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[en] Using classical properties of conformal maps, we get new exact inequalities for rational functions with prescribed poles. In particular, we prove a new Bernstein-type inequality, an inequality for Blaschke products and a theorem that generalizes the Turan inequality for polynomials. The estimates obtained strengthen some familiar inequalities of Videnskii and Rusak. They are also related to recent results of Borwein, Erdelyi, Li, Mohapatra, Rodriguez, Aziz and others
[en] National and regional radon surveys are used in many nations to produce maps detailing the spatial variation of indoor radon concentrations. National surveys which are designed to be representative use either a geographically-weighted or a population-weighted sampling scheme. Additionally, many countries collect a large number of data on indoor radon concentrations from volunteers who have chosen to have the indoor radon concentration measured in their own dwellings. This work examines the representativeness of volunteer-based samples in radon measurement and explores the effect of potential volunteer bias on radon mapping results. We also investigate the influence that media attention has on volunteer sampling of indoor radon concentrations. The result of our work indicates that volunteer measurements are biased due to over-sampling of high radon areas. Consequently such volunteer radon measurements should not be used for radon mapping purposes.
[en] It is established that Q-homeomorphisms (in the sense of O. Martio) defined in Rn, n≥2, are absolutely continuous on lines. Furthermore, they belong to the Sobolev class Wloc1,1 and are differentiable almost everywhere for Q element of L1loc
[en] If g(z) is a hyperbolic rational map of degree two which is not conjugate to z2 + c for some c is an element of C-bar and J(g), the Julia set of g, is connected, then we show that the boundary of the components of C-bar / J(g) are Jordan curves. (author). 5 refs, 1 fig
[en] The properties of systems of pairwise distances between points thrown into a Euclidean space have been poorly studied to date. These properties are described in terms of a map called the 'edge function' (the 'rigidity mapping') and defining the behaviour of actual frameworks of levers and hinges. The simplest non-trivial case is that of rigidity mappings corresponding to plane frameworks (hingers) all fastened hinges of which lie on one straight line. In this paper rigidity mappings are investigated and examples of such straightened hingers with peculiar properties are presented.
[en] In this paper, we show that quantum twist maps, introduced by Lenagan-Yakimov, induce bijections between dual canonical bases of quantum nilpotent subalgebras. As a corollary, we show the unitriangular property between dual canonical bases and Poincaré-Birkhoff-Witt type bases under the “reverse” lexicographic order. We also show that quantum twist maps induce bijections between certain unipotent quantum minors.