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    Convergence Criteria for Series of Real Numbers

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    Tema ovog završnog rada su kriteriji konvergencije redova realnih brojeva. Za potrebe njihovog definiranja, u prvom dijelu rada navedene su definicije i rezultati vezani uz osnovne pojmove kao što su red i konvergencija reda. Potom, za razumijevanje kriterija konvergencije u drugom dijelu rada je definirano i na primjerima prikazano uspoređivanje redova te apsolutna konvergencija redova. U posljednjem poglavlju iskazani su i dokazani uvjeti za određivanje konvergencije redova, a kako bismo iskazali sve kriterije bilo je potrebno uvesti i definiciju alternirajućeg reda. Dodatno, na primjerima je prikazano korištenje nekoliko važnih kriterija za određivanje konvergencije redova.The topic of this final paper is convergence criteria for sequences of real numbers. For the purpose of defining them, the first part of the paper presents definitions and results related to fundamental concepts such as series and the convergence of a series. Then, in the second part of the paper, in order to understand the convergence criteria, comparisons of series and the absolute convergence of series are defined and illustrated with examples. In the last chapter, conditions for determining the convergence of series are stated and proven. To encompass all criteria, it was necessary to introduce the definition of an alternating series. Additionally, examples are provided to demonstrate the use of several important criteria for determining the convergence of series

    Marker Gene Selection Problem

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    Ovaj rad istražuje problem selekciije marker gena na Zeisel skupu podataka.Obrađuje se usporedba između različitog broja markera s različitim ograničenjima i različitom vremenu izvršenja, tabličnim prikazom i vizualnim prikazom preko grafova. Uspoređuju se također rezultati dobiveni trima različitim metodama. Metodom ograničenja usmjerenih na centar, metodom parnih ograničenja udaljenosti i metodom parnih ograničenja usmjerenih na centar. Također, u radu se definiraju alati, koji su korišteni za rješavanje tog problema.This thesis investigates the marker gene selection problem on Zeisel dataset. It covers a comparison between different number of markers with different constraints and execution times, with tabular representation and visual representation via graphs. The results obtained from three different methods, are also compared. Center based constraints, pairwise distance constraints and pairwise center based constraints. In this thesis, as well, are defined programing tools, that are used in solving marker gene selection problem

    Digitization in libraries

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    U današnjem digitalnom dobu, uloga knjižnica i informacijskih centara značajno se transformira uslijed procesa digitalizacije. Ovaj diplomski rad istražuje ključne aspekte digitalizacije u kontekstu knjižničarstva, s posebnim naglaskom na Republiku Hrvatsku i Europsku uniju. Analiziraju se smjernice i standarde vezane uz digitalizaciju, ističući važnost prilagodbe lokalnih praksi globalnim normama. Proučavanjem pravnih aspekata, rad istražuje zaštitu autorskih prava u digitalnom okruženju, zakonske obaveze čuvanja digitalne građe, kao i pitanja sigurnosti, privatnosti i etike. Organizacijske aktivnosti nužne za uspješno upravljanje digitalnim sadržajem obuhvaćaju procese stvaranja, čuvanja i pristupa elektroničkim dokumentima, uz naglasak na potrebu za efikasnom upotrebom ljudskih resursa i tehnoloških alata.In today's digital age, the role of libraries and information centers is undergoing significant transformation due to the process of digitization. This thesis explores key aspects of digitization in the context of library science, with a specific focus on Croatia and the European Union. It analyzes guidelines and standards related to digitization, emphasizing the importance of aligning local practices with global norms. Examining legal aspects, the thesis investigates copyright protection in the digital environment, legal obligations for preserving digital content, as well as issues of security, privacy, and ethics. Organizational activities necessary for effective management of digital content encompass processes of creation, preservation, and access to electronic documents, highlighting the need for efficient utilization of human resources and technological tools

    Application of stationary battery systems in households

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    Zadatak ovog diplomskog rada je analizirati primjenu stacionarnih baterijskih sustava u kućanstvima. U ovome radu su definirani baterijski sustavi pohrane, te najpopularnije tehnologije baterijskih sustava pohrane. Opisane su karakteristike tehnologija baterijskih sustava pohrane te njihove primjene. Navedeni su izazovi te mogućnosti daljnjeg istraživanja tehnologija baterijskih sustava pohrane. Napravljena je SWOT analiza primjene baterijskih sustava pohrane u kućanstvima, te su prikazani trenutno dostupni stacionarni baterijski sustavi pohrane električne energije za kućanstva na tržištu. U praktičnome dijelu diplomskog rada, napravljena je tehno-ekonomska analiza primjene stacionarnih baterijskih sustava na primjeru jednog kućanstva u Osijeku te su se donijeli zaključci o isplativosti integracije baterijskih sustava pohrane električne energije u promatrano kućanstvo.The task of this master thesis is to analyze the application of stationary battery systems in households. In this thesis, battery storage systems and the most popular technologies of battery storage systems are defined. The characteristics of battery storage system technologies and thier applications are described. Challenges and opportunities for further research into battery storage system technologies are listed. A SWOT analysis of the application of battery storage systems in households was made, and currently available stationary battery storage systems for households on the market were presented. In the practial part of the thesis, techno-ecnomic analysis of the application of stationary battery systems for one household in Osijek was made. Conclusions were drawn on the profitability of integrating battery systems for electricity storage in the observed household

    Wireline broadband Internet access

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    U radu je dan pregled žičnog širokopojasnog pristupa Internetu i njegove karakteristike. Obrađene su DSL tehnologije, pristup mreži koaksijalnim kabelom, širokopojasni pristup internetu preko elektroenergetske mreže te svjetlovodni pristup internetu uključujući PON. Predložena je implementacija žičnog širokopojasnog pristupa internetu za naselja Sopje prema kojoj se je kasnije krenulo u realizaciju i izgradnju širokopojasnog pristupa.The paper provides an overview of wired broadband Internet access and its characteristics. DSL technologies, access to the network via coaxial cable, broadband access to internet over power line and fiber - optic Internet access are defined. The implementation of wired broadband Internet access for the settlements of Sopje was proposed, according to which the implementation and construction of broadband access was later started

    The Effect of Turmeric Powder and Black Pepper on Sensory Properties and Consumer Acceptance of Ice Cream

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    Kurkuma se zbog potencijalnih terapijskih svojstava sve češće dodaje u različite prehrambene proizvode. Međutim, kurkumin, aktivni sastojak iz kurkume, se vrlo teško apsorbira u krvotok. Budući da je dokazano da piperin iz papra povećava bioraspoloživost kurkumina, primijenit će se njihova kombinacija. Cilj ovog rada bio je ispitati senzorski profil i procijeniti prihvatljivost sladoleda s dodatkom kurkume, te kurkume i papra u različitim koncentracijama. U preliminarnim ispitivanjima senzorski panel je odabrao 3 najprihvatljivija udjela kurkume, te udio papra. Ispitanici su bili regrutirani na Prehrambeno-tehnološkom fakultetu Osijek, a ocjenjivali su 6 uzoraka s dodatkom kurkume (3 bez dodatka papra i 3 s dodatkom papra), zajedno s kontrolnim standardnim mliječnim sladoledom. Prihvatljivost senzorskih svojstava (okus, osjet u ustima, izgled, tekstura i miris) i ukupna prihvatljivost uzoraka je bila ocjenjena pomoću hedonističke skale, intenzitet odabranih senzorskih svojstava (boja, tvrdoća, topljenje, ukupni okus, slatkoća, naknadni okus, gorčina i miris) ispitan je pomoću JAR (Just-about-Right) skale, a za karakterizaciju proizvoda se primijenio CATA (Check-all-that-apply) test s 28 senzorskih pojmova (8 za teksturu, 16 za okus i miris i 4 za osjet u ustima). Zaključeno je da dodatak kurkume mijenja senzorska svojstva sladoleda te da crni papar u optimalnim koncentracijama može biti integriran u recepture sladoleda bez negativnog utjecaja na senzorska svojstva sladoleda. Dakle u proizvodnji funkcionalnog sladoleda moguće je koristiti kurkumu i papar.Turmeric is increasingly being added to various food products due to its potential therapeutic properties. However, curcumin, the active ingredient in turmeric, is very difficult to absorb into the bloodstream. Since it has been proven that piperine from pepper increases the bioavailability of curcumin, their combination will be applied. The aim of this study was to examine the sensory profile and evaluate the acceptability of ice cream with the addition of turmeric, as well as turmeric and pepper in different concentrations. In preliminary trials, a sensory panel has selected the three most acceptable turmeric ratios, as well as the pepper ratio. The participants were recruited at the Faculty of Food Technology in Osijek, and they evaluated six samples with the addition of turmeric (three without pepper and three with pepper), along with a control standard dairy ice cream. The acceptability of sensory properties (taste, mouthfeel, appearance, texture, and smell) and overall acceptability of the samples was assessed using a hedonic scale. The intensity of selected sensory properties (colour, hardness, melting, overall taste, sweetness, aftertaste, bitterness, and smell) were examined using the JAR (Just-about-Right) scale, and for product characterization, the CATA (Check-all-that-apply) test with 28 sensory terms (8 for texture, 16 for taste and smell, and 4 for mouthfeel) will be applied. It was concluded that the addition of turmeric changes the sensory properties of ice cream, and that black pepper in optimal concentrations can be integrated into ice cream recipes without negative impact on the sensory properties of ice cream. Therefore, it is acceptable to use turmeric and pepper in the production of functional ice cream

    The Effect of Mycorrhizal Fungi and Beneficial Bacteria on two Lettuce (Lactuca sativa var. capitata) Varieties under Limited Water Conditions

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    Nedostatak vode može inhibirati rast korijenskog sustava što ometa usvajanje vode i hranjivih tvari iz tla. Interakcija korijena s mikoriznim gljivama i korisnim bakterijama povećava učinkovitost iskorištenja vode što je u uvjetima vodnog stresa izuzetno važno. Cilj ovog rada bio je provjeriti otpornost dva genotipa salate (L. sativa var. capitata) “puterica” i “kristalka”, na stres izazvan sušom dodatkom komercijalnog pripravka mikoriznih gljiva s dodatkom korisnih bakterija (M) na rast i biokemijske pokazatelje u uvjetima in vivo. Zasušivanje je izazvano smanjivanjem obroka navodnjavanja gdje je 100% retencijskog kapaciteta (Rkv) predstavljalo kontrolu, 80% Rkv (umjeren vodni stres) i 60% Rkv (intenzivniji vodni stres). Uzorci salate podvrgnuti su pojedinačnim (100%, 80% i 60%) i kombiniranim tretmanima (M-100%, M-80% i M-60%) u fazi formiranja glavice. Dodatak pripravka inducirao je veću masu i broj listova glavice u puterice (M-80% i M-60%) te veću masu i promjer glavice kristalke (M-60%). Na vodnom stresu slabijeg intenziteta (80%) puterica je sintetizirala više prolina od kristalke što govori o specifičnom genotipskom odgovoru. Dodatak pripravka u kristalke reducirao je sadržaj MDA na slabijem intenzitetu vodnog stresa (M-80%) što govori o protektivnoj ulozi mikoriznih gljiva i bakterija u očuvanju integriteta biomembrana.Water scarcity can inhibit root system growth, hindering the absorption of water and nutrients from the soil. However, the interaction of roots with mycorrhizal fungi and beneficial bacteria can enhance water use efficiency, which is crucial under drought conditions. This study aimed to evaluate the drought resistance of two lettuce genotypes (L. sativa var. capitata), "Butterhead" and "Iceberg," by adding a commercial preparation of mycorrhizal fungi and beneficial bacteria (M) to assess growth and biochemical indicators under in vivo conditions. Drought stress was induced by reducing irrigation levels: 100% retention capacity (RC) served as the control, 80% RC represented moderate drought, and 60% RC represented severe drought. Lettuce samples were subjected to individual treatments (100%, 80%, and 60%) and combined treatments (M-100%, M-80%, and M-60%) during the head formation stage. The addition of the mycorrhizal preparation resulted in greater head mass and leaf number in Butterhead (M-80% and M-60%) and increased head mass and diameter in Iceberg (M-60%). Under lower-intensity stress (80%), Butterhead synthesized more proline than Iceberg, indicating a specific genotypic response. Mycorrhizal treatment also reduced MDA content in Iceberg at the moderate drought intensity (M-80%), highlighting the protective role of mycorrhizae and bacteria in maintaining biomembrane integrity

    Optimization of Ultrasound-Assisted Extraction of Phenolic Compounds from Grape Seed Meal by Response Surface Methodology

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    U ovom radu ispitan je utjecaj tri procesna uvjeta ultrazvučne ekstrakcije (temperatura ekstrakcije: 40 – 60 – 80 °C, vrijeme trajanja ekstrakcije: 10 – 25 – 40 min i koncentracija vodene otopine etanola: 30 – 60 – 90 %) na ekstraktibilnost ukupnih fenolnih tvari, ukupnih flavonoida i ukupnih ekstraktibilnih proantocijanidina iz brašna sjemenki grožđa te na antioksidacijsku aktivnost ekstrakata, metodom odzivnih površina prema Box– Behnkenovom planu pokusa. Ekstrakcija je provedena u ultrazvučnoj kupelji, a primijenjena je snaga ultrazvuka od 60 % max. efektivne snage pri 37 kHz u sweep modu. Ekstrakt brašna sjemenki grožđana analiziran je spektrofotometrijski. Proces ekstrakcije najbolje je opisivao kvadratni model gdje je utvrđena jaka pozitivna korelacija (R ˃ 0,96) između eksperimentalnih i modelom predviđenih podataka. Koncentracija otapala je imala najveći utjecaj na ekstraktibilnost svih fenolnih tvari te na antioksidacijsku aktivnost ekstrakata. Numeričkom optimizacijom određeni su optimalni uvjeti ekstrakcije fenolnih tvari kako slijedi: temperatura 80 °C, koncentracija vodene otopine etanola 50 % i vrijeme ekstrakcije 40 minuta. Prema kvadratnom modelu izračunato je da bi se pri navedenim uvjetima mogao ostvariti maksimalan prinos ukupnih fenolnih spojeva od 57,46 mgGAE/gs.t.mg_{GAE}/g_{s.t.}, ukupnih flavonida od 20,67 mgCE/gs.t. mg_{CE}/g_{s.t.}, ukupnih proantocijanidina od 11,99 mg/gs.t.mg/g_{s.t.}., te antioksidacijska aktivnost ekstrakata prema DPPH metodi od 99,63 mgtroloksa/gs.t.mg_{troloksa}/g_{s.t.}, prema ABTS metodi od 269,93 mgtroloksa/gs.t.mg_{troloksa}/g_{s.t.} i FRAP metodi od165,21 mgtroloksa/gs.t.mg_{troloksa}/g_{s.t.}In this work, the influence of three process conditions of ultrasonic extraction (extraction temperature: 40 - 60 – 80 °C, extraction duration: 10 – 25 – 40 min and concentration of the aqueous ethanol solution: 30 – 60 – 90 %) on the extractability of total phenolic compounds, total flavonoids and total extractable proanthocyanidins from grape seed meal as well as on the antioxidant activity of the extracts was investigated using the response surface method according to the Box–Behnken experimental design. The extraction was carried out in an ultrasonic bath and an ultrasonic power of 60 % maximum effective power at 37 kHz in sweep mode. The grape seed meal extract was analyzed spectrophotometrically. The extraction process was best described by the quadratic model, which showed a strong positive correlation (R ˃ 0.96) between the experimental and modelpredicted data. The solvent concentration had the greatest influence on the extractability of all phenolic compounds and on the antioxidant activity of the extracts. The optimal conditions for the extraction of the phenolic compounds were determined by numerical optimization, as follows: temperature 80 °C, concentration of aqueous ethanol solution 50 % and extraction time 40 minutes. According to the quadratic model, it is predicted that under optimal conditions a maximum yield of total phenolic compounds of 57.46 mgGAE/gdbmg_{GAE}/g_{db}, of total flavonoids of 20.67 mgCE/gdbmg_{CE}/g_{db}, of total proanthocyanidins of 11.99 mg/gdb and an antioxidant activity of the extracts of 99.63 mgtrolox/gdbmg_{trolox}/g_{db} according to the DPPH method, 269.93 mgtrolox/gdbmg_{trolox}/g_{db} according to the ABTS method and 165.21 mgtrolox/gdbmg_{trolox}/g_{db} according to the FRAP method could be achieved

    Comparison of synchronous and asynchronous population update in differential evolution

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    U radu su razmotrene dvije inačice algoritma diferencijalne evolucije, jednog od najpopularnijih evolucijskih algoritama koji se pokazao vrlo učinkovit za probleme kontinuirane optimizacije. Inačice se razlikuju samo u načinu obnavljanja populacije, jedna sa sinkronim gdje se populacija obnavlja generaciju po generaciju, a druga sa asinkronim gdje se populacija obnavlja odmah kada su nova kvalitetnija rješenja dostupna. Upotrebom ostvarenog programskog rješenja provedena je eksperimentalna analiza u kojoj su dvije inačice algoritma primijenjene na deset često korištenih testnih funkcija pri dvije različite dimenzionalnosti. Također je razmotren utjecaj parametra veličine populacije korištenjem tri različite vrijednosti istog. Ostvareni rezultati daju uvid u to kako način obnavljanja populacije direktno utječe na performanse algoritma. Daljnjom usporedbom dvije inačice primijećeno je da ona sa asinkronom implementacijom obnavljanja populacije ostvaruje bolje performanse u usporedbi sa standardnom, sinkronom inačicom u većini slučajeva.The thesis discusses two implementations of the differential evolution algorithm, one of the most popular evolutionary algorithms, which has proven to be highly effective in problems of continuous optimization. The implementations differ only in the method of population updating: one using a synchronous method, where the population is updated generation by generation, and the other using an asynchronous method, where the population is updated immediately when new, better solutions become available. Using the implemented software solution, an experimental analysis was conducted in which the two implementations of the algorithm were applied to ten commonly used benchmark functions at two different dimensionalities. The impact of the population size parameter was also examined by using three different values of it. The obtained results provide insight into how the method of population updating directly affects the algorithm's performance. Further comparison of the two variants revealed that the asynchronous implementation achieves better performance compared to the standard synchronous implementations in most cases

    Web application for real estate sales

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    U ovom završnom radu opisana je web aplikacija za prodaju nekretniona. Web aplikacija omogućuje prikaz i pretraživanje nekretnina na tržištu te dodavanje novih nekretnina na tržište, a napravljena je pomoću HTML-a, CSS-a, MongoDB-a, Express.js-a i React-a. Prikazana je usporedba s već postojećim rješenjima te njihova sličnost sa izrađenom aplikacijom. Aplikacija je lagana za korištenje te ju je moguće dodatno proširiti dodavajući mogućnost slanja poruka drugim korisnicima ili plaćanja putem aplikacije.This thesis describes a web application for real estate sales. The web application allows for the display and search of real estate listings on the market, as well as the addition of new properties to the market. It is built using HTML, CSS, MongoDB, Express.js, and React. A comparison is made with existing solutions, highlighting their similarities with the developed application. The application is easy to use and can be further expanded by adding features such as messaging between users or in-app payments

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