A multipoint Padë approximant, R, to a function of Stieltjes1 type is determined.The function R has numerator of degree n-l and denominator of degree n.The 2n interpolation points must belong to the region where f is analytic,and if one non-real point is amongst the interpolation points its complex-conjugated point must too.The problem is to characterize R and to find some convergence results as n tends to infinity. A certain kind of continued fraction expansion of f is used.From a characterization theorem it is shown that in each step of that expansion a new function, g, is produced; a function of the same type as f. The function g is then used,in the second step of the expansion,to show that yet a new function of the same type as f is produced. After a finite number of steps the expansion is truncated,and the last created function is replaced by the zero function.It is then shown,that in each step upwards in the expansion a rational function is created; a function of the same type as f.From this it is clear that the multipoint Padê approximant R is of the same type as f.From this it is obvious that the zeros of R interlace the poles, which belong to the region where f is not analytical.Both the zeros and the poles are simple. Since both f and R are functions of Stieltjes ' type the theory of Hardy spaces can be applied (p less than one ) to show some error formulas.When all the interpolation points coincide ( ordinary Padé approximation) the expected error formula is attained. From the error formula above it is easy to show uniform convergence in compact sets of the region where f is analytical,at least wien the interpolation points belong to a compact set of that region.Convergence is also shown for the case where the interpolation points approach the interval where f is not analytical,as long as the speed qî approach is not too great. / digitalisering@umu

This research was initiated after a 100-year flood caused an oil spill on the San Jacinto River (Houston, Texas) in October of 1994. After the floodwaters subsided the released petroleum floating on the water was deposited on the surrounding lands. The petroleum spill was used as an opportunity to research intrinsic petroleum biodegradation in a 9-acre petroleum impacted estuarine wetland. The first phase of this research (Phase I) began in December 1994, approximately 1.5 months after the spill of opportunity and involved the study and quantification of in-situ petroleum biodegradation. The second phase of the research (Phase II) began in March 1996 with a controlled oil release to study and evaluate the success of two bioremediation treatments versus natural biodegradation. The study of in-situ petroleum hydrocarbon degradation and the evaluation of bioremediation amendments were successfully quantified using GC-MS analytical techniques. However, the GC-MS technique is limited to the analyses of hydrocarbon compounds, a disadvantage that precludes the overall characterization of petroleum degradation. The research presented here details an analytical technique that was used to provide a full characterization of temporal petroleum biodegradation. This technique uses thin layer chromatography coupled with flame ionization detection (TLC-FID) to characterize the saturate and aromatic (hydrocarbon) fractions and the resin and asphaltene (non-hydrocarbon, polar) fractions. Other analysis techniques, such as HPLC-SARA analysis, are available for the full characterization of the four petroleum fractions. However, these techniques do not lend themselves well to the application of large sample set analysis. A significant advantage of the TLC-FID analysis to other petroleum analysis techniques is the ability to analyze several samples concurrently and quickly with relative ease and few resources. For the purposes of the Phase I and Phase II research the TLC-FID analysis method was evaluated, refined and applied to quantify the temporal biodegradation and bioremediation of petroleum. While the TLC-FID analysis produces a full characterization, it cannot supplant the GC-MS analysis for petroleum bioremediation research. However, it can be used in conjunction with the GC-MS to expand the knowledge of petroleum bioremediation and remediation strategies.

La thèse est consacrée aux divers problèmes de la théorie des systèmes dynamiques. On commence par étudier l'intégrabilité méromorphe du problème des trois corps. Alors, la renormalisation des applications unimodales asymétriques est analysée. Quelques résultats dans la théorie des fractions continues sont exposés y compris la réponse à une conjecture de Ramanujan sur les fractions infini-périodiques.

The purpose of this study was to investigate the effects of a web-based strategic, interactive computer application (Fun Fraction) on the ability of middle school students with LD, who have mathematics goals on their IEPs, to solve word problems with fractions and multiplication including two factors of a whole number (less than or equal to 4) and proper fractions. A multiple-probe single case research design across subjects was applied for the study. Three middle school students with learning disabilities participated in baseline, intervention, and maintenance test sessions over a 13-week period. Findings showed that there was an experimental effect for all three students, tested on their instructional probes; students' performance improved from baseline to intervention phases after receiving instruction through Fun Fraction. John and Alec reached the mastery level of 80% on two of the three review days. The level of change from baseline to intervention phases ranged from 28.67% to 68.89%. Even through there was no immediacy effect for John, the trend of his data (10.33) revealed a substantial growth in general. Additionally, the percentage of data showing improvement between baseline and intervention phases was 70% for Tiffany, 56% for John, and 100% for Alec. In particular, the improvement trend of Alec's data was statistically significant (Tau[subscript novlap] = 1, p < .05, CI 90% = .341<>1.659). All of them reached 80% accuracy percentage on their one-time maintenance tests. Regarding the three problem types of combine, partition, and compare for each representation and equation question, students struggled the most with combine representation questions and showed relatively better competence in compare equation questions. A learning-related social validity questionnaire and usability questionnaire indicated that students liked learning through Fun Fraction and recognized well the useful interaction design features embedded in Fun Fraction. Cognitive and metacognitive strategy questionnaires also indicated that students liked the represent strategy that allowed students to manipulate the rectangular area model, and students expressed positive views on the thinking process through metacognitive strategies embedded in Fun Fraction. / text

published_or_final_version / Educational Psychology / Master / Master of Social Sciences

No description available.

In this dissertation we investigate prior definitions for p-adic continued fractions and introduce some new definitions. We introduce a continued fraction algorithm for quadratic irrationals, prove periodicity for Q₂ and Q₃, and numerically observe periodicity for Q(p) when p < 37. Various observations and calculations regarding this algorithm are discussed, including a new type of symmetry observed in many of these periods, which is different from the palindromic symmetry observed for real continued fractions and some previously defined p-adic continued fractions. Other results are proved for p-adic continued fractions of various forms. Sufficient criteria are given for a class of p-adic continued fractions of rational numbers to be finite. An algorithm is given which results in a periodic continued fraction of period length one for √D ∈ Zˣ(p), D ∈ Z, D non-square; although, different D require different parameters to be used in the algorithm. And, a connection is made between continued fractions and de Weger’s approximation lattices, so that periodic continued fractions can be generated from a periodic sequence of approximation lattices, for square roots in Zˣ(p). For simple p-adic continued fractions with rational coefficients, we discuss observations and calculations related to Browkin’s continued fraction algorithms. In the last chapter, we apply some of the definitions and techniques developed in the earlier chapters for Q(p) and Z to the t-adic function field case F(q)((t)) and F(q)[t], respectively. We introduce a continued fraction algorithm for quadratic irrationals in F(q)((t)) that always produces periodic continued fractions.

The Third International Assessment of Educational Progress (TIMMS) and the Programme for International Student Assessment (PISA) during the last decades regarding the results of mathematics teaching shows that China have a better performance than Sweden’s.Swedish teacher-guidelines focus on developing student’s individual interest and confidence for mathematics. In the Chinese teaching-guidelines for Mathematics Curriculum Standards, Ordninary Senior Secondary, the focus is given on: Elevate their mathematics literacy necessary for future citizenship and Development of citizen´s qualities (s.3).Teachers are the primary factors that impact teaching and learning of mathematics. Two teachers from Sweden and two from China were interviewed and their methods were compared in my study. The aim of my study was to understand mathematics teaching in China and Sweden. As a conclusion, this study will give advices of which concept and method should be emphasized and chosen in Mathematics teaching.

The research work is dedicated to compose a computer – based model with graphic tests and computerese. The object of the research – actions with vulgar fractions. The usable teaching programmes in primary forms were analyzed. The requirements and the needs of such programmes were defined. The rules of the actions with fractions were depicted invoking action structuring graphs and specification of training software requirements was comprised for technical demands. According to them and using universal computerese Visual Studio 2005 and applying special system of graphic tests TestTool5 two training programmes were created. The programme „Fraction“, total size 76 KB, is composed of three operating conditions. There might be many tasks. Graphic tests „Fractions“ are also composed of three operating conditions, 94 tasks, and a teacher has a possibility to supplement the tasks. These two training programmes were introduced at school and an experimental testing was accomplished. Thirty schoolchildren participated in the experiment. The diagrams showing their learning process were received. A questionnaire survey was made. The experiments showed that both programmes present good facilities for schoolchildren to carry out experiments and to pattern. They are appropriate for constructive teaching process.

Thesis (Ph. D.)--University of Toronto, 2006. / Source: Dissertation Abstracts International, Volume: 67-06, Section: A, page: 2086. Includes bibliographical references.