1,257 research outputs found
An Erd\"os--R\'ev\'esz type law of the iterated logarithm for order statistics of a stationary Gaussian process
Let be a stationary Gaussian process with almost
surely (a.s.) continuous sample paths, , and correlation function satisfying (i) as for some , (ii) and (iii) as
for some . For any , consider mutually independent
copies of and denote by the th smallest order
statistics process, . We provide a tractable criterion for
assessing whether, for any positive, non-decreasing function , equals 0 or 1.
Using this criterion we find that, for a family of functions , such
that , , . Consequently, with , for , and
a.s.. Complementary, we prove an
Erd\"os-R\'ev\'esz type law of the iterated logarithm lower bound on
, i.e., a.s., ,
a.s., , where
Note on maximally entangled Eisert-Lewenstein-Wilkens quantum games
Maximally entangled Eisert-Lewenstein-Wilkens games are analyzed. For a
general class of gate operators defined in the previous papers of the first
author the general conditions are derived which allow to determine the form of
gate operators leading to maximally entangled games. The construction becomes
particularly simple provided one does distinguish between games differing by
relabelling of strategies. Some examples are presented.Comment: 20 pages, no figures, appendix added, references added, concluding
remarks extende
Geometric properties of semitube domains
In the paper we study the geometry of semitube domains in . In
particular, we extend the result of Burgu\'es and Dwilewicz for semitube
domains dropping out the smoothness assumption. We also prove various
properties of non-smooth pseudoconvex semitube domains obtaining among others a
relation between pseudoconvexity of a semitube domain and the number of
connected components of its vertical slices.
Finally, we present an example showing that there is a non-convex domain in
such that its image under arbitrary isometry is pseudoconvex.Comment: 6 page
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