Research
Research
Research
Research
152+ open-access research outputs.
We show the subgroup of 20 nonzero fourth powers in the finite field of order 81 is a cap set. Similarly, the subgroup of 9 nonzero seventh powers in the field of order 64 is a cap set. These are the …
We show that for quasi-compact smooth rigid analytic spaces, the extension functor sends holonomic D-modules to coadmissible D-cap-modules which are of finite length as weakly holonomic D-cap-modules.…
We prove that the information complexity (i.e., the inverse) of the classical spherical cap $L_2$ discrepancy on the $d$-dimensional sphere $\mathbb{S}^d$ decreases with dimension $d$, indicating a ``…
In this paper, we prove small cap square function and decoupling estimates for the parabola, where the small caps are essentially axis-parallel rectangles of dimensions $\delta\times \delta^\beta$ for…
Entropy correction artificial viscosity (ECAV) is an approach for enforcing a semi-discrete entropy inequality through an entropy dissipative correction term. The resulting method can be implemented a…
We establish the global well-posedness theory of small BV weak solutions to a one-dimensional compressible Navier--Stokes model for reacting gas mixtures in dynamic combustion. The unknowns of the PDE…
A cap set in projective or affine geometry over a finite field is a set of points no three of which are collinear. In this paper, we propose a new construction for complete cap sets that yields a cap …
We adapt Caro's notion of overholonomicity to give a definition of holonomic D-cap-modules on rigid analytic spaces. We prove stability under five of the six operations (both inverse image functors, d…
The ternary extended contact relation was introduced in (Ivanova, 2020) as a more expressive counterpart of the standard binary contact relation. The class of Boolean algebras expanded with the relati…
We study provability predicates $\mathrm{Pr}_T(x)$ satisfying the following condition $\mathbf{E}$ from a modal logical perspective: $\mathbf{E}:$ if $ T \vdash \varphi \leftrightarrow \psi$, then $T …
We construct a fully-faithful functor of $\infty$-categories from complexes of D-cap modules with Fr\'echet cohomology to quasi-coherent sheaves on an analytic stack. We prove various descent results …
Hadwiger's covering conjecture is that every $n$-dimensional convex body can be covered by at most $2^n$ of its smaller positive homothetic copies, with $2^n$ copies required only for affine images of…
We resolve key open questions regarding approximation properties and their permanence for Fell bundles over locally compact groups. Specifically, we establish the equivalence between the B\'edos--Cont…
We introduce fractional integrals on the $n$-dimensional spherical cap, study their boundednes in weighted $L^p$ spaces and obtain explicit inversion formulas. The results are applied to the inversion…
This paper is devoted to the proof of an isoperimetric property of the double spherical cap rearrangement of planar sets under the assumption of disconnection of non-trivial spherical slices. Addition…
This presentation abstract, presented at 12th Applied Inverse Problems Conference, to be held at FGV EMAp, Rio de Janeiro, Brazil, in 2025, describe the theory results of applying the Chebyshev pseudo…
In this article, we prove interpolation results for $BMO$ in Lorentz spaces. From these results, we derive interpolation theorems in Besov spaces, the space $BV$, and fractional Sobolev spaces. As an …
Recurrent networks of binary neurons are a foundational concept in artificial intelligence. While these networks are traditionally assumed to be fully connected, complex dynamics can emerge when the g…
The illumination conjecture asserts that any convex body in $n$-dimensional Euclidean space can be illuminated by at most $2^n$ external light sources or parallel beams of light. Despite recent progre…
A {\em hole} is an induced cycle of length at least 4, an {\em even hole} is a hole of even length, and a {\em cap} is a graph obtained from a hole by adding an additional vertex which is adjacent exa…
Free open-access publishing with Google Scholar indexing.
Submission Guide →