Zobrazeno 1 - 10
of 123
pro vyhledávání: '"Dragovic, Vladimir"'
Autor:
Dragović, Vladimir, Radnović, Milena
In this work, we introduce a novel concept of magic billiards, which can be seen as an umbrella, unifying several well-known generalisations of mathematical billiards. We analyse properties of magic billiards in the case of elliptical boundaries. We
Externí odkaz:
http://arxiv.org/abs/2409.03158
Autor:
Dragović, Vladimir, Gajić, Borislav
We provide a geometric approach to the lasso. We study the tangency of the level sets of the least square objective function with the polyhedral boundary sets $B(t)$ of the parameters in $\mathbb R^p$ with the $\ell_1$ norm equal to $t$. Here $t$ dec
Externí odkaz:
http://arxiv.org/abs/2407.08058
Autor:
Dragović, Vladimir, Radnović, Milena
Using Marden's Theorem from geometric theory of polynomials, we show that for every triangle there is a unique ellipse such that the triangle is a billiard trajectory within that ellipse. Since $3$-periodic trajectories of billiards within ellipses a
Externí odkaz:
http://arxiv.org/abs/2405.08922
Autor:
Dragović, Vladimir, Stošić, Marko
Starting from billiard partitions which arose recently in the description of periodic trajectories of ellipsoidal billiards in $d$-dimensional Euclidean space, we introduce a new type of separable integer partition classes, called type B. We study th
Externí odkaz:
http://arxiv.org/abs/2404.19078
We consider the nonholonomic systems of $n$ homogeneous balls $\mathbf B_1,\dots,\mathbf B_n$ with the same radius $r$ that are rolling without slipping about a fixed sphere $\mathbf S_0$ with center $O$ and radius $R$. In addition, it is assumed tha
Externí odkaz:
http://arxiv.org/abs/2210.11586
Autor:
Dragović, Vladimir, Gajić, Borislav
This paper enhances and develops bridges between statistics, mechanics, and geometry. For a given system of points in $\mathbb R^k$ representing a sample of full rank, we construct an explicit pencil of confocal quadrics with the following properties
Externí odkaz:
http://arxiv.org/abs/2209.01679
Publikováno v:
Regular and Chaotic Dynamics, 2022, Vol. 27, No. 4, pp. 424-442
We first construct nonholonomic systems of $n$ homogeneous balls $\mathbf B_1,\dots,\mathbf B_n$ with centers $O_1,...,O_n$ and with the same radius $r$ that are rolling without slipping around a fixed sphere $\mathbf S_0$ with center $O$ and radius
Externí odkaz:
http://arxiv.org/abs/2208.03009
Autor:
Dragović, Vladimir, Mironov, Andrey E.
We introduce a method to find differential equations for functions which define tables, such that associated billiard systems admit a local first integral. We illustrate this method in three situations: the case of (locally) integrable wire billiards
Externí odkaz:
http://arxiv.org/abs/2207.09585
We introduce and study the dynamics of Chebyshev polynomials on $d>2$ real intervals. We define isoharmonic deformations as a natural generalization of the Chebyshev dynamics. This dynamics is associated with a novel class of constrained isomonodromi
Externí odkaz:
http://arxiv.org/abs/2112.04110
The aim of this work is to put together two novel concepts from the theory of integrable billiards: billiard ordered games and confocal billiard books. Billiard books appeared recently in the work of Fomenko's school, in particular of V. Vedyushkina.
Externí odkaz:
http://arxiv.org/abs/2111.10913