M. Plakhotnyk

activity

20162020

most citedThe max-plus algebra of exponent matrices of tiled orders

4 citations · 6 across the 13 of their papers we have counts for

collaborators

14 papers

math.CO2020

The cone of quasi-semimetrics and exponent matrices of tiled orders

Mikhailo Dokuchaev, Arnaldo Mandel, Makar Plakhotnyk

Finite quasi semimetrics on $n$ can be thought of as nonnegative valuations on the edges of a complete directed graph on $n$ vertices satisfying all possible triangle inequalities.…

math.DS2019

Classification of commutative pairs of surjective maps of interval, one of which is unimodal

Makar Plakhotnyk

We introduce here a classification of unimodal maps $[0, 1] \to [0, 1]$ , which commute with piecewise linear surjective maps $[0, 1] \to [0, 1]$ . Remind that if conti…

math.DS2018★ 1 cited

Infinite sequence on 2-element alphabet as coordinates of points, determines by unimodal maps

Makar Plakhotnyk

We study in this work different $(0, 1)$ -codings of points from the unit interval $[0, 1]$ in the relation with the treatment of continuous unimodal maps.

math.DS2018

On one generalization of skew tent maps

Makar Plakhotnyk

We generalize in this work the properties of the conjugacy of skew tent maps. It is known that the conjugacy $h$ from a skew tent map $g_{1}$ to $g_{2}$ is differentiable at a point $x…

math.DS2018★ 1 cited

Piecewise linear unimodal maps with non-trivial continuous piecewise linear commutator

Makar Plakhotnyk

Let $g : [0, 1] \to [0, 1]$ be piecewise linear unimodal map. We say that $g$ has non-trivial piecewise linear commutator, if there is a continuous piecewise linear $ψ:\, […

math.DS2017

Self-semiconjugation of piecewise linear unimodal maps

Makar Plakhotnyk

We devote this work to the functional equation $ψ \circ g = g \circ ψ$ , where $ψ$ is an unknown function and $g$ is piecewise linear unimodal map, which is topologically conjugated t…

cs.OH2017

A HelloWord \textsc{Bib}\negthinspace\TeX~stile file .\textbf{bst}

Makar Plakhotnyk

A HelloWord \textsc{Bib}\negthinspace\TeX~stile file .\textbf{bst} is described

math.DS2017

The derivative of the conjugacy for the pair of tent-like maps from an interval into itself

Makar Plakhotnyk

We consider in this article the properties of the topological conjugacy of the piecewise linear unimodal maps $g : [0, 1] \to [0, 1]$ , all whose kinks belong to the com…

math.DS2017

Self semi conjugations of Ulam's Tent-map

Makar Plakhotnyk

We study the self-semiconjugations of the Tent-map $f : x \mapsto 1 - ∣2 x - 1∣$ for $x \in [0, 1]$ . We prove that each of these semi-conjugations $ξ$ is piecewise linear. For any $n\i…

math.RA2017★ 4 cited

The max-plus algebra of exponent matrices of tiled orders

Mikhailo Dokuchaev, Vladimir V. Kirichenko, Ganna Kudryavtseva +1

An exponent matrix is an $n \times n$ matrix $A = (a_{ij})$ over $N^{0}$ satisfying (1) $a_{ii} = 0$ for all $i = 1, \dots, n$ and (2) $a_{ij} + a_{j k} \geq a_{ik}$ for all pairwise…

math.HO2017

Kepler's laws with introduction to differential calculus

Makar Plakhotnyk

We explain the solution of the following two problems: obtaining of Kepler's laws from Newton's laws (so called two bodies problem) and obtaining the fourth Newton's law (the formu…

math.HO2016

On the history of the Ulam's Conjugacy

Makar Plakhotnyk

We show the results on the history of the invention of the conjugacy $h (x) = \frac{2}{π} arcsin x$ of one-dimensional $[0, 1] \to [0, 1]$ maps $f (x) = 4 x (1 - x)$ and $g(x)…

math.HO2016

Possibility of the use of Cartesian method in the proofs of fundamental theorems of school planimetry

Makar Plakhotnyk

We show how Cartesian method can be used in the proof of fundamental planimetric topics of the school course, such as introduction of trigonometric functions, equation of a line an…

math.DS2016

Topological conjugation of one dimensional maps

Makar Plakhotnyk

Topological conjugateness of one dimensional unimodal dynamical systems, which are generated by interval [0, 1] into itself maps are studied. We study the smoothness and differenti…