Given a family of graphs $\mathcal{F}$, we prove that the normalized edit distance any given graph $\Gamma$ to being induced $\mathcal{F}$-free is estimable with query complexity depends only on bounds Frieze--Kannan regularity lemma and removal for $\mathcal{F}$.

Let $ { mathcal{R}} L$ be the ring of real-valued continuous functions on a frame $L$ as the pointfree  version of $C(X)$, the ring of all real-valued continuous functions on a topological space $X$. Since $C_c(X)$ is the largest subring of $C(X)$ whose elements have countable image, this motivates us to present the pointfree  version of $C_c(X).$The main aim of this paper is to present t...

We prove regularity estimates in weighted Sobolev spaces for the $L^2$-eigenfunctions of Schr\"odinger type operators whose potentials have inverse square singularities and uniform radial limits at infinity. In particular, usual $N$-body Hamiltonians with Coulomb-type singular are covered by our result: that case, weight is $\delta_{\mathcal{F}}(x) := \min \{ d(x, \bigcup \mathcal{F}), 1\}$, wh...

Let $\mathbf{G}$ be a connected reductive group defined over locally compact non-archimedean field $F$, let $\mathbf{P}$ parabolic subgroup with Levi $\mathbf{M}$ and compatible pro-$p$ Iwahori of $G := \mathbf{G}(F)$. $R$ commutative unital ring. We introduce the Iwahori--Hecke $R$-algebra $\mathcal{H}_R(P)$ $P \mathbf{P}(F)$ construct two morphisms $\Theta^P_M\colon \mathcal{H}_R(P)\to \mathc...

Let $n > k 1$ be integers, $[n] = \{1, \ldots, n\}$. $\mathcal F$ a family of $k$-subsets $[n]$. The is called intersecting if $F \cap F' \neq \varnothing$ for all $F, \in \mathcal F$. It almost it not but to every there at most one $F'\in satisfying \varnothing$. Gerbner et al. proved that \geq 2k + 2$ then $|\mathcal F| \leqslant {n - 1\choose 1}$ holds families. Our main result implies th...