京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20153号 / 理博第4238号 / 新制||理||1609(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 坂上 貴之, 教授 上田 哲生, 教授 國府 寛司 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Indiana University-Purdue University Indianapolis (IUPUI) / The main objective of this work is to better quantify lunar surface minerals (agglutinate, clinopyroxene, orthopyroxene, plagioclase, olivine, ilmenite, and volcanic glass), particle sizes and the abundance of SMFe from the lunar soil characterization consortium (LSCC) dataset with our improved model based on Hapke's radiative transfer theory. The model is implemented for both forward and inverse modeling. Hapke's radiative transfer theory is implemented in the inverse model means Newton's method and least squares are jointly used to solve nonlinear questions rather than commonly used look-up Table (LUT). Although the effects of temperature and surface topography are incorporated into the implementation to improve the model performance for application of lunar spacecraft data, these effects cannot be extensively addressed in the current work because of the use of lab measured reflectance data. Our forward radiative transfer model (RTM) results show that the correlation coefficients between modeled and measured spectra are over 0.99. For the inverse model, the distribution of the calculated particle sizes is all within their measured range. The range of modeled SMFe for highland samples is 0.01% - 0.5 % and for mare samples is 0.03% - 1 %. The linear trend between SMFe and ferromagnetic resonance (Is) for all the LSCC samples is consistent with laboratory measurements. For quantifying lunar mineral abundances, the results show that the R-squared for the training samples (Is/FeO <= 65) are over 0.65 with plagioclase having highest correlation (0.94) and pyroxene the lowest (0.68). In the future work, the model needs to be improved for handling more mature lunar soil samples.

Recently, literary critics have increasingly drawn on methods of quantitative analysis to understand the readers and literature of the eighteenth century. Ironically, however, the eighteenth century is home to debates concerning the nature and usefulness of number, counting, and therefore, on some level, quantitative analysis. Eighteenth-century questions of number form an important part of the intellectual history of this period; these questions of number, in turn, hold important implications for language and the period's literature. I argue that the far-reaching influence of eighteenth-century questions of number can be seen especially well in the nature poetry of James Thomson. To explore this influence, I first discuss the problems of number presented to eighteenth-century mathematicians and philosophers by George Berkeley's critique of the infinitesimal calculus popularized by Isaac Newton. I then further explain the problems of number for eighteenth-century thinkers by drawing on philosopher Alain Badiou's theorization of the collapse of number in the seventeenth and eighteenth centuries. This background brings to light connections between eighteenth-century questions of number and similar questions philosophers, such as John Locke, asked of language. These connections set the stage to discuss number in Thomson's The Seasons. Because of Thomson's rather unique exposure to the Newtonian tradition through his Edinburgh education, he was introduced not only to Newton's more popular discoveries, but also the mathematical and philosophical debates that swirled around Newton's methods. Coming out of this environment, Thomson's The Seasons display a particular kind of interest in number at its limits—infinity and zero. This paper will explore Thomson's tropological expressions of infinity and zero in the poem and note how these tropes replicate the logic of the sublime. Ultimately number at its limits in Thomson suggests the problems of expression, and, reading against traditional interpretations of Thomson, the limits of the Enlightenment project.

[pt] Essa dissertação tem como objetivo principal proporcionar novos olhares sobre o Triângulo de Pascal na escola básica. Este é um assunto rico e pouco explorado nesse segmento escolar. Possibilita o desenvolvimento de aplicações e curiosidades interessantes que instigam o interesse do alunado e podem promover um processo tanto de ensino como de aprendizagem mais eficientes. Através de diversas abordagens é possível motivar ou incrementar conteúdos clássicos da Matemática da educação básica além de trabalhar com situações interdisciplinares. O trabalho apresenta um relato histórico do surgimento do Triângulo e seu uso ao longo do tempo por diversos matemáticos até Pascal. São também apresentados e demonstrados resultados matemáticos obtidos a partir da análise dos elementos deste Triângulo. Por fim, uma coletânea de abordagens interessantes que relacionam o Triângulo a diversos campos da Matemática são apresentadas visando possibilitar ao professor da educação básica o uso dessas propostas na criação de atividades da sua sala de aula. Algumas questões com conceitos matemáticos um pouco mais avançados também são explicitadas possibilitando que cada docente escolha e adapte à sua realidade àquelas que julgar pertinentes. Pretende-se assim possibilitar ao professor da escola básica mais um suporte para construção de propostas pedagógicas inovadoras e que contribuam para o desenvolvimento da educação básica de forma mais interessante e mais significativa. / [en] This thesis aims to provide new perspectives on Pascal s Triangle in elementary school. This is a rich subject and little explored in this school segment. It enables the development of interesting applications and curiosities that instigate the interest of the students and can promote a process of teaching and learning more effective. Through various approaches-gens can motivate or improve classical mathematics content of basic education as well as working with interdisciplinary situations. The paper presents a historical account of the emergence Triangle and its use over time by several mathematicians to Pascal. They are then presented and demonstrated mathematical results obtained from the analysis of the elements of this triangle. Finally, a collection of interesting approaches that relate the Triangle to various fields of mathematics are presented aiming to enable the primary education teachers use these proposals to create activities of your classroom. Some issues with mathematical concepts a little more advanced are also explicit allowing each teacher choice and adapt to their reality to those it considers relevant. The aim is to enable the teacher of primary school plus a support for building innovative educational proposals and contribute to the development of basic education more interesting and significant.

Ball and plate balancing control systems are commonly studied due to the complex dynamics associated with the instability of the system in open-loop. For simplicity, mathematical models describing the ball and plate dynamics are often linearized and the effects of complex motion are assumed to be negligible. These assumptions are rarely backed with evidence or explanations validating the simplified form of the dynamical equations of motion. This thesis focuses on developing a nonlinear model that more accurately defines the dynamics of the system, in order to quantify the error of linear and nonlinear models when compared to a Simscape physical system model. To develop the nonlinear model, this thesis considers both Newton-Euler and Lagrangian modeling methods and applies the method best suited for the ball and plate system. A linear state-feedback controller is developed to compare the stable responses of each system model. The response of each plant model in open-loop and closed-loop configurations subject to different inputs, initial conditions, and disturbances are simulated in the Simulink environment. When compared to the physical system, there was less error from the nonlinear model than from the linear model for both initial condition and disturbance responses. The differences in error were as high as 2% compared to 10% for the nonlinear and linear models, respectively. These results show that there are significant differences associated with model simplification. To optimize the performance, it may be advantageous to utilize a nonlinear model, however, the linearized model is still valid to be used in certain applications due to its stable response behavior.

We obtained four pointings of over 100 ks each of the well-studied Wolf-Rayet star WR 6 with the XMM-Newton satellite. With a first paper emphasizing the results of spectral analysis, this follow-up highlights the X-ray variability clearly detected in all four pointings. However, phased light curves fail to confirm obvious cyclic behavior on the well-established 3.766 d period widely found at longer wavelengths. The data are of such quality that we were able to conduct a search for "event clustering" in the arrival times of X-ray photons. However, we fail to detect any such clustering. One possibility is that X-rays are generated in a stationary shock structure. In this context we favor a co-rotating interaction region (CIR) and present a phenomenological model for X-rays from a CIR structure. We show that a CIR has the potential to account simultaneously for the X-ray variability and constraints provided by the spectral analysis. Ultimately, the viability of the CIR model will require both intermittent long-term X-ray monitoring of WR 6 and better physical models of CIR X-ray production at large radii in stellar winds.

Denna uppsats intresserar sig för begreppsförståelsen av krafter och tröghetslagen i gymnasiets fysik och granskar elevers uppfattning ur ett epistemologiskt perspektiv. Syftet är att belysa och klargöra vanliga missförstånd bland eleverna gällande tröghetsbegreppet i mekanik. Intervjuer av undervisande lärare genomförs och elever testas genom ett test med skriftliga konceptuella uppgifter. Synvinkeln som intervjuerna och elevlösningarna granskas genom är pragmatism med inspiration och begrepp från praktisk epistemologisk analys. De testade eleverna kommer från alla gymnasiets tre årskurser, och begreppsutveklingen över tid studeras genom att jämföra dessa årskurser. Ur detta studeras vad som utvecklas samt vilka missförstånd som kvarstår. Lärarnas praktik när det kommer till att arbeta motverkande mot missförstånden tas upp och granskas. Studien finner att trots förbättring kvarstår relativit seriösa missförstånd även efter en genomgången gymnasieutbildning på ett naturvetenskapsprogram. Dessa gäller särskilt begreppen som utgör grunden i Newtons fysik.

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The theory of Newton-Okounkov bodies can be viewed as a generalization of the theory of toric varieties; it associates a convex body to an arbitrary variety (equipped with auxiliary data). Although initial steps have been taken for formulating geometric situations under which the Newton-Okounkov body is a rational polytope, there is much that is still unknown. In particular, very few concrete and explicit examples have been computed thus far. In this thesis, we explicitly compute Newton-Okounkov bodies of some cases of Bott-Samelson and Peterson varieties (for certain classes of auxiliary data on these varieties). Both of these varieties arise, for instance, in the geometric study of representation theory. Background on the theory of Newton-Okounkov bodies and the geometry of flag and Grassmannian varieties is provided, and well as background on Bott-Samelson varieties, Hessenberg varieties, and Peterson varieties. In the last chapter we also discuss how certain techniques developed in this thesis can be generalized. In particular, a generalization of the flat family of Hessenberg varieties constructed in Chapter 6, which may allow us to compute Newton-Okounkov bodies of more general Peterson varieties, is an ongoing collaboration with H. Abe and M. Harada. / Thesis / Doctor of Philosophy (PhD)

This study seeks to validate a recently introduced global preconditioning technique for the Euler equations. Energy and enthalpy equations are nondimensionalized by means of a reference enthalpy, resulting in increased numerical accuracy for low-speed flows. A cellbased, finite volume formulation is used, with Roe flux difference splitting and both explicit and implicit time integration schemes. A Newton-linearized iterative implicit algorithm is implemented, with Symmetric Gauss-Seidel (LU/SGS) nested sub-iterations. This choice allows one to retain time accuracy, and eliminates approximate factorization errors, which become dominant at low speed flows. The linearized flux Jacobians are evaluated by numerical differentiation. Higher-order discretization is constructed by means of the MUSCL approach. Locally one-dimensional characteristic variable boundary conditions are implemented at the farfield boundary. The preconditioned scheme is successfully applied to the following traditional test cases used as benchmarks for local preconditioning techniques: point disturbance, flow angle disturbance, and stagnation point arising from the impingement of two identical jets. The flow over a symmetric airfoil and a convergentdivergent nozzle are then simulated for arbitrary Mach numbers. The preconditioned scheme greatly enhances accuracy and convergence rate for low-speed flows (all the way down to M ≈ 10E − 4). Some preliminary tests of fully unsteady flows are also conducted.