Disertacijos tyrimo objektas yra periodinė dzeta funkcija. Mokslinė problema - šios funkcijos momentų problema. Darbo tikslas - įrodyti asimptotines formules periodinės funkcijos momentams bei kai kuriems objektams, susijusiems su šios funkcijos momentais. Darbo uždaviniai yra šie: 1. Įrodyti Atkinsono tipo formulę su korektišku liekamuoju nariu kritinėje juostoje periodinei dzeta funkcijai su racionaliuoju parametru. 2. Įrodyti Atkinsono tipo formulės periodinei dzeta funkcijai kritinėje tiesėje vidurkio formulę liekamojo nario modulio kvadratui. 3. Įrodyti Atkinsono tipo formulės periodinei dzeta funkcijai kritinėje juostoje vidurkio formulę liekamojo nario modulio kvadratui. 4. Gauti asimptotinę formulę periodinės dzeta funkcijos ketvirtajam momentui. / In the thesis, problems related to the moments of the periodic zeta-function are considered. The aim of the thesis is to obtain asymptotic formulae for some analytic objects related to the periodic zeta-function. The problems are the following: 1. To prove the Atkinson-type formula with a new error term in the critical strip for the periodic zeta-function with rational parameter. 2. To prove a mean square formula for the error term in the Atkinson-type formula on the critical line for the periodic zeta-function. 3. To prove a mean square formula for the error term in the Atkinson-type formula in the critical strip for the periodic zeta-function. 4. To obtain an asymptotic formula for the fourth power moment of the periodic zeta-function.

Thesis is indirectly connected to many years of research in field of sulphate binders. Work is focused on modifying of properties of alfa and beta gypsum, mainly on reduction of water ratio. We monitored effect of addition of chloride salts, carbonates and sulphates on zeta potential and its measurement. Part of thesis is also focused on laboratory production of beta plaster from secondary materials and optimization of grinding process to achieve required criteria.

Charles University Faculty of Pharmacy in Hradcec Králové Department of Pharmaceutical Technology Supervisor: doc. RNDr. Milan Dittrich, CSc. Student: Simona Medviďová Title of thesis: Formulation and testing of branched polyesters siRNA-loaded nanoparticles The progression of development increases demand for new and more effective drug systems formulations. This diploma thesis is focused on the preparation of nanoparticles from biodegradable branched polyesters based on PLGA, which are suitable for the transport of an oligonucleotide of a small interfering nucleic acid, siRNA. The theoretical part focuses on the characteristics of usable polymers, their possible modifications, the methods of preparation with closer look at the selected nanoprecipitation method, the important parameters such as particles size, zeta potential, and polydispersity. The main part is also characterization of siRNA in terms of structure, properties, modifications, and its function. A more extensive experimental part deals with the appropriate choice of type and concentration of polyester and stabilizer, methods of preparation and characterization of nanoparticles, and the possibility of analyzing encapsulated siRNA. Chapters results and discussion compares polyesters branched on tripentaerythritol, and polyacrylic acid...

Seja E(X) a cardinalidade dos números pares menores ou iguais a X que não podem ser escritos como soma de dois primos. O objetivo central desta dissertação é apresentar uma demonstração de uma estimativa para E(X) dada por Hugh L. Montgomery e Robert C. Vaughan em [22]. Mais precisamente, estabeleceremos a existência de uma constante positiva (efetivamente computável) tal que E(X) X1 ; para todo X su cientemente grande. / Let E(X) the cardinality of even numbers not exceeding X which cannot be written as a sum of two primes. The main goal of this dissertation is to present a proof of an estimate for E(X) given by Hugh L. Montgomery e Robert C. Vaughan in [22]. More precisely, we will establish the existence of a positive constant (e ectively computable) such that E(X) X1 for all su ciently large X:

Seja E(X) a cardinalidade dos números pares menores ou iguais a X que não podem ser escritos como soma de dois primos. O objetivo central desta dissertação é apresentar uma demonstração de uma estimativa para E(X) dada por Hugh L. Montgomery e Robert C. Vaughan em [22]. Mais precisamente, estabeleceremos a existência de uma constante positiva (efetivamente computável) tal que E(X) X1 ; para todo X su cientemente grande. / Let E(X) the cardinality of even numbers not exceeding X which cannot be written as a sum of two primes. The main goal of this dissertation is to present a proof of an estimate for E(X) given by Hugh L. Montgomery e Robert C. Vaughan in [22]. More precisely, we will establish the existence of a positive constant (e ectively computable) such that E(X) X1 for all su ciently large X:

[pt] Os minérios de cobre-molibdênio são beneficiados juntos normalmente pelo processo de flotação com a ajuda de coletores sulfidrílicos de relativa seletividade. Os concentrados bulk obtidos devem ser processados com o intuito de remover aqueles coletores empregados, pois eles são prejudiciais na etapa de separação por flotação diferencial, ou seja, na obtenção de concentrados de molibdênio de alta qualidade com baixos conteúdos de cobre e ferro. O processo de flotação bulk é realizado em condições oxidantes na presença de coletores sulfidrílicos (xantatos, etc.). Na prática industrial na etapa de flotação diferencial, estes concentrados bulk são separados por modificação do potencial eletroquímico da polpa para valores considerados redutores -300 a -450 mV, com hidrosulfeto de sódio (NaSH) ou o reagente Nokes (Penta-sulfeto de fósforo dissolvido em hidróxido de sódio) além de cianeto de sódio em alguns dos casos, para melhorar a eficiência do processo. Neste quadro, o processo industrial de separação seletiva produz efluente e gases perigosos como o H2S e HCN que devem ser controlados adequadamente. Este trabalho visa avaliar o uso do reagente ácido pseudo glicol tiouréia (PGA) e ácido tioglicólico (TGA) como alternativas ao processo industrial voltado para a separação seletiva dos minerais de cobre e molibdênio. Para a avaliação do depressor foram empregadas medições de ângulo de contato, potencial zeta, testes de flotação em célula Partridge-Smith (PS), FTIR e testes em célula de bancada em um planejamento experimental. O reagente estudado apresentou boas propriedades depressoras para minerais de cobre. Nos resultados das medições de ângulo de contato, pelo método de bolha cativa, foram encontrados valores maiores para a calcopirita do que para a molibdenita (até 10 graus de diferença) e medidas entre 60 e 70 graus, porém no pH ácido esta diferença diminui e os dois minerais apresentam quase o mesmo ângulo de contato 60 mais ou menos 1 grau. Nas medidas efetuadas não foi empregado o coletor final (querosene) para a molibdenita devido a sua falta de homogeneidade na emulsão para realizar as medidas de ângulo de contato. Nos testes de flotabilidade na célula PS em misturas binarias de calcopirita-molibdenita foram encontradas na faixa ácida, valores de pH nos quais há melhores relações de concentração e recuperações, na ordem de 67 por cento para a molibdenita e apenas 10 por cento para a calcopirita no produto flutuado. Os resultados usando o reagente NaSH em condições similares apresentam recuperações similares de molibdenita, mas na faixa básica do pH. Baseados nestes resultados foram avaliadas diversas variáveis e gerado um planejamento experimental para passar à escala de bancada onde foram obtidas recuperações de 84 por cento no concentrado rougher com apenas 13 por cento de cobre corroborando as boas propriedades do depressor estudado. / [en] Copper-molybdenum porphyry deposits worldwide are exploited industrially by flotation of the ores of interest into a BULK concentrate with the aid of sulfhydryl collectors of high efficiency and low selectivity. The bulk concentrate obtained should be reprocessed in order to remove those collectors employed in the bulk stage since they impair the differential flotation during the separation step in order to obtain clean high quality molybdenite concentrates at low contents of copper and iron. The bulk flotation process is conducted under oxidizing conditions in presence of sulfhydryl collectors (xanthates, etc.). In industrial practice these bulk concentrates are then separated by modification of the pulp electrochemical potential to values considered reducing, between -300 to-450 mV, with sodium hidrosulphide (NaSH) or Nokes reagent (phosphorus pentasulfide dissolved in sodium hydroxide). Addition of sodium cyanide in some cases is used to improve process efficiency. Bulk concentrates produced are however a very small portion of the processed mineral (only 1/50 of the total ore milled), these industrial processes produce waste effluents and hazardous gases such as H2S and HCN if not adequately controlled. This dissertation seeks to assess the reagent pseudo glycol tiourea acid (PGA) and thioglycolic acid (TGA) as an alternative to industrial processing for the selective separation of minerals of copper and molybdenum. On the evaluation of this depressant were used contact angle measurements, zeta potential, flotation tests in Partridge-Smith cell (PS), FTIR and bench scale flotation testing cell with an experimental design. The reagent studied showed good depressant properties for copper minerals according to the results presented. Within the results of the contact angle measurements with the captive bubble technique were found greater contact angles for chalcopyrite than for molybdenite (up to 10 degrees difference) and values between 60 and 70 degrees, however in acidic pH this difference decreases and both minerals have almost the same contact angle as of 60 more or less 1 degree. Though on the contact angle measured values it was not employed the final collector (kerosene) for molybdenite due to lack of homogeneity on emulsions to make the contact angle measurements. On floatability tests (on PS cell) with binary mixtures of chalcopyrite-molybdenite were found pH values on the acidic range, at which good concentration ratios and recoveries in the order of 67 percent of molybdenite with only 10 percent of the chalcopyrite were obtained. The results using NaSH reagent under similar conditions gave similar recoveries for molybdenite, however it was found in the basic pH range. Based on the results, several variables were evaluated and an experimental design employed on bench scale flotation tests, the results showed recoveries of 84 percent were obtained in the rougher concentrate with 13 percent copper corroborating the good properties of this depressant.

Seja E(X) a cardinalidade dos números pares menores ou iguais a X que não podem ser escritos como soma de dois primos. O objetivo central desta dissertação é apresentar uma demonstração de uma estimativa para E(X) dada por Hugh L. Montgomery e Robert C. Vaughan em [22]. Mais precisamente, estabeleceremos a existência de uma constante positiva (efetivamente computável) tal que E(X) X1 ; para todo X su cientemente grande. / Let E(X) the cardinality of even numbers not exceeding X which cannot be written as a sum of two primes. The main goal of this dissertation is to present a proof of an estimate for E(X) given by Hugh L. Montgomery e Robert C. Vaughan in [22]. More precisely, we will establish the existence of a positive constant (e ectively computable) such that E(X) X1 for all su ciently large X:

Charles University Faculty of Pharmacy in Hradec Králové Department of Pharmaceutical Technology Consultant: doc. RNDr. Milan Dittrich, CSc. Student: Andrea Balciarová Title of Thesis: Formulation and testing of rifampicin-loaded branched polyesters nanoparticles In presented thesis, the main attention in theoretical part is focused on nanoparticles for targeted drug delivery, their types, structure and carriers used for their preparation. Moreover, in this part there is an overview of physicochemical characteristics and preparation methods of polymeric nanoparticles applicable in formulation of pharmaceutical products. The experimental part is concerned on studying the influence of the concentration of biodegradable polymers, the presence of cationic surfactants and rifampicin as model drug substance on nanoparticles΄ size and zeta-potential. The main attention is given to nanoparticles decoration with anionic biopolymers, hyaluronic acid and xanthan gum. The simple method of preparation which is usable in nanosystems formulation that influence biological functions purposefully was tried and tested in different contexts.

<p>Disertacija se bavi sumiranjem redova sa specijalnim funkcijama. Ovi redovi se posredstvom trigonometrijskih redova svode na redove sa Riemannovom zeta funkci&shy;jom i srodnim funkcijama. U određenim slučajevima sumacione formule se mogu dovesti na takozvani zatvoreni oblik, &scaron;to znači da se beskonačni redovi predstavljaju konačnim sumama. Predloženi metodi sumacije omogućavaju ubrzanje konvergencije, a mogu se primeniti i kod nekih graničnih problema matematičke fizike. Sumacione formule uključuju kao specijalne slučajeve neke formule poznate iz literature, ali i nove sume, s obzirom da su op&scaron;teg karaktera. Pomoću ovih formula sumirani su i redovi sa integralima trigonometrijskih i specijalnih funkcija.</p> / <p>This dissertation deals with the summation of series over special functions. Through<br />trigonometric series these series are reduced to series in terms of Riemann zeta and<br />related functions. They can be brought in closed form in some cases, i.e. infinite<br />series are expressed as finite sums. Closed form formulas make it possible to accele&shy;<br />rate the convergence of some series, and have many applications in various scientific<br />fields as well. For example, closed form solutions of the boundary value problem in<br />mathematical physics can be obtained. Summation formulas include particular cases<br />known from the literature, but because of their general character one can come to<br />new sums. By means of these formul&aacute;is the sums of series over integrals containing<br />trigonometric or special functions have been found.</p>

Thesis title: Formulation and characterization of oxime loaded PLGA nanoparticles Author: Ramin Hafezi Supervisor: PharmDr. Eva Šnejdrová, Ph.D. Advisor: PharmDr. Juraj Martiška, Ph.D. Department: Department of Pharmaceutical Technology The diploma thesis was focused on PLGA nanoparticles (NPs) which could be loaded with oximes, prepared by a double emulsion technique, and characterised by size, polydispersity and zeta potential. The theoretical part deals with the most common methods of the NPs preparation, the polymers and stabilizers employed, and drug delivery to brain. In the experimental part the effect of various formulation factors on NP characteristics were studied: linear or branched PLGA derivative, the concentrations of polymer, the volumes of primary emulsion. Dichloromethane (DCM) or Dimethyl sulfoxide (DMSO) as solvent for polymers were used and Poloxamer 407 or Didodecyldimethylammonium bromide (DDAB) as an outer phase stabilizer were employed. By comparison among the collected results, it seemed 1% A2 in DMSO and stabilization with poloxamer 407 could be best candidate for the oxime loaded drug delivery systems as it was possible to produce nanoparticles with size from 152 to 168 nm with PDI of below 0.15. Electrostatic stability in case of using DDAB was resulted excellent and...