- 2021/1

# 2021/1

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- ItemLatin 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
Show more 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.Show more - ItemBifurcation of positive periodic solutions to non-autonomous undamped Duffing equations(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2021) Šremr, Jiří
Show more 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.Show more - ItemAn 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
Show more 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.Show more - ItemDuality 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.
Show more 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.Show more - ItemSheffer operations in complemented posets(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2021) Chajda, Ivan; Kolařík, Miroslav
Show more We show that in every downward directed poset with an antitone involu-tion the so-called Sheffer operation can be introduced satisfying certain identities.However, also conversely, if we have given a Sheffer operation|on a setP, thenPcan be converted into a poset with an antitone involution′, where both′and theorder relation≤are derived by|. Using this, we can characterize orthoposets, i.e.bounded posets with complementation which is an antitone involution by means ofidentities satisfied by this Sheffer operation. Also conversely, if|is a Sheffer oper-ation on a given setPsatisfying these identities, thenPcan be organized into anorthoposet.Show more