arXiv subjects
Publications and source records attributed to Małgorzata Moczurad.
We provide a computer-assisted proof of the exact count of classes of central configurations for five bodies for several sets of mass values that are exceptional from the point of view of the finiteness results of Albouy and Kaloshin in the planar case and of Hampton and Jensen in the spatial case.
We study the problem of planar central configurations with $N$ heavy bodies and $k$ bodies with arbitrary small masses. We derive the equation which describe the limit of light masses going to zero, which can be seen as the equation for central configurations in the anisotropic plane. Using computer rigorous computations we compute all central configurations for $N=2$ and $k=3,4$ and for the derived limit problem. We show that the results are consistent.
We give a computer assisted proof of the full listing of central configuration for $n$-body problem for Newtonian potential on the plane for $n=5,6,7$ with equal masses. We show all these central configurations have a reflective symmetry with respect to some line. For $n=8,9,10$ we establish the existence of central configurations without any reflectional symmetry.
Inspired by computer assisted proofs in analysis, we present an interval approach to real-number computations.
We consider the algorithm for verified integration of piecewise analytic functions given by Petras. The analysis of the algorithm contained in Patras' paper is limited to a narrow class of functions and gives upper bounds only. We present an estimation of the complexity (measured by a number of evaluations of an integrand) of the algorithm, both upper and lower bounds, for a wider class of functions. We show examples with complexity $Θ(|\ln\eps|/\eps^{p-1})$, for any $p >1$, where $\eps$ is the desired accuracy of the computed integral.
We give an improved lower bound for the error of any quadrature computing $\int_{-1}^1 f(x) dα(x)$ of analytic functions bounded in the neighborhood of $[-1,1]$.