Research
Research
Research
Research
110+ open-access research outputs.
In this work we investigate the phenomenon of pathwise non-uniqueness for the stochastic incompressible Euler equations with a passive tracer on the whole Euclidean space. The stochastic perturbations…
A classical theorem of M. Jodeit Jr. implies that if a compactly supported distribution on $\mathbf{R}^d$ is the symbol of an $L^p(\mathbf{R}^d)$-$L^q(\mathbf{R}^d)$ Fourier multiplier, then its pushf…
This article focuses on some rings of integers of number fields which are known to be norm-Euclidean domains, but for which no explicit algorithm computing the Euclidean division has yet been studied …
Given a simple graph $G$, its $A_\alpha$ matrix is a convex combination with parameter $\alpha\in [0,1]$ of its adjacency matrix and its degree diagonal matrices. Here we compare two lower bounds pres…
Let $(M^5,g)$ be a five-dimensional non-trivial simply-connected compact quasi-Einstein manifold with boundary. If $M$ has constant scalar $R$, Johnatan Costa, Ernani Ribeiro Jr, and Detang Zhou show …
We resolve a $1000 Erd\H{o}s prize problem, complete with formal verification generated by a large language model. In over a dozen papers, beginning in 1976 and spanning two decades, Paul Erd\H{o}s …
In a previous joint work with Aurichi and Magalh\~aes Jr., we showed that the topological spaces arising from the edge-end structure of infinite graphs define a proper subfamily of those obtained thro…
We outline the history of the idea of deformation of space, which lead to the concept of curvature invariants, as we understand them today, including contributions of E. Bacaloglu and F. Casorati, amo…
In this paper we study the heat content for sets with positive reach. In details, we investigate the asymptotic behavior of the heat content of bounded subsets of the Euclidean space with positive rea…
We prove that the edge-end space of an infinite graph is metrizable if and only if it is first-countable. This strengthens a recent result by Aurichi, Magalhaes Jr.\ and Real (2024). Our central gra…
Motivated by random walks on subsets of the hypercube, we prove two discrete functional inequalities on the hypercube. First, we give a short, elementary proof of the Poincar\'e inequality on increasi…
The Fantappi\`e and Laplace transforms realize isomorphisms between analytic functionals supported on a convex compact set $K\subset{\mathbb C}^n$ and certain spaces of holomorphic functions associate…
We prove congruences of Hecke eigenvalues between cuspidal Hilbert newforms $f_{79}$ and $h_{79}$ over $F=\mathbb Q(\sqrt{5})$, of weights (2,2) and (2,4) respectively, level of norm 79. In the main e…
A family $\mathcal{F}$ of graphs is a \textit{Gallai family} if for every connected graph $G\in \mathcal{F}$, all longest paths in $G$ have a common vertex. While it is not known whether $P_5$-free gr…
In [Adv. Math., 321 (2017) 269-286], using the theory of ultrafilters, J. H. Johnson Jr., and F. K. Richter proved the nilpotent polynomial Hales-Jewett theorem. Using this result they proved the rest…
We study sample covariance matrices arising from multi-level components of variance. Thus, let $ B_n=\frac{1}{N}\sum_{j=1}^NT_{j}^{1/2}x_jx_j^TT_{j}^{1/2}$, where $x_j\in R^n$ are i.i.d. standard Gaus…
Two approaches to Lipschitz structures for any set are presented, studied and compared. The first approach is similar to the one proposed in Fraser, Jr. R. B., Axiom systems for Lipschitz structures, …
A classical inequality by Gr\"unbaum provides a sharp lower bound for the ratio $\mathrm{vol}(K^{-})/\mathrm{vol}(K)$, where $K^{-}$ denotes the intersection of a convex body with non-empty interior $…
We construct continuous (and even invertible) linear operators acting on Banach (even Hilbert) spaces whose restrictions to their respective closed linear subspaces of chain recurrent vectors are not …
By fully describing the lattice of subfields of some towers of number fields built by iterating square roots, we obtain infinitely many fields, each of them either contradicts Julia Robinson's problem…
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