It’s time to re-up the old story from voiceofrussia.com (since then rebranded as sputniknews.com). The old link leads to nowhere, but sputniknews still holds the grudge… On the right is what they were saying back then; on the left what the current site shows.Note the three airports! Willard, Rantoul airbase, sure, but what else? Frasca […]
a US-based university under the blue skies, among yellow fields Read More »
We all know that a generic complex plane curve of degree \(d\) has \(3d(d-2)\) inflections. Since Klein it is also known what the (strict) upper bound on the number of real inflections in real plane curves of degree \(d\) is: \(d(d-2)\), one third of the number of complex inflections. But what about the average real
averaging inflections in plane curves Read More »
Limit Cycles and Isochrones Consider smooth vector field \(v\) on a manifold with an exponentially stable limit cycle \(\gamma\): in other words, any trajectory starting close enough to \(\gamma\), converges to it exponentially fast. In this situation Guckenheimer proved the existence of isochrons, – a foliation of an open vicinity \(U\supset \gamma\) of the limit
martingales and isochrons Read More »
\(\def\Real{\mathbb{R}}\def\phd{\mathbf{P}H}\def\CAT{\mathtt{CAT}}\) The goal of this note is to define the biparametric persistence diagrams for smooth generic mappings \(h=(f,g):M\to\Real^2\) for smooth compact manifold (M). Existing approaches to multivariate persistence are mostly centered on the workaround of absence of reasonable algebraic theories for quiver representations for lattices of rank 2 or higher, or similar artificial obstacles. Singularities
singularities, biparametric persistence and cubical complexes Read More »
