2017/2

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    Application of a new type of preopen sets and related continuity
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2017) Roy, B.
    In this paper a new class of sets termed as -preopen sets has been introduced and some of its properties are discussed. A new type of separation axiom has been introduced with the help of this newly de ned sets. Finally some properties of weak forms of continuous functions have been studied.
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    Analytic solutions for singular integral equations and non-homogeneous fractional PDE
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2017) Aghili, A.
    In the last three decades, transform methods have been used for solving fractional di erential equations, singular integral equations. In this article, the author considered a new class of the inverse Laplace transforms of exponential types. We also evaluated certain types of integrals and solved partial fractional equations of Cauchy type.The result reveals that the transform method is very convenient and e ective.
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    Downstream logistics optimization at EWOS Norway
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2017) Branda, M.; Haugen, K. K; Novotný, .J.; Olstad, A.
    The Norwegian company EWOS AS produces sh feed for the salmon farming industry, supplying approximately 300 customers spread along the coast of Norway. The feed is produced at three factory locations and distributed by a eet of 10 dedicated vessels. The high seasonality of the demand and the large number of customers make the distribution planning a substantial challenge. EWOS handles it by operating a system of mostly xed routes with decentralized planning at each factory. The distribution can be described as a multi-depot vehicle routing problem with time windows, multiple vehicle usage, inter-depot routes, heterogeneous eet and a rolling horizon. The paper presents a mathematical model for this problem, which is solved by heuristics and meta heuristics. Based on detailed historical data collected by EWOS during the autumn of 2010, the model has proposed a dynamic set of routes with a signi cant reduction of travelled distance { close to 30% { and an increase of average vessel ll-rate { from 60% up to 95%. This implies a substantial fuel saving, with a positive environmental impact, and also a potential for downscaling the eet, with additional considerable cost savings for the company.
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    Traces of Hadamard and Kronecker products of matrices
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2017) Das, P. K.; Vashisht, L. K.
    We present some inequality/equality for traces of Hadamard product and Kronecker product of matrices. Some numerical examples are given to support the results.
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    Weil diffeology I: Classical differential geometry
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2017) Nishimura, H.
    Topos theory is a category-theoretical axiomatization of set theory. Model categories are a category-theoretical framework for abstract homotopy theory. They are complete and cocomplete categories endowed with three classes of morphisms (called brations, co brations and weak equivalences) satisfying certain axioms. We would like to present an abstract framework for classical di erential geometry as an extension of topos theory, hopefully comparable with model categories for homotopy theory. Functors from the category W of Weil algebras to the category Sets of sets are called Weil spaces by Wolfgang Bertram and form the Weil topos after Eduardo J. Dubuc. The Weil topos is endowed intrinsically with the Dubuc functor, a functor from a larger category eW of cahiers algebras to the Weil topos standing for the incarnation of each algebraic entity of eW in the Weil topos. The Weil functor and the canonical ring object are to be de ned in terms of the Dubuc functor. The principal objective of this paper is to present a category-theoretical axiomatization of theWeil topos with the Dubuc functor intended to be an adequate framework for axiomatic classical di erential geometry. We will give an appropriate formulation and a rather complete proof of a generalization of the familiar and desired fact that the tangent space of a microlinear Weil space is a module over the canonical ring object.