We prove that every algebraic curve X/Q is birational over C to a Teichmüller curve. keywords: algebraic curve, mapping class group, Teichmüller curve, Veech group. MSC code: 32G15, 37D40.

This study mapped and analyzed groundwater potential using two different models, logistic regression (LR) and multivariate adaptive regression splines (MARS), and compared the results. A spatial database was constructed for groundwater well data and groundwater influence factors. Groundwater well data with a high potential yield of ≥70 m3/d were extracted, and 859 locations (70%) were used for ...

We present a new approach which employs deep neural network to obtain parameters of analytical representation potential energy curve diatomic molecule. test the find spectroscopic characteristics for ground X2Σ+ electronic state MgF molecule based on experimental energies ro-vibrational transitions. The result shows that can be applied in characterisation interatomic Our is competitive with tho...

This paper covers relatively new and emerging subject of the elliptic curve crypto systems whose fundamental security is based on the algorithmically hard discrete logarithm problem. Work includes the study of the following issues: mathematical background of the elliptic curve crypto systems, discrete logarithm problem, practical use cases in the industry, common implementation mistakes, perfor...

an analytical equation of state was applied to calculate the thermodynamic properties for argon.the equation of state is that of song and mason. it is based on a statistical-mechanical perturbationtheory of the hard convex bodies and can be written as fifth-order polynomial in the density. thereexist three temperature-dependent parameters: the second virial coefficient, an effective molecularvo...