Konstrukcije pravilnog sedmerokuta

Važno mjesto u geometriji zauzimaju geometrijske konstrukcije pravilnih n-terokuta. Poznato je kako elementarno (samo uz pomoć ravnala i šestara) konstruirati jednakostraničan trokut, kvadrat, pravilni peterokut, šesterokut, osmerokut i deseterokut. Prvi koji nedostaje u ovom nizu je pravilni sedmerokut. Gauß je, proučavajući konstrukciju pravilnog sedmerokuta, dokazao koji se sve pravilni n-terokuti mogu elementarno konstruirati te da sedmerokut, nažalost, nije jedan od njih. Međutim, pravilni sedmerokut možemo konstruirati ako se poslužimo nekim sredstvima koje nisu dio elementarnih konstrukcija. Na primjer, možemo ga konstruirati umetanjem pravca ili presjekom krivulja drugog reda. U ovom radu opisujemo različite geometrijske konstrukcije pravilnog sedmerokuta, polazeći od Arhimedove analize i njegovih uvjeta za izvođenje konstrukcije. Arhimedov rad nastoje usavršiti srednjovjekovni arapski matematičari. U radu su opisane njihove konstrukcije Arhimedovih uvjeta ili Arhimedovog pravca, ali i neke originalne analize konstrukcije pravilnog sedmerokuta. Promatramo i neke algebarske konstrukcije. Rješenja ciklotomijske jednadžbe pridružene pravilnom sedmerokutu mogu se konstruirati uz pomoć krivulja drugog reda, najčešće presjekom parabole i hiperbole. U ovom radu analiziramo i nekoliko zanimljivih konstrukcija ovog tipa.The geometrical construction of regular polygons is an important part of geometry. It is known how to elementary (only by means of a ruler and a pair of compasses) construct an equilateral triangle, a square, a regular pentagon, a regular hexagon, a regular octagon, and a regular decagon. The first one missing in this sequence is a regular heptagon. While studying the construction of a regular heptagon, Gauß has determined the class of regular polygons that can be constructed elementary. Unfortunately, a heptagon is not one of them. However, a regular heptagon can be constructed if we use methods which are not parts of elementary constructions. For example, it can be constructed by inserting a line or using intersections of conics. We describe different constructions of a regular heptagon, starting from the analysis due to Archimedes and his conditions. Medieval Arab mathematicians tried to improve the work of Archimedes. We describe their constructions based on the work of Archimedes, as well as some of their original analyses concerning the construction of a regular heptagon. Some algebraic constructions have also been looked at. The solutions of an equation associated to a regular heptagon can be constructed using conics, mostly using intersections of a parabola and a hyperbola. We analyze a few interesting constructions of this type as well

Automatic System for Serving and Deploying Products into Advertising Space

The purpose of the thesis is to present the problems of deploying and serving products into advertising space,encountered daily by online marketers,planners and leaseholders of advertising spaces.The aim of the thesis is to solve the problem in question with the help of a novel web application.Therefore,we have designed an automatic system,which consists of three key components:an online store,a surveillance system and websites accommodating advertising space.In the course of this thesis,we have developed the aforementioned automatic system that employs the extraction of the products from an online store through a customized plugin.The acquired data are saved and displayed in the control system,where they're prepared in the form devised to generate advertising samples.The control system user can select among the products presented at the online store and design samples.The prepared samples can then be placed within a desired website,and subsequently administered via the control system

Konstrukcije pravilnog sedmerokuta

Važno mjesto u geometriji zauzimaju geometrijske konstrukcije pravilnih n-terokuta. Poznato je kako elementarno (samo uz pomoć ravnala i šestara) konstruirati jednakostraničan trokut, kvadrat, pravilni peterokut, šesterokut, osmerokut i deseterokut. Prvi koji nedostaje u ovom nizu je pravilni sedmerokut. Gauß je, proučavajući konstrukciju pravilnog sedmerokuta, dokazao koji se sve pravilni n-terokuti mogu elementarno konstruirati te da sedmerokut, nažalost, nije jedan od njih. Međutim, pravilni sedmerokut možemo konstruirati ako se poslužimo nekim sredstvima koje nisu dio elementarnih konstrukcija. Na primjer, možemo ga konstruirati umetanjem pravca ili presjekom krivulja drugog reda. U ovom radu opisujemo različite geometrijske konstrukcije pravilnog sedmerokuta, polazeći od Arhimedove analize i njegovih uvjeta za izvođenje konstrukcije. Arhimedov rad nastoje usavršiti srednjovjekovni arapski matematičari. U radu su opisane njihove konstrukcije Arhimedovih uvjeta ili Arhimedovog pravca, ali i neke originalne analize konstrukcije pravilnog sedmerokuta. Promatramo i neke algebarske konstrukcije. Rješenja ciklotomijske jednadžbe pridružene pravilnom sedmerokutu mogu se konstruirati uz pomoć krivulja drugog reda, najčešće presjekom parabole i hiperbole. U ovom radu analiziramo i nekoliko zanimljivih konstrukcija ovog tipa.The geometrical construction of regular polygons is an important part of geometry. It is known how to elementary (only by means of a ruler and a pair of compasses) construct an equilateral triangle, a square, a regular pentagon, a regular hexagon, a regular octagon, and a regular decagon. The first one missing in this sequence is a regular heptagon. While studying the construction of a regular heptagon, Gauß has determined the class of regular polygons that can be constructed elementary. Unfortunately, a heptagon is not one of them. However, a regular heptagon can be constructed if we use methods which are not parts of elementary constructions. For example, it can be constructed by inserting a line or using intersections of conics. We describe different constructions of a regular heptagon, starting from the analysis due to Archimedes and his conditions. Medieval Arab mathematicians tried to improve the work of Archimedes. We describe their constructions based on the work of Archimedes, as well as some of their original analyses concerning the construction of a regular heptagon. Some algebraic constructions have also been looked at. The solutions of an equation associated to a regular heptagon can be constructed using conics, mostly using intersections of a parabola and a hyperbola. We analyze a few interesting constructions of this type as well

Konstrukcije pravilnog sedmerokuta

Važno mjesto u geometriji zauzimaju geometrijske konstrukcije pravilnih n-terokuta. Poznato je kako elementarno (samo uz pomoć ravnala i šestara) konstruirati jednakostraničan trokut, kvadrat, pravilni peterokut, šesterokut, osmerokut i deseterokut. Prvi koji nedostaje u ovom nizu je pravilni sedmerokut. Gauß je, proučavajući konstrukciju pravilnog sedmerokuta, dokazao koji se sve pravilni n-terokuti mogu elementarno konstruirati te da sedmerokut, nažalost, nije jedan od njih. Međutim, pravilni sedmerokut možemo konstruirati ako se poslužimo nekim sredstvima koje nisu dio elementarnih konstrukcija. Na primjer, možemo ga konstruirati umetanjem pravca ili presjekom krivulja drugog reda. U ovom radu opisujemo različite geometrijske konstrukcije pravilnog sedmerokuta, polazeći od Arhimedove analize i njegovih uvjeta za izvođenje konstrukcije. Arhimedov rad nastoje usavršiti srednjovjekovni arapski matematičari. U radu su opisane njihove konstrukcije Arhimedovih uvjeta ili Arhimedovog pravca, ali i neke originalne analize konstrukcije pravilnog sedmerokuta. Promatramo i neke algebarske konstrukcije. Rješenja ciklotomijske jednadžbe pridružene pravilnom sedmerokutu mogu se konstruirati uz pomoć krivulja drugog reda, najčešće presjekom parabole i hiperbole. U ovom radu analiziramo i nekoliko zanimljivih konstrukcija ovog tipa.The geometrical construction of regular polygons is an important part of geometry. It is known how to elementary (only by means of a ruler and a pair of compasses) construct an equilateral triangle, a square, a regular pentagon, a regular hexagon, a regular octagon, and a regular decagon. The first one missing in this sequence is a regular heptagon. While studying the construction of a regular heptagon, Gauß has determined the class of regular polygons that can be constructed elementary. Unfortunately, a heptagon is not one of them. However, a regular heptagon can be constructed if we use methods which are not parts of elementary constructions. For example, it can be constructed by inserting a line or using intersections of conics. We describe different constructions of a regular heptagon, starting from the analysis due to Archimedes and his conditions. Medieval Arab mathematicians tried to improve the work of Archimedes. We describe their constructions based on the work of Archimedes, as well as some of their original analyses concerning the construction of a regular heptagon. Some algebraic constructions have also been looked at. The solutions of an equation associated to a regular heptagon can be constructed using conics, mostly using intersections of a parabola and a hyperbola. We analyze a few interesting constructions of this type as well

Conformity of technical products and the CE sign

Zakonodavstvo Europske unije za tehničke proizvode primjenjuje se za svaki tehnički proizvod koji u postupku korištenja istog predstavlja određenu opasnost za korisnika i/ili okoliš. Na svaki tehnički proizvod može se primijeniti jedna ili više smjernica Novog pristupa, a proizvod mora zadovoljiti bitne zahtjeve primjenjivih smjernica. Proizvođač proizvod prije plasiranja na tržište EU mora ispitati, označiti ga CE znakom i tek onda ga poslati na tržište Europske unije. CE znak simbolizira da je proizvod sukladan sa svim zahtjevima smjernica Novog pristupa koje se na njega primjenjuju.European Union legislation on technical products has to be applied on every technical product which poses a threat during its use on the user and/or the environment. One or more directives of the New Approach can be applied on a technical product, which must meet the essential requirements of applicable directives. Before placing a technical product on the EU market the manufacturer has to perform testing, apply the CE marking on the product and then place the product on the EU market. The CE sign symbolizes that the product complies with all the requirements of the New Approach Directives that apply to it

Molekularnom analizom ribljih larvi utvrđena potencijalna prisutnost rijetke vrste: Buenia massutii Kovačić, Ordines i Schliewen, 2017. u Jadranskom moru

By introduction of DNA barcodes in Adriatic larval fish identification possible presence of new Gobiidae - Buenia massutii Kovačić, Ordines, and Schliewen, 2017, was noticed. Till now, occurrence of this species was restricted only to the Western Mediterranean and to the neighbouring part of the Atlantic Ocean.Larva nedavno opisane vrste Buenia massutii Kovačić, Ordines i Schliewen, 2017, s poznatom geografskom distribucijom ograničenom na zapadno Sredozemlje i susjedni dio Atlanskog oceana, je pronađena u Jadranskom moru. Naime, tijekom ihtioplanktonskog uzorkovanja je izolirana larva navedene vrste, čija je taksonomija utvrđena molekularnom analizom (DNA barcoding)

Evaluation of DNA extraction methods and direct PCR in metabarcoding of mock and marine bacterial communities

Recent advances in new molecular biology methods and next-generation sequencing (NGS) technologies have revolutionized metabarcoding studies investigating complex microbial communities from various environments. The inevitable first step in sample preparation is DNA extraction which introduces its own set of biases and considerations. In this study, we assessed the influence of five DNA extraction methods [B1: phenol/chloroform/isoamyl extraction, B2 and B3: isopropanol and ethanol precipitations, respectively—both modifications of B1, K1: DNeasy PowerWater Kit (QIAGEN), K2: modified DNeasy PowerWater Kit (QIAGEN) and direct PCR approach (P) that completely circumvents this step on community composition and DNA yield of mock and marine sample communities from the Adriatic Sea]. B1–B3 methods generally produced higher DNA yields and more similar microbial communities, but with higher interindividual variability. Each method demonstrated significant differences in a specific community structure, where rare taxa seem to play a crucial role. There was not one superior method closest to the theoretically expected mock community composition, they all demonstrated skewed ratios, but in a similar way which might be attributed to other factors, such as primer bias or 16S rRNA gene count for specific taxa. Direct PCR represents an interesting approach when high throughput in sample processing is required. We emphasize the importance of making a cautious decision about the choice of the extraction method or direct PCR approach, but even more importantly its consistent application throughout the study

Modelling the effects of trafficking and tamping on scaled railway ballast in triaxial tests

Most of the world’s railways are on ballasted track, which is generally used in preference to slab track because of its lower initial cost and the relative ease with which track geometry can be adjusted. However, the accumulation of track movements as a result of trafficking leads to a gradual deterioration in track line and level, hence the need for periodic corrective maintenance. This is usually by tamping; a process in which the track is lifted and vibrating tines are inserted into the ballast and moved horizontally to raise the ballast surface back to the required level. The period before further maintenance is required decreases with each tamp. This paper investigates one of the reasons for the deterioration in ballast robustness following tamping, with reference to triaxial tests on scaled ballast in which vertical loading cycles and the stress reversal caused below the railseat by tamping were simulated. It is shown that the stress reversal disrupts and loosens the vertical load bearing ballast structure developed during trafficking to support vertical train loads. On re-loading after tamping, the track settles significantly and, as a result of the loss of vertical load-bearing structure, with further load cycles rapidly returns to its reduced height. The implication is that maintenance by tamping is, on its own, disruptive to the structure and resilience of the ballast to vertical cyclic loading, and should be carried out as rarely as possible

The effectiveness of balneotherapy/hydrotherapy on functional abilities, activities and quality of life of patients with rheumatoid arthritis

Balneoterapija/hidroterapija neizostavni je dio rehabilitacije bolesnika s upalnim reumatskim bolestima. Kako se njena učinkovitost često dovodi u pitanje, cilj rada je bio utvrditi učinkovitost balneoterapije/hidroterapije na funkcionalne sposobnosti, aktivnosti i kvalitetu života bolesnika s reumatoidnim artritisom (RA). U kliničku studiju su uključena 113 bolesnika s RA-om, 79 žena i 34 muškarca, koji su liječeni u Specijalnoj bolnici za medicinsku rehabilitaciju Varaždinske Toplice, u prosječnom trajanju 14 dana. Prije i poslije balneoterapije, pacijenti su ispunili upitnik o procjeni zdravlja HAQ (Health assessment questionnaire) i upitnik o kvaliteti života bolesnika s Izvorni znanstveni članak Original scientific article ISSN 1846-1867 reumatoidnim artritisom QoL-RA (Quality of life RA). Ocjena aktivnosti bolesti DAS 28 korištena je za mjerenje djelovanja bolesti prije i poslije balneoterapije/ hidroterapije. Pronašli smo značajno poboljšanje funkcionalne sposobnosti u bolesnika s RA-om. Prosječna ocjena HAQ-a prije balneoterapije/hidroterapije je 1,07 + / - 0,61, i 0,84 + / - 0,55, nakon balneoterapije/hidroterapije, što je statistički značajno niži (p <0,05). DAS 28 nakon balneoterapije/hidroterapije je i statistički značajno niži od DAS 28 prije balneoterapije/hidroterapije: srednja vrijednost DAS 28 prije balneoterapije/hidroterapije bila je 6,30 + / - 0,81 i nakon balneoterapije/hidroterapije 5,45 + / - 0,75 (p <0,01). Kvaliteta života značajno je poboljšana nakon balneoterapije/hidroterapije: srednja vrijednost QoL-RA prije balneoterapije/hidroterapije je bila 5,38 + / - 1,62 i nakon baleoterapije/hidroterapije 7,37 + / - 1,81 (p <0,05). Zaključno, balneoterapija/hidroterapija, kada se pravilno dozira, učinkovita je terapija u liječenju bolesnika s RA-om. Balneoterapija/hidroterapija ima pozitivan utjecaj na funkcionalne sposobnosti, aktivnosti bolesti i kvalitetu života bolesnika s reumatoidnim artritisom.Balneotherapy/hydrotherapy is an essential part of the rehabilitation of patients with inflammatory rheumatic diseases. Given that its effectiveness is often questioned, the goal of the study was to determine the effectiveness of balneotherapy/hydrotherapy on functional abilities, activities and quality of life of patients with rheumatoid arthritis (RA). The clinical study included 113 RA patients, 79 women and 34 men, who were treated in the Special Hospital for Medical Rehabilitation Varazdin Spa, with the average duration of 14 days. Before and after balneotherapy/hydrotherapy, patients completed a questionnaire assessing their health, HAQ (Health Assessment Questionnaire) and a questionnaire on the quality of life of patients with rheumatoid arthritis, RA-QoL (Quality of Life RA). Disease activity score DAS 28 is used to measure the effects of the disease before and after balneotherapy/hydrotherapy. We found a significant improvement of functional capacity in patients with RA. Average HAQ before balneotherapy/hydrotherapy was 1.07 + / - 0.61 and 0.84 + / - 0.55, after balneotherapy/hydrotherapy, which was significantly lower (p <0.05). DAS 28 after balneotherapy/hydrotherapy is significantly lower than the DAS 28 before balneotherapy/hydrotherapy: mean DAS 28 before balneotherapy/hydrotherapy treatment was 6.30 + / - 0.81 and after balneotherapy/hydrotherapy 5.45 + / - 0 , 75 (p <0.01). Quality of life was significantly improved after balneotherapy/ hydrotherapy: mean QoL-RA before balneotherapy/hydrotherapy treatment was 5.38 + / - 1.62 and after balneotherapy/hydrotherapy 7.37 + / - 1.81 (p <0.05 ). In conclusion, balneotherapy/hydrotherapy, when properly dosed, is an effective therapy in the treatment of patients with RA. Balneotherapy/hydrotherapy has a positive effect on disease activity, functional ability and quality of life in patients with rheumatoid arthritis

Reproduktivna biologija oslića, Merluccius merluccius (L. 1758), u Jadranskom moru

Within this paper, reproduction traits of the Adriatic population European hake, Merluccius merluccius (Linnaeus, 1758), were investigated. Specimens of the target species were monthly collected (N=1173) during 2019 along the eastern Adriatic Sea with commercial bottom trawlers. Overall, European hake total body length varied between 15.5 and 49.5 cm (mean±SD=27.5±5.0 cm) and domination of females was noted in larger length classes (TL>31.0 cm). The sexual ratio of all specimens was m/f=0.64; male prevalence was established over the year, except during the spawning peaks (December, June) when the sex ratio was in favour of the females. According to European hake’s maturity stages, gonad weights, gonadosomatic indexes and histological analysis of the gonad tissues, this species in Adriatic spawn twice in one year; the spawning period was from December to February, while second smaller signs of spawning were observed at the beginning of the summer, in June. 50% of the European hake male and female specimens sexually matured at 20.7 cm and 22.4 cm of total length, respectively.U okviru ovog rada je istražena reproduktivna biologija jadranske populacije oslića, Merluccius merluccius (Linnaeus, 1758). Uzorci istraživane vrste su prikupljeni iz uzoraka lovina ostvarenih komercijalnom pridnenom mrežom koćom s područja istočnog Jadrana (Hrvatsko ribolovno more) jednom mjesečno (N = 1173) tijekom 2019. godine. Raspon totalnih dužina tijela oslića se kretao između u rasponu od 15,5 cm do 49,5 cm (srednja vrijednost ± SD = 27,5 ± 5,0 cm) te je pri većim dužinskim razredima zabilježena dominacija ženki (TL> 31,0 cm). Omjer spolova (m/ž) je iznosio 0,64; prevalencija mužjaka je utvrđena tijekom čitave godine izuzev razdoblja mrijesta (prosinac, lipanj) kada je omjer spolova bio u korist ženki. Analizom stadija zrelosti, mase gonada, gonadosomatskog indeksa te histoloških preparata tkiva spolnih žlijezda utvrđeno je da se ova vrsta u Jadranu mrijesti dva puta u jednoj godini; utvrđeno je razdoblje mrijesta od prosinca do veljače, dok je drugo razdoblje mrijesta nešto slabijeg intenziteta utvrđeno početkom ljeta, točnije u lipnju. Prva spolna zrelost svih analiziranih jedinki oslića je nastupila pri totalnoj dužini tijela od 20,7 cm za mužjake odnosno 22,4 cm za ženke