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1.
Matematika A : za študente FKKT UM
Petra Žigert Pleteršek, Matevž Črepnjak, 2022, higher education textbook

Abstract: Visokošolski učbenik predstavlja uvod v matematično analizo na naravoslovno-tehniških fakultetah. Poleg osnovnih pojmov o množicah, logiki in številih so obravnavane realne funkcije in z njimi povezana pojma limite funkcije in zveznosti, ter zaporedja in vrste. Zajete se vsebine diferencialnega računa z aplikacijo odvoda, ter integralni račun.
Keywords: logika, množice, realne funkcije, limita in zveznost funkcije, zaporedja, vrste, odvod funkcije, integral
Published in DKUM: 18.02.2022; Views: 1460; Downloads: 607
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2.
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: 1248; Downloads: 343
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3.
An application of the Sakai's theorem to the characterization of H*-algebras
Borut Zalar, 1995, original scientific article

Abstract: The well-known Sakai's theorem, which states that every derivation acting on a von Neumann algebra is inner, is used to obtain a new elegant proof of the Saworotnow's characterization theorem for associative ▫$H^\ast$▫-algebras via two-sided ▫$H^\ast$▫-algebras. This proof completely avoids structure theory.
Keywords: mathematics, functional analysis, ▫$H^\ast$▫-algebra, involution, automorphism, derivation, centralizer, von Neumann algebra
Published in DKUM: 14.06.2017; Views: 903; Downloads: 165
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4.
Traffic safety of older drivers in various types of road intersections
Tomaž Tollazzi, Marko Renčelj, Vlasta Rodošek, Borut Zalar, 2010, review article

Abstract: In industrialized countries people over 50 years of age represent a rapidly growing part of population. Their lifestyle is also becoming more active, which means that the percentage of older drivers in the population of all drivers is also increasing. Many different studies have shown that elderly drivers are more frequently involved in specific types of accidents, especially at intersections. In the past 15 years there was a trend of increasing popularity of roundabouts in Slovenia. Their introduction was generally supported by the arguments of increased traffic-flow capacity and traffic safety as well. The studies on which these arguments are based were performed with an “ideal” type of driver in mind; the one that fully understands new rules and reacts correctly in all situations that may occur at such intersections, where there are no light signals to guide them. An elderly person does not necessarily conform to that ideal and if the percentage of elderly drivers became significant, the premises of the above mentioned studies may not be correct anymore which in turn implies that their results could also be questioned. The present study concentrated on the evaluation of traffic safety of elderly drivers, at various types of intersection, from their own perspective. Various statistical analyses of obtained data were performed. The most important finding was that we may claim, with high degree of probability, that the average person of the age of over 60 feels more unsafe at double-lane roundabouts than they would feel had the same intersection been equipped with traffic lights. Elderly traffic participants will always cause more accidents or participate in them due to hazardous factors. Challenge, arising from many different studies and researches, is in studying what measures and solutions can reduce the risk for elderly participants.
Keywords: traffic safety, road intersections, roundabouts, elderly people
Published in DKUM: 06.06.2017; Views: 1692; Downloads: 461
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5.
O praštevilih
Borut Zalar, 1995, popular article

Keywords: matematika, teorija števil, praštevila
Published in DKUM: 10.07.2015; Views: 1154; Downloads: 39
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