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We propose an efficient and flexible method for solving Abel integral equation of the first kind, frequently appearing in many fields of astrophysics, physics, chemistry, and applied sciences. This equation represents an ill-posed problem, thus solving it requires some kind of regularization. Our method is based on solving the equation on a so-called compact set of functions and/or using Tikhonovs regularization. A priori constraints on the unknown function, defining a compact set, are very loose and can be set using simple physical considerations. Tikhonovs regularization on itself does not require any explicit a priori constraints on the unknown function and can be used independently of such constraints or in combination with them. Various target degrees of smoothness of the unknown function may be set, as required by the problem at hand. The advantage of the method, apart from its flexibility, is that it gives uniform convergence of the approximate solution to the exact solution, as the errors of input data tend to zero. The method is illustrated on several simulated models with known solutions. An example of astrophysical application of the method is also given.
We present an elegant method of determining the eigensolutions of the induction and the dynamo equation in a fluid embedded in a vacuum. The magnetic field is expanded in a complete set of functions. The new method is based on the biorthogonality of
For submillimeter spectroscopy with ground-based single-dish telescopes, removing noise contribution from the Earths atmosphere and the instrument is essential. For this purpose, here we propose a new method based on a data-scientific approach. The k
We present flame, a pipeline for reducing spectroscopic observations obtained with multi-slit near-infrared and optical instruments. Because of its flexible design, flame can be easily applied to data obtained with a wide variety of spectrographs. Th
We introduce SoFiA, a flexible software application for the detection and parameterization of sources in 3D spectral-line datasets. SoFiA combines for the first time in a single piece of software a set of new source-finding and parameterization algor
We present an error analysis and further numerical investigations of the Parameterized-Background Data-Weak (PBDW) formulation to variational Data Assimilation (state estimation), proposed in [Y Maday, AT Patera, JD Penn, M Yano, Int J Numer Meth Eng