2021/1

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    Duality of conservation laws and their role in the processes of emergence of physical structures and formations
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2021) Petrova, Ludmila I.
    As it is known, the conservation laws for material media are conservationlaws for energy, linear momentum, angular momentum, and mass. Such conser-vation laws are described by differential equations. And the conservation laws forphysical fields are conservation laws that state the presence of conservative physicalquantities or objects (structures). Such conservation laws are described by closedexterior skew-symmetric forms. It can be seen that conservation laws possess dual-ity. The conservation laws for material media and the conservation laws for physicalfields are different. A peculiarity consists in the fact that there exists a connectionbetween the conservation laws for material media and those for physical fields. Thisconnection is realized discretely in the evolutionary process. It describes the emer-gence of physical structures and the observed formations, such as waves, vortices,turbulent pulsations.
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    Bifurcation of positive periodic solutions to non-autonomous undamped Duffing equations
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2021) Šremr, Jiří
    We study a bifurcation of positive solutions to the parameter-dependentperiodic problem u′′=p(t)u−h(t)|u|λsgnu+μf(t);u(0) =u(ω), u′(0) =u′(ω),whereλ >1,p,h,f∈L([0,ω]), andμ∈Ris a parameter. Both the coefficientpand the forcing termfmay change their signs, h≥0a. e. on[0,ω]. We providesharp conditions on the existence and multiplicity as well as non-existence of positivesolutions to the given problem depending on the choice of the parameter μ.
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    An incremental method for the construction of the box extents of a context
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2021) Radeleczki, Sándor; Veres, Laura
    In this paper we are improving a method proposed in [2] for the construc-tion of the box extents of a given formal context. We prove that the lattice of thebox extents can be order-embedded in the lattice generated by the atomic extentsof the given context.
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    Latin quandles and applications to cryptography
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2021) Isere, Abednego Orobosa; Adéníran, John Olúsolá; Jaiyéolá, Temitópé Gbóláhán
    This work investigated some properties of Latin quandles that are ap-plicable in cryptography. Four distinct cores of an Osborn loop (non-diassociativeand non-power associative) were introduced and investigated. The necessary andsufficient conditions for these cores to be (i) (left) quandles (ii) involutory quandles(iii) quasi-Latin quandles and (iv) involutory quasi-Latin quandles were established.These conditions were judiciously used to build cipher algorithms for cryptographyin some peculiar circumstances.
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    h-stability and boundedness results for solutions to certain nonlinear perturbed systems
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2021) Damak, Hanen; Hammani, Mohamed Ali; Kicha, Abir
    In this work, we establish some new sufficient conditions to show the uni-formh-stability for nonlinear time-varying perturbed systems which can be viewedas an extension of the uniform exponential stability and polynomial stability. Also,we study the boundedness of solutions when the origin is not necessarily an equilib-rium point of the perturbed system. The idea is to use some Gronwall type integralinequalities. As an illustration, we present some examples with simulations to showthe applicability of the obtained results.