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1.
On the integrability of persistent quadratic three-dimensional systems
Brigita Ferčec, Maja Žulj, Matej Mencinger, 2024, original scientific article

Abstract: We consider a nine-parameter familiy of 3D quadratic systems, �˙=�+�2(�,�,�), �˙=−�+�2(�,�,�), �˙=−�+�2(�,�,�), where �2,�2,�2 are quadratic polynomials, in terms of integrability. We find necessary and sufficient conditions for the existence of two independent first integrals of corresponding semi-persistent, weakly persistent, and persistent systems. Unlike some of the earlier works, which primarily focus on planar systems, our research covers three-dimensional spaces, offering new insights into the complex dynamics that are not typically apparent in lower dimensions.
Keywords: ordinary differential equations, three-dimensional systems, integrability problem, persistent systems
Published in DKUM: 23.05.2024; Views: 191; Downloads: 11
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2.
Impact of transport trends on sustainability in the Western Balkans : a future-oriented business sector perspective
Tomislav Letnik, Katja Hanžič, Matej Mencinger, Drago Sever, 2024, original scientific article

Abstract: Abstract This study examines the impact of emerging transport trends on the Western Balkans and their potential to improve the sustainability and efficiency of the transport sector in the region. In the context of global efforts to reduce environmental impacts and improve transport safety, the study aims to better understand the perspective of the business sector in order to align strategic planning for the introduction of new transport technologies and practices with the expectations of the business sector. Using a questionnaire-based survey on the Mentimeter platform, the study gathers insights from 49 transport and logistics experts. The analysis uses violin plots and heat maps to visualise the expected impact of the identified trends. The results show a consensus among the experts that the emerging trends are likely to lead to a reduction in accidents, congestion, and emissions, while at the same time increasing operating costs and investment in infrastructure. In particular, trends such as alternative fuels, electrification, and smart city initiatives are highlighted as important drivers for reducing emissions. The study concludes that while these trends are likely to lead to the achievement of environmental and safety goals, they also lead to economic challenges as operating costs increase and significant infrastructure investment is required. The study emphasises the need for strategic investment, policy adjustments, and capacity building to lead the Western Balkans towards a sustainable transport future.
Keywords: transport trends, congestion, accidents, infrastructure investment, operational costs, policy adaptation
Published in DKUM: 31.01.2024; Views: 276; Downloads: 13
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3.
Linearizability of 2:-3 resonant systems with quadratic nonlinearities
Maja Žulj, Brigita Ferčec, Matej Mencinger, 2021, original scientific article

Abstract: In this paper, the linearizability of a 2:-3 resonant system with quadratic nonlinearities is studied. We provide a list of the conditions for this family of systems having a linearizable center. The conditions for linearizablity are obtained by computing the ideal generated by the linearizability quantities and its decomposition into associate primes. To successfully perform the calculations, we use an approach based on modular computations. The sufficiency of the obtained conditions is proven by several methods, mainly by the method of Darboux linearization.
Keywords: polynomial systems, ODE's, linearizability problem, linearizability quantities, Darboux linearization, p:-q resonant system
Published in DKUM: 01.08.2023; Views: 521; Downloads: 49
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4.
Algoritmi za računanje egipčanskih ulomkov
Monia Žuran, 2022, master's thesis

Abstract: Egipčani so ulomke izražali kot vsote med seboj različnih, pozitivnih enotskih ulomkov. Takšne ulomke danes imenujemo egipčanski ulomki. V magistrskem delu obravnavamo algoritme za računanje egipčanskih ulomkov, ki temeljijo na aproksimacijah, na dvojiškem sistemu, na verižnih ulomkih, na metodi majhnih števcev in na obratni požrešni metodi. V prvem delu spoznamo številske sisteme, ki so jih poznali v starodavnem Egiptu, definiramo egipčanski ulomek ter spoznamo osnove algoritmov. V drugem delu posamezne algoritme opišemo in predstavimo na primerih. Izbran algoritem udejanjimo v programskem jeziku C++.
Keywords: Enotski ulomek, Egipčanski ulomek, Algoritem, Požrešna metoda, Dvojiška metoda, Verižni ulomek, Obratna požrešna metoda.
Published in DKUM: 12.07.2022; Views: 1030; Downloads: 91
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5.
Integrabilnost in linearizabilnost persistentnih p : -q resonantnih polinomskih sistemov navadnih diferencialnih enačb
Maja Žulj, 2022, doctoral dissertation

Abstract: Eden izmed osrednjih problemov teorije navadnih diferencialnih enačb je problem integrabilnosti, ki je pomemben za razumevanje bistva teorije diferencialnih enačb in za uporabo diferencialnih enačb pri študiju dinamičnih procesov v realnem svetu. Osrednji problemi te doktorske disertacije so problem središča in z njim povezana integrabilnost ter problem linearizabilnosti p:-q resonantnih sistemov s kvadratnimi nelinearnostmi. Obravnavana je tudi povezava med $p:-q$ resonantnimi sistemi in njim pripadajočimi persistentnimi sistemi. V uvodu so predstavljeni osnovni pojmi komutativne računske algebre, s poudarkom na lastnostih polinomskih idealov in njihovih raznoterosti. Predstavljene so tudi normalne forme, problem središča in linearizabilnosti sistema ter postopek kompleksifikacije realnih sistemov. Drugo poglavje je namenjeno posplošitvi pojma p:-q resonantnega središča na persistentno p:-q resonantno središče. Izračunamo vse potrebne in zadostne pogoje za nastop persistentnih središč za pet družin p:-q resonantnih sistemov s kvadratnimi nelinearnostmi. Raziskana je povezava med integrabilnostjo p:-q resonantnih sistemov in integrabilnostjo pripadajočih persistentnih sistemov. V tretjem poglavju so predstavljeni pogoji za nastop linearizabilnega središča za družino 2:-3 resonantnih sistemov, ki jih dobimo z dekompozicijo raznoterosti ideala, generiranega s količinami linearizabilnosti. Zaradi zahtevnosti izračunov uporabimo pristop, ki temelji na modularni aritmetiki. Za dokazovanje zadostnosti tako pridobljenih pogojev uporabimo več različnih metod, najpogosteje uporabimo metodo, ki temelji na Darbouxjevi teoriji linearizabilnosti. V zadnjem poglavju obravnavamo relativno nov problem (šibko) persistentnega linearizabilnega središča, ki ga posplošimo na problem (šibko) persistentnega linearizabilnega p:-q resonantnega središča. Obravnavana je povezava med linearizacijsko transformacijo p:-q resonantnega sistema in linearizacijsko transformacijo ustreznega persistentnega p:-q resonantnega sistema. Povezava je ponazorjena na 1:-2 in 2:-3 resonantnih kvadratnih sistemih.
Keywords: polinomski sistem NDE, p:-q resonantni sistem, problem integrabilnosti, problem linearizabilnosti, količine integrabilnosti, količine linearizabilnosti, persistentno resonantno središče, prvi integral
Published in DKUM: 08.06.2022; Views: 681; Downloads: 54
.pdf Full text (1,21 MB)

6.
Simetrijske grupe končnih vzorcev
Matej Mencinger, 2021

Abstract: Končni vzorci so najprej definirani intuitivno, kasneje pa še eksaktno (matematično). Simetrije končnih vzorcev so definirane s pomočjo izometrij ravnine. Obravnavani so štirje osnovni razredi izometrij ravnine: zrcaljenje, rotacija, translacija ter drsno zrcaljenje. V klasifikacijskem izreku je dokazano, da vsaka izometrija spada v enega od osnovnih štirih razredov. Pri obravnavi vektorjev in matrik se omejimo na ravnino in trirazsežni vektorski prostor. Dokazano je, da izometrijam ravnine s fiksno točko pripadajo natanko ortogonalne matrike. V poglavju o grupah so obravnavani pojmi: (pod)grupa, red grupe, izomorfizem grup ter generatorji grupe. Glavni rezultat je klasifikacija simetrijskih grup končnih vzorcev v ciklične ali diedrske, kar danes imenujemo Leonardov izrek. Podano je tudi nekaj informacij o zgodovinski dobi, v kateri je deloval Leonardo da Vinci in nekaterih povezavah med njegovim delom in matematiko. Učbenik je namenjen študentom arhitekture in vsebuje številne primere, rešene naloge ter obsežno slikovno gradivo.
Keywords: izometrija ravnine, končni vzorec, simetrija, končna grupa, Leonardov izrek
Published in DKUM: 21.12.2021; Views: 1199; Downloads: 287
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7.
Supplementary material for paper Comparison of the evolution of the COVID-19 disease between Romania and Italy
Ciprian Chiruţa, Emilian Bulgariu, Jurij Avsec, Brigita Ferčec, Matej Mencinger, 2020, complete scientific database of research data

Keywords: COVID-19 pandemic evolution, time dependent SIR model, coronavirus
Published in DKUM: 23.12.2020; Views: 5340; Downloads: 1610
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8.
Comparison of the evolution of the COVID-19 disease between Romania and Italy
Ciprian Chiruţa, Emilian Bulgariu, Jurij Avsec, Brigita Ferčec, Matej Mencinger, 2020, original scientific article

Abstract: After the outbreak of COVID-19 in Italy, thousands of Romanian citizens who worked in Northern Italy, Spain or Germany returned to Romania. Based on the time-dependent susceptible–infected–recovered—SIR model, this paper compares the evolution of the COVID-19 disease between Romania and Italy, assuming that the parameter value of R0 in the time-dependent SIR model decreases to R1 < R0 after publicly announced restrictions by the government, and increases to a value of R2 < R1 when the restrictions are lifted. Among other things, we answer the questions about the date and extent of the second peak in Italy and Romania with respect to different values of R2 and the duration of the restrictions.
Keywords: COVID-19 pandemic evolution, time dependent SIR model, coronavirus
Published in DKUM: 22.12.2020; Views: 1052; Downloads: 197
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9.
Analiza računalniških orodij za načrtovanje in optimizacijo transportnih poti
Matjaž Majcen, 2019, undergraduate thesis

Abstract: Diplomska naloga obravnava analizo programov in orodij za načrtovanje transportnih poti. Prikazana so teoretična spoznanja na področju transporta, logistike in logističnih trendov. Predstavljeni so različni tipi problema usmerjanja vozil in osnovni pojmi teorije grafov, ki je vodila do nastanka algoritmov in programov za optimizacijo. Izvedena je analiza komercialnih in prosto dostopnih programov. Uporabo najprimernejšega orodja smo preverili na realnem primeru dostave kosil v Domu Danice Vogrinec Maribor in izvedli optimizacijo. Simulirali smo različne scenarije in prikazali potencialno zmanjšanje opravljenih poti in prihranke, ki bi nastopili z novo razporeditvijo voznega parka.
Keywords: transport, optimizacija poti, teorija grafov, računalniška orodja, simulacije, dostava hrane
Published in DKUM: 16.09.2019; Views: 1436; Downloads: 198
.pdf Full text (5,68 MB)

10.
Algebraične metode v dinamičnih sistemih
Brigita Ferčec, Matej Mencinger, scientific monograph

Published in DKUM: 05.03.2019; Views: 1638; Downloads: 98
.pdf Full text (16,42 MB)

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