Let $d\geq2$ be an integer. The set $\mathbf{F}(d)$ of foliations degree $d$ on the complex projective plane can identified with a Zariski's open space dimension $d^2+4d+2$ which $\mathrm{Aut}(\mathbb P^2_{\mathbb C})$ acts. We show that there are exactly two orbits $\mathcal{O}(\mathcal{F}_{1}^{d})$ and $\mathcal{O}(\mathcal{F}_{2}^{d})$ minimal $6$, necessarily closed in $\mathbf{F}(d)$. This...

In this paper, characterizations of the degree to which a mapping $mathcal{T} : L^{X}longrightarrow M$ is an $(L, M)$-fuzzy topology are studied in detail.What is more, the degree to which an $L$-subset is an $L$-open set with respect to $mathcal{T}$ is introduced.Based on that, the degrees to which a mapping $f: Xlongrightarrow Y$ is continuous,open, closed or a quotient mapping with respect t...

In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-Archimedean $mathcal{L}$-fuzzy normed spaces.

The main purpose of this manuscript is to prove a common fixed point theorem for two weakly compatible maps satisfying the following integral type contraction in \(G\)-metric space:\[\int^{G(\mathcal{F}x,\mathcal{F}y,\mathcal{F}z)}_0\varphi (t)dt\le \alpha \int^{L(x,y,z)}_0\varphi (t)dt,\] all \(x,y, z\in X\), where\begin{align*}L(x,y,z)&=\max\{G(gx, gy, gz), G(gx, \mathcal{F}x, \mathcal{F}...

in this paper‎, ‎we investigate the influence of some subgroups of sylow subgroups with semi cover-avoiding property and‎ ‎$mathcal{f}$-supplementation on the structure of finite groups and generalize a series of known results‎.

We revisit the topic of polynomial kernels for Vertex Cover relative to structural parameters. Our starting point is a recent paper due to Fomin and Str{\o}mme [WG 2016] who gave a kernel with $\mathcal{O}(|X|^{12})$ vertices when $X$ is a vertex set such that each connected component of $G-X$ contains at most one cycle, i.e., $X$ is a modulator to a pseudoforest. We strongly generalize this re...

in this paper‎, ‎we investigate the influence of some subgroups of sylow subgroups with semi cover-avoiding property and‎ ‎$mathcal{f}$-supplementation on the structure of finite groups and generalize a series of known results‎.

Let F be a family of graphs. A canonical vertex deletion problem corresponding to F is defined as follows: given an n-vertex undirected graph G and a weight function w : V (G)→ R, find a minimum weight subset S ⊆ V (G) such that G− S belongs to F . This is known as Weighted F Vertex Deletion problem. In this paper we devise a recursive scheme to obtain O(logO(1) n)-approximation algorithms for ...

In this paper, we introduce the concept of ternary antiderivation on Banach algebras and investigate stability in algebras, associated to $(\alpha,\beta)$-functional inequality: \begin{align*} &\Vert \mathcal{F}(x+y+z)-\mathcal{F}(x+z)-\mathcal{F}(y-x+z)-\mathcal{F}(x-z)\Vert \nonumber\\ &\leq \Vert \alpha (\mathcal{F}(x+y-z)+\mathcal{F}(x-z)-\mathcal{F}(y))\Vert + \beta (\mathcal{F}(x-...