Colorings, determinants and Alexander polynomials for spatial graphs

A {\em balanced} spatial graph has an integer weight on each edge, so that the directed sum of the weights at each vertex is zero. We describe the Alexander module and polynomial for balanced spatial graphs (originally due to Kinoshita \cite{ki}), and examine their behavior under some common operations on the graph. We use the Alexander module to define the determinant and $p$-colorings of a balanced spatial graph, and provide examples. We show that the determinant of a spatial graph determines for which $p$ the graph is $p$-colorable, and that a $p$-coloring of a graph corresponds to a representation of the fundamental group of its complement into a metacyclic group $\Gamma(p,m,k)$. We finish by proving some properties of the Alexander polynomial.Comment: 14 pages, 7 figures; version 3 reorganizes the paper, shortens some of the proofs, and improves the results related to representations in metacyclic groups. This is the final version, accepted by Journal of Knot Theory and its Ramification

ExoMol line lists – XLVIII. High-temperature line list of thioformaldehyde (H2CS)

A comprehensive rotation-vibration (ro-vibrational) line list of thioformaldehyde (1H212C32S) that is applicable for elevated temperatures (2000K) is presented. The new MOTY line list covers the 0 to 8000 cm−1 range (wavelengths λ > 1.3μm and contains around 43.5billion transitions between 52.3million states with rotational excitation up to J = 120. Line list calculations utilise a newly determined empirically refined potential energy surface (PES) – the most accurate H2CS PES to date – a previously published high-level ab initio dipole moment surface, and the use of an exact kinetic energy operator for solving the ro-vibrational Schrödinger equation. Post-processing of the MOTY line list is performed by replacing calculated energy levels with empirically-derived values, vastly improving the accuracy of predicted line positions in certain spectral windows and making the line list suitable for high-resolution applications. The MOTY line list is available from the ExoMol database at www.exomol.com and the CDS astronomical database

The 2020 release of the ExoMol database:Molecular line lists for exoplanet and other hot atmospheres

The ExoMol database (www.exomol.com) provides molecular data for spectroscopic studies of hot atmospheres. While the data is intended for studies of exoplanets and other astronomical bodies, the dataset is widely applicable. The basic form of the database is extensive line lists; these are supplemented with partition functions, state lifetimes, cooling functions, Land\'e g-factors, temperature-dependent cross sections, opacities, pressure broadening parameters, $k$-coefficients and dipoles. This paper presents the latest release of the database which has been expanded to consider 80 molecules and 190 isotopologues totaling over 700 billion transitions. While the spectroscopic data is concentrated at infrared and visible wavelengths, ultraviolet transitions are being increasingly considered in response to requests from observers. The core of the database comes from the ExoMol project which primarily uses theoretical methods, albeit usually fine-tuned to reproduce laboratory spectra, to generate very extensive line lists for studies of hot bodies. The data has recently been supplemented by line lists deriving from direct laboratory observations, albeit usually with the use of ab initio transition intensities. A major push in the new release is towards accurate characterisation of transition frequencies for use in high resolution studies of exoplanets and other bodies

The 2024 release of the ExoMol database: molecular line lists for exoplanet and other hot atmospheres

The ExoMol database (www.exomol.com) provides molecular data for spectroscopic studies of hot atmospheres. These data are widely used to model atmospheres of exoplanets, cool stars and other astronomical objects, as well as a variety of terrestrial applications. The 2024 data release reports the current status of the database which contains recommended line lists for 91 molecules and 224 isotopologues giving a total of almost 10$^{12}$ individual transitions. New features of the database include extensive "MARVELization" of line lists to allow them to be used for high resolutions studies, extension of several line lists to ultraviolet wavelengths, provision of photodissociation cross sections and extended provision of broadening parameters. Some of the in-house data specifications have been rewritten in JSON and moved to conformity with other international standards. Data products, including specific heats, a database of lifetimes for plasma studies, and the ExoMolHR web app which allows exclusively high resolution data to be extracted, are discussed

The 2024 release of the ExoMol database: Molecular line lists for exoplanet and other hot atmospheres

The ExoMol database (www.exomol.com) provides molecular data for spectroscopic studies of hot atmospheres. These data are widely used to model atmospheres of exoplanets, cool stars and other astronomical objects, as well as a variety of terrestrial applications. The 2024 data release reports the current status of the database which contains recommended line lists for 91 molecules and 224 isotopologues giving a total of almost 1012 individual transitions. New features of the database include extensive “MARVELization” of line lists to allow them to be used for high resolutions studies, extension of several line lists to ultraviolet wavelengths, provision of photodissociation cross-sections and extended provision of broadening parameters. Some of the in-house data specifications have been rewritten in JSON and moved for conformity with other international standards. Data products, including specific heats, a database of lifetimes for plasma studies, and the ExoMolHR web app which allows exclusively high resolution data to be extracted, are discussed

Alquimia, Ocultismo, Maçonaria: o ouro e o simbolismo hermético dos cadinhos (Séculos XVIII e XIX)

Este artigo apresenta a arqueologia das enigmáticas marcas impressas na base de cadinhos dos séculos XVIII e XIX recuperados nas escavações da Casa da Moeda do Rio de Janeiro, na década de 1980, e a explanação do seu significado simbólico à luz da alquimia, do ocultismo e da Maçonaria. Espraiando-se extraordinariamente mundo afora através de uma bem-sucedida estratégia de comunicação visual, a Maçonaria utilizou símbolos herméticos para a difusão de seus princípios nos mais diferentes suportes. Aparentemente estamos diante de um sinal de reconhecimento maçônico, o sinal exterior de uma organização oculta, só partilhado por iniciados e incompreensível para os demais, que contribuiu para difundir veladamente a doutrina maçônica por diferentes pontos do globo

Église catholique et Franc-Maçonnerie. Perspectives d'avenir

Mellor Alec. Église catholique et Franc-Maçonnerie. Perspectives d'avenir. In: Revue théologique de Louvain, 5ᵉ année, fasc. 1, 1974. pp. 55-60