Estudo Comparativo de gráaficos de probabilidade normal para Anáalise de experimentos fatoriais não replicados

Two-level factorial designs are widely used in industrial experimentation. However, many factors in such a design require a large number of runs to perform the experiment, and too many replications of the treatments may not be feasible, considering limitations of resources and of time, making it expensive. In these cases, unreplicated designs are used. But, with only one replicate, there is no internal estimate of experimental error to make judgments about the significance of the observed efects. One of the possible solutions for this problem is to use normal plots or half-normal plots of the efects. Many experimenters use the normal plot, while others prefer the half-normal plot and, often, for both cases, without justification. The controversy about the use of these two graphical techniques motivates this work, once there is no register of formal procedure or statistical test that indicates \which one is best". The choice between the two plots seems to be a subjective issue. The central objective of this master's thesis is, then, to perform an experimental comparative study of the normal plot and half-normal plot in the context of the analysis of the 2k unreplicated factorial experiments. This study involves the construction of simulated scenarios, in which the graphics performance to detect significant efects and to identify outliers is evaluated in order to verify the following questions: Can be a plot better than other? In which situations? What kind of information does a plot increase to the analysis of the experiment that might complement those provided by the other plot? What are the restrictions on the use of graphics? Herewith, this work intends to confront these two techniques; to examine them simultaneously in order to identify similarities, diferences or relationships that contribute to the construction of a theoretical reference to justify or to aid in the experimenter's decision about which of the two graphical techniques to use and the reason for this use. The simulation results show that the half-normal plot is better to assist in the judgement of the efects, while the normal plot is recommended to detect outliers in the data

Modelagem Matemática e Computacional de fenômenos eletrocinéticos em meios porosos carregados eletricamente

In this work we present a mathematical and computational modeling of electrokinetic phenomena in electrically charged porous medium. We consider the porous medium composed of three different scales (nanoscopic, microscopic and macroscopic). On the microscopic scale the domain is composed by a porous matrix and a solid phase. The pores are filled with an aqueous phase consisting of ionic solutes fully diluted, and the solid matrix consists of electrically charged particles. Initially we present the mathematical model that governs the electrical double layer in order to quantify the electric potential, electric charge density, ion adsorption and chemical adsorption in nanoscopic scale. Then, we derive the microscopic model, where the adsorption of ions due to the electric double layer and the reactions of protonation/ deprotanaç~ao and zeta potential obtained in modeling nanoscopic arise in microscopic scale through interface conditions in the problem of Stokes and Nerst-Planck equations respectively governing the movement of the aqueous solution and transport of ions. We developed the process of upscaling the problem nano/microscopic using the homogenization technique of periodic structures by deducing the macroscopic model with their respectives cell problems for effective parameters of the macroscopic equations. Considering a clayey porous medium consisting of kaolinite clay plates distributed parallel, we rewrite the macroscopic model in a one-dimensional version. Finally, using a sequential algorithm, we discretize the macroscopic model via the finite element method, along with the interactive method of Picard for the nonlinear terms. Numerical simulations on transient regime with variable pH in one-dimensional case are obtained, aiming computational modeling of the electroremediation process of clay soils contaminated

Uma proposta alternativa para o ensino progressões relacionadas a funções

Generally, arithmetic and geometric progressions are taught separately from ane and exponential functions, only by the use of memorized formulas and without any concern of showing students how these contents are related. This paper aims at presenting a way of teaching such contents in an integrated way, starting with the definition of ane and exponential functions relating them to situations from the daily life of the students. Then, characteristics and graphics of those functions are presented and, subsequently, arithmetic and geometric progression are shown as a restriction of the ane and exponential functions. Thus, the study of the progressions is introduced based on the functions mentioned above using situations from students daily lives as examples

O estudo das funções quadráticas e sua relação com o cotidiano

Across the centuries, Mathematics - exact science as it is - has become a determining role in the life of man, which forms to use suprir needs of their daily lives. With this trajectory, is characterized the importance of science as an instrument of recovery not only conteudstica, but also a mathematician to know that leads the apprentice to be a dynamic process of learning ecient, able to find solutions to their real problems. However, it is necessary to understand that mathematical knowledge today requires a new view of those who deal directly with the teaching-learning process, as it is for them - Teachers of Mathematics - desmistificarem the version that mathematics, worked in the classroom, causes difficulties for the understanding of students. On this view, we tried to find this work a methodology that helps students better understand the Quadratic functions and its applications in daily life. Making use of knowledge Ethnomathematics, contextualizing the problems relating to the content and at the same time handling the software GeoGebra, aiming a better view of the behavior of graphs of functions cited

Probabilidade no ensino médio

This thesis aims to show teachers and students in teaching and learning in a study of Probability High School, a subject that sharpens the perception and understanding of the phenomea of the random nature that surrounds us. The same aims do with people who are involved in this process understand basic ideas of probability and, when necessary, apply them in the real world. We seek to draw a matched between intuition and rigor and hope therebyto contribute to the work of the teacher in the classroom and the learning process of students, consolidating, deepening and expaning what they have learned in previous contents