Related papers: Descartes-Newton-Young rainbow
A short history of prisms from Lucius Anneus Seneca to George Ravenscroft.
In these Canberra summer school lectures we treat a number of topical issues in neutrino astrophysics: the solar neutrino problem, including the physics of the standard solar model, helioseismology, and the possibility that the solution…
During the past one hundred years three related elementary particles - the electron, the muon, and the tau - were discovered by very different scientific techniques. The author, who received the Wolf Prize and the Nobel Prize for the…
The Six Circles Theorem of C. Evelyn, G. Money-Coutts, and J. Tyrrell concerns chains of circles inscribed into a triangle: the first circle is inscribed in the first angle, the second circle is inscribed in the second angle and tangent to…
This thesis deals with three different aspects of the combinatorics of permutations. In the first two papers, two flavours of pattern avoiding permutations are examined; and in the third paper Young tableaux, which are closely related to…
A short phenomenological account of the genesis and evolution of the universe is presented with emphasis on the primordial phases as well as its physical composition, i.e. dark matter and dark energy. We discuss Einstein's theory of General…
We revisit the large-$N_c$ phase diagram of $\cal{N}$ = 4 super Yang-Mills theory at finite $R$-charge density and strong coupling, by means of the AdS/CFT correspondence. We conjecture new phases that result from a black hole shedding some…
$\alpha$+$\alpha$ scattering has a long history since the first experiment by Rutherford and Chadwick in 1927 and has been studied thoroughly experimentally and theoretically. However, $\alpha$+$\alpha$ scattering has never been paid…
The four-color theorem states that no more than four colors are required to color all nodes in planar graphs such that no two adjacent nodes are of the same color. The theorem was first propounded by Francis Guthrie in 1852. Since then,…
The introduction to this review summarizes chromosphere observation in two figures. The first part showcases the historical emphasis on the eclipse chromosphere in the development of NLTE line formation theory and criticizes 1D modeling.…
Motivated by the recent SuperKamiokande results on atmospheric neutrinos, we incorporate massive neutrinos, with large angle oscillation between the second and third generations, in a theory with R-parity violating supersymmetry. The…
Four light isotopes - D, ^3He, ^4He and ^7Li - were produced by nuclear reactions a few seconds after the big bang. New measurements of ^3He in the ISM by Gloeckler and Geiss and of deuterium in high redshift hydrogen clouds by Tytler and…
Let $G$ be a graph of order $n$ with an edge-coloring $c$, and let $\delta^c(G)$ denote the minimum color degree of $G$. A subgraph $F$ of $G$ is called rainbow if all edges of $F$ have pairwise distinct colors. There have been a lot…
The concept of rainbow connection number of a graph was introduced by Chartrand et al. in 2008. Inspired by this concept, other concepts on colored version of connectivity in graphs were introduced, such as the monochromatic connection…
A famous theorem of Dirac states that any graph on $n$ vertices with minimum degree at least $n/2$ has a Hamilton cycle. Such graphs are called Dirac graphs. Strengthening this result, we show the existence of rainbow Hamilton cycles in…
An edge-colored graph $G$ is {\em rainbow connected} if any two vertices are connected by a path whose edges have distinct colors. The {\em rainbow connection} of a connected graph $G$, denoted $rc(G)$, is the smallest number of colors that…
It may seem a funny notion to write about theorems as old and rehashed as Descartes's rule of signs, De Gua's rule or Budan's. Admittedly, these theorems were proved numerous times over the centuries. However, despite the popularity of…
These lectures, given at the Chinese Academy of Sciences for the BeiJing/HangZhou International Summer School in Mathematical Physics, are intended to introduce, to the beginning student in string theory and mathematical physics, aspects of…
This is a pedagogical paper which explains some ideas in cosmology at a level accessible to undergraduate students. It does not use general relativity, but uses the ideas of Newtonian cosmology worked out by Milne and McCrea. The…
The idea of atoms is old but X-rays provided the first probe into the physical atom. Photographs of X-ray scattering from crystals -Laue spots- were the first visual proof for the physical existence of atoms arranged in a perfect geometric…