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Thesis (doctoral)--Universität Bern, 1911.

Thesis--Universität Bern, 1911.

Daniel K. Inouye Solar Telescope (formerly known as Advanced Technology Solar Telescope) will be the largest optical solar telescope ever built to provide greatly improved image, spatial and spectral resolution and to collect sufficient light flux of Sun. To meet the requirements of the telescope the design adopted a 4m aperture off-axis parabolic primary mirror with challenging specifications of the surface quality including the surface figure, irregularity and BRDF. The mirror has been completed at the College of Optical Sciences in the University of Arizona and it meets every aspect of requirement with margin. In fact this mirror may be the smoothest large mirror ever made. This paper presents the detail fabrication process and metrology applied to the mirror from the grinding to finish, that include extremely stable hydraulic support, IR and Visible deflectometry, Interferometry and Computer Controlled fabrication process developed at the University of Arizona.

This thesis investigates the geometry of polymers and other miscellaneous results in the Kardar-Parisi-Zhang (KPZ) universality class. Directed polymers have enjoyed a rich history in both probability theory and mathematical physics and have connections to several families of statistical mechanical and random growth models that belong to the KPZ universality class [77]. In this thesis, we focus on 2 integrable polymer models, the (1+1)-dimensional continuum directed random polymer (CDRP) and the half-space log-gamma (HSLG) polymer, and study their path properties. For the CDRP, we show both of its superdiffusivity and localization features. Namely, the annealed law of polymer of length t, upon t²/³ superdiffusive scaling, is tight in the space of C( [0, 1])-valued random variables and the quenched law of any point distance pt from the origin on the path a point-to-point polymer (or the endpoint of a point-to-line polymer) concentrates in a O(1) window around a random favorite point Mp,t. The former marks the first pathwise tightness result for positive temperature models and the latter result confirms the “favorite region conjecture” for the CDRP. Moreover, we provide an explicit random density for the quenched distribution around the favorite point Mp,t. The proofs of both results utilize connections with the KPZ equation and our techniques also allow us to prove properties of the KPZ equation itself, such as ergodicity and limiting Bessel behaviors around the maximum. For the HSLG polymers, we combine our localization techniques from the CDRP and the recently developed HSLG line ensemble results [22, 27] with an innovative combinatorial argument to obtain its limiting quenched endpoint distribution from the diagonal in the boundphase (α < 0). This result proves Kardar’s “pinning” conjecture in the case of HSLG polymers[158]. Finally, this thesis also contains two separate works on the tightness of the Bernoulli Gibbsian line ensemble under mild conditions and the upper-tail large deviation principle (LDP) of the asymmetric simple exclusion process (ASEP) with step initial data. In the first work, we prove that under a mild but uniform control of the one-point marginals of the top curve of the line ensemble, i.e. the shape of the top curve as approximately an inverse parabola and asymptotically covering the entire real line after scaling and recentering, the sequence of line ensembles is tight. With a characterization of [109], our tightness result implies the convergence of the Bernoulli Gibbsian line ensemble to the parabolic Airy line ensemble if the top curve converges to the parabolic Airy2 process in the finite dimensional sense. Compared to a similar work of [93], our result applies to line ensembles with possibly random initial and terminal data, instead of a packed initial condition, and does not rely on exact formulas. In our work on the ASEP, we obtain the exact Lyapunov exponent for the height function of ASEP with step initial data and subsequently its upper-tail LDP, where the rate function matches with that of the TASEP given in a variational form in [156].

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Title: Utilization of the internet by teaching conics at high school Author: Bc. Věra Effenberger Department: Department of Mathematics Education Supervisor: RNDr. Jana Hromadová, Ph.D. Supervisor's e-mail address: Jana.Hromadova@mff.cuni.cz Abstract This diploma thesis is dealing with conics' problems. It is mainly destined for high school (or university) teachers of descriptive geometry and for students too. It can by used in aid of education of conics or by self-study, because it includes many of illustrative pictures and dynamic applets made in the program GeoGebra, which support the written theoretical text. In the work are enumerated definitions, properties and various constructions of individual conics. Further there is their origin as an intersection of a right circular cone (as the case may be of a right circular cylinder) with a plane, their osculating circle and conjugate diameters. Compilation of examples constitutes an addition of this work. The examples have various difficulty and also can serve as a control over got knowledge. Keywords: ellipse, hyperbola, parabola, foci, tangents, normals, construction of conics

[pt] A ideia principal desta dissertação é apresentar as cônicas e demonstrar suas equações cartesianas bem como suas propriedades reflexivas. O trabalho está focado em abordar tais propriedades reflexivas com o auxílio do software GeoGebra. / [en] The main idea of this dissertation is to present the conics and demonstrate their cartesian equations and their reflective properties. The work is focused on addressing such reflective properties with the aid of software GeoGebra.

Made available in DSpace on 2015-06-17T19:34:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-09-17. Added 1 bitstream(s) on 2015-06-18T12:49:07Z : No. of bitstreams: 1 000832159.pdf: 1810864 bytes, checksum: 45d2b4ffb0e214843e13e9e6262e28bd (MD5) / Em cursos regulares de Ensino Médio as Cônicas são estudadas a partir de uma de nição que leva à uma equação e nalmente chega-se à gura da curva. Com esse trabalho pretendemos apresentá-las de outra forma. Começamos com a construção da curva com compasso e régua não graduada a partir de uma de suas propriedades, em seguida a de nimos formalmente e nalmente encontramos sua equação e características algébricas. De niremos alguns conceitos prévios para o estudo das cônicas. Em seguida estudaremos cada uma das cônicas elipse, hipérbole e parábola respectivamente, a partir de sua construção. Finalmente apresentaremos uma proposta de aulas que esperamos possam ser utilizadas por professores de Ensino Médio / On high school courses the study of Conics starts with the de nition which leads to an equation and nally the picture of the conic is presented. In this work we shall introduce the Conics in a di erent approach. We will start with the construction using only ruler and compass based on some of its properties and then we will de ne Conics. Finally we will obtain its equation and its algebraic characteristics. We will start with some basic concepts which will guide us to the study of Conics: ellipse, hyperbole and parabola. Finally we will present a proposal of classes that we hope can be used by high school teachers

[pt] A presente dissertação, que tem como Título O Outro que me justifica, trata-se de uma análise exegético/hermenêutica sobre a perícope Lucana 18, 9-14, a parábola do Fariseu e do Publicano. A metodologia adotada é a aplicação dos passos do Método Histórico Crítico, trazendo também algumas considerações para a realidade geral da teologia e algumas ciências afins, como a filosofia e a psicologia. A parábola de Lc 18, 9-14, conhecida como a do Fariseu e do Publicano, ao longo da história vem sido interpretada como uma parábola que trate sobre a oração, ou seja a forma adequada com que o discípulo deve se referir a Deus. Outra linha recorrente ao longo da história é a de que esta tenha sido uma parábola sobre a humildade, já que a atitude soberba do fariseu contrasta com a figura humilde do publicado que nem sequer ousa levantar os olhos aos céus, e que desce para casa recebendo os favores divinos. O presente trabalho continua a mostrar a validez dessas interpretações, ao mesmo tempo mostra que eles não são suficientes para mostrar a riqueza de significado do texto. O presente trabalho se propõe a mostrar a parábola como um exemplo presente já nos sinóticos da doutrina da justificação pela fé, que será posteriormente desenvolvida pelo apóstolo Paulo, e que abarca com maior totalidade o sentido semântico desta, e que abarca também as interpretações anteriores que foram feitas desta. / [en] This work, which has the title The Other justifying me, this is an exegetical analysis / hermeneutics on the pericope Lucana 18, 9-14, the parable of the Pharisee and the Publican. The methodology is the implementation of the steps of the Critical History Method, also bringing some considerations to the overall reality of theology and some related sciences, such as philosophy and psychology. The parable of Luke 18: 9-14, known as the Pharisee and the Publican, throughout history has been interpreted as a parable that deals on prayer, that is the proper way in which the student must refer to God. Another recurring line throughout history is that this was a parable about humility, as the superb attitude of the Pharisee contrasts with the humble figure of published that dares not even raise his eyes to heaven, and down home receiving the divine favors. This study continues to show the validity of these interpretations, at the same time shows that they are not enough to display the text meaning of wealth. This paper aims to explain the parable as an example already present in the synoptic of the doctrine of justification by faith, which will be further developed by the apostle Paul, and that includes most all the semantic meaning of this, and that also includes previous interpretations They were made from this.