Ce travail introduit la notion de schéma d'Atiyah et Hitchin. Une variété algébrique raisonnable Y étant fixée, il s'agit d'une famille de nouveaux schémas, indexée par un entier positif m et notée $R_m(Y)$. Nous étudions les propriétés homotopiques de ces « espaces » au sens de Morel et Voevodsky. Les schémas $F_m$ des fractions rationnelles pointées de degré m constituent un exemple fondateur et fondamental. Du point de vue topologique, les travaux de G. Segal et F. Cohen et al. montrent que l'espace $F_m(C)$ approxime l'espace de lacets $Ω^2 S^3$. Nous formulons une série précise de conjectures visant à généraliser ces résultats dans un cadre algébrique. Le schéma $R_m(Y)$ approximerait l'espace de lacets motivique $Ω^{P¹} Σ^{P¹} Y$. Nous obtenons plusieurs résultats dans cette direction. En particulier : 1) Nous déterminons l'ensemble des composantes connexes algébriques naïves du schéma de fractions rationnelles $F_m$, au-dessus d'un corps de base. Le calcul est simple et élémentaire. On retrouve, à une complétion près, le groupe des classes d'homotopie d'endomorphismes pointés de la droite projective $P¹$, tel que calculé par Morel. 2) Nous construisons un morphisme algébrique reliant $R_mY$ à $Ω^{P¹} Σ^{P¹} Y$. 3) Lorsque Y est une variété algébrique complexe, nous explicitons le type d'homotopie de l'espace topologique $R_m(Y)(C)$ comme un foncteur en $Y(C)$. De plus, nous montrons que l'espace $R_m(Y)(C)$ admet un scindement stable dont les facteurs sont ceux du scindement de Snaith de l'espace $Ω² Σ² Y (C)$.

Over the course of normal oil well operations, pipes used downhole in the oil and petroleum industry tend to accumulate a mineral deposit on their interior, which restricts the flow of oil. This deposit, termed scale, will eventually occlude the interior diameter of the pipe making removal from service and descaling a cost effective option. The pipes are sent to cleaning yards where they remain until descaling can be performed. This storage period can potentially create a health concern not only because of the external radiation exposure but also because of the radon gas emissions, both of which are due to the radioactive minerals contained in the scale. It was believed that the structure of the scale is formed tightly enough to prevent much of the radon from becoming airborne. The goal of this research was to determine the emanation fractions for the rattled scale samples from three formations. A high purity germanium detector was used to measure the activities of the parents and progeny of radon, and electret ion chambers were used to measure the concentration of radon emanated from the scale. The emanation fractions of between 4.9x10-5 and 1.08x10-3 for radon were a factor of approximately 100 smaller than previous research results. For thoron, the fractions were and 5.72x10-8 and 4.92x10-7 for thoron with no previous research to compare. However, information that pertains to the temperature dependence of emanation was included in this research and was not available for previous, similar research. Therefore, differences in the environment (e.g., temperature, humidity, etc.) in which the previous experiments were conducted, as well as differences in the scale formation types used, could account for the discrepancy. In addition, measuring the emanation fractions of the rattled scale was a method of determining whether surface to volume ratio dependence existed. After acquiring the emanation fractions, insufficient evidence of any surface to volume ratio dependence could be found.

The goal of this study is to align teachers’ Mathematical Knowledge for Teaching (MKT) with their classroom instruction. To reduce the classroom complexity while keeping the connection between teaching and learning, I focused on Teacher Responses to Student Errors and Difficulties (TRED) in teaching equivalent fractions with an eye on students’ cognitive gains as the assessment of teaching effects. This research used a qualitative paradigm. Classroom videos concerning equivalent fractions from six teachers were observed and triangulated with tests of teacher knowledge and personal interviews. The data collection and analysis went through a naturalistic inquiry process. The results indicated that great differences about TRED existed in different classrooms around six themes: two learning difficulties regarding critical prior knowledge; two common errors related to the learning goal, and two emergent topics concerning basic mathematical ideas. Each of these themes affected students’ cognitive gains. Teachers’ knowledge as reflected by teacher interviews, however, was not necessarily consistent with their classroom instruction. Among these six teachers, other than one teacher whose knowledge obviously lagged behind, the other five teachers demonstrated similar good understanding of equivalent fractions. With respect to the basic mathematical ideas, their knowledge and sensitivity showed differences. The teachers who understood equivalent fractions and also the basic mathematical ideas were able to teach for understanding. Based on these six teachers’ practitioner knowledge, a Mathematical Knowledge Package for Teaching (MKPT) concerning equivalent fractions was provided as a professional knowledge base. In addition, this study argued that only when teachers had knowledge bases with strong connections to mathematical foundations could they flexibly activate and transfer their knowledge (CCK and PCK) to their use of knowledge (SCK) in the teaching contexts. Therefore, further attention is called for in collaboratively cultivating teachers’ mathematical sensitivity.

This thesis work was made for Södra Cell Mörrums bruk in Blekinge. The purpose of the work was to develop a computer model in the simulation program Extend for the removal and balance of organic oxygen consuming substances, measured as COD (Chemical Oxygen Demand), in the new biological treatment plant in the mill. The plant produces two different pulp products, TCF- (Totally Chlorine Free) pulp and ECF- (Elementary Chlorine Free) pulp, for sale. The different bleaching procedures affect the characteristic of the wastewater and thus the effectiveness of the biological treatment plant. In the model that was developed the COD in the wastewater was divided into five different COD-fractions: soluble easily degradable (SS), soluble hardly degradable (SR), soluble inert (SI), particulate inert (XI) and particulate biomass (XB). To create the model FlowMac™ was used as a base. FlowMac™ is a library module in Extend adapted for pulp and paper mills. Some of the blocks only needed a slight modification while others, for example the sedimentation basin and the bioblocks, had to be done from scratch. The calibration of the model was made from data from a period of eleven weeks and a validation was made from data that differed as much as possible from the calibration data. Then the model was used to find out in what way an increase in production to 480 000 annual tons should affect the discharge of organic oxygen consumption substances. Results from the model indicates that the goals for the total COD-discharge will be hard to achieve with an increase in production to 480 000 annual tons. Despite the fact that production of TCF-pulp generates more COD than ECF-production the total discharge of COD is lower at TCF-production. The reason is that easier degradable COD is generated in TCF-bleaching. One of the major problems is that the torrent of water that is bypassed the biological treatment plant contains a large amount of COD and the efficiency of the treatment plant must be very high if the goals for the total COD-discharge shouldn’t be exceeded. / Det här examensarbetet gjordes för Södra Cell på Mörrums Bruk i Blekinge. Arbetet bestod i att göra en modell i simuleringsprogrammet Extend över nedbrytningen och massbalansen av organiska syreförbrukande ämnen, mätt som COD (Chemical Oxygen Demand), i den nybyggda biologiska reningsanläggningen på bruket. Mörrums bruk är en sulfatmassafabrik som producerar både TCF- (Totally Chlorine Free) och ECF- (Elementary Chlorine Free) massa för avsalu. De olika blekningsmetoderna påverkar sammansättningen på avloppsvattnet och därmed också den biologiska reningsanläggningens reduktion av COD. I modellen som utvecklades delades inkommande COD i obehandlat vatten upp i fem olika COD-fraktioner: löst lättnedbrytbart (SS), löst svårnedbrytbart (SR), löst inert (SI), partikulärt inert (XI) och partikulärt nedbrytbart COD i form av biomassa (XB). För att bygga modellen användes FlowMac™ som utgångspunkt. FlowMac™ är en biblioteksmodul i Extend avpassad för pappersbruk. En del block behövde bara modifieras medan andra block, t.ex. sedimenteringen och bioblocken, fick byggas till. Modellen kalibrerades med medelvärden från en elvaveckorsperiod och en validering gjordes med data från några veckor med mer extrema värden på inkommande vatten. Med modellen gjordes en simulering för att undersöka vad en produktionsökning till 480 000 årston skulle innebära med avseende på utsläppen av organiska syreförbrukande ämnen. Resultat från modellen tyder på att det vid en ökning av produktionen till 480 000 årston blir svårt att nå de uppställda totala utsläppsmålen för COD. Vid produktion av TCF-massa bildas mer COD men utsläppsmängderna är lägre än vid ECF-produktion. Anledningen är att den COD som bildas ut vid TCF-blekning innehåller en större mängd lättnedbrytbart COD. En bidragande orsak till att det blir svårt att hålla utsläppsmålen för COD är att de flöden som leds förbi reningsanläggningen innehåller mycket COD vilket gör att verkningsgraden över reningsanläggningen måste vara hög för att klara målen för totala COD-utsläppet.

The goal of this study is to align teachers’ Mathematical Knowledge for Teaching (MKT) with their classroom instruction. To reduce the classroom complexity while keeping the connection between teaching and learning, I focused on Teacher Responses to Student Errors and Difficulties (TRED) in teaching equivalent fractions with an eye on students’ cognitive gains as the assessment of teaching effects. This research used a qualitative paradigm. Classroom videos concerning equivalent fractions from six teachers were observed and triangulated with tests of teacher knowledge and personal interviews. The data collection and analysis went through a naturalistic inquiry process. The results indicated that great differences about TRED existed in different classrooms around six themes: two learning difficulties regarding critical prior knowledge; two common errors related to the learning goal, and two emergent topics concerning basic mathematical ideas. Each of these themes affected students’ cognitive gains. Teachers’ knowledge as reflected by teacher interviews, however, was not necessarily consistent with their classroom instruction. Among these six teachers, other than one teacher whose knowledge obviously lagged behind, the other five teachers demonstrated similar good understanding of equivalent fractions. With respect to the basic mathematical ideas, their knowledge and sensitivity showed differences. The teachers who understood equivalent fractions and also the basic mathematical ideas were able to teach for understanding. Based on these six teachers’ practitioner knowledge, a Mathematical Knowledge Package for Teaching (MKPT) concerning equivalent fractions was provided as a professional knowledge base. In addition, this study argued that only when teachers had knowledge bases with strong connections to mathematical foundations could they flexibly activate and transfer their knowledge (CCK and PCK) to their use of knowledge (SCK) in the teaching contexts. Therefore, further attention is called for in collaboratively cultivating teachers’ mathematical sensitivity.

In this thesis, four different crude oil samples and their saturate, aromatic and resin fractions were analyzed by two different thermoanalytical methods, thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). The experiments were performed at three different heating rates (5, 10 and 15 &deg / C/min) under air atmosphere. Same gas flow rate and same pressure were applied to all samples. The aim is to determine the kinetic analysis and combustion behavior of crude oils and their fractions and also determining the effect of heating rate on all samples. For all samples two main reaction regions were observed in thermogravimetry (TG), differential thermogravimetry (DTG) and DSC curves due to the oxidative degradation of crude oil components. It was deduced that the free moisture, volatile hydrocarbons were evaporated from the crude oils, light hydrocarbons were burned and fuel was formed in the first reaction region. The second reaction region was the main combustion region where the fuel was burned. From the TGA curves, it was detected that the heavier fraction, resins, lost considerable amounts of their initial mass, approximately 35%, while saturates lost only approximately 3% of their initial mass in the second reaction region. DSC curves of the samples were also examined and observed that as the sample got heavier, the heat of the reaction increased. Saturates, lightest part of the crude oil fractions, gave minimum heat of reaction. As the heating rate increased, shift of peak temperatures to high values and higher reaction regions were observed. The kinetic analysis of crude oils and their fractions were also performed using different kinetic methods. Activation energies (E), mean activation energies (Emean) and Arrhenius constants were found for crude oils and fractions. It was deduced that the resins gave the highest activation energy and Arrhenius constant for both reaction regions. Moreover, it was encountered that heating rate has no effect on activation energies.

The purpose of this study was to investigate mistakes made by elementary fifth grade students regarding basic fractional concepts and operations, and difficulties that they encounter. The other purpose was to investigate underlying misconceptions and reasons of those difficulties and mistakes. For this purpose, a mixed-method research combining quantitative and qualitative approach respectively was performed. Data were collected from elementary fifth grade students at the end of the spring semester of 2009-2010. Operation with Fraction Questionnaire (OFQ) was administered to 151 fifth grade students who were chosen from the two public elementary schools in Eskisehir province. By this way, difficulties that elementary fifth grade students encounter and mistakes they make regarding basic fractionalconcepts and operations was analyzed. Afterwards, sixteen of these students participated in a semi-structured interview which was designed to investigate underlying reasons and misconceptions behind those mistakes and difficulties. Results were presented in two phases. In the first phase, common mistakes and difficulties of students were analyzed in detail and representative examples of these errors were introduced. In the second phase, students&#039 / mistakes were grouped under five categories as: algorithmically based mistakes, intuitively based mistakes, mistakes based on formal knowledge on fractions, misunderstanding on problem, and missing information in solution. In this phase, misconceptions and underlying reasons of those mistakes and difficulties which students may encounter while learning fractions were described. Results revealed that there was evidence that fifth grade students made various mistakes regarding fractional concepts and operations in the fifth grade elementary mathematics curriculum and they had many misconceptions regarding fraction concepts and operations.

This study examined teachers' learning and understanding of mathematical representation through the Middle School Mathematics Project (MSMP) professional development, investigated teachers' use of mathematics representations in teaching fractions and algebraic functions, and addressed patterns of teachers' changes in learning and using representation corresponding to Teachers' Zone of Proximal Development (TZPD). Using a qualitative research design, data were collected over a 2-year period, from eleven participating 6th and 7th grade mathematics teachers from four school districts in Texas in a research-designed professional development workshop that focused on helping teachers understand and use of mathematical representations. Teachers were given two questionnaires and had lessons videotaped before and after the workshop, a survey before the workshop, and learning and discussion videotapes during the workshop. In addition, ten teachers were interviewed to find out the patterns of their changes in learning and using mathematics representations. The results show that all teachers have levels of TZPD which can move to a higher level with the help of capable others. Teachers' knowledge growth is measurable and follows a sequential order of TZPD. Teachers will make transitions once they grasp the specific content and strategies in mathematics representation. The patterns of teacher change depend on their learning and use of mathematics representations and their beliefs about them. This study advocates teachers using mathematics representations as a tool in making connections between concrete and abstract understanding. Teachers should understand and be able to develop multiple representations to facilitate students' conceptual understanding without relying on any one particular representation. They must focus on the conceptual developmental transformation from one representation to another. They should also understand their students' appropriate development levels in mathematical representations. The findings suggest that TZPD can be used as an approach in professional development to design programs for effecting teacher changes. Professional developers should provide teachers with opportunities to interact with peers and reflect on their teaching. More importantly, teachers' differences in beliefs and backgrounds must be considered when designing professional development. In addition, professional development should focus on roles and strategies of representations, with ongoing and sustained support for teachers as they integrate representation strategies into their daily teaching.

Over the course of normal oil well operations, pipes used downhole in the oil and petroleum industry tend to accumulate a mineral deposit on their interior, which restricts the flow of oil. This deposit, termed scale, will eventually occlude the interior diameter of the pipe making removal from service and descaling a cost effective option. The pipes are sent to cleaning yards where they remain until descaling can be performed. This storage period can potentially create a health concern not only because of the external radiation exposure but also because of the radon gas emissions, both of which are due to the radioactive minerals contained in the scale. It was believed that the structure of the scale is formed tightly enough to prevent much of the radon from becoming airborne. The goal of this research was to determine the emanation fractions for the rattled scale samples from three formations. A high purity germanium detector was used to measure the activities of the parents and progeny of radon, and electret ion chambers were used to measure the concentration of radon emanated from the scale. The emanation fractions of between 4.9x10-5 and 1.08x10-3 for radon were a factor of approximately 100 smaller than previous research results. For thoron, the fractions were and 5.72x10-8 and 4.92x10-7 for thoron with no previous research to compare. However, information that pertains to the temperature dependence of emanation was included in this research and was not available for previous, similar research. Therefore, differences in the environment (e.g., temperature, humidity, etc.) in which the previous experiments were conducted, as well as differences in the scale formation types used, could account for the discrepancy. In addition, measuring the emanation fractions of the rattled scale was a method of determining whether surface to volume ratio dependence existed. After acquiring the emanation fractions, insufficient evidence of any surface to volume ratio dependence could be found.

Woodlot and natural woodland systems in the semi-arid regions in Tanzania are believed to have a high potential to sequester carbon (C) in their biomass and the soil which may qualify for C credits under the current voluntary C market schemes like, the REDD program. However, our understanding of the processes influencing storage and dynamics of C in soils under semi-arid agroforestry systems such as these woodlot systems is limited. This study evaluated C pools in soil and tree biomass in woodlot species of Albizia lebbeck, Leucaena leucocephala, Melia azedarach, and Gmelina arborea; and in farmland and ngitili systems. Synchrotron-based C K-edge x-ray absorption near-edge structure (XANES) spectroscopy was also used to study the influence of these land use systems on the soil organic matter (SOM) chemistry to understand the mechanisms of soil C changes. Soil samples were collected to 1 m depth and subsamples for each land use system to 0.4 m depth were fractionated into macroaggregates (2000-250 μm), microaggregates (250-53 μm), and silt and clay-sized aggregates (<53 μm) to provide information of C dynamics and stabilization in various land uses. SOC was analyzed in whole and soil aggregates and biomass C was estimated using developed biomass models from the literatures. Aboveground biomass carbon in the woodlots from the Kahama district ranged from 11.76 Mg C ha-1 to 24.40 Mg C ha-1. Based on the age of woodlots and the rate of carbon sequestration potential (CSP), Gmelina arborea had the highest rate of aboveground C sequestration (3.59 Mg C ha-1 year-1). The SOC stocks in whole soil for the land use systems from the two districts ranged from 43-67 Mg C ha-1. The degraded ngitili did not show a reduction in SOC stocks despite reducing aboveground biomass C stocks by 15.11 Mg C ha-1. SOC in the woodlots were found to be associated more with the micro and silt-and clay-sized aggregates than the macroaggregates, reflecting high stability of SOC in the woodlot systems. The XANES C K-edge spectra revealed the stabilization of recalcitrant aromatic C compounds in the silt and clay-sized aggregates. This study demonstrates the significant contributions of woodlots in biomass C accumulation as well as long-term SOC stabilization in soil fractions. Thus, these agroforestry practices hold promise to meet household energy needs while contributing to climate change mitigation and adaption.