Related papers: Descartes-Newton-Young rainbow
I present a review of the recent advancements in scattering theory, which provides a unified approach to studying dispersive and hyperbolic equations with general interaction terms and data. These equations encompass time-dependent…
Let $\mathbf{G}:=(G_1, G_2, G_3)$ be a triple of graphs on a common vertex set $V$ of size $n$. A rainbow triangle in $\mathbf{G}$ is a triple of edges $(e_1, e_2, e_3)$ with $e_i\in G_i$ for each $i$ and $\{e_1, e_2, e_3\}$ forming a…
A rainbow spanning tree in an edge-colored graph is a spanning tree in which each edge is a different color. Carraher, Hartke, and Horn showed that for $n$ and $C$ large enough, if $G$ is an edge-colored copy of $K_n$ in which each color…
The notes provide a short introduction to de Branges--Rovnyak spaces. They cover some basic facts and are intended to give the reader a taste of the theory, providing sufficient motivation to make it interesting.
This manuscript summarizes a series of three lectures on interactions of neutrinos . The lectures begin with a pedagogical foundation and then explore topics of interest to current and future neutrino oscillation and cross-section…
We study the strength of $\RRT^3_2$, Rainbow Ramsey Theorem for colorings of triples, and prove that $\RCA + \RRT^3_2$ implies neither $\WKL$ nor $\RRT^4_2$. To this end, we establish some recursion theoretic properties of cohesive sets and…
A new hidden variable theory is proposed, according to which particles follows definite trajectories, as in Bohmian Mechanics or Nelson's stochastic mechanics; in the new theory, however, the trajectories are classical, i.e. Newtonian. This…
The Newton line and the associated theorems by Newton and Gauss for tetragons and quadrilaterals are closely linked to some other theorems of Euclidean geometry: a theorem by Bocher on the existence of a nine-point conic of a quadrangle, a…
We establish a sharp upper bound on the number of properly $3$-edge-colored $K_4$'s in graphs with $R$ red, $G$ green and $B$ blue edges. We give a computer-free flag-algebra proof of this bound, and we also convert our proof into a…
I review the main features of the color charge degree of freedom in particle physics, sketch the paradox in the early quark model that led to color, give a personal perspective on the discovery of color and describe the introduction of the…
We review theoretical ideas, problems and implications of neutrino masses and mixing angles. We give a general discussion of schemes with three light neutrinos. Several specific examples are analyzed in some detail, particularly those that…
We introduce a way to color the regions of a classical knot diagram using ternary operations, so that the number of colorings is a knot invariant. By choosing appropriate substitutions in the algebras that we assign to diagrams, one obtains…
These lecture notes in the De Rham-Hodge theory are designed for a 1-semester undergraduate course (in mathematics, physics, engineering, chemistry or biology). This landmark theory of the 20th Century mathematics gives a rigorous…
String theories in principle address the origin and values of the quark and lepton masses. Perhaps the small values of neutrino masses could be explained generically in string theory even if it is more difficult to calculate individual…
Newtonian gravity can be regarded as a hypothetic-deductive system where the inverse square law is the starting point from which gravitational phenomena are deduced. This operational form of presenting gravity endorses problem solving and…
Let [n]=\{1,\,2,...,\,n\} be colored in k colors. A rainbow AP(k) in [n] is a k term arithmetic progression whose elements have diferent colors. Conlon, Jungic and Radoicic [10] had shown that there exists an equinumerous 4-coloring of [4n]…
Scientific discussions of the arrow of time often get quite confusing due to highly complex systems they deal with. Popular literature then often coveys messages that tend to get lost in translation. The purpose of this note is to demystify…
The basis of new ideas in the old theory is the Majorana and Ahluwalia constructs, modified versions of the Weinberg $2(2j+1)$ theory, and the Barut's self-field quantum electrodynamics.
By defining multiplicities for zeros of polynomials over hyperfields, Baker and Lorscheid were able to provide a unifying perspective on Descartes's rule and the Newton polygon rule for polynomials over a formally-real and valued field…
An edge-colored graph $F$ is rainbow if each edge of $F$ has a unique color. The rainbow Tur\'an number $ex^*(n,F)$ of a graph $F$ is the maximum possible number of edges in a properly edge-colored $n$-vertex graph with no rainbow copy of…