We introduce non-Abelian Kuramoto model on \begin{document}$ S^3 $\end{document} in the most general form. Following an analogy with the classical Kuramoto model (on the circle \begin{document}$ S^1 $\end{document} ), we study some interesting variations of the model on \begin{document}$ S^3 $\end{document} that are obtained for particular coupling functions. As a partial case, by choosing "standard" coupling function one obtains a previously known model, that is referred to as Kuramoto-Lohe model on \begin{document}$ S^3 $\end{document} . We briefly address two particular models: Kuramoto models on \begin{document}$ S^3 $\end{document} with frustration and with external forcing. These models on higher dimensional manifolds have not been studied so far. By choosing suitable values of parameters we observe different nontrivial dynamical regimes even in the simplest setup of globally coupled homogeneous population. Although non-Abelian Kuramoto models can be introduced on various symmetric spaces, we restrict our analysis to the case when underlying manifold is the 3-sphere. Due to geometric and algebraic properties of this specific manifold, variations of this model are meaningful and geometrically well justified.

Extracurricular activities as a variety of organizational forms of students gathering in free extracurricular time at elementary school have predominantly cultural, artistic, sporting, technical, recreational or scientific character (Cindrić, 1992). Through them, students meet their needs and develop the culture of using their leisure time. Thanks to its pedagogic potential, chess is increasingly used as an educational tool and taught in elementary schools around the world. This trend begins to follow Croatia, where chess in many schools is carried out as an extracurricular and/or extracurricular activity. In this paper we will present and analyze the advantages that chess has for the elementary school students and empirically determine the occurrence of chess as an extracurricular activity in the schools in the City of Zagreb. Also, based on the results of the qualitative research, the views of the chess teachers regarding advantages of chess implementation, ways of determining the interests of students, and teaching methods used in chess teaching will be presented.

Izvannastavne aktivnosti kao različiti organizacijski oblici okupljanja učenika u slobodno izvannastavno vrijeme u školi imaju pretežito kulturnoumjetničko, športsko, tehničko, rekreacijsko ili znanstveno obilježje (Cindrić, 1992). Kroz njih učenici zadovoljavaju svoje potrebe i razvijaju kulturu korištenja slobodnog vremena. Zahvaljujući svom pedagoškom potencijalu, šah se sve više implementira u kurikulume škola i poučava na svim razinama obrazovanja. Ovaj trend počinje pratiti i Hrvatska, u kojoj se šah u mnogo škola provodi kao izvannastavna i/ili izvanškolska aktivnost. U ovome radu prikazat će se i analizirati prednosti koje bavljenje šahom ima za učenike osnovnih škola te će se empirijskim istraživanjam utvrditi pojavnost izvannastavne aktivnosti šaha u školama Grada Zagreba. Temeljem rezultata kvalitativnog istraživanja prikazat će se stavovi voditelja šaha kao izvannastavne aktivnosti o prednostima njegove implementacije, načinima utvrđivanja interesa te o načinima rada voditelja i polaznika/učenika.

: We construct bijections between certain energetically favorable resonance-like structures in several classes of benzenoid compounds and some well- known combinatorial structures enumerated by Catalan and related numbers. In that way we derive explicit formulas for the n umber of such structures in the considered classes of compounds. We also list some open problems and indicate some possible d irections for future research.

Recent trends in the development of autonomous vehicles focus on real-time processing of vast amounts of data from various sensors. The data can be acquired using multiple cameras, lidars, ultrasonic sensors, and radars to collect useful information about the state of the traffic and the surroundings. Significant computational power is required to process the data fast enough, and this is even more pronounced in vehicles that not only assist the driver but are capable of fully autonomous driving. This article proposes speed and accuracy improvement of traffic sign detection and recognition in high-definition images, based on focusing on different regions of interest in traffic images. These regions are determined with efficient and parallelized preprocessing of every traffic image, after which convolutional neural network is applied for detection and recognition in parallel on graphics processing units. We employed different “You Only Look Once” (YOLO) architectures as baseline detectors, due to their speed, straightforward architecture, and high accuracy in general object detection tasks. Several preprocessing procedures were proposed, to achieve real-time performance requirement. Our experiments using a large-scale traffic sign dataset show that we can achieve real-time detection in high-definition images with high recognition accuracy.

Background. The most common cause of early death in acute myocardial infarction with ST elevation are malignant heart rhythm disorders, generally occurring in the first four hours of myocardial infarction. The incidence of ventricular fibrillation is greatest in the early stage of the myocardial infarction, and sudden cardiac deaths occur most often in outpatient conditions. Case reports. This paper presents a patient whose first manifestation of coronary artery disease was myocardial infarction with ST elevation complicated by early ventricular fibrillation. Rapid measures of cardiopulmonal resuscitation enabled quick establishment of normal sinus rhythm. Primary percutaneous intervention was performed, with revascularization of artery responsible for acute myocardial infarction. In order to reduce ischemic brain damage, therapeutic hypothermia was applied since the patient was presented in post-reanimation coma. Conclusion. Better treatment of patients with cardiac arrest in outpatient conditions and faster revascularization of the infarct artery are crucial for a reduction of mortality in acute myocardial infarction.

Mercury (Hg) has been listed as a global high priority pollutant by many international organizations due to its mobility and persistence in the environments and high toxicity to organisms. This research was conducted with the aims to determine: (i) total Hg content (THg) and its spatial distribution in sediments of river Tisa along the river course, (ii) possible sources of THg and (iii) degree of THg pollution in sediments from the river Tisa through different criteria. Total Hg in the sediments ranged from 0.07 to 0.49 mg kg-1, with mean ? S.D. value of 0.26 ? 0.10 mg kg-1. The highest mean value of THg (0.30 mg kg-1) was found in the lower stream, while the lowest (0.13 mg kg-1) was found in the tributary. According to Principal Component Analyses (PCA) strong positive loading of metals in all parts of the river Tisa is mainly controlled from the same sources. These sources are related to anthropogenic activities based on calculated Enrichment Factor (EF) values. Total Hg are higher than background value. According to the Republic of Serbia official standard, THg values of river Tisa sediments were within the range of maximum permissible values. Compared with National Oceanic and Atmospheric Administration (NOAA) guideline, 80.49% of sediment samples indicated that THg in the river Tisa sediments represented minimal and possible risk towards the living organisms. Integrating the results of pollution assessment, it could be concluded that THg in river Tisa sediments in Serbia demonstrates considerable contamination according to Geoaccumulation Index (Igeo), and Contaminant Factor (CF), and high pollution risk according to Potential Environmental Risk Index (PERI).