Related papers: Combinatorics of Dyadic Intervals: Consistent Colo…
The synchronization problem is investigated for the class of locally strongly transitive automata introduced in a previous work of the authors. Some extensions of this problem related to the notions of stable set and word of minimal rank of…
Given a hypergraph $H$, the conflict-free colouring problem is to colour vertices of $H$ using minimum colours so that each hyperedge in $H$ sees a unique colour. We present a polynomial time reduction from the conflict-free colouring…
We study the existence and stability of cnoidal periodic wave arrays propagating in uniform quadratic nonlinear media and discover that they become completely stable above a threshold light intensity. To the best of our knowledge, this is…
In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude…
In this paper we extend previous results on convergent perturbative solutions of the Schroedinger equation of a class of periodically time-dependent two-level systems. The situation treated here is particularly suited for the investigation…
The project has carried out the re-optimization of image coloring in accordance with the existing Autocolorization direction model DDColor. For the experiments on the existing weights of DDColor, we found that it has limitations in some…
An edge-coloring of a graph $G$ with consecutive integers $c_{1},\ldots,c_{t}$ is called an \emph{interval $t$-coloring} if all colors are used, and the colors of edges incident to any vertex of $G$ are distinct and form an interval of…
We study the expanding properties of random perturbations of regular interval maps satisfying the summability condition of exponent one. Under very general conditions on the interval maps and perturbation types, we prove strong stochastic…
An edge-coloring of a graph $G$ with colors $1,...,t$ is an interval $t$-coloring if all colors are used, and the colors of edges incident to each vertex of $G$ are distinct and form an interval of integers. A graph $G$ is interval…
We address partition regularity problems for homogeneous quadratic equations. A consequence of our main results is that, under natural conditions on the coefficients $a,b,c$, for any finite coloring of the positive integers, there exists a…
We discuss the higher order stabilization of the coefficients of the colored Jones polynomial. In particular, we find an expression for the second stable sequence of the colored Jones polynomial of a certain class of knots. We also…
A proper edge-coloring of a graph is an interval coloring if the labels on the edges incident to any vertex form an interval of consecutive integers. Interval thickness s(G) of a graph G is the smallest number of interval colorable graphs…
Two colourings of a graph are orthogonal if they have the property that when two vertices are coloured with the same colour in one colouring, then those vertices receive distinct colours in the other colouring. In this paper, orthogonal…
We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high…
An edge coloring of a graph $G$ with colors $1,2,..., t$ is called an interval $t$-coloring if for each $i\in \{1,2,...,t\}$ there is at least one edge of $G$ colored by $i$, the colors of edges incident to any vertex of $G$ are distinct…
Let $X,Y$ be finite sets, $r,s,h, \lambda \in \mathbb{N}$ with $s\geq r, X\subsetneq Y$. By $\lambda \binom{X}{h}$ we mean the collection of all $h$-subsets of $X$ where each subset occurs $\lambda$ times. A coloring of…
This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable…
For a family of second-order parabolic systems with rapidly oscillating and time-dependent periodic coefficients, we investigate the asymptotic behavior of fundamental solutions and establish sharp estimates for the remainders.
In this paper, we consider a linear heat equation with constant coefficients and a single constant delay. Such equations are commonly used to model and study various problems arising in ecology and population biology when describing the…
We prove that a wide range of coloring problems in graphs on surfaces can be resolved by inspecting a finite number of configurations.