- 2017/2

# 2017/2

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- ItemWeil diffeology I: Classical differential geometry(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2017) Nishimura, H.
Show more 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.Show more - ItemAnalytic solutions for singular integral equations and non-homogeneous fractional PDE(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2017) Aghili, A.
Show more 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.Show more - ItemNecessary conditions for hyponormality of Toeplitz operators on the Fock space(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2017) Gupta, A.; Singh, S. K.
Show more In this article, the necessary conditions for the hyponormality of Toeplitz operator T with harmonic polynomial symbols on the Fock space are explored.Show more - ItemEquilibrium team selection in football under win or profit maximisation(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2017) Haugen, K. K.
Show more This article applies mathematical methods to investigating (extremely) simpli ed versions of the team selection problem for football managers. The team selection problem { obviously a game problem { is analysed game theoretically, but some funny results of a combinatorial nature are also added. In general, the ndings indicate that the problem of selecting a football team is a very demanding task. Still, a simple comparison between win and pro t maximising game models indicate surprising complexity in game prediction.Show more - ItemTraces of Hadamard and Kronecker products of matrices(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2017) Das, P. K.; Vashisht, L. K.
Show more We present some inequality/equality for traces of Hadamard product and Kronecker product of matrices. Some numerical examples are given to support the results.Show more