2023/1

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    On the ultra-quasi-tight extensions
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2023) Mukongo, Demco Kalusokoma; Otafudu, Olivier Olela; Toko, Wilson Bombe
    In their previous paper [4], Künzi and Olela Otafudu constructed the ultra-quasi-metric hull of a T0-ultra-quasi-metric space. In this article, we continue these studies by investigating the tightness and essentiality of extension maps in the category of ultra-quasi-metric spaces and nonexpansive maps. We show, for instance, that q-spherical completeness is preserved by a retraction map. Furthermore, we point out some categorical aspects of ultra-quasi-metrically injective hulls.
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    A comparison of geometric algebra and harmonic domain for linear circuit analysis
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2023) Sundriyal, Nitin; Ramirez, Juan Manuel; Corrochano, Eduardo Bayro
    For a long time, non-sinusoidal, non-linear electric circuit analysis has been a prevalent topic. The supplementary analysis tool and domain are subjects of debate in many scientific groups, leading to a range of norms and definitions. Since its beginnings, the electric power system has advanced thanks to the development of Power Electronic devices, converters, and Renewable Energy sources. Electronic equipment has transformed the electrical system and brought industrial applications a plethora of benefits. Unfortunately, this results in distortions in the power system (voltage and current). For this, it is necessary to comprehend power flow in nonsinusoidal linear and non-linear circuit situations. Therefore, it is always necessary to use a distinct mathematical framework to examine the circuit in such a setting. Finally, an agreement on norms that adhere to well-known, established standards can be obtained under non-sinusoidal circumstances. To show the precision of geometric algebra in power flow calculations, the work presented here combines the usage of the harmonic domain and geometric algebra in circuits with disturbances for sinusoidal and non-sinusoidal excitation.
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    All maximal unit-regular elements of Relhyp((m),(n))
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2023) Kunama, Pornpimol; Leeratanavalee, Sorasak
    Any relational hypersubstitution for algebraic systems of type (τ, τ′) = ((mi)i∈I , (nj )j∈J ) is a mapping which maps any mi-ary operation symbol to an mi-ary term and maps any nj-ary relational symbol to an nj-ary relational term preserving arities, where I, J are indexed sets. The set of all relational hypersubstitutions for algebraic systems of type (τ, τ′) together with a binary operation defined on the set and its identity forms a monoid. The properties of this structure are expressed by terms and formulas. Some algebraic properties of the monoid of a special type, especially the set of all unit-regular elements, were studied. In this paper, we determine all maximal unit-regular submonoids of this monoid of type ((m), (n)) for arbitrary natural numbers m, n ≥ 2.
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    Topologies induced by graph metrics on the vertex set of graphs
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2023) Lalithambigai, K.; Gnanachandra, Paulraj; Jafari, Saeid
    This paper presents a method of constructing topologies on the vertex set of a graph G induced by open balls with respect to the graph metric viz. geodesic distance, detour distance, circular distance and circular D-distance on the vertex set of G. Also, this paper explores the topologies induced by eccentric neighbourhoods of vertices of a graph and presents the nature of topologies generated by various graph metrics on the vertex set of some standard graphs.
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    On complex trinomial roots distribution
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2023) Jánský, Jiří; Tomášek, Petr
    The paper deals with a certain trinomial with two strictly complex coef- ficients. The root locus technique is utilized to obtain a distribution of roots with respect to a unit circle in the complex plane. A number of roots inside the unit disk is described in a relation with the two parameter values. Several appropriate graphs illustrate the trinomial roots distribution in particular cases.