Research
Research
Research
Research
7,093+ open-access research outputs.
J. Conway defined useful operations on the Class of combinatorial games and also introduced a notion of equivalence between games. Conway showed that, under his equivalence, games form a Group. Howeve…
This work is concerned with the probabilistic representation of solutions to the $p$-Laplace evolution equation $\frac{\partial u}{\partial t}={\rm div}(|\nabla u|^{p-2}\nabla u)$ in $(0,\infty)\times…
We show that isomorphisms of fundamental groups of elementary anabelian varieties -- varieties obtained as iterated fibrations of hyperbolic curves -- over sub-$p$-adic fields correspond bijectively t…
A residual-based a posteriori error estimator is proposed for the incompressible Oseen problem in the convection-dominated regime. The SUPG/PSPG/grad-div stabilized finite element method is used as di…
In 2002, Bourgain and Brezis proved that for the space $X=W^{1,d}$ (on $\mathbb{T}^{d}$, with $d\geq2$) we have the equality of images \begin{equation} \operatorname{div} (L^{\infty}\cap X)=\operatorn…
Higham's conjecture on the growth factor of complex symmetric positive definite matrices is a longstanding problem in the stability theory of Gaussian elimination without pivoting. It asserts that eve…
We introduce the notion of timed-Gromov--Hausdorff distance for timed-metric spaces. We prove that this distance is bi-Lipschitz equivalent to the intrinsic timed-Hausdorff distance of Sakovich--Sorma…
Recent work of Piotr Oprocha and his collaborators has provided a number of delicate examples of dynamical systems separating specification, shadowing, and periodic-point density, primarily in symboli…
We develop a family of $H(\mathrm{div})$-conforming hybridizable discontinuous Galerkin methods for the steady Stokes equations based on BDM and RT velocity spaces with either discontinuous or continu…
We study the existence of negative eigenvalues for two-dimensional Schr\"odinger operators with real-valued potentials in the weak coupling regime. In his pioneering paper [Simon 1976] from half a cen…
This Part develops structural consequences of the thermodynamic formalism for Axiom A diffeomorphisms. The Pesin Entropy Formula equates the metric entropy of the SRB measure to the sum of positive Ly…
In 1963, Rapha\"el Salem concluded his highly influential book ``Algebraic Numbers and Fourier Analysis'' with a list of four unsolved problems. The first two problems remain wide open while the last …
We prove a suitable fibration theorem over quasi-trivial tori that, through an approach developed by Harpaz and Wittenberg, implies so-called solvable descent. In particular, this gives a positive ans…
In the winter semester of 1890--1891 Adolf Hurwitz delivered a lecture course at the Albertina University in K\"onigsberg entitled -Theorie der algebraischen Gleichungen-. These lectures contain a par…
In this paper we study the existence and summability of the solutions to the following parabolic-elliptic system of partial differential equations with discontinuous coefficients: \begin{equation*} \b…
I was interested in the work of Solomon Marcus in Mathematical Linguistics as a high-school student. Later, I had the opportunity to discuss with him about many topics. He was a polymath. We wrote a p…
We study a one-dimensional cross-diffusion system for two interacting populations on the torus, with a linear pressure law and different mobilities. For arbitrary bounded non-negative initial data, we…
In this paper, we investigate the local boundedness of weak solutions to degenerate parabolic double phase equation of type $$ u_t-\textrm{div}(|Du|^{p-2}Du+a(x,t)|Du|^{q-2}Du)=0\quad \text{in } \Omeg…
Even if it has been less than a decade and a half since Tian introduced his concept of evolution algebras to represent algebraically non-Mendelian rules in Genetics, their study is becoming increasing…
There are at least two ways to approach the homotopy theory of spaces `at chromatic height $n$': one may localize with respect to $T(n)$-homology or with respect to $v_n$-periodic homotopy groups. It …
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