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math.FA2023
Anisotropic refinable functions and the tile B-splines
Vladimir Yu. Protasov, Tatyana Zaitseva
The regularity of refinable functions has been analysed in an extensive literature and is well-understood in two cases: 1) univariate 2) multivariate with an isotropic dilation mat…
math.MG2023
Closed simple geodesics on a polyhedron
Vladimir Yu. Protasov
It is well-known that every isosceles tetrahedron (disphenoid) admits infinitely many simple closed geodesics on its surface. They can be naturally enumerated by pairs of co-prime…
math.OC2023
How do the lengths of switching intervals influence the stability of a dynamical system?
Vladimir Yu. Protasov, Rinat Kamalov
If a linear switching system with frequent switches is stable, will it be stable under arbitrary switches? In general, the answer is negative. Nevertheless, this question can be an…