Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING / Bibliography: leaf 45. / by Ron Yair Pinter. / M.S.

abstract: The attractiveness of a reward depends in part on the delay to its receipt, with more distant rewards generally being valued less than more proximate ones. The rate at which people discount the value of delayed rewards has been associated with a variety of clinically and socially relevant human behaviors. Thus, the accurate measurement of delay discounting rates is crucial to the study of mechanisms underlying behaviors such as risky sex, addiction, and gambling. In delay discounting tasks, participants make choices between two alternatives: one small amount of money delivered immediately versus a large amount of money delivered after a delay. After many choices, the experimental task will converge on an indifference point: the value of the delayed reward that approximates the value of the immediate one. It has been shown that these indifference points are systematically biased by the direction in which one of the alternatives adjusts. This bias is termed a sequencing effect. The present research proposed a reference-dependent model of choice drawn from Prospect Theory to account for the presence of sequencing effects in a delay discounting task. Sensitivity to reference frames and sequencing effects were measured in two computer tasks. Bayesian and frequentist analyses indicated that the reference-dependent model of choice cannot account for sequencing effects. Thus, an alternative, perceptual account of sequencing effects that draws on a Bayesian framework of magnitude estimation is proposed and furnished with some preliminary evidence. Implications for future research in the measurement of delay discounting and sensitivity to reference frames are discussed. / Dissertation/Thesis / Masters Thesis Psychology 2018

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2016-05-31T09:41:38Z No. of bitstreams: 2 Dissertação - Josiana Gomes Barbosa Arenhardt - 2016.pdf: 10764471 bytes, checksum: 8fee3bbd62885870474ad3578760ac1a (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-05-31T09:46:51Z (GMT) No. of bitstreams: 2 Dissertação - Josiana Gomes Barbosa Arenhardt - 2016.pdf: 10764471 bytes, checksum: 8fee3bbd62885870474ad3578760ac1a (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2016-05-31T09:46:52Z (GMT). No. of bitstreams: 2 Dissertação - Josiana Gomes Barbosa Arenhardt - 2016.pdf: 10764471 bytes, checksum: 8fee3bbd62885870474ad3578760ac1a (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2016-03-28 / In this dissertation we will cover the study of conic sections: ellipse, hyperbola and parabola. This subject is quite rarely addressed in high school books. We therefore propose an approach that favors the development of students’ ability to algebraically classify, geometrically compare, and understand the constructions in a simple and pleasant way. We atempt address the subject in a detailed and rigorous manner, telling the historical development, talking about its applications, and classifing the conic sections through the reduced equations. Starting from the general equation of conic sections, we discuss the role of rotation and translation processes that lead the general classification of conic sections. Since the aim of this work is to be a comprehensive source for teachers and students interested in the subject, we also present a way to classify the conic sections using definitions and theorems from linear algebra, enabling the reader to choose between methods and taking him to realize that Analytical Geometry and Linear Álgebra complement theirselves. For the sake of strenghtening the intuition on this process we will use some features of the mathematical software Geogebra. / Neste trabalho de conclusão de curso abordaremos o estudo das seções cônicas: elipse, hipérbole e a parábola. Tal assunto é muito pouco abordado nos livros de ensino médio. Por isso propomos uma abordagem ao tema que favoreça o desenvolvimento da habilidade dos alunos em classificar algebricamente, comparar geometricamente, e entender as construções de forma simples e prazerosa. Abordaremos o assunto de forma detalhada e rigorosa, contaremos a parte histórica, suas aplicações, classificaremos as cônicas através das equações reduzidas. Partindo da equação geral das cônicas discutimos a natureza dos processos de rotação e translação que levam a classificação geral das cônicas. Como o objetivo deste trabalho é ser fonte de referência aos professores e estudantes que se interessam pelo tema, apresentaremos também uma forma de classificar as cônicas usando definições e teoremas da Álgebra Linear, possibilitando ao leitor escolher qual método utilizar e levá-lo a perceber que a Geometria Analítica e a Álgebra Linear se complementam. E, para enriquecer a intuição à este processo utilizaremos alguns recursos do software matemático Geogebra.

Submitted by JÚLIO HEBER SILVA (julioheber@yahoo.com.br) on 2017-04-18T19:26:13Z No. of bitstreams: 2 Dissertação - Danielle Michaelsen Lago - 2017.pdf: 6057418 bytes, checksum: 82697fc49062f88da2b3e99b2791a358 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-04-20T12:34:22Z (GMT) No. of bitstreams: 2 Dissertação - Danielle Michaelsen Lago - 2017.pdf: 6057418 bytes, checksum: 82697fc49062f88da2b3e99b2791a358 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-04-20T12:34:22Z (GMT). No. of bitstreams: 2 Dissertação - Danielle Michaelsen Lago - 2017.pdf: 6057418 bytes, checksum: 82697fc49062f88da2b3e99b2791a358 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-03-31 / This work was carried out to help teachers and students of high school in the study of geometric gures known as ellipse, parabola and hyperbola obtained through the cone section. We will present how the main characters in the story in uenced the ndings. We will demonstrate the respective canonical (reduced) equations of each of the gures as well as the general equation. We will present some of the applications o ered by these structures emphasizing the importance of studying this theme. / Este trabalho foi realizado para auxiliar professores e alunos do ensino médio no estudo das guras geométricas conhecidas como elipse, parábola e hipérbole obtidas através da secção do cone. Apresentaremos como os principais personagens da história in uenciaram nas descobertas relativas ao conteúdo. Demonstraremos as respectivas equações canônicas (reduzidas) de cada uma das guras bem como a equação geral para a obtenção dessas estruturas. Apresentaremos algumas das as aplicações oferecidas por estas estruturas ressaltando a importância do estudo deste tema.

In this investigation an attempt was made to determine how learners and teachers use computers in the teaching and learning of hyperbolic graphs in Mathematics. A comprehensive literature study showed that there are many benefits in using computers to study Mathematics. The investigation was done in two phases. In the first phase, a questionnaire was given to learners. The second phase involved interviewing learners and teachers. Findings indicate that learners and teachers enjoy using computers in the teaching and learning of Mathematics. Analysis of the results shows that the use of computers in teaching and learning of Mathematics, in particular the teaching and learning of hyperbolic graphs is beneficial. / Mathematical Sciences / M.Sc. (Mathematics Education)

The diploma thesis deals with preparing the production process of the winning prize, which contains a selection in the form of a hyperbolic paraboloid in its upper part. The work is divided into four main chapters. First of all, the introduction part of the diploma thesis presents the possibilities of programming in the Sinumerik control system. Next, the mathematical requirements of the selected surface - hyperbolic paraboloid - are explained. The practical part consists of creating an NC program where all the theoretical knowledge from the introduction is applied. Finally, the diploma thesis ends with an economic evaluation of the selected element.

Synthetic aperture radar (SAR) was originally designed as an airborne ground-imaging radar technology. But it has long been desired to also be able to use SAR imaging systems to detect, locate, and track moving ground targets, a process called Ground Moving Target Indication (GMTI). Unfortunately, due to the nature of how SAR works, it is inherently poorly suited to the task of GMTI. SAR only focuses targets and image features that remain stationary during the data collection. A moving ground target therefore does not focus in a conventional SAR image, which complicates the process of performing GMTI with SAR systems. This thesis investigates the feasibility of performing GMTI with single-channel, unsquinted, broadside stripmap SAR despite this inherent limitation. This study focuses solely on the idealized case of direct energy returns from point targets on flat ground, where they and the airborne radar platform all move rectilinearly with constant speed. First, the various aspects of how SAR works, the signal processing used to collect the SAR data, and the backprojection image formation algorithm are explained. The effects of target motion are described and illustrated in actual and simulated SAR images. It is shown how the backprojection (BPJ) algorithm, typically used to image a stationary landscape scene, can also focus on moving targets when the target motion is known a priori. A SAR BPJ ambiguity function is also derived and presented. Next, the time-changing geometry between the airborne radar and a ground target is mathematically analyzed, and it is shown that the slant range between the radar and any ground target, moving or stationary, is a hyperbolic function of time. It is then shown that this hyperbolic range history causes the single-channel SAR GMTI problem to be underdetermined. Finally, a method is then presented for resolving the underdetermined nature of the problem. This is done by constraining a target's GMTI solution using contextual information in the SAR image. Using constraining information, a theoretical way is presented to perform limited GMTI with a single-channel SAR system by using a modified form of the BPJ imaging algorithm, and practical considerations are addressed that complicate the process. Instead of focusing on stationary pixels, this GMTI method uses the BPJ ambiguity function to search for moving targets on a straight path, such as a road, by performing matched filtering on a collection of moving pixels in a position-velocity image space. Nevertheless, it is concluded that for moving point targets, general GMTI with no path constraints is infeasible in practice with a single-channel SAR.

Text in Afrikaans / Real empowerment of school learners requires preparing them for the age of technology. This empowerment can be achieved by developing their higher-order thinking skills. This is clearly the intention of the proposed South African FET National Curriculum Statements Grades 10 to 12 (Schools). This research shows that one method of developing higher-order thinking skills is to adopt an integrated curriculum approach. The research is based on the assumption that an integrated curriculum approach will produce learners with a more integrated knowledge structure which will help them to solve problems requiring higher-order thinking skills. These assumptions are realistic because the empirical results of several comparative research studies show that an integrated curriculum helps to improve learners' ability to use higher-order thinking skills in solving nonroutine problems. The curriculum mentions four kinds of integration, namely integration across different subject areas, integration of mathematics with the real world, integration of algebraic and geometric concepts, and integration into and the use of dynamic geometry software in the learning and teaching of geometry. This research shows that from a psychological, pedagogical, mathematical and historical perspective, the theme conic sections can be used as an integrating factor in the new proposed FET mathematics curriculum. Conics are a powerful tool for making the new proposed curriculum more integrated. Conics can be used as an integrating factor in the FET band by means of mathematical exploration, visualisation, relating learners' experiences of various parts of mathematics to one another, relating mathematics to the rest of the learners' experiences and also applying conics to solve real-life problems. / Mathematical Sciences / D.Phil. (Wiskundeonderwys)

Text in Afrikaans / Real empowerment of school learners requires preparing them for the age of technology. This empowerment can be achieved by developing their higher-order thinking skills. This is clearly the intention of the proposed South African FET National Curriculum Statements Grades 10 to 12 (Schools). This research shows that one method of developing higher-order thinking skills is to adopt an integrated curriculum approach. The research is based on the assumption that an integrated curriculum approach will produce learners with a more integrated knowledge structure which will help them to solve problems requiring higher-order thinking skills. These assumptions are realistic because the empirical results of several comparative research studies show that an integrated curriculum helps to improve learners' ability to use higher-order thinking skills in solving nonroutine problems. The curriculum mentions four kinds of integration, namely integration across different subject areas, integration of mathematics with the real world, integration of algebraic and geometric concepts, and integration into and the use of dynamic geometry software in the learning and teaching of geometry. This research shows that from a psychological, pedagogical, mathematical and historical perspective, the theme conic sections can be used as an integrating factor in the new proposed FET mathematics curriculum. Conics are a powerful tool for making the new proposed curriculum more integrated. Conics can be used as an integrating factor in the FET band by means of mathematical exploration, visualisation, relating learners' experiences of various parts of mathematics to one another, relating mathematics to the rest of the learners' experiences and also applying conics to solve real-life problems. / Mathematical Sciences / D.Phil. (Wiskundeonderwys)

[pt] O presente trabalho tem como objetivo facilitar o estudo das cônicas e ainda despertar o interesse do aluno para o desenho geométrico. Será apresentado que as curvas cônicas estão em nosso dia a dia, não só como beleza estética, mas também provocando fenômenos físicos amplamente utilizado pela arquitetura e engenharia civil, como acústica e reflexão da luz. Utilizaremos instrumentos para desenhar curvas que despertem a curiosidade dos alunos e faremos uso das equações e lugares geométricos a fim de demostrar tais recursos. Pretende-se assim que ao adquirir tais conhecimentos o aluno aprimore seu entendimento matemático e amplie seu horizonte cultural. / [en] The present research aims to facilitate the study of the conics and also to arouse the interest of the student for the geometric drawing. The conic curves will be presented not only as they are in our day to day as aesthetic beauty but also as responsible for the physical phenomena widely used by architecture and civil engineering as well as acoustics and reflection of light. We will use instruments to draw curves that arouse the curiosity of the students, making use of the equations and locus in order to demonstrate such resources. It is intended that the student acquire this knowledge, improving his mathematical understanding and broadening his cultural horizon.