Related papers: Superposition de calques monochromes d'opacit\'es …

In astronomy multiple images are frequently obtained at the same position of the sky for follow-up co-addition as it helps one go deeper and look for fainter objects. With large scale panchromatic synoptic surveys becoming more common,…

We present a recursive formula for the number of ways to color $j$ vertices blue in an r-uniform hyperpath of size $n$ while avoiding a blue monochromatic sub-hyperpath of length k. We use this result to solve the corresponding problem for…

The chromatic number of the finite projective space $\mathrm{PG}(n-1,q)$, denoted $\chi_q(n)$, is the minimum number of colors needed to color its points so that no line is monochromatic. We prove subadditivity of $\chi_q(n)$ with respect…

In this revised form, the proof of the principal lemma has been simplified and the main theorem has been extended to all characteristics for those varieties which are smooth in codimension one. This principal theorem essentially says the…

We present a new explicit formula for the $m$-th Bernoulli number $B_m$, which involves two integer parameters $a$ and $n$ with $0\le a\le m\le n$. If we set $a=0$ and $n=m$, then the formula reduces to the celebrated Kronecker formula for…

In attempting to understand how combinatorial modifications alter algebraic properties of monomial ideals, several authors have investigated the process of adding "whiskers" to graphs. In this paper, we study a similar construction to build…

Experimental mechanisms that yield the growth of homochiral copolymers over their heterochiral counterparts have been advocated by Lahav and co-workers. These chiral amplification mechanisms proceed through racemic {\beta}-sheet-controlled…

A unified approach to the representation of solutions of linear PDE's with constant coefficients in high dimensions in terms of solutions of the same PDE's in lower dimensions is presented. It is based on the observation that if a function…

We study a reconstruction problem for colorings. Given a finite or countable set $X$, a coloring on $X$ is a function $\varphi: [X]^{2}\to \{0,1\}$, where $[X]^{2}$ is the collection of all 2-elements subsets of $X$. A set $H\subseteq X$ is…

We generalize Sylvester single sums to multisets (sets with repeated elements), and show that these sums compute subresultants of two univariate polyomials as a function of their roots independently of their multiplicity structure. This is…

Liquid structure at solid-liquid interfaces is critical for many natural and engineered processes ranging from biological signal transduction to electrochemical energy conversion. Advanced experimental and computational methods have…

The chromatic number for properly colouring the facets of a combinatorial simple $n$-polytope $P^n$ that is the orbit space of a quasitoric manifold satisfies the inequality $n\leq P^n\leq 2^n-1$. The inequality is sharp for $n=2$ but not…

Spectral lines of heavy atomic elements in the ejecta of supernovae and neutron star mergers can have important contribution to the opacity of the ejecta matter even when the abundance of the elements is very small. Under favorable…

Let $G = (V,E)$ be a finite simple graph. Recall that a proper coloring of $G$ is a mapping $\varphi: V\to\{1,\ldots,k\}$ such that every color class induces an independent set. Such a $\varphi$ is called a semi-matching coloring if the…

We consider a generalisation of the classical Ramsey theory setting to a setting where each of the edges of the underlying host graph is coloured with a {\em set} of colours (instead of just one colour). We give bounds for monochromatic…

Let $K_{\mathbb{N}}$ be the complete symmetric digraph on the positive integers. Answering a question of DeBiasio and McKenney, we construct a $2$-colouring of the edges of $K_{\mathbb{N}}$ in which every monochromatic path has density~$0$.…

The Ramsey multiplicity problem asks for the minimum asymptotic density of monochromatic labelled copies of a graph $H$ in a red/blue colouring of the edges of $K_n$. We introduce an off-diagonal generalization in which the goal is to…

Working in subsystems of second order arithmetic, we formulate several representations for hypergraphs. We then prove the equivalence of various vertex coloring theorems to ${\sf WKL}_0$, ${\sf ACA}_0$ and $\Pi ^1_ 1$-${\sf CA}_0$.

A linearly ordered (LO) $k$-colouring of an $r$-uniform hypergraph assigns an integer from $\{1, \ldots, k \}$ to every vertex so that, in every edge, the (multi)set of colours has a unique maximum. Equivalently, for $r=3$, if two vertices…

The classical Lie method is applied to a nonisospectral problem associated with a system of partial differential equations in 2+1 dimensions (Maccari A, J. Math. Phys. 39, (1998), 6547-6551). Identification of the classical Lie symmetries…