En esta tesis se analiza de manera detallada los sistemas de refrigeración solar con equipos de absorción de doble efecto con captadores solares de concentración en términos de energía primaria consumida. El análisis de estos sistemas permite compararlos con sistemas de refrigeración por absorción de simple efecto accionados con energía solar térmica de baja temperatura y con sistemas convencionales de compresión. Estos tres tipos de sistemas han sido modelizados mediante el software de simulación TRNSYS para cubrir la demanda frigorífica de un edificio genérico de oficinas localizado en Sevilla (España). Un aspecto importante en esta tesis es la modelización de las enfriadoras de absorción de simple y doble efecto mediante el método de la ecuación característica. Este método permite modelizar las prestaciones térmicas del equipo de absorción de manera sencilla y robusta, además que debido a su estructura puede ser aplicado a cualquier sistema de refrigeración por absorción. / This thesis presents a detailed analysis of solar cooling systems, with double-effect absorption chillers activated by concentrating solar collectors, in terms of primary energy savings. This analysis allows comparing this type of systems with solar assisted air-conditioning installations composed by single-effect absorption chillers and flat plate solar collectors, and conventional compression systems. These three types of systems have been modeled in a TRNSYS simulation environment and applied to a generic building located in the city of Seville (Spain) to cover its cooling demand. An important aspect of this thesis is the modeling of single and double-effect absorption chillers by means of the characteristic equation method (ChEM). This method permits modeling of thermal performance of the absorption machine in a simple and robust manner, and due to its structure, the method can be applied to any absorption refrigeration system.

As equações de diferenças desempenham papel fundamental na modelagem de problemas em que o tempo é medido em intervalos discretos, por exemplo, horas, dia, mês, ano. Elas têm aplicações em Matemática, Física, Engenharia, Economia, Biologia e Sociologia. O objetivo desse trabalho é estudar as equações de diferenças lineares de ordem superior, focando aspectos teóricos, métodos de determinação das soluções destas equações e análise da estabilidade de soluções de equações de diferenças de 2a ordem com coeficientes constantes. Exemplos e aplicações ilustram a teoria desenvolvida. É apresentada uma proposta didática relacionada ao tema para ser trabalhada no ensino médio. / The difference equations play a key role in shaping problems in which time is measured in discrete intervals, e.g., hour, day, month, year. They may be applied to Mathematics, Physics, Engineering, Economics, Biology and Sociology. The aim of this work is to study the higher-order linear difference equations, focusing on the theoretical aspects, on the methods used to determine the solutions of these equations and also on the analysis of the stability of 2nd-order difference equations with constants coefficients. Examples and applications depict the developed theory. In addition, a didactic proposal related to the topic to be worked on high school is presented.

As equações de diferenças desempenham papel fundamental na modelagem de problemas em que o tempo é medido em intervalos discretos, por exemplo, horas, dia, mês, ano. Elas têm aplicações em Matemática, Física, Engenharia, Economia, Biologia e Sociologia. O objetivo desse trabalho é estudar as equações de diferenças lineares de ordem superior, focando aspectos teóricos, métodos de determinação das soluções destas equações e análise da estabilidade de soluções de equações de diferenças de 2a ordem com coeficientes constantes. Exemplos e aplicações ilustram a teoria desenvolvida. É apresentada uma proposta didática relacionada ao tema para ser trabalhada no ensino médio. / The difference equations play a key role in shaping problems in which time is measured in discrete intervals, e.g., hour, day, month, year. They may be applied to Mathematics, Physics, Engineering, Economics, Biology and Sociology. The aim of this work is to study the higher-order linear difference equations, focusing on the theoretical aspects, on the methods used to determine the solutions of these equations and also on the analysis of the stability of 2nd-order difference equations with constants coefficients. Examples and applications depict the developed theory. In addition, a didactic proposal related to the topic to be worked on high school is presented.

Submitted by Luanna Matias (lua_matias@yahoo.com.br) on 2015-05-15T18:05:08Z No. of bitstreams: 2 Dissertação - Ricardo da Silva Santos - 2015.pdf: 789332 bytes, checksum: 923307ee147a03d1a874647f6dcf4c9e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luanna Matias (lua_matias@yahoo.com.br) on 2015-05-15T18:08:48Z (GMT) No. of bitstreams: 2 Dissertação - Ricardo da Silva Santos - 2015.pdf: 789332 bytes, checksum: 923307ee147a03d1a874647f6dcf4c9e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-05-15T18:09:06Z (GMT). No. of bitstreams: 2 Dissertação - Ricardo da Silva Santos - 2015.pdf: 789332 bytes, checksum: 923307ee147a03d1a874647f6dcf4c9e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-03-27 / This work was divided into three chapters , the rst we have some basic de nitions for the study of di erential equations, and basic results as Euler's formula and Wronskian . In the second chapter, we talked about Di erential Equations of First Order Linear, and commenting on PVI, and the Theorem of Existence and Uniqueness for ODEs. In the third and main chapter, we work with resolution methods Di erential Equations. In particular, we present a unnusual in mathematics literature to solve Linear Di erential Equations, which is by Equation Characteristic. / Este trabalho foi dividido em 3 capítulos. No primeiro temos algumas de finições básicas para o estudo de Equações Diferenciais, e resultados básicos como a fórmula de Euler e Wronskiano. No segundo capítulo, falamos sobre Equações Diferenciais Lineares de Primeira Ordem, além de comentarmos sobre o que vem a ser Problema do Valor Inicial (PVI), e o Teorema da Existência e Unicidade para EDO's. No terceiro e principal capítulo, trabalhamos com métodos de resolução de uma Equação Diferencial Ordinária Com Coe ficentes Constantes. Em especial, apresenta-mos um método não tão usual na literatura Matemática pra resolver EDOs Lineares, que é através da Derivação da Equação Caraterística.

The thesis is paid to design frequency filters steerable jet active elements of the MO–CF (Multiple-Output Current Follower) and also newly-developed current active element DACA (Digitally Adjustable Current Amplifier) in the company ON Semiconductor. The first three chapters focus on basic properties of frequency filters, used components and circuit design methods. The digitally controllable current amplifier DACA is used for managing the radio frequency filters and adjust it using the current amplification parameter A through the digital input CTR. For the design of filters of the second order a method of M-C Signal flow graphs is used. This method is in the work proved very useful and contributed to the modification of already designed frequency filters. The fourth chapter describes the actual detailed design of circuits with quality management, or marginal frequencies to the two parameters. Involvement of the proposed filter is simulated in the OrCAD program for different levels of models of the circuit elements. At the end of each filter design there is a comparison of theoretical and simulated values of the adjustable parameters circuit. The conclusion was one of the districts selected for experimental verification, followed by comparing the measured and simulated transmission characteristics.

Submitted by Maria Medeiros (maria.dilva1@ufcg.edu.br) on 2018-11-08T12:05:44Z No. of bitstreams: 1 JOSÉ NILTON SILVA - TESE (PPGEQ) 2013.pdf: 1910479 bytes, checksum: 59c6bfc5fdbee46bc17470e9b2c8c2e5 (MD5) / Made available in DSpace on 2018-11-08T12:05:44Z (GMT). No. of bitstreams: 1 JOSÉ NILTON SILVA - TESE (PPGEQ) 2013.pdf: 1910479 bytes, checksum: 59c6bfc5fdbee46bc17470e9b2c8c2e5 (MD5) Previous issue date: 2013-08-01 / Este trabalho trata do desenvolvimento de uma metodologia baseada nos conceitos clássicos de estatística e probabilidade para a análise e avaliação da robustez da estabilidade e do desempenho de sistemas de controle, particularmente àqueles que usam o PID (Proporcional, Integral, Derivativo) como lei de controle. Visando estabelecer as condições para a aplicação da metodologia, um sistema de identificação do processo foi desenvolvido de forma recursiva, no qual modelos de convolução e fenomenológico foram empregados como representação do modelo e processo, agrupado a um procedimento de auto sintonia, necessário para considerar os parâmetros de sintonia como variáveis aleatórias e, por conseguinte as raízes da equação característica do sistema em malha fechada.O mapeamento da região de robustez tem sido realizado a partir das raízes da equação característica, considerando a distância estatística como a métrica representativa da robustez da estabilidade a qual permite estabelecer a região com certo grau de significância.Os resultados obtidos demonstram o potencial analítico exigido pela metodologia, permitindo também a análise online, com baixo esforço computacional e operacional mostrando ser um poderoso instrumento de avaliação de sistema de controle. / This study discusses the development of a methodology based on classical concepts of statistics and probability to analyze and evaluate the robustness of the stability and performance of the control system, particularly those that use the PID as control law. To establish the conditions for the application of the methodology, a recursive system identification method process was developed, in which convolution and phenomenological models were used to represent model and process, together with a self-tuning procedure that is necessary to consider tuning parameters as random variables, and hence the roots of the characteristic equation of the closed loop system. The mapping of the region of robustness has been achieved from the roots of the characteristic equation, considering the statistical distance as the metric represented to the robustness of stability which allows the region to establish a degree of significance. The results obtained demonstrate the potential analytical and evaluation required by the methodology, allowing such analysis also "online" with low computational effort and operational proving to be a powerful tool in the analysis of control system.

Submitted by Kilvya Braga (kilvyabraga@hotmail.com) on 2018-04-18T13:53:36Z No. of bitstreams: 1 ALISSON CASTRO DO NASCIMENTO - DISSERTAÇÃO (PPGEQ) 2016.docx: 5565605 bytes, checksum: c2e8a916a77d583ce8d664d0ec023fce (MD5) / Made available in DSpace on 2018-04-18T13:53:36Z (GMT). No. of bitstreams: 1 ALISSON CASTRO DO NASCIMENTO - DISSERTAÇÃO (PPGEQ) 2016.docx: 5565605 bytes, checksum: c2e8a916a77d583ce8d664d0ec023fce (MD5) Previous issue date: 2016-04-14 / CNPq / Este trabalho apresenta uma metodologia baseada em princípios da estatística clássica para determinar as regiões de estabilidade robusta de sistemas lineares ou não lineares, com um nível de conservadorismo muito menor que àqueles apresentados pelas metodologias determinísticas. O caráter aleatório das raízes da equação características do sistema, representado pelas distribuições de probabilidades diz respeito ao universo de todos os resultados possíveis para o fenômeno, sendo assim possível estabelecer o mapeamento das raízes através da métrica da distância estatística associada a função chi-quadrado para um nível de significância α. Desta forma, as raízes podem ser coletadas, gerando as distribuições de probabilidade, bem como também determinada a região no plano complexo que as contém. Um dos problemas da metodologia determinista reside em não considerar as interações entre as variáveis, como também o assim chamado “problema inverso”. Ainda no âmbito da análise determinística, pode-se observar que tal análise considera as raízes da equação característica distribuídas de acordo com a distribuição uniforme. Comparações com os métodos clássicos de análise da estabilidade como o lugar das raízes, o conceito de entrada limitada/saída limitada, ou ainda a teoria de estabilidade definida por Liapunov, também estão inclusas nas análises realizadas neste trabalho. Tais comparações têm indicado que os resultados obtidos através da metodologia desenvolvida são menos conservativos, e consequentemente produz uma análise e mapeamento da região de estabilidade robusta mais realista, pois considera todas as variáveis, os parâmetros e as interações simultâneas entre eles, sem a necessidade de avaliar contribuições isoladas relativas a análise de estabilidade. O método proposto permite também monitorar continuamente a região de estabilidade, avaliando a sua tendência, e com isso determinando a necessidade de tomada de decisão, em tempo hábil, a fim de restaurar tal região. A fim de analisar o comportamento da metodologia e os efeitos que a descreve,é utilizado um sistema reativo e outro sistema não reativo. / This work presents a methodology based on classical statistics principles with a view to determining the regions of robust stability of linear or non-linear systems, with a reduced level of conservatism relative to deterministic methods. The random nature of the roots of the characteristics equation of the system represented by their probability distributions is with regard to the universe of all possible outcomes for the phenomenon. This means that it is possible to map the roots by using the statistical distance as a metric associated with the chi-squared function to a level of significance α. Thus, the roots can be collected, thereby generating the probability distributions. In addition, the region in the complex plane that contains them is thereby established. One of the problems of deterministic methodology lies in not considering interactions between variables and another problem is the so-called "inverse problem". Within the scope of deterministic analysis, it is observed that such an analysis considers the roots of the characteristic equation are distributed uniformly. Comparisons with the classical methods of analysis of stability such as the root-locus, the concept of bounded input/bounded output and Lyapunov stability theory, are also included in the analysis made in this article. Such comparisons have indicated that the results obtained using the methodology presented are less conservative, and therefore producing an analysis and mapping of robustness of stability more realistically, because it considers all variables, parameters and simultaneous interactions between them, without the need to assess the individual contributions of each variable, related to stability analysis. The proposed method also allows a check on the stability region to be run continuously, thus assessing its tendency, and therefore determining the need for decision-making, in a timely manner, in order to restore such a region. In work is used a reactive system and other non-reactive system, in order to evaluate the behavior of the methodology and it is effects.

Thesis (Ph.D. (Statistics)) -- University of Limpopo, 2017 / Operations Research (OR) is a scientific method for developing quantitatively well-grounded recommendations for decision making. While it is true that it uses a variety of mathematical techniques, OR has a much broader scope. It is in fact a systematic approach to solving problems, which uses one or more analytical tools in the process of analysis. Over the years, OR has evolved through different stages. This study is motivated by new real-world challenges needed for efficiency and innovation in line with the aims and objectives of OR – the science of better, as classified by the OR Society of the United Kingdom. New real-world challenges are encountered on a daily basis from problems arising in the fields of water, energy, agriculture, mining, tourism, IT development, natural phenomena, transport, climate change, economic and other societal requirements. To counter all these challenges, new techniques ought to be developed. The growth of global markets and the resulting increase in competition have highlighted the need for OR techniques to be improved. These developments, among other reasons, are an indication that new techniques are needed to improve the day-to-day running of organisations, regardless of size, type and location. The principal aim of this study is to modify and develop new OR techniques that can be used to solve emerging problems encountered in the areas of linear programming, integer programming, mixed integer programming, network routing and travelling salesman problems. Distribution models, resource allocation models, travelling salesman problem, general linear mixed integer ii programming and other network problems that occur in real life, have been modelled mathematically in this thesis. Most of these models belong to the NP-hard (non-deterministic polynomial) class of difficult problems. In other words, these types of problems cannot be solved in polynomial time (P). No general purpose algorithm for these problems is known. The thesis is divided into two major areas namely: (1) network models and (2) resource allocation and distribution models. Under network models, five new techniques have been developed: the minimum weight algorithm for a non-directed network, maximum reliability route in both non-directed and directed acyclic network, minimum spanning tree with index less than two, routing through 0k0 specified nodes, and a new heuristic to the travelling salesman problem. Under the resource allocation and distribution models section, four new models have been developed, and these are: a unified approach to solve transportation and assignment problems, a transportation branch and bound algorithm for the generalised assignment problem, a new hybrid search method over the extreme points for solving a large-scale LP model with non-negative coefficients, and a heuristic for a mixed integer program using the characteristic equation approach. In most of the nine approaches developed in the thesis, efforts were done to compare the effectiveness of the new approaches to existing techniques. Improvements in the new techniques in solving problems were noted. However, it was difficult to compare some of the new techniques to the existing ones because computational packages of the new techniques need to be developed first. This aspect will be subject matter of future research on developing these techniques further. It was concluded with strong evidence, that development of new OR techniques is a must if we are to encounter the emerging problems faced by the world today. Key words: NP-hard problem, Network models, Reliability, Heuristic, Largescale LP, Characteristic equation, Algorithm.

It the thesis, we study retarded functional differential equations. As a result of the Banach fixed point theorem, it is easy to show that there exists a unique solution to such problems. Alas, this theorem gives us no information on the form of the solution. Therefore, we are particularly interested in expressing it. We achieve that by applying Laplace transform to both sides of the equation, we get a solution to this modified problem and subsequently claim that we can apply the inverse Laplace transform to express the solution of the former problem. At the end of the thesis, we formulate and prove the exponential estimate of the solution. 1

Sequences often occur in many branches of applied mathematics. Recurrence relation is a powerful tool to characterize and study sequences. Some commonly used methods for solving recurrence relations will be investigated. Many examples with applications in algorithm, combination, algebra, analysis, probability, etc, will be discussed. Finally, some well-known contest problems related to recurrence relations will be addressed.