9 papers
Unique expansions in number systems via refinement equations
Sergei V. Konyagin, Vladimir Yu. Protasov, Alexey L. Talambutsa
Using the subdivision schemes theory, we develop a criterion to check if any natural number has at most one representation in the -ary number system with a set of non-negative i…
Perron matrix semigroups
Vladimir Yu. Protasov
We consider multiplicative semigroups of real dxd matrices. A semigroup S is called Perron if each of its matrices has a Perron eigenvalue, i.e., an eigenvalue equal to the spectra…
Autopolar conic bodies and polyhedra
Maxim Makarov, Vladimir Yu. Protasov
An antinorm is a concave analogue of a norm. In contrast to norms, antinorms are not defined on the entire space but on a cone . They are applied in the matrix…
Chebyshev approximation by non-Chebyshev systems
Vladimir Yu. Protasov, Rinat Kamalov
We address the problem of the best uniform approximation by linear combinations of a finite system of functions. If the system is Chebyshev and the problem is unconstrained, then t…
Stability under dwell time constraints: Discretization revisited
Thomas Mejstrik, Vladimir Yu. Protasov
We decide the stability and compute the Lyapunov exponent of continuous-time linear switching systems with a guaranteed dwell time. The main result asserts that the discretization…
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…
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…
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…
Elements of mathematics in problems. Through olympiads and circles to profession
M. Berstein, A. Blinkov, V. Bragin +14
This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the…