Research
Research
Research
Research
22,475+ open-access research outputs.
Let $k\in\mathbb{N}$. Wigert's divisor function $d^{\left(\frac{1}{k}\right)}(j)$ counts the number of representations of $j$ of the form $m^k+mn$ with $m\geq1 , n\geq0$. Let $\mathcal{F}_k(s)$ denote…
We address the question of the large-time behavior of solutions to reaction-diffusion equations in periodic media. We start with the description of the asymptotic shape of the invasion set, which is c…
We study the asymptotic behavior of Stiefel--Whitney classes of irreducible orthogonal representations of the finite general linear groups $\mathrm{GL}_n(\mathbb{F}_q)$. Building on recent formulas ex…
We will generalize the concept of aggregation function for mathematical structures as a certain function between quantales. In fact, these functions turn to be exactly the lax morphism of quantales. T…
In many analyses the object reported at the end is not fixed in advance, but is chosen after a preliminary search over variables, subgroups, transformations, models or contrasts. Classical selective-i…
Let $\mathcal{OP}_n$ be the monoid of all orientation-preserving full transformations on $X_n=\{1,\dots, n\}$ with the natural order. For $\alpha \in \mathcal{OP}_n$, let $F(\alpha)=\{y\in X_n: y\alph…
We show that under $\mathsf{ZF} + \mathsf{CC}_{\mathbb R}$, if the Ramsey property holds for all sets in a good pointclass $\Gamma$, then there is no MAD family in $\Gamma$, proving a long-standing co…
In this note we formulate a conjecture about two group ring identities and prove that it would imply the Alon-Jaeger-Tarsi conjecture.…
Power grid infrastructure is an increasingly significant source of wildfire ignitions and poses severe risks to communities in fire-prone regions. Public Safety Power Shutoffs (PSPS) have emerged as a…
Defant and Kravitz introduced generalizations of West's stack-sorting map $s$ from permutations to finite words. This raises questions as to how such generalizations could be applied in the field of c…
From an identity connecting a combinatorial sum and Legendre polynomials, we derive closed forms for a number of combinatorial sums. Some of them are obtained via results about the integrals of functi…
Our research is closely related to ontological studies in mathematics. It provides crucial insights into the nature of decisions and strategies characterized by Markov moments. In a stopping game, a…
We establish a direct connection between the analytic data of weakly isolated mixed singularities and the topology of their associated links. More precisely, we prove that the existence of essential t…
Minahan and the author recently proved results that allow the calculation of the second rational cohomology group of the Torelli group. This builds on two key ingredients: Hain's calculation of the im…
We discuss an example of a non-complete normed space with the Daugavet property such that the norm is G\^ateaux differentiable at every nonzero point. In contrast, we note that the dual norm of a norm…
Measures of association in contingency tables, such as odds ratios and their generalizations, are often studied under different sampling schemes that either fix or leave random the margins of the tabl…
For $s \geq 0$ and a parameter $0 < \beta < 1$, the weak pair correlation function $f_{N,\beta}(s)$ for the first $N \in \mathbb{N}$ elements of a sequence $(x_n)_{n \in \mathbb{N}} \subset[0,1]$ is e…
In the early 1990s, J.Bourgain proved a general result $K$-closedness result in the context of classical harmonic analysis. In this paper, we extend Bourgain's method to the semicommutative setting, m…
We study the free-boundary equation \[ \Delta u=\chi_{\{|\nabla u|>0\}} \] near the origin. We prove that, at a singular point of \(\partial\{|\nabla u|>0\}\), the quadratic blow-up is unique. As no…
Zeroth-order optimization aims to minimize an objective function using only function evaluations, and is therefore fundamental in black-box optimization, hyperparameter tuning, bandit learning, and ad…
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