2020/2

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    Note on a class of k-paranormal weighted composition operators on the Fock space Fp(C)
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2020) Santhoshkumar, C.; Veluchamy, T.
    In this paper, we characterize the k-paranormal, isometric, spectral radius and the numerical radius of the weighted composition operator C.
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    On increasing solutions of half-linear delay differential equations
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2020) Matucci, Serena; Řehák, Pavel
    We establish conditions guaranteeing that all eventually positive increas-ing solutions of a half-linear delay differential equation are regularly varying andderive precise asymptotic formulae for them. The results presented here are new alsoin the linear case and some of the observations are original also for non-functionalequations. A substantial difference is pointed out between the delayed and non-delayed case for eventually positive decreasing solutions.
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    On bornological induced pseudonearness
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2020) Leseberg, Dieter; Vaziry, Zohreh
    Pseudonearness is considered a common tool for studying bornology,b-topology, pseudoproximity, and last but not least,classicalnearness. For anypseudonear space we construct ab-completion, which generalizes the classical com-pletion of nearness spaces. Then, b-compactification is introduced in the context ofstrictbornotopologicalextensions.
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    In-game betting and the Kelly criterion
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2020) Andersen, Robin; Hassel, Vegard; Hvattum, Lars Magnus; Stalhane, Magnus
    When a bet with a positive expected return is available, the Kelly crite-rion can be used to determine the fraction of wealth to wager so as to maximizethe expected logarithmic return on investment. Several variants of the Kelly cri-terion have been developed and used by investors and bettors to maximize theirperformance in inefficient markets. This paper addresses a situation that has not,hitherto, been discussed in academic literature: when multiple bets can be placedon the same object and the available odds, true probabilities, or both, vary overtime. Such objects are frequently available in sports betting markets, for example,in the case of in-game betting on outcomes of soccer matches. We adapt the Kellycriterion to support decisions in such live betting scenarios, and provide numericalexamples of how optimal bet sizes can sometimes be counter-intuitive.
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    Huffman coding and chains in partition lattices
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2020) Foldes, Stephan
    The Huffman coding algorithm is interpreted in the context of the lat-tice of partitions of the source alphabet. Maximal chains in the partition latticecorrespond to linear extensions of tree orders, and those among the chains thatexhibit a simple greedy property correspond precisely to executions of the Huffmanalgorithm