The design of power amplifiers within a circuit simulator requires a good non-linear model that accurately predicts the electormagnetic behaviour of the power transistor. In recent years, a certain class of large signal frequency-dependent black-box behavioural modeling techniques known as Poly-Harmonic Distortion (PHD) models has been devised to mimic the non-linear unmatched RF transistor. These models promise a good prediction of the device behaviour under multi-harmonic periodic continuous wave inputs. This thesis describes the capabilities of the PHD modeling framework and the theoretical type of behaviour that it is capable of predicting. Specifically, the PHD framework cannot necessarily predict the response of a broadband aperiodic signal. This analysis will be performed by deriving the PHD modeling framework as a simplification of the Volterra series kernel functions under the assumption that the power transistor is operating under continuous periodic multi-harmonic voltage and current signals in a stable circuit. A PHD model will be seen as a set of describing functions that predict the response of the Device Under Test (DUT) for any given non-linear periodic continuous-wave inputs that have a specific fundamental frequency. Two popular implementations of PHD models that can be found in the literature are the X-parameter and Cardiff models. Each model formulates the describing functions of the general PHD model differently. The mathematical formulation of the X-parameter and Cardiff models will be discussed in order to provide a theoretical ground for comparing their robustness. The X-parameter model will be seen as the first-order Taylor series approximation of the PHD model describing functions around a Large Signal Operating Point (LSOP) of the device under test. The Cardiff large-signal model uses Fourier series coefficient functions that vary with the magnitude of the large signal(s) as the PHD model describing functions. This thesis will provide a breakdown of the measurement procedure required for the extraction of these models, the challenges involved in the measurement, as well as the mathematical extraction of the model coe cients from measurement data. As each of these models contain have extended versions that enhance the predictive capability of the model under stronger nonlinear modes of operation, a comparison is used to represent the cost of increasing model accuracy as a function of the increasing model complexity for each model. The order of complexity of each model can manifest itself in terms of the mathematical formulation, the number of parameters required and the measurement time that is required to extract each model for a given DUT. This comparison will fairly assess the relative strengths and weaknesses of each model.

In recent decades, the landscape of the U.S. classroom has been drastically changing. Schools at every level are enrolling increasingly higher numbers of culturally and linguistically diverse learners, many in the process of learning English. These students, frequently called English language learners (ELLs), present new and unique challenges to educators. Many of these challenges concern language and the many ways it affects the educational experience. One concern of great interest involves better understanding the ways language and academic content interact. Language is a pivotal component of the learning experience, and likely to affect students’ perceptions of the classroom environment and themselves, as well as interactions with teachers and peers. This concern remains critical to consider in secondary mathematics, where language demands are high, but teachers may not be trained to attend to both language and content in the mainstream classroom. The present research used data from the High School Longitudinal Study of 2009 to investigate the secondary mathematics experiences of ELL and non-ELL students in two studies conducted at distinct levels: student and teacher. At the student-level, hierarchical linear modeling was used to compare the effects of several student variables on both access to and achievement in mathematics, as well as how these effects differed between ELL and non-ELL students. Findings indicated that both mathematics self-efficacy and interest in early coursework were positively related to access to and achievement in mathematics, and these relationships were significantly stronger for ELL students. Conversely, positive perceptions of the learning environment and classroom engagement were often related to gains in outcomes for non-ELL students, but decreases for ELL students. This study highlighted several key factors of the secondary mathematics experience that behaved differently for ELL and non-ELL students. Implications of these findings are further discussed in Chapter 2. At the teacher-level, hierarchical linear modeling was used to compare the effects of teacher experience, classroom practices, and perceptions of departmental support on the access to and achievement in mathematics of their students, and how these effects differed between ELL and non-ELL students. Findings indicated that more conceptually-oriented teaching practices were beneficial to both students, with greater gains long-term for both ELL and non-ELL students. Procedurally-oriented teaching was beneficial to ELL students in nearly all cases, but detrimental to non-ELL students’ mathematics outcomes. The effects of perceptions of departmental support varied, with mixed effects for some (e.g. principal support) and detrimental effects for others (e.g. sense of responsibility). Implications of these findings are further discussed in Chapter 3. Finally, Chapter 4 discusses overarching themes across studies at both levels, summarizing the results with regards to student variables, teacher variables, and student-teacher-school relationships. Implications for administrators, teachers, and teacher educators are discussed.

Recently, with growing application of wind power, the system based on the doubly fedinduction generator (DFIG) has become the one of the most popular concepts. Theproblem of connecting to the grid is also gradually revealed. As an effective solution toconnect offshore wind farm, VSC-HVDC line is the most suitable choice for stabilityreasons. However, there are possibilities that the converter of a VSC-HVDC link canadversely interact with the wind turbine and generate poorly damped sub-synchronousoscillations. Therefore, this master thesis will derive the linear model of a single DFIG aswell as the linear model of several DFIGs connecting to a VSC-HVDC link. For thelinearization method, the Jacobian transfer matrix modeling method will be explainedand adopted. The frequency response and time-domain response comparison betweenthe linear model and the identical system in PSCAD will be presented for validation. / Nyligen, med ökande tillämpning av vindkraft, det system som bygger på den dubbeltmatad induktion generator (DFIG) har blivit en av de mest populära begrepp. Problemetmed att ansluta till nätet är också gradvis avslöjas. Som en effektiv lösning för att anslutavindkraftpark är VSC -HVDC linje det lämpligaste valet av stabilitetsskäl. Det finns dockmöjligheter att omvandlaren en VSC-HVDC länk negativt kan interagera medvindturbinen och genererar dåligt dämpade under synkron svängningar. Därför kommerdetta examensarbete härleda den linjära modellen av en enda DFIG liksom den linjäramodellen av flera DFIGs ansluter till en VSC-HVDC -länk. För arise metoden kommerJacobian transfer matrix modelleringsmetodförklaras och antas. Jämförelse mellan denlinjära modellen och identiskt system i PSCAD frekvensgången och tidsdomänensvarkommer att presenteras för godkännande.

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This study compared 3 approaches for handling a fourth level of nesting structure when analyzing data from a cluster-randomized trial (CRT). CRTs can include 3 levels of nesting: repeated measures, individual, and cluster levels. However, above the cluster level, there may sometimes be an additional potentially important fourth level of nesting (e.g., schools, districts, etc., depending on the design) that is typically ignored in CRT data analysis. The current study examined the impact of ignoring this fourth level, accounting for it using a model-based approach, and accounting it using a design-based approach on parameter and standard error (SE) estimates. Several fixed effect and random effect variance parameters and SEs were biased across all 3 models. In the 4-level model, most SE biases decreased as the number of level 3 clusters increased and as the number of level 4 clusters decreased. Also, random effect variance biases decreased as the number of level 3 clusters increased. In the 3-level and complex models, SEs became more biased as the weight level 4 carried increased (i.e., larger intraclass correlation, more clusters at that level). The current results suggest that if a meaningful fourth level of nesting exists, future researchers should account for it using design-based approach; the model-based approach is not recommended. If the fourth level is not practically important, researchers may ignore it altogether.

本研究以TIMSS 2003台灣數學科資料為資料來源，使用階層線性模式為統計分析方式，探討國小四年級及國中二年級，學生數學家庭作業完成時間與教師指派數學家庭作業頻率，對於學生數學學習成就的影響。研究結果顯示：在國小四年級，學生數學家庭作業完成時間與學生數學學習成就為負相關；教師指派數學家庭作業頻率與學生數學學習成就之間為正相關，但並不顯著。在國中二年級，學生數學家庭作業完成時間與教師指派數學家庭作業頻率，對學生數學學習成就皆有正向的影響。在國小四年級中，學生數學家庭作業完成時間與教師指派數學家庭作業頻率的交互作用，對學生數學學習成就為負相關，但不顯著。在國中二年級中，學生數學家庭作業完成時間與教師指派數學家庭作業頻率的交互作用，對學生數學學習成就為正相關，但不顯著。 / The research was to explore the effects of mathematics homework time and mathematics homework frequency on mathematics achievement in the fourth and eighth grades, using TIMSS 2003 Taiwan mathematics data as the resources and Hierarchical Linear Modeling as the statistical analysis method. The results showed that in the fourth grades, mathematics homework time had a negative relationship with mathematics achievement while mathematics homework frequency had a positive, but non-significant, relationship with mathematics achievement. In the eighth grades, both mathematics homework time and mathematics homework frequency had positive effects on mathematics achievement. In the fourth grades, the interaction between mathematics homework time and mathematics homework frequency had negative, but non-significant, effects on mathematics achievement while in the eighth grades, the interaction between mathematics homework time and mathematics homework frequency had positive, but non-significant, effects on mathematics achievement.

The changing landscape of demographics, technology, and diversity in the learning environment is challenging schools around the world to rethink their approaches to the implementation of high-quality teaching practices. Classroom practices are becoming more complex because educators have to ensure that their students are well-equipped with 21st century skills (e.g., Darling-Hammond, 2010; Dede, 2010; Griffin, McGaw, & Care, 2012). Educators, curriculum developers, and school administrators need to be more than experts in pedagogy. They are now required to keep up with current ideas, innovative instructional practices, and the results of a variety of educational reform efforts. Believing that teachers’ beliefs are the most important psychological construct with regard to instructional practices (Pajares, 1992) and that teachers’ beliefs are related to their choice of classroom practices and, ultimately, the students’ performance (Bybee, Taylor, Gardner, Van Scotter, Powell, Westbrook, & Landes, 2006; Staub & Stern, 2002), the author of this study utilizes the international data set of the Teaching and Learning International Study (TALIS) 2013 to examine the associations between teachers’ constructivist beliefs, their self-efficacy beliefs, professional activities, and the school principals’ instructional leadership as related to lower secondary school teachers and principals in South Korea, Finland, and Mexico. These three countries represent the high and low performers in the global index of cognitive skills and educational attainment (Pearson, 2014). An account of their educational practices will provide some insights for stakeholders in school systems across nations. Nevertheless, it is important to understand that each country has unique teaching and learning conditions, and that conclusions reached in relation to such conditions do not apply across nations. A series of hierarchical linear modeling (HLM) studies were performed for the present work to provide evidence-based information with practical implications to school administrators and educational policymakers regarding the development and implementation of leadership programs and teacher professional development. Additionally, an understanding of how the constructivist beliefs associate with the level of self-efficacy and professional activities will assist curriculum developers in higher educational institutions in the development of quality teacher preparation programs for the future teaching workforce.