1951. Domains without parabolic minimal submanifolds and weakly hyperbolic domainsFranc Forstnerič, 2023, original scientific article Abstract: We show that if $\Omega$ is an $m$-convex domain in $\mathbb{R}^n$ for some $2 \le m < n$ whose boundary $b\Omega$ has a tubular neighbourhood of positive radius and is not $m$-flat near infinity, then $\Omega$ does not contain any immersed parabolic minimal submanifolds of dimension $\ge m$. In particular, if $M$ is a properly embedded non-flat minimal hypersurface in $\mathbb{R}^n$ with a tubular neighbourhood of positive radius, then every immersed parabolic hypersurface in $\mathbb{R}^n$ intersects $M$. In dimension $n=3$, this holds if $M$ has bounded Gaussian curvature function. We also introduce the class of weakly hyperbolic domains $\Omega$ in $\mathbb{R}^n$, characterised by the property that every conformal harmonic map $\mathbb{C} \to \Omega$ is constant, and we elucidate their relationship with hyperbolic domains, and domains without parabolic minimal surfaces.
Keywords: minimal surfaces, m-plurisubharmonic functions, hyperbolic domain
Published in DiRROS: 10.04.2024; Views: 823; Downloads: 542
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1952. The Waring problem for matrix algebras, IIMatej Brešar, Peter Šemrl, 2023, original scientific article Abstract: Let $f$ be a noncommutative polynomial of degree $m\ge 1$ over an algebraically closed field $F$ of characteristic $0$. If $n\ge m-1$ and $\alpha_1,\alpha_2,\alpha_3$ are nonzero elements from $F$ such that $\alpha_1+\alpha_2+\alpha_3=0$, then every trace zero $n\times n$ matrix over $F$ can be written as $\alpha_1 A_1+\alpha_2A_2+\alpha_3A_3$ for some $A_i$ in the image of $f$ in $M_n(F)$.
Keywords: Waring problem, noncommutatative polynomials, matrix algebras
Published in DiRROS: 10.04.2024; Views: 446; Downloads: 195
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1953. Variety of mutual-visibility problems in graphsSerafino Cicerone, Gabriele Di Stefano, Lara Drožđek, Jaka Hedžet, Sandi Klavžar, Ismael G. Yero, 2023, original scientific article Abstract: If $X$ is a subset of vertices of a graph $G$, then vertices $u$ and $v$ are $X$-visible if there exists a shortest $u,v$-path $P$ such that $V(P)\cap X \subseteq \{u,v\}$. If each two vertices from $X$ are $X$-visible, then $X$ is a mutual-visibility set. The mutual-visibility number of $G$ is the cardinality of a largest mutual-visibility set of $G$ and has been already investigated. In this paper a variety of mutual-visibility problems is introduced based on which natural pairs of vertices are required to be $X$-visible. This yields the total, the dual, and the outer mutual-visibility numbers. We first show that these graph invariants are related to each other and to the classical mutual-visibility number, and then we prove that the three newly introduced mutual-visibility problems are computationally difficult. According to this result, we compute or bound their values for several graphs classes that include for instance grid graphs and tori. We conclude the study by presenting some inter-comparison between the values of such parameters, which is based on the computations we made for some specific families.
Keywords: mutual-visibility, total mutual-visibility, dual mutual-visibility number, outer mutual-visibility, grid graphs, torus graphs, computational complexity
Published in DiRROS: 10.04.2024; Views: 539; Downloads: 204
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1954. On a definition of logarithm of quaternionic functionsGraziano Gentili, Jasna Prezelj, Fabio Vlacci, 2023, original scientific article Abstract: For a slice-regular quaternionic function $f$, the classical exponential function ${\mathrm exp} f$ is not slice-regular in general. An alternative definition of an exponential function, the $\ast$-exponential ${\mathrm exp}_\ast$, was given in the work by Altavilla and de Fabritiis (2019): if $f$ is a slice-regular function, then ${\mathrm exp}_\ast f$ is a slice-regular function as well. The study of a $\ast$-logarithm ${\mathrm log}_\ast f$ of a slice-regular function $f$ becomes of great interest for basic reasons, and is performed in this paper. The main result shows that the existence of such a ${\mathrm log}_\ast f$ depends only on the structure of the zero set of the vectorial part $f_v$ of the slice-regular function $f = f_0 + f_v$, besides the topology of its domain of definition. We also show that, locally, every slice-regular nonvanishing function has a $\ast$-logarithm and, at the end, we present an example of a nonvanishing slice-regular function on a ball which does not admit a $\ast$-logarithm on that ball.
Keywords: regular functions over quaternions, quaternionic logarithm of slice-regular functions
Published in DiRROS: 10.04.2024; Views: 440; Downloads: 184
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1955. Critical edges in Rips complexes and persistencePeter Goričan, Žiga Virk, 2023, original scientific article Abstract: We consider persistent homology obtained by applying homology to the open Rips filtration of a compact metric space $(X, d)$. We show that each decrease in zero-dimensional persistence and each increase in one-dimensional persistence is induced by local minima of the distance function $d$ When $d$ attains local minimum at only finitely many pairs of points, we prove that each above mentioned change in persistence is induced by a specific critical edge in Rips complexes, which represents a local minimum of $d$. We use this fact to develop a theory (including interpretation) of critical edges of persistence. The obtained results include upper bounds for the rank of one-dimensional persistence and a corresponding reconstruction result. Of potential computational interest is a simple geometric criterion recognizing local minima of $d$ that induce a change in persistence. We conclude with a proof that each locally isolated minimum of $d$ can be detected through persistent homology with selective Rips complexes. The results of this paper offer the first interpretation of critical scales of persistent homology (obtained via Rips complexes) for general compact metric spaces.
Keywords: persistent homology, Rips complex, critical simplex, reconstruction result
Published in DiRROS: 10.04.2024; Views: 595; Downloads: 326
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1956. Does age matter? : The well-being of migrant children in comparative perspectiveZorana Medarić, Barbara Gornik, 2024, original scientific article Abstract: This article explores the subjective perceptions of well-being of migrant children attending primary school (9-14 years) and secondary school (15-18 years) in Slovenia. It focuses on how they conceptualise their fears, worries and concerns, what is important for them to feel accepted and safe, and how they think about their past and the future. Using a comparative perspective, similarities and differences in the experience of well-being of these two age groups of migrants are explored. The analysis is based on open-ended narrative interviews with migrant children and revolves around the question of whether and how age influences their subjective perception of well-being. The article sheds light on age-specific meanings and understandings of migration processes based on the views and experiences of migrant children and youth regarding their well-being, bringing to the fore the perspectives of children that are often missing or underrepresented in integration policy.
Keywords: acceptance, agency, well-being, age differences, migrant children
Published in DiRROS: 09.04.2024; Views: 501; Downloads: 182
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1958. Researching the change in the weight of split oak firewood due to different drying methodsAmina Gačo, 2021, published scientific conference contribution Abstract: In this paper, the influences of stacking methods and drying places of split oak firewood in winter conditions (Quercus cerris) have been experimentally and theoretically investigated, due to the great importance of use in heating with such wood. The research was conducted on a sample of 48 pieces of logs with bark made of freshly cut oak. The logs were obtained by mechanized technology with the help of grafting by a hydraulic splitter and a chainsaw. Each log was measured for a research length of 0.30 m, marked with numbers 1-24. On each log, the weight was measured on a scale of 5 kg with an accuracy of 0.5 grams. Drying of logs was performed in two places. The first drying place was in outdoor conditions, sheltered from the snow and ventilated. The second place was indoors, at approximately constant room temperature. The logs were stacked in a crossed way for better air circulation. They were dried between 15/12/2020 and 15/02/2021, a total of 62 days. The average initial weight of logs dried in the facility was 1130.3 g, in the dried state the average weight was 952.87 g, which represented 84.3% of the original weight. The average initial weight of logs dried in outdoor conditions was 1192.125 g, in the dried state 1076.37 g, which represented 90.29% of the original weight. The average initial water content in the logs dried in the facility was 37.9%, in the dried state it was 27.5%. For logs dried in outdoor conditions, the average initial amount of water was 36.6%, in the dried state the average amount of water was 31.2%.
Keywords: weight, drying methods, splitting firewood, oak, stacking methods
Published in DiRROS: 09.04.2024; Views: 794; Downloads: 556
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1959. Bio-based tannin-furanic-silk adhesives : applications in plywood and chemical cross-linking mechanismsEmanuele Cesprini, Johannes Jorda, Marco Paolantoni, Luca Valentini, Primož Šket, Valerio Causin, Diana E. Bedolla, Michela Zanetti, Gianluca Tondi, 2023, original scientific article Published in DiRROS: 09.04.2024; Views: 510; Downloads: 188
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1960. Effects of high-intensity interval training (HIIT) on physical performance in female team sports : a systematic reviewMima Stanković, Dusan Djordjevic, Nebojša Trajković, Zoran Milanović, 2023, review article Abstract: Abstract Background There is limited information regarding adaptation of HIIT in female athletes which is important since the adaptation to HIIT may be diferent compared to male athletes. Therefore, the aim of this systematic review was to summarize the efects of HIIT on physical performance in female team sports athletes. Methods The following databases Google Scholar, PubMed, Web of Science, Cochrane Library, ProQuest and Science Direct were searched prior to September 2nd, 2022. The inclusion criteria were longitudinal studies written in English, elite, sub-elite or college female team sports participants, and HIIT intensity had to be at 80–100% maximal heart rate. There were no exclusion criteria regarding the age of the participants or their training experience. The primary outcome measures were maximal oxygen uptake (VO2max), repeated sprint ability (RSA), change of direction speed, speed, explosive strength and body composition. Results A total of 13 studies met the inclusion criteria, with a total of 230 participants. HIIT improved VO2max in fve studies (ES from 0.19 to 1.08), while three studies showed improvement in their RSA (ES from 0.32 to 0.64). In addition, change of direction speed was improved in fve studies (ES from 0.34 to 0.88), while speed improved in four studies (ES from 0.12 to 0.88). Explosive strength results varied (ES from 0.39 to 1.05), while in terms of body composition, the results were inconsistent through observed team sports. Conclusion HIIT has signifcant efects on VO2max, RSA, change of direction speed, speed and explosive strength in female team sports, regardless of the competition level.
Keywords: interval training, output, VO2max, physical fitness
Published in DiRROS: 09.04.2024; Views: 553; Downloads: 308
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