Conselho Nacional de Desenvolvimento Científico e Tecnológico / The processes of erosion and sedimentation in a watershed cause numerous problems. Knowledge of the amount of sediment transported by rivers is really important to planning and using water resources, since the damage caused by sediments depend on the amount and nature of them, which depend on the processes of erosion, transport and deposition. This study aimed to evaluate the sediment transport in the Vacacaí-Mirim River, through measured data in the cross-section in Restinga Sêca. Thus, it was possible to quantify the average of the sediment discharge in cross-section of the river; to characterize the particle size of the transported materials; to relate the sediment discharge (Qs) and liquid discharge (Q) to the hydraulic and geometric characteristics of the section; and to indicate the sediment discharge calculation method most suitable to estimate sediment transport. To calibrate the quality of collected data, it was used the Pearson correlation coefficient (r), and the index of dispersion (ID) presented by Aguirre et al. (2004), which is the average of the deviations between the calculated and measured values in the field. When it was related the Qs and Q to the hydraulic and geometric parameters of the section, it was found that Q had very strong correlation (r> 0.90) with the wet area, cross-sectional width, wetted perimeter, hydraulic radius and the stage of the section. The best fit to the Qs were using the stream stage and average depth of the flow.The sediment discharge of the river was almost all wash load. The wash load particle size distribution was 57.05% of silt, 39.81% of coarse clay and 3.14% fine sand. The greater coefficient of variation was found to diameter D90 (64.31% to bed material and 73.21% to drag material. Related to particle size analysis of the bed material, it was found a predominance of sand (97.21%) and silt (2.79%), which does not differ significantly from the drag material, 97.06% sand and 2.94 % silt. After determining the rating curve of sediments, it was possible to estimate the total average of sediments discharge for the considered period, which resulted in more than 182 tons of sediment per year for the considered section. Related to procedures used to evaluate the sediment discharge, Einstein modified method was which best fit the QST measure (ID = 0.07), followed by Colby (1957), Toffaleti (1969) with ID equal to 2.04 and 3.53, respectively. To estimate the bed load discharge, the best method was Meyer-Peter & Müller (1948), resulting in a ID equal to 7.02 followed by methods of Karim (1998), Van Rijn (1984) and Cheng (2002). The methods of Modified Einstein and Colby (1957), which incorporate measured data of suspended sediment concentration (SSC), resulted in better evaluations related to sediment discharge calculated and measured. Thus, it is recommended to measure SSC and subsequently applying these two methods to determine the sediment discharge in the Vacacaí-Mirim River. / Os processos de erosão e sedimentação em uma bacia hidrográfica trazem inúmeros problemas. O conhecimento da quantidade de sedimentos transportado pelos rios é de fundamental importância para o planejamento e aproveitamento dos recursos hídricos, uma vez que os danos causados pelos sedimentos dependem da sua quantidade e natureza, os quais por sua vez, dependem dos processos de erosão, transporte e deposição. O presente trabalho teve como objetivo principal avaliar o transporte de sedimentos no rio Vacacaí-Mirim, mediante coletas realizadas na seção transversal em Restinga Sêca. Com isso, foi possível quantificar a descarga sólida média na seção transversal do rio; caracterizar a granulometria dos materiais transportados; relacionar a descarga sólida (Qs) e líquida (Q) com as características hidráulicas e geométricas da seção; e indicar os métodos de cálculo de descarga sólida mais adequados para estimar o transporte de sedimentos. Para aferir a qualidade dos dados coletados, foi utilizado o índice de correlação de Pearson (r) e o Índice de Dispersão (ID) apresentado por Aguirre et al. (2004) que representa a média dos desvios entre os valores calculados e medidos a campo. Relacionando a Qs e Q com os parâmetros hidráulicos e geométricos da seção, verificou-se que a Q teve correlação muito forte (r>0,90) com a área molhada, largura da seção transversal, perímetro molhado, raio hidráulico e a cota da seção. Os melhores ajustes da Qs foram com a cota da régua e profundidade média do escoamento. O material em suspensão correspondeu quase que a totalidade da descarga sólida no rio. A composição granulométrica deste material foi de 57,05% silte, 39,81% de argila muito grossa e 3,14% de areia muito fina. Já para o material de leito e de arraste, o maior coeficiente de variação foi encontrado para diâmetro D90, 64,31% e 73,21%, respectivamente. Da análise granulométrica do material de leito, constatou-se a predominância de areia (97,21 %) e silte (2,79 %), o que não difere significativamente do material de arraste, 97,06% de areia e 2,94 % de silte. Após a determinação da curva-chave de sedimentos, foi possível estimar a descarga sólida total média para o período considerado, que resultou em mais de 182 mil toneladas de sedimentos ano para a seção considerada. Dos procedimentos empregados para avaliar a descarga sólida, o método Einstein modificado foi o que melhor se ajustou a QST medida (ID=0,07), seguido por Colby (1957), Toffaleti (1969) com ID igual a 2,04 e 3,53 respectivamente. Já para estimar a descarga sólida de fundo, o melhor método foi o de Meyer- Peter & Müller (1948), com ID igual a 7,02 seguido dos métodos de Karim (1998), Van Rijn (1984) e Cheng (2002). Os métodos de Einstein Modificado e Colby (1957), que incorporam dados medidos de concentração de sedimentos em suspensão (Css), resultaram em melhores avaliações com relação da descarga sólida calculada e medida. Assim, recomenda-se a realização de medidas de Css e posteriormente a aplicação destes dois métodos a fim de determinar a descarga sólida no rio Vacacaí-Mirim.

This diploma thesis describes historical evolution of calculation of sphere's volume and surface and provides an analysis of textbooks for secondary and primary schools. It is made with the intention to inspire high school teachers with various approaches of teaching the volume and surface of solid bodies. It can help teachers with motivation of students as well as with selection of textbook and teaching methods for the issue. This thesis is meant to inspire high school students interested in history of mathematics, too. It includes analysis of preserved exercises on the topic from ancient Egypt and Mesopotamia as well as findings from Archimedes' works, which were devoted to this topic. Moreover it describes contribution of enlighteners on the subject and shows exact procedures of derivation of formulas using integral calculus.

<p>In this qualitative study of students’ methods of calculating subtractions, I have used interviews, subtraction exercises and analysis of teaching material. The purpose of my study was to explore which methods students in grade three uses when calculating subtractions. I also wanted to highlight which strategies the students use and their comprehension of the concept of subtraction. In the study, I also highlight the different pedagogical ideas on which the teaching material is based on and the students’ choice of methods.  The study shows that the students choose to use the methods”deduct” and “kind of number” independently. Further it also shows that the students choose to switch from the method “deduct” to “kind of number” when the numbers in the exercises are further up on the number axis. When asked, the students answered that subtraction means “minus” which they in turn explained as removing something, an explanation confirmed by the Swedish Academy dictionary. The students’ choice of methods and teaching material is based on different fundamental pedagogical view.</p><p> </p>

In this qualitative study of students’ methods of calculating subtractions, I have used interviews, subtraction exercises and analysis of teaching material. The purpose of my study was to explore which methods students in grade three uses when calculating subtractions. I also wanted to highlight which strategies the students use and their comprehension of the concept of subtraction. In the study, I also highlight the different pedagogical ideas on which the teaching material is based on and the students’ choice of methods.  The study shows that the students choose to use the methods”deduct” and “kind of number” independently. Further it also shows that the students choose to switch from the method “deduct” to “kind of number” when the numbers in the exercises are further up on the number axis. When asked, the students answered that subtraction means “minus” which they in turn explained as removing something, an explanation confirmed by the Swedish Academy dictionary. The students’ choice of methods and teaching material is based on different fundamental pedagogical view.

In the adaptive finite element method, the solution of a p.d.e. is approximated from finer and finer meshes, which are controlled by error estimators. So, starting from a given coarse mesh, some elements are subdivided a couple of times. We investigate the question of avoiding instabilities which limit this process from the fact that nodal coordinates of one element coincide in more and more leading digits. In a previous paper the stable calculation of the Jacobian matrices of the element mapping was given for straight line triangles, quadrilaterals and hexahedrons. Here, we generalize this ideas to linear and quadratic triangles on curved boundaries.

Text in Afrikaans, abstract in Afrikaans and English / Different methods of calculation of the loss of support of minor children, are investigated. According to one method (A), one first has to establish that the deceased's income was not all absorbed for his/her own maintenance. Only if there is surplus income available, it can be inferred that the deceased contributed towards the maintenance of the minor children and that the children have suffered a loss. According to another method (B) both parents' income are added and then divided between the family members. The minor child's loss of support is an amount which represent his/her share in the deceased's own income - a child automatically suffers a loss according to this method, in the event of death of a parent. Method B ought to be applied, because it is consistent with the reciprocal duty of support between spouses and the duty of spouses to maintain children. / Verskillende metodes om die verlies aan onderhoud van afhanklike kinders te bereken word ondersoek. Volgens een benadering (A) moet eers vasgestel word of die oorledene se inkomste nie alles geabsorbeer is vir sy /haar eie onderhoud nie. Slegs indien daar surplusinkomste was, kan aanvaar word dat die oorledene bygedra het tot die onderhoud van die minderjarige kinders en dat die kinders 'n verlies ly. Volgens die ander benadering (B) word beide ouers se inkomste bymekaar getel en dan tussen die gesinslede verdeel. Elke minderjarige kind se verlies aan onderhoud is 'n bedrag wat sy/haar aandeel in die oorlede ouer se afsonderlike inkomste verteenwoordig - 'n kind ly outomaties volgens hierdie metode 'n verlies. Metode B behoort meestal aanwending te vind, aangesien dit in ooreenstemming is met die wederkerige onderhoudsplig tussen gades en die plig van ouers om hul kinders te onderhou. / Private Law / LL. M. (Law)

<p>Examensarbetet handlar om en jämförelsestudie av beräkningseffektivitet med avseende på energi- och tidsförbrukning mellan grafikkort och processorer i persondatorer och PlayStation 3.</p><p>Problemet studeras för att göra allmänheten uppmärksam på att det går att lösa en del av energiproblematiken med beräkningar genom att öka energieffektiviteten av beräkningsenheterna.</p><p>Undersökningen har genomförts på ett explorativt sätt och studerar förhållandet mellan processorer, grafikkort och vilken som presterar bäst i vilket sammanhang. Prestandatest genomförs med molekylberäkningsprogrammet F@H och med filkomprimeringsprogrammet WinRAR. Testerna utförs på MultiCore- och SingleCorePCs och PS3s av olika karaktär. I vissa test mäts effektförbrukning för att kunna räkna ut hur energieffektiva vissa system är.</p><p>Resultatet visar tydligt hur den genomsnittliga effektförbrukningen och energieffektiviteten för olika testsystem skiljer sig vid belastning, viloläge och olika typer beräkningar.</p> / <p>The thesis is a comparative study of computational efficiency in terms of energy and time consumption of graphics cards and processors in personal computers and Playstation3’s.</p><p>The problem is studied in order to make the public aware that it is possible to solve some of the energy problems with computations by increasing energy efficiency of the computational units.</p><p>The audit was conducted in an exploratory way, studying the relationship between the processors, graphics cards and which one performs best in which context. Performance tests are carried out by the molecule calculating F@H-program and the file compression program WinRAR. Tests performed on MultiCore and SingleCore PC’s and PS3’s with different characteristics. In some tests power consumption is measured in order to figure out how energy-efficient certain systems are.</p><p>The results clearly show how the average power consumption and energy efficiency for various test systems at differ at load, sleep and various calculations.</p><p> </p>

Text in Afrikaans, abstract in Afrikaans and English / Different methods of calculation of the loss of support of minor children, are investigated. According to one method (A), one first has to establish that the deceased's income was not all absorbed for his/her own maintenance. Only if there is surplus income available, it can be inferred that the deceased contributed towards the maintenance of the minor children and that the children have suffered a loss. According to another method (B) both parents' income are added and then divided between the family members. The minor child's loss of support is an amount which represent his/her share in the deceased's own income - a child automatically suffers a loss according to this method, in the event of death of a parent. Method B ought to be applied, because it is consistent with the reciprocal duty of support between spouses and the duty of spouses to maintain children. / Verskillende metodes om die verlies aan onderhoud van afhanklike kinders te bereken word ondersoek. Volgens een benadering (A) moet eers vasgestel word of die oorledene se inkomste nie alles geabsorbeer is vir sy /haar eie onderhoud nie. Slegs indien daar surplusinkomste was, kan aanvaar word dat die oorledene bygedra het tot die onderhoud van die minderjarige kinders en dat die kinders 'n verlies ly. Volgens die ander benadering (B) word beide ouers se inkomste bymekaar getel en dan tussen die gesinslede verdeel. Elke minderjarige kind se verlies aan onderhoud is 'n bedrag wat sy/haar aandeel in die oorlede ouer se afsonderlike inkomste verteenwoordig - 'n kind ly outomaties volgens hierdie metode 'n verlies. Metode B behoort meestal aanwending te vind, aangesien dit in ooreenstemming is met die wederkerige onderhoudsplig tussen gades en die plig van ouers om hul kinders te onderhou. / Private Law / LL. M. (Law)

Examensarbetet handlar om en jämförelsestudie av beräkningseffektivitet med avseende på energi- och tidsförbrukning mellan grafikkort och processorer i persondatorer och PlayStation 3. Problemet studeras för att göra allmänheten uppmärksam på att det går att lösa en del av energiproblematiken med beräkningar genom att öka energieffektiviteten av beräkningsenheterna. Undersökningen har genomförts på ett explorativt sätt och studerar förhållandet mellan processorer, grafikkort och vilken som presterar bäst i vilket sammanhang. Prestandatest genomförs med molekylberäkningsprogrammet F@H och med filkomprimeringsprogrammet WinRAR. Testerna utförs på MultiCore- och SingleCorePCs och PS3s av olika karaktär. I vissa test mäts effektförbrukning för att kunna räkna ut hur energieffektiva vissa system är. Resultatet visar tydligt hur den genomsnittliga effektförbrukningen och energieffektiviteten för olika testsystem skiljer sig vid belastning, viloläge och olika typer beräkningar. / The thesis is a comparative study of computational efficiency in terms of energy and time consumption of graphics cards and processors in personal computers and Playstation3’s. The problem is studied in order to make the public aware that it is possible to solve some of the energy problems with computations by increasing energy efficiency of the computational units. The audit was conducted in an exploratory way, studying the relationship between the processors, graphics cards and which one performs best in which context. Performance tests are carried out by the molecule calculating F@H-program and the file compression program WinRAR. Tests performed on MultiCore and SingleCore PC’s and PS3’s with different characteristics. In some tests power consumption is measured in order to figure out how energy-efficient certain systems are. The results clearly show how the average power consumption and energy efficiency for various test systems at differ at load, sleep and various calculations.