arXiv subjects
Publications and source records attributed to Borbála Fazekas.
We investigate the explicit convex relaxation of the ideal magnetohydrodynamics equations. We provide a non-trivial lower estimate on the lamination hull and an upper estimate on the $Λ$-convex hull, the latter providing inequalities which will be satisfied by weak limits of weak solutions of the ideal MHD equations, which serve as a model of averaged turbulent magnetohydrodynamical flows.
In this paper, sequences of trials having three outcomes are studied. The outcomes are labelled as success, failure of type I and failure of type II. A run is called at most 1+1 contaminated, if it contains at most 1 failure of type I and at most 1 failure of type II. The limiting distribution of the first hitting time and the accompanying distribution for the length of the longest at most 1+1 contaminated run are obtained. This paper contains the detailed mathematical proofs. Simulation results supporting the theorems are also presented.
We study the length of $T$-contaminated runs of heads in the well-known coin tossing experiment. A $T$-contaminated run of heads is a sequence of consecutive heads interrupted by $T$ tails. For $T=1$ and $T=2$ we find the asymptotic distribution for the first hitting time of the $T$ contaminated run of heads having length $m$; furthermore, we obtain a limit theorem for the length of the longest $T$-contaminated head run. We prove that the rate of the approximation of our accompanying distribution for the length of the longest $T$-contaminated head run is considerably better than the previous ones. For the proof we use a powerful lemma by Csáki, Földes and Komlós.