Sequence converges is an important research object in topology and analysis, since it closely related to continuity, compactness other properties. In this article, we use the notion of regularly convergence, which a generalization convergence notion, define sequentially closed sets operator sequential closure; then consider thier charactarizations prove that are coincide regular spaces. Finally...

in this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $e_k(1, f^{n}(z)f(z+c))=e_k(1, g^{n}(z)g(z+c))$. then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...

Building on the weak CSR approach developed in a previous paper by Merlet, Nowak and Sergeev, we establish new bounds for periodicity threshold of powers tropical matrix. According to that approach, ultimate take form T=max(T_1,T_2), where T_1 is bound time after which expansion starts hold T_2 first term dominate. The established this make use cyclicity associated graph (tropical) factor rank ...

By $\mathcal{A}^2$ denote the class of analytic functions formBy form$f(z)=\sum_{n+m=0}^{+\infty}a_{nm}z_1^nz_2^m,$with {the} domain convergence $\mathbb{T}=\{z=(z_1,z_2)\in\mathbb C^2\colon|z_1|<1,\ |z_2|<+\infty\}=\mathbb{D}\times\mathbb{C}$ and$\frac{\partial}{\partial z_2}f(z_1,z_2)\not\equiv0$ in $\mathbb{T}.$ In this paper we prove some analogue Wiman's inequalityfor $f\in\mathcal{A...

Let $T_1, T_2$ be regular trees of degrees $d_1, d_2 \geq 3$. also $\Gamma \leq \mathrm{Aut}(T_1) \times \mathrm{Aut}(T_2)$ a group acting freely and transitively on $VT_1 VT_2$. For $i=1$ $2$, assume that the local action $\Gamma$ $T_i$ is $2$-transitive; if moreover $d_i 7$, contains $\mathrm{Alt}(d_i)$. We show irreducible, unless $(d_1, d_2)$ belongs to an explicit small set exceptional val...

In this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. Suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $E_k(1, f^{n}(z)f(z+c))=E_k(1, g^{n}(z)g(z+c))$. Then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...