Abstract We prove that under the log-Hölder continuity condition of variable exponent $$p(\cdot )$$ p ( · ) , a new type maximal operators, $$U_{\gamma ,s}$$ U γ , s<...

Let $$\ell $$ be a prime and let $$n\ge 1$$ . In this note we show that if there is non-cuspidal, non-CM isolated point x with rational j-invariant on the modular curve $$X_1(\ell ^n)$$ , then =37$$ of either $$7\cdot 11^3$$ or $$-7.137^3\cdot 2083^3$$ The reverse implication holds for first but it currently unknown whether not second.

Let T be a triangulation of a set P of n points in the plane, and let e be an edge shared by two triangles in T such that the quadrilateral Q formed by these two triangles is convex. A flip of e is the operation of replacing e by the other diagonal of Q to obtain a new triangulation of P from T . The flip distance between two triangulations of P is the minimum number of flips needed to transfor...

&lt;p style='text-indent:20px;'&gt;In this paper, we investigate the optimal time-decay rates of global classical solutions for compressible Oldroyd-B model in &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ \mathbb{R}^n(n = 2,3) $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;. Global two space dimensions are still open. We first complete proof dimensions. Based on and F...

Many programming languages in the OO tradition now support pattern matching some form. Historical examples include Scala and Ceylon, with more recent additions of Java, Kotlin, TypeScript, Flow. But on generic class hierarchies currently results puzzling type errors most these languages. Yet this combination features occurs naturally many scenarios, such as when manipulating typed ASTs. To it p...

We study Kauffman's model of folded ribbon knots: knots made a thin strip paper flat in the plane. The ribbonlength is length to width ratio such knot. show for any knot or link type that there exist constants $c_1, c_2>0$ bounded above by $c_1\cdot Cr(K)^2$, and also $c_2\cdot Cr(K)^{3/2}$. use different method each bound. constant $c_1$ quite small comparison $c_2$, first bound lower than sec...

For $n\geq 1$, let $C_n$ denote a cyclic group of order $n$. Let $G=C_n\oplus C_{mn}$ with 2$ and $m\geq $k\in [0,n-1]$. It is known that any sequence $mn+n-1+k$ terms from $G$ must contain nontrivial zero-sum length at most $mn+n-1-k$. The associated inverse question to characterize those sequences maximal $mn+n-2+k$ fail subsequence $k\leq this the for Davenport Constant. $k=n-1$, $\eta(G)$ i...

The concept of residuated relational systems ordered under a quasi-order relation was introduced in 2018 by S. Bonzio and I. Chajda as structure $\mathfrak{A} = \langle A, \cdot, \rightarrow, 1, \preccurlyeq \rangle$, where $(A,\cdot)$ is commutative semigroup with the identity $1$ top element this monoid $\preccurlyeq$. In 2020, author analyzed concepts filters type algebraic structures. addit...