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Knowledge of the binary population in stellar groupings provides important information about the outcome of the star forming process in different environments. Binarity is also a key ingredient in stellar population studies and is a prerequisite to calibrate the binary evolution channels. In these proceedings we present an overview of several commonly used methods to pair individual stars into binary systems, which we refer to as the pairing function. Many pairing functions are frequently used by observers and computational astronomers, either for the mathematical convenience, or because they roughly describe the expected outcome of the star forming process. We discuss the consequences of each pairing function for the interpretation of observations and numerical simulations. The binary fraction and mass ratio distribution generally depend strongly on the selection of the range in primary spectral type in a sample. These quantities, when derived from a binary survey with a mass-limited sample of target stars, are thus not representative for the population as a whole.
Knowledge of the binary population in stellar groupings provides important information about the outcome of the star forming process in different environments (see, e.g., Blaauw 1991, and references therein). Binarity is also a key ingredient in stel
One of the central problems in supernova theory is the question how massive stars explode. Understanding the physical processes that drive the explosion is crucial for linking the stellar progenitors to the final remnants and for predicting observabl
We construct a symmetric invertible binary pairing function $F(m,n)$ on the set of positive integers with a property of $F(m,n)=F(n,m)$. Then we provide a complete proof of its symmetry and bijectivity, from which the construction of symmetric invert
The multielectron LDA+GTB approach has been developed to calculate electronic structure of strongly correlated cuprates. At low energies the effective Hamiltonian of the $t - t - t - {t_ bot } - {J^ * } - {J_ bot }$-model has been derived with parame
In this review, I present a brief summary of the impact of nucleon pairing at supra-nuclear densities on the cooling of neutron stars. I also describe how the recent observation of the cooling of the neutron star in the supernova remnant Cassiopeia A