Let p ( · ) $p(\cdot )$ be a measurable function defined on R d ${\mathbb {R}}^d$ and − : = inf x ∈ $p_-:=\inf _{x\in {\mathbb {R}}^d}p(x)$ . In this paper, we generalize the Hardy–Littlewood maximal operator. definition, instead of cubes or balls, take supremum over all rectangles side lengths which are in cone-like set by given ψ. Moreover, integral means, consider L q $L_{q(\cdot )}$ -means....

Abstract We generalize the usual Doob maximal operator as well fractional and introduce $$M_{\gamma ,s,\alpha }$$ M γ , s α , a new for martingales. prove that under log-Hölder continuity conditio...

let $l$ be a completely regular frame and $mathcal{r}l$ be the ‎ring of continuous real-valued functions on $l$‎. ‎we show that the‎ ‎lattice $zid(mathcal{r}l)$ of $z$-ideals of $mathcal{r}l$ is a‎ ‎normal coherent yosida frame‎, ‎which extends the corresponding $c(x)$‎ ‎result of mart'{i}nez and zenk‎. ‎this we do by exhibiting‎ ‎$zid(mathcal{r}l)$ as a quotient of $rad(mathcal{r}l)$‎, ‎the‎ ‎...

In late 2012 and early 2013 the discrete logarithm problem (DLP) in finite fields of small characteristic underwent a dramatic series of breakthroughs, culminating in a heuristic quasipolynomial time algorithm, due to Barbulescu, Gaudry, Joux and Thomé. Using these developments, Adj, Menezes, Oliveira and Rodŕıguez-Henŕıquez analysed the concrete security of the DLP, as it arises from pairings ...

A skew brace is a triplet $(A,\cdot,\circ)$, where $(A,\cdot)$ and $(A,\circ)$ are groups such that the relation $x\circ (y\cdot z) = (x\circ y)\cdot x^{-1}\cdot z)$ holds for all $x,y,z\in A$. In this paper, we study number of finite braces up to isomorphism, both isomorphic $T^n$ with $T$ non-abelian simple $n\in\mathbb{N}$. We prove it equal unlabeled directed graphs on $n+1$ vertices, one d...

‎We show that for all normalized Hecke eigenforms $f$‎ ‎with weight one and of CM type‎, ‎the number $(f,f)$ where $(cdot‎, ‎cdot )$ denotes‎ ‎the Petersson inner product‎, ‎is a linear form in logarithms and‎ ‎hence transcendental‎.