Benford’s Law states that the first significant digit for most data is not uniformly distributed. Instead, it follows the distribution: P(d = d1) = log10(1 + 1/d1) for d1 ϵ {1, 2, …, 9}. In 2006, my supervisor, Dr. Mary Lesperance et. al tested the goodness-of-fit of data to Benford’s Law using the first significant digit. Here we extended the research to the first two significant digits by performing several statistical tests – LR-multinomial, LR-decreasing, LR-generalized Benford, LR-Rodriguez, Cramѐr-von Mises Wd2, Ud2, and Ad2 and Pearson’s χ2; and six simultaneous confidence intervals – Quesenberry, Goodman, Bailey Angular, Bailey Square, Fitzpatrick and Sison. When testing compliance with Benford’s Law, we found that the test statistics LR-generalized Benford, Wd2 and Ad2 performed well for Generalized Benford distribution, Uniform/Benford mixture distribution and Hill/Benford mixture distribution while Pearson’s χ2 and LR-multinomial statistics are more appropriate for the contaminated additive/multiplicative distribution. With respect to simultaneous confidence intervals, we recommend Goodman and Sison to detect deviation from Benford’s Law.

In this study, we consider the Operational Fixed Job Scheduling Problem on identical parallel machines. The problem is to select a subset of jobs for processing among a set of available jobs with fixed arrival times and deadlines, so as to maximize the total weight. We analyze the problem under three environments: Working time constraints, Spread time constraints, and Machine dependent job weights. We show that machine eligibility constraints appear as a special case of the last environment. We settle the complexity status of all problems, and show that they are NP-hard in the strong sense and have several polynomially solvable special structures. For all problems, we propose branch and bound algorithms that employ powerful reduction mechanisms and efficient lower and upper bounds. The results of our computational runs reveal that, the algorithms return optimal solutions for problem instances with up to 100 jobs in reasonable solution times.

In this thesis, two methods are proposed in order to rank units: Target-direction-set value efficiency analysis (TDSVEA) and mixed integer programming (MIP) technique. Besides its ranking ability based on preferences of a decision maker (DM), TDSVEA, which modifies the targeted projection approach of Value Efficiency Analysis (VEA) and Data Envelopment Analysis (DEA), provides important information to analyzer: targets and distances of units from these targets, proposed input allocations in order to project these targets, the lack of harmony between the DM and the manager of the unit etc. In MIP technique, units select weights of the criteria from a feasible weight space in order to outperform maximum number of other units. Units are then ranked according to their outperforming ability. Mixed integer programs in this technique are simplified by domination and weight-domination relations. This simplification procedure is further simplified using transitivity between relations. Both TDSVEA and MIP technique are applied to rank research universities and these rankings are compared to those of other ranking techniques.

ABSTRACT PARAMETER OPTIMIZATION OF CHEMICALLY ACTIVATED MORTARS CONTAINING HIGH VOLUMES OF POZZOLAN BY STATISTICAL DESIGN AND ANALYSIS OF EXPERIMENTS Aldemir, BaSak M.S., Department of Industrial Engineering Supervisor: Prof. Dr. &Ouml / mer Saat&ccedil / ioglu Co-Supervisor: Assoc. Prof. Dr. Lutfullah Turanli January 2006, 167 pages This thesis illustrates parameter optimization of early and late compressive strengths of chemically activated mortars containing high volumes of pozzolan by statistical design and analysis of experiments. Four dominant parameters in chemical activation of natural pozzolans are chosen for the research, which are natural pozzolan replacement, amount of pozzolan passing 45 &amp / #956 / m sieve, activator dosage and activator type. Response surface methodology has been employed in statistical design and analysis of experiments. Based on various second-order response surface designs / experimental data has been collected, best regression models have been chosen and optimized. In addition to the optimization of early and late strength responses separately, simultaneous optimization of compressive strength with several other responses such as cost, and standard deviation estimate has also been performed. Research highlight is the uniqueness of the statistical optimization approach to chemical activation of natural pozzolans.

[Truncated abstract] The scaled boundary finite element method is a novel computational method developed by Wolf and Song which reduces partial differential equations to a set of ordinary linear differential equations. The method, which is semi-analytical, is suitable for solving linear elliptic, parabolic and hyperbolic partial differential equations. The method has proved to be very efficient in solving various types of problems, including problems of potential flow and diffusion. The method out performs the finite element method when solving unbounded domain problems and problems involving stress singularities and discontinuities. The scaled boundary finite element method involves solution of a quadratic eigenproblem, the computational expense of which increases rapidly as the number of degrees of freedom increases. Consequently, to a greater extent than the finite element method, it is desirable to obtain solutions at a specified level of accuracy while using the minimum number of degrees of freedom necessary. In previous work, no systematic study had been performed so far into the use of elements of higher order, and no consideration made of p adaptivity. . . The primal problem is solved normally using the basic scaled boundary finite element method. The dual problem is solved by the new technique using the fundamental solution. A guaranteed upper error bound based on the Cauchy-Schwarz inequality is derived. A iv goal-oriented p-hierarchical adaptive procedure is proposed and implemented efficiently in the scaled boundary finite element method.

We review the construction of three Smale spaces associated to a unimodular Pisot substitution on d letters: a subshift of finite type (SFT), a substitution tiling space, and a hyperbolic toral automorphism on the Euclidean d-torus. By considering an SFT whose elements are biinfinite, rather than infinite, paths in the graph associated to the substitution, we modify a well-known map to obtain a factor map between our SFT and the hyperbolic toral automorphism on the d-torus given by the incidence matrix of the substitution. We prove that if the tiling substitution forces its border, then this factor map is the composition of an s-resolving factor map from the SFT to a one-dimensional substitution tiling space and a u-resolving factor map from the tiling space to the d-torus.

In this investigation an attempt was made to determine the misconceptions that engineering students have of the idea of a limit. A comprehensive literature study showed that there are a number of common misconceptions that students normally form. The empirical investigation was done in two phases. A questionnaire on the idea of a limit was given to the students during the first phase. During the second phase six interviews were conducted. The findings were grouped according to the nature of a limit and students' views on the relationship between the continuity of a function at a point and the limit at that point. An analysis of these findings led to the identification of the misconceptions that these students have of the idea of a limit. / In hierdie ondersoek is gepoog om die wanbegrippe wat ingenieursstudente van die limietbegrip vorm, bloot te stel. 'n Omvattende literatuurstudie het 'n aantal algemene wanbegrippe aan die lig gebring. Die empiriese ondersoek het in twee fases plaasgevind. Tydens die eerste fase is 'n vraelys aan die studente gegee in 'n poging om meer te wete te kom van hulle begrip van 'n limiet. Die vraelys is opgevolg deur ses onderhoude. Die responsies is gegroepeer in terme van die aard van 'n limiet en studente se sienings van die kontinuiteit van 'n funksie by 'n punt en die limiet by daardie punt. Die analisering van hierdie responsies het die identifisering van 'n aantal wanbegrippe by hierdie groep studente moontlik gemaak. / Educational Studies / M.Ed. (with specialisation in Mathematics Education)

Este trabalho apresenta a construção, a aplicação e a avaliação de uma unidade de ensino potencialmente significativa em uma turma da disciplina de Pré-Cálculo, de cursos de Engenharia, visando à ocorrência de uma aprendizagem significativa de conceitos relacionados a funções matemáticas. A escolha dos conteúdos “Função de Primeiro Grau”, “Função Exponencial” e “Função Logarítmica”, nessa unidade de ensino, deve-se, primordialmente, ao fato de que o conceito de função é um dos conceitos fundamentais da Matemática, dadas suas inúmeras aplicações na Engenharia. Nesse contexto, trata-se do ponto de partida para a construção dos conceitos de derivada e de integral, que são a base do Cálculo Diferencial e Integral. Além disso, dificuldades em relação às funções aqui abordadas têm sido expressivas, também, em outras disciplinas dos cursos de Engenharia, o que motivou a escolha para este trabalho de pesquisa. A pesquisa realizou-se por meio de uma abordagem qualitativa; de natureza aplicada; descritiva, quanto aos objetivos; participante, quanto aos procedimentos. A unidade de ensino foi organizada em oito momentos com atividades específicas para cada tipo de função. A análise dos resultados da aplicação da proposta foi feita por meio de instrumentos de avaliação inicial e final, além da construção de mapas conceituais. A pesquisa foi realizada com base na Teoria da Aprendizagem Significativa de Ausubel, com a análise dos mapas conceituais fundamentada em uma adaptação da Taxonomia Topológica de Novak e Cañas, e os resultados apontaram que a metodologia adotada é um método de ensino com potencial para promover a aprendizagem significativa, reduzir a evasão e diminuir a retenção no contexto da educação em Engenharia. / Submitted by Ana Guimarães Pereira (agpereir@ucs.br) on 2017-06-28T17:49:19Z No. of bitstreams: 1 Dissertacao Bruna Cavagnoli Boff.pdf: 4803451 bytes, checksum: 54626eb94b1c8ffad6d4cf39354eef6c (MD5) / Made available in DSpace on 2017-06-28T17:49:19Z (GMT). No. of bitstreams: 1 Dissertacao Bruna Cavagnoli Boff.pdf: 4803451 bytes, checksum: 54626eb94b1c8ffad6d4cf39354eef6c (MD5) Previous issue date: 2017-06-28 / This work presents the elaboration, the application and the evaluation of a potentially meaningful teaching unit in a Pre-Calculus course of engineering courses, aiming at the occurrence of a meaningful learning of concepts related to mathematical functions. The choice of the "first degree function", "exponential function" and "logarithmic function" contents in this teaching unit is primarily due to the fact that the concept of function is one of the fundamental concepts of mathematics, given its many applications in Engineering. In this context, it is the starting point for the construction of the derivative and integral concepts, which are the basis of Differential and Integral Calculus. In addition, difficulties in relation to the functions discussed here have been significant, also, in other Engineering courses, which motivated the choice for this research work. The research was carried out through a qualitative approach; of applied nature; descriptive in relation to the objectives; participant, regarding the procedures. The teaching unit was organized in eight steps with specific activities for each type of function. The results analysis of the application of the proposal was done through instruments of initial and final evaluation, besides the construction of conceptual maps. The research was carried out based on the Ausubel’s Theory of Meaningful Learning, with the analysis of the conceptual maps based on an adaptation of the Topological Taxonomy of Novak and Cañas, and the results pointed out that the adopted methodology is a methodological strategy with potential to promote meaningful learning, reduce evasion and increase retention rates in the context of engineering education.

Este trabalho apresenta a construção, a aplicação e a avaliação de uma unidade de ensino potencialmente significativa em uma turma da disciplina de Pré-Cálculo, de cursos de Engenharia, visando à ocorrência de uma aprendizagem significativa de conceitos relacionados a funções matemáticas. A escolha dos conteúdos “Função de Primeiro Grau”, “Função Exponencial” e “Função Logarítmica”, nessa unidade de ensino, deve-se, primordialmente, ao fato de que o conceito de função é um dos conceitos fundamentais da Matemática, dadas suas inúmeras aplicações na Engenharia. Nesse contexto, trata-se do ponto de partida para a construção dos conceitos de derivada e de integral, que são a base do Cálculo Diferencial e Integral. Além disso, dificuldades em relação às funções aqui abordadas têm sido expressivas, também, em outras disciplinas dos cursos de Engenharia, o que motivou a escolha para este trabalho de pesquisa. A pesquisa realizou-se por meio de uma abordagem qualitativa; de natureza aplicada; descritiva, quanto aos objetivos; participante, quanto aos procedimentos. A unidade de ensino foi organizada em oito momentos com atividades específicas para cada tipo de função. A análise dos resultados da aplicação da proposta foi feita por meio de instrumentos de avaliação inicial e final, além da construção de mapas conceituais. A pesquisa foi realizada com base na Teoria da Aprendizagem Significativa de Ausubel, com a análise dos mapas conceituais fundamentada em uma adaptação da Taxonomia Topológica de Novak e Cañas, e os resultados apontaram que a metodologia adotada é um método de ensino com potencial para promover a aprendizagem significativa, reduzir a evasão e diminuir a retenção no contexto da educação em Engenharia. / This work presents the elaboration, the application and the evaluation of a potentially meaningful teaching unit in a Pre-Calculus course of engineering courses, aiming at the occurrence of a meaningful learning of concepts related to mathematical functions. The choice of the "first degree function", "exponential function" and "logarithmic function" contents in this teaching unit is primarily due to the fact that the concept of function is one of the fundamental concepts of mathematics, given its many applications in Engineering. In this context, it is the starting point for the construction of the derivative and integral concepts, which are the basis of Differential and Integral Calculus. In addition, difficulties in relation to the functions discussed here have been significant, also, in other Engineering courses, which motivated the choice for this research work. The research was carried out through a qualitative approach; of applied nature; descriptive in relation to the objectives; participant, regarding the procedures. The teaching unit was organized in eight steps with specific activities for each type of function. The results analysis of the application of the proposal was done through instruments of initial and final evaluation, besides the construction of conceptual maps. The research was carried out based on the Ausubel’s Theory of Meaningful Learning, with the analysis of the conceptual maps based on an adaptation of the Topological Taxonomy of Novak and Cañas, and the results pointed out that the adopted methodology is a methodological strategy with potential to promote meaningful learning, reduce evasion and increase retention rates in the context of engineering education.

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