2014/2

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    Dynamic pricing with capacity constraints and inventory replenishment
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2014) Olstad, Asmund
    This paper describes a fast algorithm for solving a capacitated dynamic pricing problem where the producer has the ability to store inventory. The pricing problem described is a quadratic programming problem with a structure that can be solved e ectively by a dual algorithm. The proposed algorithm gives a solution satisfying the Karush-Kuhn-Tucker conditions. This, combined with the fact that the problem has a convex feasible region with a concave objective function which we want to maximize, implies that the proposed algorithm gives a globally optimal solution. The algorithm is illustrated by numerical examples for both the single-item and the multi-item cases.
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    New bounds for irrationality measures of some fast converging series
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2014) Šustek, Jan
    This paper presents new upper bounds for irrationality measures of some fast converging series of rational numbers. The results depend only on the speed of convergence of the series and do not depend on the arithmetical properties of the terms.
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    Lifting connections to the r-jet prolongation of the cotangent bundle
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2014) Mikulski, Włodzimierz M.
    We show that the problem of finding all Mfm -natural operators C : Q "M QJ r T ∗ lifting classical linear connections ∇ on m-manifolds M into classical linear connections CM (∇) on the r-jet prolongation J r T ∗M of the cotangent bundle T ∗M p of M can be reduced to that of finding all Mfm -natural operators D : Q "M® T ⊗ q ® T ∗ sending classical linear connections ∇ on M into tensor fields DM (∇) of type (p, q) on M .
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    Synthetic differential geometry of Chen's iterated integrals
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2014) Nishimura, Hirokazu
    Chen's iterated integrals are treated within synthetic di erential geometry. The main result is that iterated integrals produce a subcomplex of the de Rham complex on the free path space as well as based path spaces.
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    Extensions in bounded topology
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2014) Leseberg, Dieter
    In a series of papers, Leseberg has studied and examined several fundamental aspects of generalized nearness in the realm of bounded topology. This paper deals with an alternate, detailed description of so-called bounded nearness and bounded topology by certain subdensity spaces and related maps. This type of spaces contains, in particular, b-near spaces as well as b-topological spaces in a nice fashion. Moreover, we found a one-to-one correspondence between suitable subdensity spaces and the related strict topological extensions. We point out that this newly established connection generalize the extensions which were studied by Bentley, Hušek, Ivanova, Ivanov, Lodato and Smirnov.