Dissertations / Theses on the topic 'Operations on determinants and matrices'

Matrices whose rows (or columns) consists of monomials of sequential powers are called Vandermonde matrices and can be used to describe several useful concepts and have properties that can be helpful for solving many kinds of problems. In this thesis we will discuss this matrix and some of its properties as well as a generalization of it and how it can be applied to curve fitting discharge current for the purpose of ensuring electromagnetic compatibility. In the first chapter the basic theory for later chapters is introduced. This includes the Vandermonde matrix and some of its properties, history, applications and generalizations, interpolation and regression problems, optimal experiment design and modelling of electrostatic discharge currents with the purpose to ensure electromagnetic compatibility. The second chapter focuses on finding the extreme points for the determinant for the Vandermonde matrix on various surfaces including spheres, ellipsoids, cylinders and tori. The extreme points are analysed in three dimensions or more. The third chapter discusses fitting a particular model called the p-peaked Analytically Extended Function (AEF) to data taken either from a standard for electromagnetic compatibility or experimental measurements. More specifically the AEF will be fitted to discharge currents from the IEC 62305-1 and IEC 61000-4-2 standards for lightning protection and electrostatic discharge immunity as well as some experimentally measured data of similar phenomena.

Let $U_\infty\Z_p$ be the group of infinite invertible upper triangular matrices with entries in the $p$-adic integers. Also let $\Aut_{\text{left-}\ell\text{-mod}}^0(\ell\wedge\ell)$ be the group of left $\ell$-module automorphisms of $\ell\wedge\ell$ which induce the identity on mod $p$ homology, where $\ell$ is the Adams summand of the $p$-adically complete connective $K$-Theory spectrum. In this thesis we construct and prove there is an isomorphism between these two groups. We will then determine a specific matrix (up to conjugacy) which corresponds to the automorphism $1\wedge\psi^q$ of $\ell\wedge\ell$ where $\psi^q$ is the Adams operation and $q$ is an integer which generates the $p$-adic units $\Z_p^\times$. We go on to look at the map $1\wedge\phi_n$ where $\phi_n=(\psi^q-1)(\psi^q-r)\cdots(\psi^q-r^{n-1})$ and $r=q^{p-1}$ under a generalisation of the map which gave us the isomorphism. Lastly we use some of the ideas presented to give us a new way of looking at the ring of degree zero operations on the connective $p$-local Adams summand via upper triangular matrices.

By first looking at the orthonormal basis: Γ = {∑i 4 ibi ∈{0, 1}, finite sums} and the related orthonormal basis 5Γ = {5∑i 4i bi : bi ∈ {0, 1}, finite sums} we find several interesting relationships with the unitary matrix Uα,β arising from the operator U: Γ → 5Γ. Further, we investigate the relationships between U and the operators So : Γ → 4Γ defined by Soe4γ where eγ = e2ΠiΓ and S1: Γ → 4Γ+1 defined by S1eγ = e4γ+1. Most intriguing, we found that when taking powers of the aforementioned Uα,β matrix that although there are infinitely many 1's occurring in the entries of Uα,β only one such 1 occurs in the subsequent higher powers Ukα,β. This means that there are infinitely many γ ∈ Γ ∩ 5Γ, but only one such γ in the intersection Γ and 5kΓ, for k ≥ 2.

Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2006.<br>Title from electronic title page (viewed Oct. 10, 2007). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics." Discipline: Mathematics; Department/School: Mathematics.

Doctor of Philosophy<br>Department of Apparel, Textiles, and Interior Design<br>Melody L. A. LeHew<br>Fashion is the second most polluting industry and accounts for 10% of global carbon emissions. Consuming fossil fuel based electricity, the primary source of energy in the apparel production process, causes a great deal of greenhouse gas (GHG) emissions. Due to ever-increasing apparel demand and population growth, this industry’s carbon footprint will only grow bigger. As attention on sustainability issues in our world intensifies, research on environmental sustainability in the apparel manufacturing industry is needed. The purpose of this exploratory study was to investigate energy consumption (EC) of the apparel sewing process. The objectives are to (a) identify the most influential EC factors and develop a model to capture EC levels, (b) determine factor interrelationships, (c) identify steps to reduce EC, and (d) explore experts' level of concern regarding EC of the apparel manufacturing and its contribution to greenhouse gas emissions and climate change. A mixed method research study was employed in this study: a qualitative method was utilized to assess expert perceptions and a quantitative method was used to measure EC and build a regression model. This study determined dominant EC and GHG emissions factors from sewing process so that apparel manufacturers can understand which factors need to be controlled to reduce environmental damage. Findings from the study indicated sewing machine motor capacity, sewing speed, and standard allocated minute (SAM) were the most influential EC factors, and shortening the sewing time was found as the best solution to reduce energy consumption in the apparel sewing process. The energy consumption model was found as: Log (EC) = 9.283 + 0.771* log (SAM) + 0.386*knit fabric type + 0.260*sportswear fabric type + 0.080*SPI - 0.008*capacity + 0.004*seam length - 0.001* speed + 0.495. The EC model along with GHG calculator (a tool to convert GHG from EC) will help the industry to determine their EC and GHG emissions level to boost their awareness and to encourage greater impetus for environmental actions. Finally, this study will help designers, retailers, and consumers to pursue environmentally friendly actions in terms of decisions regarding apparel design, sourcing, and purchasing.

Thesis (M.A. in National Security Affairs (Defense Decision Making and Planning))--Naval Postgraduate School, September 2006.<br>Thesis Advisor(s): James Wirtz, Thomas Johnson. "September 2006." Includes bibliographical references (p.85-91). Also available in print.

Approved for public release; distribution is unlimited<br>Despite the political impetus for greater multilateralism in international military operations, recent coalitions including U.S. forces reflect a trend toward increasing U.S. dominance and decreasing allied participation. As the United States continues to invest in its military with research, development and acquisition budgets at least double that of any other nation, it fields technologies so advanced with respect to its allies as to leave them incompatible for combined operations. Recent coalition operations suggest that there is a close relationship between technological asymmetries created by partner contributions and the structures formed as the coalition assembles. Using Desert Storm and Operation Allied Force as case studies, this thesis identifies a systemic relationship between technological advantage and coalition dominance. As a coalition seeks to reduce aggregate risk, it relies on technologies that offer the greatest effectiveness. This reliance causes the coalition to divert combat burden to the technologically dominant partner which, in turn, imposes its operational culture. This thesis concludes that the technological transformation currently underway in the U.S. Department of Defense conflicts with U.S. political initiatives to promote greater multilateralism in combat operations by forcing allies to rely on U.S. technologies thereby creating more unilateral operations.<br>Outstanding Thesis

The determinants that affect the financial performance of an insurance company are complicated due to the intangible nature of insurance products and the lack of transparency in the market. Consequently, the financial performance of insurance companies is important to various stakeholders such as policyholders, insurance intermediaries and policymakers. This study aims to investigate the determinants of financial performance of insurance companies based on their financial strength rating performance. The empirical data are drawn from A.M. Best Insurance Report Online: Non- US Database. The sample consists of 57 insurers in the United Kingdom over the period of 2006 to 2010. The analyses include eight firm-specific variables, which are leverage, profitability, liquidity, size, reinsurance, growth, type of business and organisational form. Rating transition matrices and regression models are employed in this study. Rating transition analysis demonstrates a significant degree of rating changes, as reflected in the rating fluctuations. Based on the empirical results, this study establishes that profitability, liquidity, size and organisational form are statistically significant determinants of financial performance of insurance companies in the United Kingdom. This study recommends an alternative to measure the size of an insurance company, which is based on the gross premium written. In addition, this study provides insights into the effects of the global financial crisis on the financial performance of the insurance companies.

This thesis aims to investigate determinants of fear of failure in entrepreneurial activity that could inhibit starting a business. The study uses cross-sectional, pooled OLS, and panel regressions. The dependent variable is fear of failure regarding entrepreneurship, measured with the Global Entrepreneurship Monitor (GEM) survey question of whether fear of failure would prevent the responder from starting a firm. The unit of analysis is at country level. I categorize determinants into demographic, property rights, and procedural variables. A population of higher working age ratio (measured as the population aged 15-64 divided by the population aged 65 and over) correlates with a decreasing fear of failure. Additionally, stronger property rights appear to decrease fear of failure. I do not find a statistically significant relationship between fear of failure and procedural variables in my datasets. A binary variable for whether the country is in Asia appears to show a positive association with fear of failure, increasing it by ten percentage points. Since decreasing fear of failure is desirable to promote greater entrepreneurial activity, a better understanding of the determinants of fear of failure is essential to inform public policies to spur entrepreneurial growth. The findings from this study, while not conclusive, identify the importance of further research based on larger datasets and variables that are more robust.

The paper explores the driving forces behind corporate cash holdings by analyzing past literature and extending this research to the behavior of firms after the 2008 recession. I look at the cash to assets and net debt to assets ratios from October 1980 to October 2011 to obtain an understanding of the past and current state of cash holdings. A comprehensive literature review is done on agency costs and transactional motives to give the reader an overview of the costs and benefits of holding cash. This provides the foundation for the precautionary motives for companies today to keep cash as a risk management tool.

In this paper, I analyze how firm attributes such as their age, industry, nature of industry, spinoff status and debt ratio influence venture-capital financing decision. I look at a sample of 280 firms that went public in the United States between 2015- 2019. This paper finds that firm age and debt are negatively related to the likelihood of being venture-capital backed. It also finds that firms in technology and biotechnology industries are more likely to be backed by a venture-capitalist.

The purpose of this study was to examine many factors associated with family-owned businesses that lead to business success and profitability. The panel data used in this study came from the 1997 and 2000 waves of the National Family Business Study (NFBS). Many independent variables from the 1997 wave (e.g., age, gender, managerial activities, business size, home-based, business problems) were tested to predict business success and profitability (dependent variables), which were variables from the 2000 wave. Some of the descriptive analyses indicated that, compared to female managers, male managers perceived less business success, participated more in managerial activities, managed older businesses, experienced more business problems, and experienced fewer business cash-flow problems. Compared to businesses that are not home-based, home-based businesses reported less perceived business success, less business profitability, were smaller businesses, experienced fewer business problems, had fewer business liabilities, and had managers with poorer health and less education. Overall, the ordinary least squares regression analyses yielded results indicating that managerial activities, home-based businesses, business age, business problems, and business cash-flow problems were all statistically significantly associated with perceived business success. Business size was shown to be significantly associated with business profitability. Implications of the findings, limitations of the current study, and recommendations for future research were presented in the final section.

Este trabalho tem como objetivo apresentar os conteúdos de matrizes, determinantes e sistemas lineares aos professores de matemática que lecionam no ensino médio, ressaltando as situações-problema bem como suas aplicações, contextualizando através de problemas.<br>The goal of this work is to present an introduction to matrices, determinants, and linear systems to high school mathematics teachers highlighting some applications.

Greenhouse gas emissions are caused, in part, by human activities. However, consumers may assume that the burden of environmental problems, such as carbon emissions reduction through sustainable energy practices, should be borne by the entire society. The purpose of this cross-sectional study was to test whether behavioral determinants and demographic factors could influence homeowners' intent to conserve energy. Empirical data were collected from 436 sampled homeowners in the Northeast region of the United States using an online survey questionnaire. The survey instrument was adapted from Ajzen's theory of planned behavior instrument. Variables aligned with the theory of planned behavior, alongside sociodemographic factors, were used to explain any impact the predictors had on the outcome. A multiple ordinary least squares regression model was used to answer the 3 research questions. According to the study findings, the most significant positive relationship was found between homeowners' beliefs about energy conservation and the intent to conserve energy. There was also a significant positive relationship between the other predictors and the outcome at varying levels. Policymakers could generate support for energy efficiency and conservation by educating consumers about alternative energy options as a means of mitigating carbon emissions and air pollution. This study may lead to a positive social change by supporting regional policymakers in designing and promoting cost-effective behavioral solutions and demographic change support systems as an alternative policy tool that could encourage a sustainable energy consumption practice at the household level.

This paper investigates the influence of various macroeconomic variables on Japan’s merger and acquisition (M&A) activity, both in terms of total deal value and total number of deals. Looking at monthly data from June 1997 to December 2013, I use econometric time-series analysis to find that: First, total deal value per month is not well explained by our macroeconomic variables, but about half of the variation in number of deals per month can be explained by our dataset. Second, the most important determinant in the total number of deals per month during our period is the level of national debt, and interest rates had the opposite effect from what was originally expected. Third, adding lag variables to our analysis proved to be relatively fruitless. Finally, when taking a look at only the past couple of years to determine the effects of “Abenomics” on M&A activity in Japan, I conclude that there is not enough data, and better results would be obtained in the future.

Made available in DSpace on 2015-03-03T15:36:09Z (GMT). No. of bitstreams: 1 AgamenonHCT_DISSERT.pdf: 1109440 bytes, checksum: 1e3e3f703ff180a7a76461fb8e7b74b7 (MD5) Previous issue date: 2013-02-22<br>Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior<br>In this work we studied the method to solving linear equations system, presented in the book titled "The nine chapters on the mathematical art", which was written in the first century of this era. This work has the intent of showing how the mathematics history can be used to motivate the introduction of some topics in high school. Through observations of patterns which repeats itself in the presented method, we were able to introduce, in a very natural way, the concept of linear equations, linear equations system, solution of linear equations, determinants and matrices, besides the Laplacian development for determinants calculations of square matrices of order bigger than 3, then considering some of their general applications<br>Neste trabalho, estudamos o m?todo apresentado no livro "Os nove cap?tulos sobre a arte matematica", escrito no s?culo I da era crist?, a em de revelar como a hist?ria pode ser uma motivadora na introdu??o de t?picos da matem?tica do ensino m?dio. Atrav?s de observa??es dos padr?es que se repetem no m?todo apresentado, fomos capazes de introduzir, de maneira natural, o conceito de equa??es lineares, sistema de equa??es lineares, solu??o de sistemas de equa??es lineares, determinantes e matrizes, al?m do desenvolvimento de Laplace para c?lculo de determinantes de matrizes quadradas de ordem maior que 3, considerando, em seguida, algumas de suas aplica??es gerais

Made available in DSpace on 2017-07-21T20:56:31Z (GMT). No. of bitstreams: 1 Marta Lena Jahn.pdf: 1783494 bytes, checksum: c6497fd4a435d106076c444a8c6fc4cc (MD5) Previous issue date: 2013-04-11<br>The objective of this study is to propose a different approach to teaching of matrices, seeking value the geometric aspect of them, and determinants. In fact, the matrices are important not only as a way to organize numerical data (tables), but also by the different properties of the operations that define the matrix algebra. However, the traditional way of teaching matrices and determinants in a secondary education, such as tables of numbers and a number associated with a matrix, respectively, the definitions of matrix operations and determinants, as well as their properties become quite unnatural. The Geometry not only turns these concepts more natural, but also develops our intuition about it. Furthermore, the geometrical aspects of the matrices and determinants are present in technological applications such as in Computer Graphics, for example. We begin this work by analyzing some textbooks adopted in secondary education, in order to see how the theory of matrices and determinants have been approached in classrooms, and to relate it to national education curriculum guidelines. Later, we explore the geometric content of matrices and determinants and propose a methodology for teaching, which brings out this aspect. This approach by middle of the Geometry is intended to stimulate the student to deduce properties and reflect on the results in operations with matrices, for example, addition, multiplication and also in the calculation of determinants. In proposing this methodology, we use the free software Geogebra, with the intent of providing a better view of the content for the student.<br>O objetivo deste estudo é propor uma abordagem diferente para o ensino das matrizes, buscando valorizar o aspecto geométrico delas, e dos determinantes. De fato, as matrizes são importantes não apenas como forma de organizar dados numéricos (tabelas), mas também pelas diversas propriedades das operações que definem a álgebra matricial. Todavia, na forma tradicional de ensinar matrizes e determinantes no ensino médio, como tabelas de números e um número associado a uma matriz, respectivamente, as definições das operações matriciais e determinantes, assim como as suas propriedades, tornam-se bastante artificiais. A Geometria não apenas ajuda a tornar estes conceitos mais naturais, como também desenvolve a nossa intuição sobre o assunto. Além disso, os aspectos geométricos das matrizes e determinantes estão presentes em aplicações tecnológicas tais como em Computação Gráfica, por exemplo. Começaremos este trabalho analisando alguns livros didáticos adotados no ensino médio, para verificar como a teoria de matrizes e determinantes vem sendo abordada em sala de aula; e relacionar essa teoria com os parâmetros curriculares nacionais do ensino médio. Posteriormente, exploraremos o conteúdo geométrico de matrizes e determinantes e proporemos uma metodologia para o seu ensino que valorize este aspecto. Esta abordagem por meio da geometria tem a finalidade de estimular o aluno a deduzir propriedades e refletir sobre os resultados obtidos nas operações realizadas com matrizes, por exemplo, a adição, a multiplicação e também, no cálculo de determinantes. Ao propor esta metodologia, faremos uso do software livre Geogebra, com o intento de propiciar uma melhor visualização do conteúdo pelo aluno.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>A melhoria na qualidade do ensino matemático resulta de diversos fatores como: qualificação dos professores, busca de novos modelos pedagógicos e inclusão da tecnologia aos processos de aprendizagem. Existe um grande distanciamento entre a tecnologia e a sala de aula, principalmente quando se fala em ensino público, e é nessa problemática que este trabalho busca contribuir com soluções alternativas. Aproveitando a enorme demanda dos aparelhos móveis e a forte influência que esses dispositivos detém sobre os jovens, buscou-se fundamentar o trabalho realizando pesquisas sobre os aspectos pedagógicos da aprendizagem móvel e, em virtude do fascínio exercido pelos jogos digitais, foram estudadas as técnicas de gamificação. Nesse contexto, foi desenvolvido um aplicativo tipo perguntas e respostas (QUIZ), de acordo com os preceitos da aprendizagem móvel e utilizando os recursos motivacionais da gamificação. Como tópico matemático, foi utilizado matrizes e determinantes devido a contemporaneidade do assunto e sua diversidade de aplicações. Com a finalidade de validar os objetivos, foi realizado um experimento com alunos do Ensino Médio do Colégio de Aplicação da Universidade Federal de Roraima, onde após a utilização do aplicativo foi distribuído um questionário a alunos e professores. E, com a tabulação dos resultados, foi realizada uma breve avaliação de alguns aspectos deste trabalho.<br>The improvement in the quality of mathematics teaching is the result of several factors such as the qualification of teachers, the search for new pedagogical models and the inclusion of technology to learning processes.There is a large gap between the technology and the classroom, especially when it comes in public education, and it is this problem that this work seeks to contribute to alternative solutions. Taking advantage of the huge demand of mobile phones and the strong influence that this device has on young people, we seek to support our application conducting research on the pedagogical aspects of mobile learning and, because of the fascination exerted by digital games, we studied the techniques of gamification. In this context, it was developed an application questions and answers (QUIZ), according to the precepts of mobile learning and using the motivational resources of gamification. As mathematical topic was used matrices and determinants due to this matter be current and its range of applications. For the purpose to validate the goals was carried out an experiment with high school students of the College Application of the Federal University of Roraima, where after using the application has distributed a questionnaire to students and teachers. And with the tabulation of results, there was a brief review of some aspects of this work.

Made available in DSpace on 2016-04-27T16:57:03Z (GMT). No. of bitstreams: 1 Roberto Meconi Junior.pdf: 3600051 bytes, checksum: 15b0b72b464227929325b5bdebbe8f28 (MD5) Previous issue date: 2010-11-24<br>Conselho Nacional de Desenvolvimento Científico e Tecnológico<br>This work describes an investigative experience related to High School Math teachers Studies, more precisely about their performance in relation to the use of technologies as mediators during their classes. Through a Math Educational Didactic and technological work- shop offered in the ambit of activities in the Programa de Estudos Pós-Graduados em Educação Matemática da PUC/SP (grupo TecMEM), where a group of teachers from Estado de São Paulo Public School were under observation in the realization in dynamic activities using the software WinMat as well as in the executions of tasks with traditional medias, all of them related to the theme "matrices and determinants". Through qualitative analysis of data, it was possible to verify several difficulties by these groups of researchers, conceptual and technical, but these difficulties could decrease as soon as this articulation was being reached between the interface technological domain and the recover of mathematics concepts involved. Besides, the teachers who are in this investigation have noticed the importance of pedagogical strategies in which mathematics technological classes should be included, more than the simple use of software or other artifact to the students use<br>Este trabalho relata uma experiência investigativa relacionada à formação continuada de professores de Matemática do Ensino Médio, mais precisamente no que tange ao preparo dos mesmos em relação ao uso de tecnologias como mediadoras em suas aulas. Através de uma Oficina Didática de Educação Matemática e Tecnologias, oferecida no âmbito das atividades do Programa de Estudos Pós-Graduados em Educação Matemática da PUC/SP (grupo TecMEM), um grupo de professores da rede pública do Estado de São Paulo foi acompanhado na realização de atividades dinâmicas com uso do software Winmat, bem como na consecução de tarefas em com mídias tradicionais, todas relacionadas ao tema matrizes e determinantes . Através de análise qualitativa dos dados, foi possível constatar diversas dificuldades por parte dos sujeitos da pesquisa, tanto conceituais quanto técnicas, que puderam ser minoradas à medida que se alcançava uma articulação entre o desenvolvimento do domínio tecnológico da interface e a recuperação dos conceitos matemáticos envolvidos. Além disso, os docentes envolvidos nesta investigação indicaram perceber a importância das estratégias pedagógicas que incluam tecnologias nas aulas de Matemática, muito além da mera inserção de softwares e ou artefatos para o uso de seus estudantes

Made available in DSpace on 2015-05-15T11:46:13Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-08-15<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>This work is a study of linear systems from the perspective of linear algebra. We will use the concepts of matrix, vector, linear combination, linear dependence and independence, vector space, basis and dimension. We will also calculate the determinants and implications. Our aim is to present the rudiments of Linear Algebra as helper tool in solving linear systems and display its geometry. We want it to manufacture a auxiliary text that can be explored by students and high school teachers, and so gently introducing this powerful mathematical tool. Throughout the text will be covered also some historical aspects.<br>Este trabalho é um estudo de sistemas lineares sob uma perspectiva da Álgebra Linear. Utilizaremos os conceitos de matriz, vetor, combinação linear, dependência e independência linear, espaço vetorial, base e dimensão. Faremos também o cálculo de determinantes e implicações. Nosso intuito é apresentar os rudimentos da álgebra linear como ferramenta auxiliadora na resolução de sistemas lineares e exibir a sua geometria. Queremos com isto confeccionar um texto auxiliar que possa ser explorado por estudantes e professores do Ensino Médio e, assim, suavemente introduzindo esta poderosa ferramenta da matemática. No decorrer do texto serão abordados também alguns aspectos históricos.

Made available in DSpace on 2018-06-27T19:12:51Z (GMT). No. of bitstreams: 2 DISSERTACAO Lucilene.pdf: 12972661 bytes, checksum: 4339127e1b922dbeb99adb7dfb8522ff (MD5) DISSERTACAO Lucilene.pdf.jpg: 3259 bytes, checksum: 3959e9e09c4690ab37a327eab7cdf742 (MD5) Previous issue date: 2008-08-15<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>It is presented in this work, the results of a qualitative research associated to the teaching of mathematics, in which it was adopted the methodology of teaching through the problem solving. Thus, the goal was to analyze the possibilities that the resolution of problems with matrices and determinants could provide for a meaningful learning of mathematical concepts. The methodological procedures used to gather data were: interview-type semi-structured with teachers from the school, questionnaires with pupils, the participant observation in the classroom and the daily field of the teacher-researcher. The survey was developed with 26 students from the 3º grade of high school at the Technical School José Cañellas of Frederico 8 Westhapen - R/S in the second semester of 2007. For the application and development of activities using the resolution of problems, were followed the steps suggested by Onuchic (1999), which are: 1) To form groups and deliver the activity, 2) The role of the teacher, 3) Results on board; 4) Plenary and analysis of results; 5) Consensus and formalization of activities. Based on theoretical and practical assumptions, it was noticed the importance and necessity of exercise at schools, the problem-solving, since it contemplate the skills and competences developed and proposals in the teaching of mathematics. For this, are vital that the lessons are more participatory, where the teacher is the mediator of the teaching-learning and the students the active subjects of this process. It was thus offer to learners the interpretation of problems as well as the remove of the requested information for later resolution, and by this way allowed to verifying the implementation of such content in several real-life situations. Therefore, the research supplied the understanding of the concepts of matrices and determinants easier, and significantly, since working with the methodology of problem solving awakened the interest and motivation of the students involved, leading them to more autonomy and construction of other problems from the studied ones.<br>Apresenta-se, nesse trabalho, os resultados de uma pesquisa qualitativa associada ao ensino da matemática, em que se adotou a metodologia de ensino por meio da resolução de problemas. Desse modo, o objetivo foi analisar as possibilidades que a resolução de problemas com matrizes e determinantes pode oferecer para uma aprendizagem significativa de conceitos matemáticos. Os procedimentos metodológicos utilizados para a coleta de dados foram: entrevista do tipo semi-estruturada com professores da escola, questionários com os alunos, a observação participante em sala de aula e o diário de campo da professora-pesquisadora. A pesquisa foi desenvolvida com 26 alunos do 3º ano do Ensino Médio da Escola Técnica José Cañellas de Frederico Westhapen R/S, no segundo semestre de 2007. Para a aplicação e o desenvolvimento das atividades utilizando a resolução de problemas, foram seguidos os passos sugeridos por Onuchic (1999), os quais são: 1) Formar grupos e entregar a atividade;2) O papel do professor; 3) Resultados na lousa; 4) Plenária e análise dos resultados; 5) Consenso e formalização das atividades. Com base nos pressupostos teóricos e práticos, percebeu-se a importância e a necessidade de que se exercite nas escolas a resolução de problemas, já que esta contempla as competências e as habilidades desenvolvidas e propostas no ensino de matemática. Para isso, são imprescindíveis que as aulas sejam mais participativas, em que o professor seja o mediador do processo de ensino-aprendizagem e os alunos os sujeitos ativos desse processo. Procurou-se assim, oportunizar aos educandos a interpretação de problemas, bem como a retirada das informações solicitadas, para posterior resolução. Dessa forma, possibilitou-se a verificação da aplicação desses conteúdos em várias situações da vida real. Portanto, a investigação oportunizou a compreensão dos conceitos de matrizes e determinantes com maior facilidade e de forma significativa, já que trabalhar com a metodologia de resolução de problemas despertou o interesse e a motivação dos educandos envolvidos, levando-os a maior autonomia na construção e resolução de outros problemas a partir dos estudados.

[ES] La calidad superficial en las piezas mecanizadas depende del acabado superficial, resultado de las marcas dejadas por la herramienta durante el proceso de corte. Las aproximaciones teóricas tradicionales indican que estas marcas están relacionadas con los parámetros de corte (velocidad de corte, avance, profundidad de corte...), el tipo de máquina, el material de la pieza, la geometría de la herramienta, etc. Pero no todos los tipos de mecanizado y selección de materiales pueden dar un resultado ambiguo. Hoy en día, de manera progresiva, se están utilizando las técnicas de fresado de Alta Velocidad sobre materiales de difícil mecanizado cada vez más. El fresado de Alta Velocidad implica a un considerable número de parámetros del proceso que pueden afectar a la formación topográfica 3D de la superficie. La hipótesis de que los parámetros de rugosidad superficial dependen de las huellas dejadas por la herramienta, determinadas por las condiciones de trabajo y las propiedades del entorno, condujo al desarrollo de una metodología de investigación personalizada. Este trabajo de investigación muestra como la combinación de los parámetros, inclinación del eje de la herramienta, deflexión geométrica de la herramienta y comportamiento vibracional del entorno, influencian sobre el parámetro de rugosidad superficial 3D, Sz. El modelo general fue dividido en varias partes, donde se ha descrito la influencia de parámetros del proceso adicionales, siendo incluidos en el modelo general propuesto. El proceso incremental seguido permite al autor desarrollar un modelo matemático general, paso a paso, testeando y añadiendo los componentes que más afectan a la formación de la topografía de la superficie. En la primera parte de la investigación se seleccionó un proceso de fresado con herramientas de punta plana. Primero, se analiza la geometría de la herramienta, combinada con múltiples avances, para distinguir los principales parámetros que afectan a la rugosidad superficial. Se introduce un modelo de predicción con un componente básico para la altura de la rugosidad, obtenida por la geometría de la herramienta de corte. A continuación, se llevan a cabo experimentos más específicamente diseñados, variando parámetros tecnológicos. Esto empieza con el análisis de la inclinación del eje de la herramienta contra la mesa de fresado. Los especímenes de análisis son muestras con cuatro recorridos de corte rectos con corte en sentido contrario. Las trayectorias lineales con diferentes direcciones dan la oportunidad de analizar la inclinación del husillo de fresado en la máquina. Un análisis visual reveló diferencias entre direcciones de corte opuestas, así como marcas dejadas por el filo posterior de la herramienta. Considerando las desviaciones de las marcas de corte observadas en las imágenes de rugosidad superficial obtenidas a partir de las medidas, se introdujo un análisis sobre el comportamiento dinámico del equipo y de la herramienta de corte. Las vibraciones producen desviaciones en la mesa de fresado y en la herramienta de corte. Estas desviaciones fueron detectadas e incluidas en el modelo matemático para completar la precisión en la predicción del modelo. Finalmente, el modelo de predicción del parámetro de rugosidad Sz fue comprobado con un mayor número de parámetros del proceso. Los valores de Sz medidos y predichos, fueron comparados y analizados estadísticamente. Los resultados revelaron una mayor desviación de la rugosidad predicha en las muestras fabricadas con diferentes máquinas y con diferentes avances. Importantes conclusiones sobre la precisión del equipo de fabricación han sido extraídas y de ellas se desprende que la huella de la herramienta de corte está directamente relacionada con los parámetros de la topografía de la superficie. Además, la influencia de la huella está afectada por la geometría de la herramienta de corte, la rigidez de la herramienta y la precisión del equipo. La geometría de la herramienta conforma la base del parámetro Sz, desviación de la altura de la superficie. Las conclusiones alcanzadas son la base para recomendaciones prácticas, aplicables en la industria.<br>[CA] La qualitat superficial en les peces mecanitzades depèn de l'acabat superficial, resultat de les marques deixades per l'eina durant el procés de tall. Les aproximacions teòriques tradicionals indiquen que aquestes marques estan relacionades amb els paràmetres de tall (velocitat de tall, avanç, profunditat de tall...), el tipus de màquina, el material de la peça, la geometria de l'eina, etc. Però no tots els tipus de mecanitzat i selecció de materials poden donar un resultat ambigu. Avui en dia, de manera progressiva, s'estan utilitzant les tècniques de fresat d'Alta Velocitat sobre materials de difícil mecanització cada vegada més. El fresat d'Alta Velocitat implica un considerable nombre de paràmetres del procés que poden afectar la formació topogràfica 3D de la superfície. La hipòtesi que els paràmetres de rugositat superficial depenen de les empremtes deixades per l'eina, determinades per les condicions de treball i les propietats de l'entorn, va conduir al desenvolupament d'una metodologia d'investigació personalitzada. Aquest treball de recerca mostra com la combinació dels paràmetres, inclinació de l'eix de l'eina, deflexió geomètrica de l'eina i comportament vibracional de l'entorn, influencien sobre el paràmetre de rugositat superficial 3D, Sz. El model general va ser dividit en diverses parts, on s'ha descrit la influència de paràmetres addicionals del procés, sent inclosos en el model general proposat. El procés incremental seguit permet a l'autor desenvolupar un model matemàtic general, pas a pas, testejant i afegint els components que més afecten a la formació de la topografia de la superfície. En la primera part de la investigació es va seleccionar un procés de fresat amb eines de punta plana. Primer, s'analitza la geometria de l'eina, combinada amb múltiples avanços, per distingir els principals paràmetres que afecten la rugositat superficial. S'introdueix un model de predicció amb un component bàsic per a l'altura de la rugositat, obtinguda a través de la geometria de l'eina de tall. A continuació, es duen a terme experiments més específicament dissenyats, variant paràmetres tecnològics. Això comença amb l'anàlisi de la inclinació de l'eix de l'eina contra la taula de fresat. Els espècimens d'anàlisi són mostres amb quatre recorreguts de tall rectes amb tall en sentit contrari. Les trajectòries lineals amb diferents direccions donen l'oportunitat d'analitzar la inclinació del fus de fresat en la màquina. Una anàlisi visual revelà diferències entre direccions de tall oposades, així com marques deixades pel tall posterior de l'eina. Considerant les desviacions de les marques de tall observades en les imatges de rugositat superficial obtingudes a partir de les mesures, es va introduir una anàlisi sobre el comportament dinàmic de l'equip i de l'eina de tall. Les vibracions produeixen desviacions en la taula de fresat i en l'eina de tall. Aquestes desviacions van ser detectades i incloses en el model matemàtic per completar la precisió en la predicció de el model. Finalment, el model de predicció de el paràmetre de rugositat Sz va ser comprovat amb un major nombre de paràmetres del procés. Els valors de Sz mesurats i predits, van ser comparats i analitzats estadísticament. Els resultats van revelar una major desviació de la rugositat predita en les mostres fabricades amb diferents màquines i amb diferents avanços. Importants conclusions sobre la precisió de l'equip de fabricació han estat extretes i d'elles es desprèn que l'empremta de l'eina de tall està directament relacionada amb els paràmetres de la topografia de la superfície. A més, la influència de la empremta està afectada per la geometria de l'eina de tall, la rigidesa de l'eina i la precisió de l'equip. La geometria de l'eina conforma la base del paràmetre Sz, desviació de l'altura de la superfície. Les conclusions assolides són la base per recomanacions pràctiques, aplicables en la indústria.<br>[EN] Surface quality of machined parts highly depends on the surface texture that reflects the marks, left by the tool during the cutting process. The traditional theoretical approaches indicate that these marks are related to the cutting parameters (cutting speed, feed, depths of cut...), the machining type, the part material, the tool geometry, etc. But, different machining type and material selection can give a variable result. In nowadays, more progressively, High Speed milling techniques have been applied on hard-to-cut materials more and more extensively. High-speed milling involves a considerable number of process parameters that may affect the 3D surface topography formation. The hypothesis that surface topography parameters depends on the traces left by the tool, determined by working conditions and environmental properties, led to the development of a custom research methodology. This research work shows how the parameters combination, tool axis inclination, tool geometric deflection, cutting tool geometry and environment vibrational behavior, influence on 3D surface topography parameter Sz. The general model was divided in multiple parts, where additional process parameters influence has been described and included in general model proposed. The incremental process followed allows the author to develop a general mathematical model, step by step, testing and adding the components that affect surface topography formation the most. In the first part of the research a milling procedure with flat end milling tools was selected. First, tool geometry, combined with multiple cutting feed rates, is analyzed to distinguish the main parameters that affect surface topography. A prediction model is introduced with a basic topography height component, performed by cutting tool geometry. Next, specifically designed experiments were conducted, varying technological parameters. That starts with cutting tool axis inclination against the milling table analysis. The specimens of analysis are samples with 4 contrary aimed straight cutting paths. Linear paths in different directions give a chance to analyze milling machine spindle axis topography, as well as marks left from cutting tool back cutting edge. Considering the deviations of cutting marks observed in the images of the surface topography obtained through the measurements, the milling equipment and cutting tool dynamical behavior analysis were introduced. Vibrations produce deviations in the milling table and cutting tool. These deviations were detected and included in the mathematical model to complete the prediction model accuracy. Finally, the prediction model of the topography parameter SZ was tested with increased number of process parameters. Measured and predicted SZ values were compared and analyzed statistically. Results revealed high predicted topography deviation on samples manufactured with different machines and with different feed rates. Relevant conclusions about the manufacturing equipment accuracy have been drawn and they state that cutting tool's footprint is directly related with surface topography parameters. Besides, footprint influence is affected by cutting tool geometry, tool stiffness and equipment accuracy.<br>Logins, A. (2021). High speed milling technological regimes, process condition and technological equipment condition influence on surface quality parameters of difficult to cut materials [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/164122<br>TESIS

碩士<br>國立交通大學<br>應用數學系所<br>99<br>In this thesis we are concerned with the properties of totally nonnegative ( resp. positive ) matrices. An m-by-n entry-wise nonnegative matrix is totally nonnegative (resp. positive) if the determinant of any square submatrix is nonnegative (resp. positive). A totally nonnegative matrix plays an important role in various mathematical branches. The primary propose here is to introduce the basic properties of nonnegative (resp. positive) matrix and to collect the known results in matrix theory with the totally nonnegative (resp. positive) property involved. We will recall the relation between Hadamard product and the positive semidefinite property, and study the relation between Hadamard product and the totally nonnegative (resp. totally positive) property. Furthermore, we also discuss the eventually totally positive property.

A research report submitted to the Faculty of Science, University of the Witwatersrand, in partial fulfillment of the degree of Master of Science.<br>The Toeplitz form is a most useful and important teo! in many areas of applied. mathematics today including signal processing, time-series analysis and prediction theory. It is even used in quantum mechanics in Ising model correlation functions. (Abbreviation abstract)<br>AC 2018

Large dense matrices are ubiquitous in scientific computing, arising from the discretization of integral operators associated with elliptic pdes, Schur complement methods, covariances in spatial statistics, kernel-based machine learning, and numerical optimization problems. Hierarchical matrices are an efficient way for storing the dense matrices of very large dimension that appear in these and related settings. They exploit the fact that the underlying matrices, while formally dense, are data sparse. They have a structure consisting of blocks many of which can be well-approximated by low rank factorizations. A hierarchical organization of the blocks avoids superlinear growth in memory requirements to store n × n dense matrices in a scalable manner, requiring O(n) units of storage with a constant depending on a representative rank k for the low rank blocks. The asymptotically optimal storage requirement of the resulting hierarchical matrices is a critical advantage, particularly in extreme computing environments, characterized by low memory per processing core. The challenge then becomes to develop the parallel linear algebra operations that can be performed directly on this compressed representation. In this dissertation, I implement a set of hierarchical basic linear algebra subroutines (HBLAS) optimized for GPUs, including hierarchical matrix vector multiplication, orthogonalization, compression, low rank updates, and matrix multiplication. I develop a library of open source batched kernel operations previously missing on GPUs for the high performance implementation of the H2 operations, while relying wherever possible on existing open source and vendor kernels to ride future improvements in the technology. Fast marshaling routines extract the batch operation data from an efficient representation of the trees that compose the hierarchical matrices. The methods developed for GPUs extend to CPUs using the same code base with simple abstractions around the batched routine execution. To demonstrate the scalability of the hierarchical operations I implement a distributed memory multi-GPU hierarchical matrix vector product that focuses on reducing communication volume and hiding communication overhead and areas of low GPU utilization using low priority streams. Two demonstrations involving Hessians of inverse problems governed by pdes and space-fractional diffusion equations show the effectiveness of the hierarchical operations in realistic applications.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. Johannesburg, 2014.<br>A multi-dimensional data model provides a good conceptual view of the data in data warehousing and On-Line Analytical Processing (OLAP). A typical representation of such a data model is as a multi-dimensional array which is well suited when the array is dense. If the array is sparse, i.e., has a few number of non-zero elements relative to the product of the cardinalities of the dimensions, using a multi-dimensional array to represent the data set requires extremely large memory space while the actual data elements occupy a relatively small fraction of the space. Existing storage schemes for Multi-Dimensional Sparse Arrays (MDSAs) of higher dimensions k (k > 2), focus on optimizing the storage utilization, and offer little flexibility in data access efficiency. Most efficient storage schemes for sparse arrays are limited to matrices that are arrays in 2 dimensions. In this dissertation, we introduce four storage schemes for MDSAs that handle the sparsity of the array with two primary goals; reducing the storage overhead and maintaining efficient data element access. These schemes, including a well known method referred to as the Bit Encoded Sparse Storage (BESS), were evaluated and compared on four basic array operations, namely construction of a scheme, large scale random element access, sub-array retrieval and multi-dimensional aggregation. The four storage schemes being proposed, together with the evaluation results are: i.) The extended compressed row storage (xCRS) which extends CRS method for sparse matrix storage to sparse arrays of higher dimensions and achieves the best data element access efficiency among the methods compared; ii.) The bit encoded xCRS (BxCRS) which optimizes the storage utilization of xCRS by applying data compression methods with run length encoding, while maintaining its data access efficiency; iii.) A hybrid approach (Hybrid) that provides the best control of the balance between the storage utilization and data manipulation efficiency by combining xCRS and BESS. iv.) The PATRICIA trie compressed storage (PTCS) which uses PATRICIA trie to store the valid non-zero array elements. PTCS supports efficient data access, and has a unique property of supporting update operations conveniently. v.) BESS performs the best for the multi-dimensional aggregation, closely followed by the other schemes. We also addressed the problem of accelerating some selected array operations using General Purpose Computing on Graphics Processing Unit (GPGPU). The experimental results showed different levels of speed up, ranging from 2 to over 20 times, on large scale random element access and sub-array retrieval. In particular, we utilized GPUs on the computation of the cube operator, a special case of multi-dimensional aggregation, using BESS. This resulted in a 5 to 8 times of speed up compared with our CPU only implementation. The main contributions of this dissertation include the developments, implementations and evaluations of four efficient schemes to store multi-dimensional sparse arrays, as well as utilizing massive parallelism of GPUs for some data warehousing operations.

博士<br>國立政治大學<br>應用數學研究所<br>95<br>Classical and generalized Vandermonde matrices are ubiquitous in mathematics, and various studies on their determinants, inverses, explicit LU factorizations with applications are done recently by many authors. In this thesis we shall focus on two topics: One is generalized Vandermonde matrices revisited and the other is various decompositions of some generalized Vandermonde matrices. In the first topic, we prove the well-known determinant formulas of two types of generalized Vandermonde matrices using only mathematical induction, different from the proofs of Fulin Qian's and Flowe-Harris'. In the second topic, which constitutes the main results of this thesis, we devote ourself to two themes. Firstly, we study a special class which is the transpose of the generalized Vandermonde matrix of the first type and succeed in obtaining its LU factorization in an explicit form. Furthermore, we express the LU factorization into 1-banded factorizations and get the inverse explicitly. Secondly, we consider a totally positive(TP) generalized Vandermonde matrix and obtain its unique LU factorization without using Schur functions. The result is better than Demmel and Koev's which is involved Schur functions. As by-products, we gain the determinant and the inverse of the required matrix and express any Schur function in an explicit form. Basing on the above result, we obtain a way to calculate Kostka numbers by expanding Schur functions.

This paper examines the determinants of profitability using operations strategy, productivity, and service measures in the context of the U.S. domestic airline industry. Data on ten carriers was collected on a quarterly basis between 1995 and 2007. An analysis is performed separately on data prior and post 9/11 attack. It is found that operations strategy and productivity measures are significant both before and after the 9/11 attack, whereas service measures are only significant before 9/11. Some managerial implications are provided. Additionally, it is found that the profitability of full-service carriers is improving faster than low-cost carriers after 9/11.

Tese de Doutoramento em Gestão de Empresas, na especialidade de Estratégia, apresentada à Faculdade de Economia da Universidade de Coimbra<br>Para melhorar o seu desempenho, as empresas transformadoras enfrentam o paradoxo da escolha entre o alinhamento com o contexto externo e a exploração de novas formas de inovar. Acresce a necessidade de desenvolverem flexibilidade produtiva para enfrentar uma procura variável. Estas empresas deparam-se com concorrência, gamas crescentes de complexas soluções tecnológicas, tendências de mercado em mudança e ocasionais choques económicos externos. Neste contexto, acedem a conhecimento externo, que assimilam e transformam em conhecimentos específicos aplicáveis ao desenvolvimento das suas capacidades internas. Esta tese foca a indústria portuguesa e explora as relações entre a capacidade absortiva, orientações para o mercado, orientações das competências de inovação e flexibilidade produtiva, para compreender o balanço que traduz melhor desempenho de negócio e de operações. Os resultados realçam o papel da capacidade absortiva na abordagem aos paradoxos exploitation-exploration (flexibilidade de inovação) e da mudança-conservação (flexibilidade produtiva). Adicionalmente, a orientação das competências de inovação (exploitation-exploration) revela-se mais importante para o desempenho de negócio do que a orientação para o mercado (reativa-proativa) - capítulo 3 - ao passo que a criação de conhecimento contribui para explicar um melhor desempenho através da flexibilidade produtiva (capítulo 4). Finalmente, uma estratégia de fiabilidade na inovação afeta positivamente a flexibilidade produtiva (capítulo 5), enquanto as orientações das competências de inovação (exploitation-exploration) e a flexibilidade produtiva se revelam essenciais ao desempenho sob condições de maior turbulência (capítulos 3 e 4).<br>Manufacturing firms are challenged by the paradox of aligning to their environment while exploring new ways to innovate, in their efforts to enhance business performance. They also need to develop manufacturing flexibility to address varying demand and embrace the paradox of change versus preservation. These firms have to face the competition, a growing plethora of complex technological solutions, fast changing customer trends and occasional economic shocks. In such a dynamic context, a growing volume of external information needs to be accessed, assimilated and transformed into firm-specific applicable knowledge enabling developments in core capabilities. This thesis focuses on the Portuguese industry and explores the relationships between absorptive capacity, market and innovation competences orientations, and manufacturing flexibility, to understand the balances resulting in higher business and operations performance. Overall, the findings support the key role of absorptive capacity for firms to cope with the paradoxes of exploitation-exploration (innovation flexibility) and change-preservation (manufacturing flexibility). Additionally, innovation competences orientation (exploitation-exploration) are more important than market orientation (responsive-proactive) to improve business performance – chapter 3. Moreover, knowledge creation helps explaining why some firms are better than others at enhancing operations performance through manufacturing flexibility – chapter 4. Lastly, an innovation reliability strategy is found to positively affect manufacturing flexibility (chapter 5), while innovation competences orientation (exploitation-exploration) and manufacturing flexibility are shown to be essential for the perf

The thesis studies the role of human figure drawing in Orientační test školní zralosti (i. e. Jirasek's Orientation Test of School Readiness). The starting point is the correspondence between human figure drawing and other tasks in both verbal and non-verbal thinking. For the empirical material we have chosen pre-school children results in Orientační test školní zralosti, including the verbal thinking test and Raven's Coloured Progressive Matrices. The aim is to examine correspondence of human figure drawing with other tasks taking into account verbal and non-verbal thinking and logical and infralogic operations. The data was collected in two stages with the interval of four months and therefore it is able to assess durability of findings in time. The thesis is beneficial in terms of qualitative analysis of discovered correspondences and also in developing a theory of abilities tested by the test, especially regarding human figure drawing. Last but not least it is helpful in examining similarities and differences in the ability of children to analyse and synthetize. KEY WORDS: school maturity, drawing, figure, man, writing, points, matrices, verbal thinking, non-verbal thinking, logical operations, infralogic operations, analysis, synthesis

Indiana University-Purdue University Indianapolis (IUPUI)<br>We study the one-parameter family of determinants $det(I-\gamma K_{PII}),\gamma\in\mathbb{R}$ of an integrable Fredholm operator $K_{PII}$ acting on the interval $(-s,s)$ whose kernel is constructed out of the $\Psi$-function associated with the Hastings-McLeod solution of the second Painlev\'e equation. In case $\gamma=1$, this Fredholm determinant describes the critical behavior of the eigenvalue gap probabilities of a random Hermitian matrix chosen from the Unitary Ensemble in the bulk double scaling limit near a quadratic zero of the limiting mean eigenvalue density. Using the Riemann-Hilbert method, we evaluate the large $s$-asymptotics of $\det(I-\gamma K_)$ for all values of the real parameter $\gamma$.