Maps on positive definite matrices preserving Bregman and Jensen divergences

In this paper we determine those bijective maps of the set of all positive definite $n\times n$ complex matrices which preserve a given Bregman divergence corresponding to a differentiable convex function that satisfies certain conditions. We cover the cases of the most important Bregman divergences and present the precise structure of the mentioned transformations. Similar results concerning Jensen divergences and their preservers are also given

A kárpátaljai magyarok munkavállalói migrációja

The political and economic crisis of recent years has intensified the migrational activity from Ukraine to European countries with higher standards of living. Among the Transcarpathian Hungarians there are especially intensive migration processes for employment and other purposes, which was facilitated by owning Hungarian language skills on the one hand and possibility of obtaining Hungarian citizenship on the other. However, the number of Transcarpathian hungarians affected by migration, as well as the nature, duration and purpose of their migration, have not yet been investigated quantitatively. Our paper attempts to answer the above questions by evaluating the results of a questionnaire survey