Fourierova transformacija i Paley-Wienerov prostor

U ovome radu izložene su osnove Fourierove transformacije na Banachovom prostoru $L^1(\mathbb{R})$ i Hilbertovom prostoru $L^2(\mathbb{R})$. Također, opisana su glavna svojstva Paley-Wienerovog prostora i dokazan je teorem o uzorkovanju na tom prostoru. Rad je podijeljen u četiri idejne cjeline, u prvom poglavlju navedeni su rezultati iz teorije normiranih prostora, te mjere i integrala koji su potrebni u proučavanju Fourierove transformacije. U drugome dijelu pažnju smo posvetili baznim okvirima koji se pokazuju korisnima u samom teoremu o uzorkovanju. Treće poglavlje posvećeno je Fourierovoj transformaciji. U četvrtom poglavlju uvodi se Paley-Wienerov prostor, proučavaju se svojstva tog prostora i na samom kraju, dokaže se teorem o uzorkovanju.In this thesis we introduce outlines of Fourier transform in Banach space $L^1(\mathbb{R})$ and Hilbert space $L^2(\mathbb{R})$. Also, main properties of Paley-Wiener space is disscused and Sampling theorem has been proved. The thesis consists of four parts. Chapter 1 is a review of normed linear spaces theory and measure and integration theory, needed in coming chapters. Chapter 2 is devoted to frames, which will show useful in the Sampling theorem. In Chapter 3 we commit to Fourier transform. In final chapter, Paley-Wiener space has been introduced, main properties have been brought up and Classical Sampling Theorem has been demonstrated

Fourierova transformacija i Paley-Wienerov prostor

U ovome radu izložene su osnove Fourierove transformacije na Banachovom prostoru $L^1(\mathbb{R})$ i Hilbertovom prostoru $L^2(\mathbb{R})$. Također, opisana su glavna svojstva Paley-Wienerovog prostora i dokazan je teorem o uzorkovanju na tom prostoru. Rad je podijeljen u četiri idejne cjeline, u prvom poglavlju navedeni su rezultati iz teorije normiranih prostora, te mjere i integrala koji su potrebni u proučavanju Fourierove transformacije. U drugome dijelu pažnju smo posvetili baznim okvirima koji se pokazuju korisnima u samom teoremu o uzorkovanju. Treće poglavlje posvećeno je Fourierovoj transformaciji. U četvrtom poglavlju uvodi se Paley-Wienerov prostor, proučavaju se svojstva tog prostora i na samom kraju, dokaže se teorem o uzorkovanju.In this thesis we introduce outlines of Fourier transform in Banach space $L^1(\mathbb{R})$ and Hilbert space $L^2(\mathbb{R})$. Also, main properties of Paley-Wiener space is disscused and Sampling theorem has been proved. The thesis consists of four parts. Chapter 1 is a review of normed linear spaces theory and measure and integration theory, needed in coming chapters. Chapter 2 is devoted to frames, which will show useful in the Sampling theorem. In Chapter 3 we commit to Fourier transform. In final chapter, Paley-Wiener space has been introduced, main properties have been brought up and Classical Sampling Theorem has been demonstrated

Fourierova transformacija i Paley-Wienerov prostor

U ovome radu izložene su osnove Fourierove transformacije na Banachovom prostoru $L^1(\mathbb{R})$ i Hilbertovom prostoru $L^2(\mathbb{R})$. Također, opisana su glavna svojstva Paley-Wienerovog prostora i dokazan je teorem o uzorkovanju na tom prostoru. Rad je podijeljen u četiri idejne cjeline, u prvom poglavlju navedeni su rezultati iz teorije normiranih prostora, te mjere i integrala koji su potrebni u proučavanju Fourierove transformacije. U drugome dijelu pažnju smo posvetili baznim okvirima koji se pokazuju korisnima u samom teoremu o uzorkovanju. Treće poglavlje posvećeno je Fourierovoj transformaciji. U četvrtom poglavlju uvodi se Paley-Wienerov prostor, proučavaju se svojstva tog prostora i na samom kraju, dokaže se teorem o uzorkovanju.In this thesis we introduce outlines of Fourier transform in Banach space $L^1(\mathbb{R})$ and Hilbert space $L^2(\mathbb{R})$. Also, main properties of Paley-Wiener space is disscused and Sampling theorem has been proved. The thesis consists of four parts. Chapter 1 is a review of normed linear spaces theory and measure and integration theory, needed in coming chapters. Chapter 2 is devoted to frames, which will show useful in the Sampling theorem. In Chapter 3 we commit to Fourier transform. In final chapter, Paley-Wiener space has been introduced, main properties have been brought up and Classical Sampling Theorem has been demonstrated

The Mechanism of Peptide Hydrolysis Catalysed by Dipeptidyl Peptidase III from Bacteroides thetaiotaomicron

Dipeptidyl peptidase III (DPP III) is a zinc- dependent peptidase that cleaves dipeptides off of N-termini of its substrates. Previous studies on human DPP III reveal a reaction mechanism similar to that of thermolysin. Since the active site is conserved within the DPP III family, it is not surprising that the mechanism determined for Bacteroides thetaiotaomicron DPP III (BtDPP III) closely resembles that of hDPP III. However, the hydrogen bond network within the model differs slightly from that in the human ortholog, which results in two proposed pathways. The calculated Gibbs activation energy of 90.1 kJ mol–1 is larger than the one calculated from kinetic data for the preferred substrate Arg2-2-naphthylamide at room temperature (69 kJ mol–1), suggesting the importance of treating the whole DPP III enzyme in the calculations

Lignocellulosic Materials as Dye Adsorbents: Adsorption of Methylene Blue and Congo Red on Brewers’ Spent Grain

Brewers’ spent grain (BSG), a lignocellulosic waste material, was evaluated as a low-cost adsorbent for the removal of synthetic dyes methylene blue (MB) and Congo red (CR) from aqueous solutions in a batch process. Characterisation of the BSG was performed by chemical analysis, FTIR and SEM. The effects of contact time, initial dye concentration, adsorbent particle size, adsorbent concentration and pH on the adsorption process were investigated. High removal of both dyes ranging from 70 to over 90 % was achieved. It was shown that in both cases (MB and CR adsorption) the process could be interpreted in terms of Langmuir and Freundlich adsorption isotherms. The kinetics of the adsorption process was well described by the pseudo-second-order model. The results indicated the potential use of BSG as a low-cost adsorbent for MB and CR dye removal from aqueous solutions. This work is licensed under a Creative Commons Attribution 4.0 International License

Antibacterial Properties of mTiO2 Filler in Biocomposites Based on Low Density Polyethylene and Rice Husks

Polietilen niske gustoće (LDPE) sintetski je nerazgradljiv polimer koji se najčešće upotrebljava kao ambalažni materijal za pakiranje hrane, međutim njegova nerazgradljivost ima loš utjecaj na okoliš. Razvoj i uporaba biorazgradljivih polimernih materijala ili plastike kao ambalažnog materijala za pakiranje hrane danas je u značajnom porastu. Biopolimeri predstavljaju jednu od najznačajnijih alternativa za razvoj ekološki prihvatljive ambalaže u prehrambenoj industriji zbog njihove biorazgradljivosti. Cilj ovoga rada bio je pripremiti biokompozite na osnovi linearnog polietilena niske gustoće (LDPE), rižinih ljuskica (RLJ) i punila mikro titanijeva dioksida (mTiO2) kako bi se dobili biorazgradljivi biokompoziti s antibakterijskim učinkom, pogodni za primjenu kao ambalažni materijali u prehrambenoj industriji. Biokompoziti su pripremljeni umješavanjem u laboratorijskoj Brabender gnjetilici. Ispitan je utjecaj različitog masenog udjela mTiO2 (w = 0,5, 1,0, 1,5 i 2,0 %) na inhibiciju bakterijske kulture Escherichia coli, Pseudomonas aeruginosa i Bacillus subtilis. Rezultati pokazuju da je mTiO2 inhibirao rast bakterijske kulture Escherichia coli, Pseudomonas aeruginosa i Bacillus subtilis kod masenog udjela mTiO2 od 1,5 i 2,0 % (broj stanica bakterijskih kultura se smanjivao). Rezultati TGA i DSC mjerenja pokazuju prisutnost mTiO2 u biokompozitima. Ovo djelo je dano na korištenje pod licencom Creative Commons Imenovanje 4.0 međunarodna.Low-density polyethylene (LDPE) is a synthetic, non-degradable polymer most commonly used as a food packaging material; however, its non-degradability has an adverse effect on the environment. The development and use of biodegradable polymeric materials or plastics as packaging materials for food packaging has significantly increased. Biopolymers present one of the best alternatives for development of environmentally friendly packaging materials in the food industry due to their biodegradability. The aim of this study was to prepare biocomposites of low-density polyethylene (LDPE), rice husk (RH) and micro titanium dioxide (mTiO2) as a filler in order to obtain a biodegradable and antibacterial material suitable for use as a packaging material in the food industry. The biocomposites were prepared by melt mixing in laboratory Brabender mixer. Antibacterial effect of different mass fraction of mTiO2 (w = 0.5; 1.0; 1.5, and 2.0 %) on bacterial cultures of Escherichia coli, Pseudomonas aeruginosa, and Bacillus subtilis was investigated. The results showed that mTiO2 inhibited the growth of bacterial cultures of Escherichia coli, Pseudomonas aeruginosa, and Bacillus subtilis at the mTiO2 mass fraction of 1.5 and 2.0 % (the number of bacterial culture cells decreased). The results of TGA and DSC measurements showed that TiO2 was blended successfully into the biocomposites. This work is licensed under a Creative Commons Attribution 4.0 International License

Тhe importance of effective communication between teachers, parents and children

Остваривање вишедимензионалне сарадње и партнерског односа између породице и предшколске установе директно се рефлектује на добробит детета. Циљ овог рада је да укаже у којој мери се ефективна комуникација између родитеља и васпитача позитивно рефлектује на добробит детета. Заправо, дискурс који деле васпитачи и родитељи преноси се и на дете, чиме се добија квалитативно нови однос у којем су сви актери равноправни чланови. Квалитетна сарадња у великој мери зависи и од комуникативних способности васпитача. Интегративни приступ у учењу предшколске деце се примењује у Србији већ деценијама, а званично од 2018. године. Овај приступ захтева грађење партнерства између породица и предшколске установе и ефективну комуникацију међу свим актерима васпитно-образовног рада. У овом раду фокус је на компатибилности комуникације на релацији: родитељи/породица – дете – васпитач. Ово ће допринети да дете уз подршку васпитача и родитеља истражује, испробава користећи искуства која је претходно стекло. Кроз ефективну комуникацију и размену информација васпитач у васпитно-образовној групи развија индивидуализован приступ и стил подучавања прилагођава детету. Васпитач о свему обавештва родитеље, који су комплементарна страна у комуникацији, и који активности детета код куће усмеравају ка томе да изражава своја интересовања и потребе и развија критичко мишљење. Ово се остварује интегративним приступом учењу. Ефективна комуникација између родитеља и васпитача омогућава праћење учења и напредовања детета и мењања стратегија кад год се за то укаже потреба.Achieving multidimensional cooperation and partnership between the family and the preschool institution is reflected in the wellbeing of the child. The aim of this paper is to show to what extent effective communication between parents and educators reflects on the well-being of the child. In fact, the discourse between educators and parents is also transferred to the child, which results in a new relationship in which all involved parties are equal. Quality cooperation depends to a great extent on the communicative abilities of the teacher. The integrative approach to the learning of preschool children has been applied in Serbia for decades, and officially since 2018. This approach requires building of a partnership between families and preschool institutions and effective communication among all actors of educational work. In this paper, the focus is on the compatibility of communication in the relationship: parents/family - child - educator. Support of educators and parents will contribute the child to explore, try out and use the experiences he has gained. Through effective communication and exchange of information, the teacher in the educational group develops individualised approache and adapts the teaching style to the child. The teacher informs about everything the parents, who are a complementary party in communication and who direct the child’s activities at home to express his interests and needs and develop critical thinking. This is achieved through an integrative approach to learning. Effective communication between parents and educators enables monitoring of the child’s learning and progress, and changing strategies whenever the need arises

The users’ tendency to different packaging materials regarding to the type of product

The most important role of packaging is protecting a product, but also stimulating purchasing decision. Products on store shelfs can often be found packaged in different materials, even when they are of the same net weight. This study investigated how different packaging materials affect purchasing decision. The aim was to evaluate the user’s tendency towards a particular packaging material in relation to its functionality and environmental protection. Test samples were three common powder products: instant coffee, cocoa and sugar. Respondents’ task was to select one of the following packaging materials: glass, tin and composite material for coffee; rigid and flexible plastics for cocoa and sugar. The results showed that the user’s tendency towards packaging material is influenced by packaging functionality. In addition, technical (protection, recyclability) and ergonomic (presence of the lid, easy to dose and reusability) attributes have found to be essential criteria for the choice of packaging. Furthermore, this study showed that customers are ecologically aware since they tend to re-use the packaging, thus enhancing environmental care

Dominant microflora of fermented horse meat sausages

Budući da se proizvodi od konjskog mesa, u našoj zemlji, proizvode u malim domaćinstvima na tradicionalan način, a konačan pro- izvod ovisi o prisutnosti i aktivnosti prirodne mikroore, svrha ovog rada bila je odrediti mikrobnu populaciju i kemijske parametre u fermentiranim kobasicama od konjskog mesa, te izolirati i karakterizirati prisutne autohtone starter kulture i istražiti njihovu spo- sobnost inhibicije rasta patogenih bakterija. U uzorku kobasice od konjskog mesa biokemijskim API testovima dokazane su bakterija Serratia odorifera iz obitelji Enterobacteriaceae, Staphylococcus aureus, bakterija Listeria grayi, bakterije iz roda Salmonella i sul- toreducirajuće klostridije nisu utvrđene, a dokazan je i kvasac – Candida zeylanoides. Dominantna mikroflora u uzorku kobasice bio je izolat bakterija mliječne kiseline Lactococcus lactis ssp. lactis 5K1 u broju 8,301 log10cfu g-1. Na MRS podlozi (selektivnoj podlozi za bakterije mliječne kiseline) L. lactis ssp. lactis 5K1 proizveo je 13,83gL-1 mliječne kiseline (HPLC), te zakiselio podlogu na 4,16 pH vrijednost i pokazao znatno antimikrobno djelovanje prema patogenim test mikroorganizmima. U radu su praćeni i kemijski para- metri: udio vode (41,12%), masti (20,93%), proteina (27,29%), natrijevog klorida (3,78%), pH (4,94) i sadržaj nitrita (0,983 mgkg-1).Since the products of horse meat in our country, produced in small households in the traditional way, and the nal product depends on the presence and activity of natural microora, the purpose of this study was to determine the microbial population and chemical parameters in dry fermented sausages of horse meat, and isolate and characterize the presence of autochthonous starter cultures and to investigate their ability to inhibit growth of pathogenic bacteria. In the samples of horse meat sausages were detected bacteria Seratia odorifera from the family Enterobacteriaceae, Staphylococcus aureus, API Listeria test conrmed the bacteria L. grayi, bacteria of the genus Salmonella and Sulphite reducing clostridia not established, and detected yeast - Candida zeylanoides. The dominant microora in the samples of sausages were lactic acid bacteria Lactococcus lactis ssp. lactis 5K1 in the number log10cfu 8.301 g-1. On the MRS medium (selective medium for lactic acid) Lactococcus lactis ssp. lactis 5K1 produced 13,83gL-1 of lactic acid (HPLC) and acidify media at pH value of 4.16 and showed significant antimicrobial activity against pathogenic test microorganisms. In the paper were also observed chemical parameters: water content (41,12%), fat (20,93%), protein (27,29%), sodium chloride (3,78%), pH (4,94) and nitrite content (0,983 mgkg-1)