Related papers: Rainbow formation: from Descartes to Venus
The origin of rings around giant planets remains elusive. Saturn's rings are massive and made of 90-95% of water ice. In contrast, the much less massive rings of Uranus and Neptune are dark and likely to have higher rock fraction. Here we…
A famous conjecture of Caccetta and H\"aggkvist is that in a digraph on $n$ vertices and minimum out-degree at least $\frac{n}{r}$ there is a directed cycle of length $r$ or less. We consider the following generalization: in an undirected…
% context heading (optional) {Thanks to the Venus Express Mission, new data on the properties of Venus could be obtained in particular concerning its rotation.} % aims heading (mandatory) {In view of these upcoming results, the purpose of…
The concept of rainbow connection was introduced by Chartrand et al. in 2008. It is fairly interesting and recently quite a lot papers have been published about it. In this survey we attempt to bring together most of the results and papers…
A model based on celestial geometry and atmospheric physics predicts the dimming and the color of lunar eclipses. Corresponding visual magnitudes and color indices for eclipses from year 2000 through 2050 are listed. The enlargement of the…
Rainbows and boat wakes may seem unrelated, but they share deep mathematical connections through ray folding, caustics, and Airy interference. This paper explores these principles, which are also relevant for explaining phenomena such as…
Accurate and thorough characterization of the chemistry of compounds containing the third-row elements sulfur and chlorine is critical for modeling the composition of the atmosphere of Venus. We have used a combination of ab initio quantum…
Aharoni and Berger conjectured that in every proper edge-colouring of a bipartite multigraph by $n$ colours with at least $n+1$ edges of each colour there is a rainbow matching using every colour. This conjecture generalizes a longstanding…
The main observations of 1761 by M. Lomonossov and those that followed are recalled by extending the discussion to other remarkable visual observations of the passages, then with more and more powerful imagers producing images in profusion.…
Many of the general-relativity-tests such as bending of light near a star and gravitational red/blue shift are explained without general-relativity and without Newtonian-approach. The author first casts doubts on both, the Newtonian and the…
Long-term measurements (1972-2015) of the reflectivity of Uranus at 472 and 551 nm display variability that is incompletely explained by seasonal effects. Spectral analysis shows this non-seasonal variability tracks the 11-year solar cycle.…
Context: The superrotation phenomenon in the atmosphere on Venus has been known since the late 60's. But until now no mechanism proposed has satisfactorily explained this phenomenon. Objective: The aim of this research is to propose a…
In this paper, we consider a spherical symmetric metric to extract the hydrostatic equilibrium equation of stars in $(3+1)-$dimensional gravity's rainbow in the presence of cosmological constant. Then, we generalize the hydrostatic…
The superrotation of the atmosphere of Venus requires a large torque on the up- per atmosphere. Mechanisms for providing a net balancing of this through waves or ionospheric motions to other parts of the atmosphere have been proposed but…
An edge-coloured cycle is rainbow if the edges have distinct colours. Let $G$ be a graph such that any $k$ vertices lie in a cycle of $G$. The $k$-rainbow cycle index of $G$, denoted by $crx_k(G)$, is the minimum number of colours required…
We report, {for the first time, the emergence of} a secondary bow with ripples in $^{12}$C+$^{12}$C nuclear rainbow scattering. This finding was achieved by studying the experimental angular distributions in $^{12}$C+$^{12}$C scattering at…
The gravity's rainbow function is derived in terms of a new varying speed of light (VSL) theory that varying velocity of light in the rainbow gravity becomes smaller when the energy of photons increases. In light of the new theory we…
It is shown how repeated observations of the sunset from various points up a tall building can be used to determine the Earth's radius. The same observations can also be used, at some latitudes, to deduce an approximate value for the amount…
An edge-coloured graph $G$ is {\it rainbow connected} if any two vertices are connected by a path whose edges have distinct colours. This concept was introduced by Chartrand et al. in \cite{ch01}, and it was extended to oriented graphs by…
Planetary-scale waves at the Venusian cloud-top cause periodic variations in both winds and ultraviolet (UV) brightness. While the wave candidates are the 4-day Kelvin wave and 5-day Rossby wave with zonal wavenumber 1, their temporal…