Title: Curves of constant width Author: Miroslav Němec Department: Department of Mathematics Education Supervisor: RNDr. Antonín Slavík, Ph.D., Department of Mathematics Education Abstract: The aim of this thesis is to familiarize the reader with the notion of the width of a given plane curve, and with curves having the same width in all directions. We focus our attention especially on those curves that are constructible using straightedge and compass. The chapters presenting the definition and measurement of curve width, as well as the construction of curves from circular arcs, are accessible to high-school students. We also briefly mention other related topics, such as the solids of constant width. Keywords: Width of a curve, constant width, construction, properties

My dissertation focuses on (i) the development of new analysis tools and methodologies for analyzing X-ray photoelectron spectroscopy (XPS) and time-of-flight secondary ion mass spectrometry (ToF-SIMS) data, and (ii) the comprehensive characterization of materials (nanodiamonds) using a multi-instrument approach. Chapter 1 contains (i) a discussion of the two techniques I focused on most in my work: XPS and ToF-SIMS, (ii) a discussion of the common chemometrics techniques used to analyze data from these methods, and (iii) the advantages/rationale behind the multi-instrument characterization of materials. Chapter 2 describes various good practices for obtaining reasonable peak fits in XPS, which can also be applied to peak fitting data from different techniques. To address the issue of user subjectivity/bias in XPS peak fitting, I introduce two less biased mathematical functions for characterizing XPS narrow scans, namely the equivalent width (EW) and the autocorrelation width (AW). These functions are discussed in Chapters 3 and 4. In Chapter 5, I then introduce uniqueness plots as simple and straightforward graphical tools for assessing the quality of XPS peak fits and for determining whether fit parameters are correlated. This tool is extensively used in spectroscopic ellipsometry, and the mathematics behind it is known in XPS. However, to the best of my knowledge, this graphical tool has never been applied to XPS. ToF-SIMS data analysis is somewhat challenging due to the enormous amounts of data that are collected, and also the matrix effect in SIMS. This amount of information is significantly increased when depth profiles are performed on samples. Chapter 6 discusses a new chemometrics tool that I introduce for analysis of complex data sets, with emphasis on XPS and ToF-SIMS depth profiling data. The new approach is called the Information Content (IC) or entropy, which is adapted from Claude Shannon's work on Information Theory. Chapter 7 then contains a presentation of the comprehensive characterization of five nanodiamond samples used to manufacture particles for liquid chromatography. The advantages of a multi-instrument approach for material characterization and the lack of comprehensive material characterization in the literature are emphasized. To the best of my knowledge this is the most comprehensive characterization of nanodiamonds that has been reported in the literature. Chapter 8 presents conclusions of my work and future work. This thesis also contains six appendices. Appendix 1 contains an article from a scientific magazine that I wrote to highlight the importance and applications of the EW and AW to characterize XPS narrow scans. Appendices 2-5 are application notes I wrote on separations I performed on a nanodiamond based HPLC column. Finally, Appendix 6 describes the ToF-SIMS analysis of the tungsten species in the nanodiamond samples characterized in Chapter 7.

A high efficiency driver circuit is proposed for Light Emitting Diode (LED) lamps with dimming feature. The current regulation is accomplished by processing partial power of the power conversion circuit so that a high overall efficiency can be realized. The detailed description and analysis of circuit operation are provided. The dimming feature can be accomplished by means of linear current regulation, pulse-width modulation (PWM) or double pulse-width modulation (DPWM). Based on the circuit analyses and derived equations, a laboratory circuit is designed for an LED lamp which is composed of 40 high-brightness white LEDs in series. The performances with three dimming schemes are compared from the measured results. LEDs dimmed by DPWM have less color shift than those dimmed by linear current regulation and PWM. On the other hand, the dimming scheme with linear current regulation has the highest light efficiency over the entire dimming range. The circuit efficiency can be as high as 95.5% at the rated output and deteriorates slightly to 90.5% as the lamp is dimmed to 10% of the rated power.

No description available.

No description available.

The invisible width of the Z boson is its partial width to neutrinos and is a well known Standard Model quantity. A direct measurement of the Z boson’s invisible width has been performed using the ATLAS detector. The width was measured to be Γ(Z → inv) = 481 ± 5(stat.) ± 22(syst.), which rivals the precision of the direct measurements performed by the LEP experiments. Such a precise was measurement performed by measuring the ratio of Z → νν to Z → ee events and correcting for the differences between the neutrino and electron selections. The measurement is sensitive to any non Standard Model interactions with a jet(s) + undetected particle final state. No evidence was found for a deviation from the Standard Model, however improvements have been suggested to allow more sensitivity to new phenomena at high energies.

No description available.

International Telemetering Conference Proceedings / October 26-29, 1992 / Town and Country Hotel and Convention Center, San Diego, California / This paper describes a biotelemetric application whereby information of tooth contact pressure from within the mouth of a human subject is transmitted to a bedside receiver where it is processed and used in the biofeedback treatment of nocturnal bruxism (grinding of the teeth). Bruxing information is encoded on a pulse width modulated 313 MHZ carrier. Issues that are addressed include miniaturization of the transmitter, minimization of power requirements, stabilization of carrier frequency, receiver selection, and the various problems associated with getting a radio frequency signal out of the mouth.

Graph immersions are a natural counterpart to the widely studied concepts of graph minors and topological graph minors, and yet their theory is much less developed. In the present work we search for sufficient conditions for the existence of the immersions and the properties of the graphs avoiding an immersion of a fixed graph. We prove that large tree-with of 4-edge-connected graph implies the existence of immersion of any 4-regular graph on small number of vertices and that large maximum degree of 3-edge-connected graph implies existence of immersion of any 3-regular graph on small number of vertices.

A demanda por qualidade nas aplicações envolvendo radiação laser exigiu melhorias no seu desempenho. Conseqüentemente, equipamentos mais rápidos e precisos nas medidas dos seus parâmetros são indispensáveis. Nas áreas onde o laser é empregado, três parâmetros sobressaem-se nas suas aplicações: (1) potência ou energia, (2) freqüência e (3) comprimento espacial ou largura do feixe. A determinação das bordas, isto é, da largura do feixe, está ligada a um percentual do máximo valor atingido pela energia. O diâmetro do feixe, juntamente com a energia, determina-se a densidade do feixe. Outros parâmetros como: divergência e fator de qualidade (M2), podem ser determinados também. O presente trabalho busca desenvolver um sistema de translação bidimensional que possa ser empregado na caracterização espacial do feixe de lasers. Para determinar o perfil do feixe de lasers utiliza-se o método borda-da-lâmina (knife-edge), relacionando o deslocamento da lâmina posicionada transversalmente ao feixe, com a energia transmitida. Obstruindo o feixe com uma lâmina opaca, obtêm-se a variação da energia do feixe em função da posição da lâmina. Esta variação representa a integral do perfil Gaussiano do feixe. Para a automação do sistema foi empregado o programa Labview (National Instruments). O funcionamento do protótipo mostrou-se eficiente na caracterização de feixes laser e com uma instrumentação de baixo custo para a comercialização nacional. No entanto, apresentou-se lento na aquisição de dados, tornando a tarefa de caracterização do laser mais demorada. Fatores como velocidade do motor de passo e linguagem de programação contribuíram para tornar a aquisição lenta. / The demand for quality in the applications involving laser radiation demanded improvements in its performance. Faster equipments in the measures of its parameters are indispensable. In the areas where the laser is employee, three parameters are important in its applications: (1) power or energy, (2) frequency and (3) beam spatial. The determination of the edges, i. e., the width of the beam, is correlated to a percentage of the maximum reached energy. This parameter, together with the energy, determines beam density; beyond this parameter it also possible to determine the divergence and quality factor (M2). This work searches to develop a system of bi-dimension translation that can be used in the spatial characterization of laser beam. To determine the profile of laser beam it is used the knife-edge method, that it relates the displacement of the blade located transversally to the beam, with the transmitted energy. Blocking the beam with a blade the energy variation of the beam is correlated with blade position; this variation represents the integral of the beam Gaussian profile. For the automation it will be used the Labview program(National Instruments). The prototype had showed to be efficient in the characterization of laser beams and a low cost for national commercialization; however was slow in the data acquisition resulting a longer time to acquire the laser parameters. Instrumental components as step motors or programming language had contributed to slowly acquisition.