AMF Fastigheter is shortly for the procurement of a waste contractor for all of its commercial properties. The investigation will identify the problem of how the waste is handled in shopping centers and inform AMF Fastigheter about how this can be improved. Through study visits and interviews, necessary information is gathered to make concrete proposals. A comprehensive analysis of the waste generated in the properties describes in the report that large waste volumes consist of combustible. The authors provide suggestions on how this can be avoided, as well as highlighting fractions that should be recycled to a greater extent. According to the authors, there may be problems about the waste contractors' intentions in the properties visited, as recycling is not a priority. The human factor is considered to be a major problem where it is difficult to achieve long-term changes in tenants' behavior regarding waste sorting. Initial explanation of these issues is presented in the report and details that the property owner should consider in the procurement of waste contractor. / AMF Fastigheter står inom kort inför upphandling av en avfallsentreprenör för samtliga av sina kommersiella fastigheter. Utredningen ska identifiera problematiken i hur avfallet hanteras i köpcentrum och upplysa AMF Fastigheter om hur detta kan förbättras. Genom studiebesök och intervjuer samlas nödvändig information för att komma med konkreta förslag. En övergripande analys av det avfall som uppstår i fastigheterna beskriver i rapporten att stora avfallsvolymer består av brännbart. Författarna ger i rapporten förslag på hur detta kan undvikas, samt lyfter fram fraktioner som bör återvinnas i större utsträckning. Enligt författarna kan det finnas problem kring avfallsentreprenörernas intentioner i de besökta fastigheterna då återvinning prioriteras för lite. Den mänskliga faktorn upplevs vara en stor problematik där det är svårt att nå långsiktiga förändringar kring hyresgästernas beteende och avfallssortering. Ingående förklaring om dessa problem presenteras i rapporten samt detaljer fastighetsägaren ska tänka på vid upphandling av avfallsentreprenör.

As procedural flexibility, previously understood as adaptive reasoning, emerges as an important consideration in math skill development, it is important to account for executive functioning in that process as well, as executive functioning a well-researched factor in math performance. The current study, a secondary data analysis, explores how students rate themselves on the Executive Skills Questionnaire – Revised (ESQ-R), an informal executive skills measure, and how those scores relate to procedural flexibility scores, which accounts for students’ efficiency in math problem solving. Using the factor structure relevant to the current sample, which varies significantly from the current ESQ-R, findings indicate that procedural flexibility is lower in seventh grade when compared to sixth and eighth grades. Perceived executive skills vary positively across sixth, seventh, and eighth grades, indicating more perceived difficulties with executive skills as students move up in grade. Additional analyses explored the relationships between procedural flexibility and ESQ-R scores. Although there was no evidence of a significant relationship between procedural flexibility and ESQ-R scores, the relationship varied across grade level, yielding a negative relationship for sixth grade, a neutral relationship fore seventh grade, and a positive relationship for eighth grade. This pattern indicates that procedural flexibility may become more readily demonstrated, and possibly more valuable, as students gain mastery of skills and procedures and students may become more critical of their executive skills. Procedural flexibility is also highly sensitive to context and curriculum, based on the Common Core State Standards for Mathematics. / School Psychology

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This study investigated three pre-service elementary teachers' understanding of fractions and fraction multiplication and division. The motivation for this study was lack of conceptual understanding of fractions and fraction multiplication and division. Pre-service elementary teachers were chosen because teachers are the conduit of information for their students. The subjects were followed through the fractions unit in a mathematics methods course for pre-service elementary teachers at Brigham Young University. Each subject volunteered to participate and were interviewed and videotaped throughout the study, and they also provided copies of all work done in the fractions unit in the course. The data is presented as three case studies, each beginning with a discussion of the subject's math history and prior understanding of fractions. Then the case studies discuss the subject's change in understanding of fractions, fraction multiplication, and fraction division. Finally, at the end of each case study, a discussion of the subject's conceptual understanding is discussed. Each participant showed a deepened conceptual understanding of fractions, fraction multiplication, and fraction division. The subjects' prior knowledge of fractions and fraction multiplication and division did affect their growth of understanding. Each participant had unique levels of growth and inhibitors to growth of understanding. At the times of most growth of understanding, the subjects' inhibitors of growth were also the most evident.

This study examined the use of the set, area, and linear models of fraction representation to enhance elementary students' conceptual understanding of fractions. Students' preferences regarding the set, area, and linear models of fractions during independent work was also investigated. This study took place in a 5th grade class consisting of 21 students in a suburban public elementary school. Students participated in classroom activities which required them to use manipulatives to represent fractions using the set, area, and linear models. Students also had experiences using the models to investigate equivalent fractions, compare fractions, and perform operations. Students maintained journals throughout the study, completed a pre and post assessment, participated in class discussions, and participated in individual interviews concerning their fraction model preference. Analysis of the data revealed an increase in conceptual understanding. The data concerning student preferences were inconsistent, as students' choices during independent work did not always reflect the preferences indicated in the interviews.

The purpose of this action research study was to evaluate my own practice of teaching writing word problems with fraction subtraction and fraction multiplication using appropriate context. I wanted to see how focusing my instruction on the use of the area model and manipulatives could develop students’ understanding of fractions when writing word problems. I chose this topic because Florida has adopted the Common Core State Standards and will be implementing them in the coming years. These standards encourage the development of deeper understanding of mathematics, including fractions. I hoped this research would give my students the opportunity to make sense of fraction subtraction and fraction multiplication word problems on a deeper level, while giving me insight into my own practice in teaching context within word problems. Through this study, I learned that my students continued to switch the context of subtraction with multiplication within word problems. Students did make clear gains in their writing of fraction subtraction and fraction multiplication word problems. Although there is a limited amount of research on students mixing their context within fraction word problems, this study offers additional insight into a teacher’s practice with writing fraction word problems

This study examined the effects of a ratio-based supplemental teaching sequence on third grade students‘ equivalent fraction performance as measured by a curriculum-based measure and a standardized test. Participants included students identified as being learning disabled in mathematics (MLD), struggling (SS), or typically achieving (TA). Nineteen students were assigned to the experimental group and 19 additional students formed the control group. The difference between the two groups was that the experimental group received the ratio-based teaching sequence. Both groups continued to receive textbook based instruction in fraction equivalency concepts in their regular mathematics classroom. Qualitative interviews were employed to further investigate the thinking of each of the three types of students in the study. Analyses of the data indicated that students in the experimental group outperformed the control group on both the curriculum-based measure and the standardized measure of fraction equivalency. All students who participated in ratio-based instruction had a higher performance in fraction equivalency than those who did not. Performance on the CBM and the standardized measure of fraction equivalency improved significantly from pre to post test for students who struggled; their performance also transferred to standardized measures. Qualitative analyses revealed that a focal student with MLD, while improving his ability to think multiplicatively, had misconceptions about fractions as ratios that persisted even after the intervention was completed. Implications for instruction, teacher preparation, and future research are provided

Within a low-performing seventh grade mathematics classroom, communication techniques including discourse, collaborative groups, listening, reading, and writing were implemented during a six week period. This study shows how the use of these techniques led to the twenty four students' conceptual understanding of fraction and decimal concepts. This research study provides insight to the deep-seeded beliefs of low-performing students. It provides a record of how the teacher used communication techniques in the classroom and had a strong positive impact on the attitudes and performance of these struggling students.

<p>The main focus of this dissertation is to find and explain the periodic points of certain algebraic functions that are related to some modular functions, which themselves can be represented by continued fractions. Some of these continued fractions are first explored by Srinivasa Ramanujan in early 20th century. Later on, much work has been done in terms of studying the continued fractions, and proving several relations, identities, and giving different representations for them.</p> <p><br></p> <p>The layout of this report is as follows. Chapter 1 has all the basic background knowledge and ingredients about algebraic number theory, class field theory, Ramanujan’s theta functions, etc. In Chapter 2, we look at the Ramanujan-Göllnitz-Gordon continued fraction that we call v(τ) and evaluate it at certain arguments in the field K = Q(√−d), with −d ≡ 1 (mod 8), in which the ideal (2) = ℘₂℘′₂  is a product of two prime ideals. We prove several identities related to itself and with other modular functions. Some of these are new, while some of them are known but with different proofs. These values of v(τ) are shown to generate the inertia field of ℘₂ or ℘′₂ in an extended ring class field over the field K. The conjugates over Q of these same values, together with 0, −1 ± √2, are shown to form the exact set of periodic points of a fixed algebraic function ˆF(x), independent of d. These are analogues of similar results for the Rogers-Ramanujan continued fraction. See [1] and [2]. This joint work with my advisor Dr. Morton, is submitted for publication to the New York Journal.</p> <p><br> In Chapters 3 and 4, we take a similar approach in studying two more continued fractions c(τ) and u(τ), the first of which is more commonly known as the Ramanujan’s cubic continued fraction. We show what fields a value of this continued fraction generates over Q, and we describe how the periodic points for described functions arise as values of these continued fractions. Then in the last chapter, we summarise all these results, give some possible directions for future research as well as mentioning some conjectures.</p>

Planning, scheduling and real time optimization (RTO) are currently implemented by using different types of models, which causes discrepancies between their results. This work presents a single model of a crude distillation unit (preflash, atmospheric, and vacuum towers) suitable for all of these applications, thereby eliminating discrepancies between models used in these decision processes. Hybrid model consists of volumetric and energy balances and partial least squares model for predicting product properties. Product TBP curves are predicted from feed TBP curve, operating conditions (flows, pumparound heat duties, furnace coil outlet temperatures). Simulated plant data and model testing have been based on a rigorous distillation model, with 0.5% RMSE over a wide range of conditions. Unlike previous works, we do not assume that (i) midpoint of a product TBP curve lies on the crude distillation curve, and (ii) midpoint between the back-end and front-end of the adjacent products lies on the crude distillation curves, since these assumptions do not hold in practice. Associated properties (e.g. gravity, sulfur) are computed for each product based on its distillation curve. Model structure makes it particularly amenable for development from plant data. High model accuracy and its linearity make it suitable for optimization of production plans or schedules. / Thesis / Master of Applied Science (MASc)