[0-9]{4} https://revistaschilenas.uchile.cl/handle/2250/42584 2026-05-11T16:26:25Z 2026-05-11T16:26:25Z https://revistaschilenas.uchile.cl/handle/2250/241520 2024-04-16T14:16:58Z

On a class of fractional Γ(.)-Kirchhoff-Schrödinger system type This paper focuses on the investigation of a Kirchhoff-Schrödinger type elliptic system involving a fractional \(\gamma(.)\)-Laplacian operator. The primary objective is to establish the existence of weak solutions for this system within the framework of fractional Orlicz-Sobolev Spaces. To achieve this, we employ the critical point approach and direct variational principle, which allow us to demonstrate the existence of such solutions. The utilization of fractional Orlicz-Sobolev spaces is essential for handling the nonlinearity of the problem, making it a powerful tool for the analysis. The results presented herein contribute to a deeper understanding of the behavior of this type of elliptic system and provide a foundation for further research in related areas.

https://revistaschilenas.uchile.cl/handle/2250/241518 2024-04-16T14:16:58Z

Double asymptotic inequalities for the generalized Wallis ratio Asymptotic estimates for the generalized Wallis ratio \(W^*(x):=\frac{1}{\sqrt{\pi}}\cdot\frac{\Gamma(x+\frac{1}{2})}{\Gamma(x+1)}\) are presented for \(x\in\mathbb{R}^+\) on the basis of Stirling's approximation formula for the \(\Gamma\) function. For example, for an integer \(p\ge2\) and a real \(x>-\tfrac{1}{2}\) we have the following double asymptotic inequality\[A(p,x)\,<\,W^*(x)\,<\,B(p,x),\] where\begin{align*}A(p,x):=&W_p(x)\left(1-\tfrac{1}{8(x+p)}+\tfrac{1}{128(x+p)^2}+\tfrac{1}{379(x+p)^3}\right), \\B(p,x):= &W_p(x)\left(1-\tfrac{1}{8(x+p)}+\tfrac{1}{128(x+p)^2}+\tfrac{1}{191(x+p)^3}\right),\\W_p(x):=&\frac{1}{\sqrt{\pi\,(x+p)}}\cdot\frac{(x+1)^{(p)}}{(x+\frac{1}{2})^{(p)}},\end{align*} with \(y^{(p)}\equiv y(y+1)\cdots(y+p-1)\), the Pochhammer rising(upper) factorial of order \(p\).

https://revistaschilenas.uchile.cl/handle/2250/241515 2024-04-16T14:16:58Z

On uniqueness of \(L\)-functions in terms of zeros of strong uniqueness polynomial In this article, we have mainly focused on the uniqueness problem of an \(L\)-function \(\mathcal{L}\) with an \(L\)-function or a meromorphic function \(f\) under the condition of sharing the sets, generated from the zero set of some strong uniqueness polynomials. We have introduced two new definitions, which extend two existing important definitions of URSM and UPM in the literature and the same have been used to prove one of our main results. As an application of the result, we have exhibited a much improved and extended version of a recent result of Khoai-An-Phuong [23]. Our remaining results are about the uniqueness of \(L\)-function under weighted sharing of sets generated from the zeros of a suitable strong uniqueness polynomial, which improve and extend some results in [12].

https://revistaschilenas.uchile.cl/handle/2250/241519 2024-04-16T14:16:58Z

Multiplicative maps on generalized \(n\)-matrix rings Let \(\mathfrak{R}\) and \(\mathfrak{R}'\) be two associative rings (not necessarily with identity elements). A bijective map \(\varphi\) of \(\mathfrak{R}\) onto \(\mathfrak{R}'\) is called an \textit{\(m\)-multiplicative isomorphism} if {\(\varphi (x_{1} \cdots x_{m}) = \varphi(x_{1}) \cdots \varphi(x_{m})\)} for all \(x_{1}, \dotsc ,x_{m}\in \mathfrak{R}.\) In this article, we establish a condition on generalized matrix rings, that assures that multiplicative maps are additive. And then, we apply our result for study of \(m\)-multiplicative isomorphisms and \(m\)-multiplicative derivations on generalized matrix rings.