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pro vyhledávání: '"Protasov IS"'
Invariant norms, also called Barabanov norms, are defined in $R^d$ for any compact family $\mathcal A$ of $d \times d$ matrices. They correspond to the linear switching system, which is a differential equation $\dot x(t) = A(t)x(t)$, where $A(t) \in
Externí odkaz:
http://arxiv.org/abs/2407.07861
Autor:
Makarov, Maxim, Protasov, Vladimir Yu.
An antinorm is a concave analogue of a norm. In contrast to norms, antinorms are not defined on the entire space $R^d$ but on a cone $K\subset R^d$. They are applied in the matrix analysis, optimal control, and dynamical systems. Their level sets are
Externí odkaz:
http://arxiv.org/abs/2407.04137
Autor:
Khrabrov, Kuzma, Ber, Anton, Tsypin, Artem, Ushenin, Konstantin, Rumiantsev, Egor, Telepov, Alexander, Protasov, Dmitry, Shenbin, Ilya, Alekseev, Anton, Shirokikh, Mikhail, Nikolenko, Sergey, Tutubalina, Elena, Kadurin, Artur
Methods of computational quantum chemistry provide accurate approximations of molecular properties crucial for computer-aided drug discovery and other areas of chemical science. However, high computational complexity limits the scalability of their a
Externí odkaz:
http://arxiv.org/abs/2406.14347
Local minima in Newton's aerodynamical problem and inequalities between norms of partial derivatives
Autor:
Plakhov, Alexander, Protasov, Vladimir
The problem considered first by I. Newton (1687) consists in finding a surface of the minimal frontal resistance in a parallel flow of non-interacting point particles. The standard formulation assumes that the surface is convex with a given convex ba
Externí odkaz:
http://arxiv.org/abs/2405.05415
Autor:
Protasov, Vladimir Yu., Kamalov, Rinat
We address the problem of the best uniform approximation of a continuous function on a convex domain. The approximation is by linear combinations of a finite system of functions (not necessarily Chebyshev) under arbitrary linear constraints. By modif
Externí odkaz:
http://arxiv.org/abs/2403.16330
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 method with step size~$h$ approximates the Lyapunov exponent with the
Externí odkaz:
http://arxiv.org/abs/2402.04795
We consider the problem of partitioning a two-dimensional flat torus $T^2$ into $m$ sets in order to minimize the maximal diameter of a part. For $m \leqslant 25$ we give numerical estimates for the maximal diameter $d_m(T^2)$ at which the partition
Externí odkaz:
http://arxiv.org/abs/2402.03997
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 matrix. The general (non-isotropic) case offered a great resistance. It w
Externí odkaz:
http://arxiv.org/abs/2312.11182
Autor:
Protasov, Vladimir Yu.
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 integers $n > m > 1$ with two additional cases $(1,0)$ and $(1,1)$. Th
Externí odkaz:
http://arxiv.org/abs/2312.10554
Autor:
Protasov, Vladimir Yu., Kamalov, Rinat
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 answered in an explicit form for any concrete system. This is done by fi
Externí odkaz:
http://arxiv.org/abs/2312.10506