $t$ with $$\Bigl | \frac{1}{\psi_\alpha(t)} \frac{1}{\psi_\beta(t)} \Bigl \geqslant \sqrt5\left(1-\sqrt{\frac{\sqrt5-...

In this paper, we discuss the Bianchi type-I cosmological model in framework of symmetric teleparallel gravity say $f(Q)$ which non-metricity term $Q$ is responsible for gravitational interaction. We consider a special form $f\left( Q\right) $ function can be cast as =\lambda Q^{n}$, where $\lambda and $n$ both are dynamical parameters. Such choice viewed hybrid scale factor that leads to relat...

Hyperbolic beta integrals are analogues of Euler’s beta integral in which the role of Euler’s gamma function is taken over by Ruijsenaars’ hyperbolic gamma function. They may be viewed as (q, q̃ )-bibasic analogues of the beta integral in which the two bases q and q̃ are interrelated by modular inversion, and they entail q-analogues of the beta integral for |q| = 1. The integrals under considerat...

Hyperbolic beta integrals are analogues of Euler’s beta integral in which the role of Euler’s gamma function is taken over by Ruijsenaars’ hyperbolic gamma function. They may be viewed as (q, q̃ )-bibasic analogues of the beta integral in which the two bases q and q̃ are interrelated by modular inversion, and they entail q-analogues of the beta integral for |q| = 1. The integrals under considerat...

For $$\beta > 1$$ a real algebraic integer (the base), the finite alphabets $${\mathcal {A}} \subset {\mathbb {Z}}$$ which realize identity $${\mathbb {Q}}(\beta ) = \mathrm{Per}_{{\mathcal {A}}}(\beta )$$ , where $$\mathrm{Per}_{{\mathcal is set of complex numbers are $$(\beta {\mathcal {A}})$$ -eventually periodic representations, investigated. Comparing with greedy algorithm, minimal and nat...

Numerical simulations are used to investigate the multiaffine exponent alpha(q) and multigrowth exponent beta(q) of ballistic deposition growth for noise obeying a power-law distribution. The simulated values of beta(q) are compared with the asymptotic function beta(q)=1/q that is approximated from the power-law behavior of the distribution of height differences over time. They are in good agre...