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Includes bibliographical references (leaves 37-39). / Bozdogan [8] [6] [7] developed a new model selection criteria called information measure of complexity (ICOMP) for model selection. In contrast to Akaike's [1] information criterion (AIC) and other AIC type criteria that are traditionally used for regression analysis, ICOMP takes into account the interdependencies of the parameter estimates. This paper is divided into two parts. In the first part we compare and contrast ICOMP with AIC and other AIC type selection criterion for model selection in regression analysis involving stock market securities. While in the second part we apply the definition of information theoretic measure of complexity to portfolio analysis. We compare the complexity of a portfolio of securities with its' measure of diversification (PDI) and examine the similarities and differences between the two quantities as it affects portfolio management.

The purpose of this study was to investigate whether the Test-Taking Strategy would improve performance on math curriculum-based assessments of students with disabilities, and if students reported an increased sense of math self-efficacy as a result of learning the Test-Taking Strategy. The Test-Taking Strategy uses mnemonics to teach strategies to help students successfully navigate through assessments. This study used an experimental, single-subject, multiple-probe, multiple base-line design (Horner & Baer, 1978). The design featured multiple participants, and followed the design features of quantitative research (Horner & Baer, 1978, McMillan, 2004, & Mitchell & Jolley, 2004). The Test-Taking Strategy did result in improved performance on CBA (math quizzes) for some of the students in this study. However, some students did not increase performance on math CBA (math quizzes). Findings also indicated most students did not report an increased sense of math efficacy. Results of this study and the impact of these findings are discussed.

The purpose of my job “The Systematic and Optimization of Exercises Solution Of Primary Mathematics Exercises in 3-4 Classes” was to overlook newly and to value mathematic exercises, which was given in mathematic textbooks. To reach this purpose, I chose and analyzed B. Balchychio, A. Kiseliovo ir D. Kiseliovos bei D. Shalnienes ir L. Hoshteterienės mathematic textbooks of 3-4 classes. I made three problems for this job: to detect peculiarities of mathematics exercises systematic; to analyze mathematic textbooks of different authors of 3-4 classes; to analyze derivation ways of 3-4 mathematic exercises in different ways. When I was writing my job I used these methods: the analyze of different literature derivations, questionnaire poll, the analyze of mathematic textbooks and mathematic statistics. I ascertained which exercises authors render a lot in their textbooks, which sort is textual and geometric exercises, which are most arithmetic operations. I made the questionnaire poll of nine exercises of chosen textbooks too, I gave three geometric, three arithmetic and three textual exercises in this questionnaire poll. There was chosen one by one from all kinds of exercises from different textbooks. The poll was given to pupils of 4 classes on purpose to see are the pupils able to solve exercises of different authors, do the authors give not difficult or not easy exercises. In this investigation pupils were from 12 schools: main school of Pryshmanchiai, secondary school of... [to full text]

O objetivo deste trabalho e determinar a solução de algumas equações de coeficientes intervalares. Este estudo utiliza uma Teoria das Aproximações Intervalares, a qual foi descrita por [ACI91]. Nesta teoria a igualdade para intervalos e substituída pela relação de aproximação . Esta substituição deve-se ao fato da igualdade utilizada na Teoria Clássica dos Intervalos para resolução de equações de coeficientes intervalares não apresentar uma solução satisfatória, visto que a solução encontrada não contem todas as soluções das equações reais que compõe a equação intervalar. Pela substituição da igualdade intervalar por uma relação de aproximação é possível determinar a solução de equações de coeficientes intervalares, de maneira que esta solução contenha todas as possíveis soluções das equações reais pertencentes a equação intervalar. Apresenta-se alguns conceitos básicos, bem como analisa-se algumas propriedades no espaço solução ( /(R), +, •, C, 1). São representadas graficamente diferentes tipos de funções neste espaço intervalar, com os objetivos de obtenção da imagem, caracterização da solução e identificação gráfica da região de solução (ótima e externa), para cada tipo de função. Como a representação de intervalos de /(R) esta determinada num semiplano de eixos X - X+, onde X - representa o extremo inferior de cada intervalo e X+ representa o extremo superior dos intervalos, apresenta-se o espaço intervalar estendido /(R). Neste espaço intervalar estão definidos os intervalos não-regulares, representados no outro semi-piano de eixos X - X+ Em /(R) serão apresentados alguns conceitos fundamentais, assim como operações aritméticas e algumas considerações referentes aos intervalos não-regulares. No espaço intervalar /(R) e possível resolver equações de coeficientes intervalares de maneira análoga a resolução de equações reais no espaço real, pois este espaço intervalar possui a estrutura semelhante a de um corpo. Com isto apresenta-se a solução de equações de coeficientes intervalares lineares, obtida diretamente, assim como determina-se a Formula de Bascara Intervalar para resolução da Equação Quadrática Intervalar. Para funções que possuem grau maior que 2 apresenta-se alguns métodos iterativos intervalares, tais como o Método de Newton Intervalar, o Método da Secante Intervalar e o Método híbrido Intervalar, que permitem a obtenção do intervalo solução para funções intervalares. Por fim apresenta-se alguns conceitos básicos no espaço intervalar matricial M„,„(/(R)), bem como apresenta-se alguns métodos diretos para resolução de sistemas de equações lineares intervalares. / The aim of this work is to determine the solution set of some Equations of Interval Coefficients. The study use a Theory of Interval Approximation. The begining of this theory was described by [ACI91]. In this theory the equality for intervals is replaced by an approximation relation. When we make use of that relation to solve interval equations, it's possible to obtain an optimal solution, i.e., to get an interval solution that contain all of real solutions of the real equations envolved in the interval equation. By using the equality of Classical Interval Theory for solving interval equations we can not get an optimal solution, that is, the interval solution in the most of equations not consider some real solutions of real equations that belong to the interval equation. We present some basic concepts and analyse some properties at the interval space (1(R), E, -a x , 1). Different kind of functions are showed in this space in order to obtain the range, the solution caracterization and the graphic identification of the optimal and external solution region, for each kind of function. The representation of intervals in /(R) is determined in a half plane of axes X - , X+, where X - represent the lower endpoint and X+ represent the upper endpoint of the intervals. The nonregular intervals are defined in /(R), which are determined in an other half plane. In this interval space are presenting some specific concepts, as well as arithmetical operations and some remarks about nonregular intervals. The interval space (1(R), +, •, C, Ex , 1) have a similar structure to a field, so it's possible to solve interval coefficients equations analogously as to solve real equations in the real space. We present the solution of linear interval equations and we determine an interval formula to solve square interval equation. We present some intervals iterated methods for functions that have degree greater than 2 that allow to get an interval solution of interval functions. Finally we show some basic concepts about the interval matrix space Af,„„(IR)) and present direct methods for the resolution of linear interval sistems.

The objective of this thesis is to provide the modeling procedure for a tubular permanent magnet generator with Halbach array. The cylindrical-coordinated magnetic flux distributions generated by the stator winding currents and permanent magnets can be realized by deriving the magnetic vector potential in Bessel form from the Maxwell's equations. Then, the functional expressions of inductance matrix and magnetic flux linkage can be obtained. The detailed mathematic model of the proposed system combined with the actual operational properties can be further established and implemented by using the Matlab/Simulink software. The applicability of such mathematic model is also confirmed with experimental results.

Students must be good problem solvers in order to compete in today’s global economy. However, many students, including students with disabilities, do not have adequate problem-solving skills, thus eliminating potential job opportunities. In order to increase opportunities for problem-solving success, schools must find strategies that are effective and efficient for students to use and simulate real-world scenarios. Therefore, the purpose of this study was to investigate whether a direct, cognitive-strategy, problem-solving program (Solve It!), which is designed to enhance student skills in word-problem solving, could increase the accuracy with which students with and without disabilities correctly solved word problems and whether it affected students beliefs about problem solving. The research questions developed for this study were (a) does the Solve It! method affect the math problem-solving achievement of Grade 6 students, and (b) what are teacher and student perceptions of the efficacy of the Solve It! method of teaching word-problem solving? A quantitative case study was used for this study to determine the efficacy of a specific cognitive instructional strategy with Grade 6 students. Participants in this study included 54 Grade 6 students, 7 with disabilities, from a middle school in Southwestern Colorado. Data were gathered from students through the use of pre- and posttests containing 10 word math problems. Students were also given short weekly quizzes to monitor progress and check for proper usage of the strategy. Finally, data were gathered from the Northwest Evaluation Association (NWEA) instrument, winter and spring testing periods, to investigate changes on the problem-solving strand of the mathematics test. Teacher interviews and student surveys were also used to gain deeper insight into the effectiveness of the strategy. From this analysis, conclusions were drawn to answer the research questions. Comparison of means showed that although the Solve It! strategy did not statistically significantly improve students’ mathematical problem-solving abilities on the standardized NWEA test, it did improve their scores in word-problem solving on the 10-item word-problem test. In addition, the students’ perceived self-efficacy to solve word problems increased. / text

Children born very preterm (VPT) are known to be at high risk of under-achievement in mathematics. However the nature of these difficulties is poorly understood. In this study, a regionally representative cohort of 102 children born VPT and a comparison group of 108 children born full term (FT) during 1998-2000 were followed from birth to nine years. At age nine, children were tested using the Woodcock-Johnson III maths fluency subtest, and teacher reports of mathematical achievement and curriculum-based (numeracy project) achievement data were collected. The data was analysed using group comparisons and multiple regression. Parent and teacher ratings of executive function at age six were included as predictors. Findings indicated that children born VPT had elevated rates of mathematical difficulties across all measures including the standardised and curriculum-based measures, and teacher ratings. They also had higher rates of mathematical learning disability. With the exception of curriculum-based measures, these results remained significant even after controlling for socioeconomic status and severe neurodevelopmental impairment. Children born VPT showed particular difficulty using operational strategies, rather than with factual knowledge, and this effect was most marked for addition and multiplication. As well as difficulties in mathematics, children born VPT also showed more difficulty than children born FT in almost all areas of executive function. Difficulties with working memory at age six were significantly associated with poor performance in aspects of curriculum-based measures at age nine.

The purpose with this essay is to compare two classes in an international school during their mathematic lesson. The international school offers education to their pupils in two languages; in Swedish and in English. Through this study I want to find out how teachers are working with language and communication during school hours. I will compare the work of two teachers and two classes to find out the differences and similarities between their work methods concerning language and communication during mathematic lessons. The main questions for the essay: How do the teachers work with language and communication in this school during the mathematic lessons? What similarities and differences are there between the two teachers in matter of methods of working with language and communication during the mathematic lessons? The research is based on interviews with the teachers and also on observations in the classroom during mathematic lessons. The difference between the two classes is that one class only speaks English during their lessons while the other class speaks both English and Swedish. The study is based on a socio-cultural perspective.  Education and development that takes place through interaction with other people is a significant part of the social-cultural perspective. In my result I learned that the two teachers I observed have more similarities than differences concerning their methods in the classroom regarding language and communication.

O objetivo deste trabalho e determinar a solução de algumas equações de coeficientes intervalares. Este estudo utiliza uma Teoria das Aproximações Intervalares, a qual foi descrita por [ACI91]. Nesta teoria a igualdade para intervalos e substituída pela relação de aproximação . Esta substituição deve-se ao fato da igualdade utilizada na Teoria Clássica dos Intervalos para resolução de equações de coeficientes intervalares não apresentar uma solução satisfatória, visto que a solução encontrada não contem todas as soluções das equações reais que compõe a equação intervalar. Pela substituição da igualdade intervalar por uma relação de aproximação é possível determinar a solução de equações de coeficientes intervalares, de maneira que esta solução contenha todas as possíveis soluções das equações reais pertencentes a equação intervalar. Apresenta-se alguns conceitos básicos, bem como analisa-se algumas propriedades no espaço solução ( /(R), +, •, C, 1). São representadas graficamente diferentes tipos de funções neste espaço intervalar, com os objetivos de obtenção da imagem, caracterização da solução e identificação gráfica da região de solução (ótima e externa), para cada tipo de função. Como a representação de intervalos de /(R) esta determinada num semiplano de eixos X - X+, onde X - representa o extremo inferior de cada intervalo e X+ representa o extremo superior dos intervalos, apresenta-se o espaço intervalar estendido /(R). Neste espaço intervalar estão definidos os intervalos não-regulares, representados no outro semi-piano de eixos X - X+ Em /(R) serão apresentados alguns conceitos fundamentais, assim como operações aritméticas e algumas considerações referentes aos intervalos não-regulares. No espaço intervalar /(R) e possível resolver equações de coeficientes intervalares de maneira análoga a resolução de equações reais no espaço real, pois este espaço intervalar possui a estrutura semelhante a de um corpo. Com isto apresenta-se a solução de equações de coeficientes intervalares lineares, obtida diretamente, assim como determina-se a Formula de Bascara Intervalar para resolução da Equação Quadrática Intervalar. Para funções que possuem grau maior que 2 apresenta-se alguns métodos iterativos intervalares, tais como o Método de Newton Intervalar, o Método da Secante Intervalar e o Método híbrido Intervalar, que permitem a obtenção do intervalo solução para funções intervalares. Por fim apresenta-se alguns conceitos básicos no espaço intervalar matricial M„,„(/(R)), bem como apresenta-se alguns métodos diretos para resolução de sistemas de equações lineares intervalares. / The aim of this work is to determine the solution set of some Equations of Interval Coefficients. The study use a Theory of Interval Approximation. The begining of this theory was described by [ACI91]. In this theory the equality for intervals is replaced by an approximation relation. When we make use of that relation to solve interval equations, it's possible to obtain an optimal solution, i.e., to get an interval solution that contain all of real solutions of the real equations envolved in the interval equation. By using the equality of Classical Interval Theory for solving interval equations we can not get an optimal solution, that is, the interval solution in the most of equations not consider some real solutions of real equations that belong to the interval equation. We present some basic concepts and analyse some properties at the interval space (1(R), E, -a x , 1). Different kind of functions are showed in this space in order to obtain the range, the solution caracterization and the graphic identification of the optimal and external solution region, for each kind of function. The representation of intervals in /(R) is determined in a half plane of axes X - , X+, where X - represent the lower endpoint and X+ represent the upper endpoint of the intervals. The nonregular intervals are defined in /(R), which are determined in an other half plane. In this interval space are presenting some specific concepts, as well as arithmetical operations and some remarks about nonregular intervals. The interval space (1(R), +, •, C, Ex , 1) have a similar structure to a field, so it's possible to solve interval coefficients equations analogously as to solve real equations in the real space. We present the solution of linear interval equations and we determine an interval formula to solve square interval equation. We present some intervals iterated methods for functions that have degree greater than 2 that allow to get an interval solution of interval functions. Finally we show some basic concepts about the interval matrix space Af,„„(IR)) and present direct methods for the resolution of linear interval sistems.