Top Hat was created by students for students, with the goal of helping everyone succeed in higher education. Whether you're logging in for the first time or looking to get the most out of our platform...

We give a counterexample to Theorem 9 in [T.K. Subrahmonian Moothathu, Syndetically proximal pairs, J. Math. Anal. Appl. 379 (2011) 656--663]. We also provide sufficient conditions for the conclusion ...

Experience a seamless connection between Top Hat and your LMS. Enjoy easy navigation, direct links to course materials, and synced grades for better teaching and learning.

We analyze the convergence of piecewise collocation methods for computing periodic solutions of general retarded functional differential equations under the abstract framework recently developed in [S...

Sign up for a Top Hat account. Professors and students can quickly and easily register online by following these steps. Experience everything Top Hat has to offer.

We provide a sharp lower bound for the perimeter of the inner parallel sets of a convex body $Ω$. The bound depends only on the perimeter and inradius $r$ of the original body and states that \[|\par...

Ergodicity for local and nonlocal stochastic singular $p$-Laplace equations is proven, without restriction on the spatial dimension and for all $p\in[1,2)$. This generalizes previous results from [Ges...

In this paper we prove that every Stein manifold $S$ admits a proper holomorphic immersion into any Stein manifold $X$ of dimension $2\mathrm{dim}S$ enjoying the density property or the volume density...

Given $p,N>1,$ we prove the sharp $L^p$-log-Sobolev inequality on noncompact metric measure spaces satisfying the ${\sf CD}(0,N)$ condition, where the optimal constant involves the asymptotic volume r...

Data visualization and analytics are nowadays one of the corner-stones of Data Science, turning the abundance of Big Data being produced through modern systems into actionable knowledge. Indeed, the B...

We study generalizations of Lorentzian warped products with one-dimensional base of the form $I\times_f X$, where $I$ is an interval, $X$ is a length space and $f$ is a positive continuous function. T...

Fog computing serves as a computing layer that sits between the edge devices and the cloud in the network topology. They have more compute capacity than the edge but much less so than cloud data cente...

Astrobiology is the field of science devoted to searching for life elsewhere in the Universe. It is inherently interdisciplinary, integrating results from multiple fields of science, and in this respe...