1,720,955 research outputs found
Paradoxical sets and the Axiom of Choice
No full textParadoxe Mengen treten in vielen Bereichen der Mathematik auf. Diese Mengen werden unter Verwendung des Auswahlaxioms konstruiert und weisen kontraintuitive Eigenschaften auf, wie beispielsweise die Vitali-Menge oder das Banach-Tarski-Paradoxon. Die zentrale Frage dieser Arbeit ist, ob bestimmte Fragmente des Auswahlaxioms aus der Existenz spezifischer paradoxer Mengen abgeleitet werden können. Wir liefern mehrere negative Antworten auf diese Frage. Insbesondere zeigen wir, dass es Modelle der ZFC-Mengenlehre ohne eine Wohlordnung der reellen Zahlen gibt, die dennoch eine Zerlegung des dreidimensionalen euklidischen Raums in Einheitskreise enthalten. Darüber hinaus entwickeln wir einen allgemeinen Rahmen für die Konstruktion ähnlicher Modelle für andere paradoxe Mengen unter bestimmten Bedingungen der Erweiterbarkeit und Amalgamierung. Zudem präsentieren wir einige Ergebnisse zum Transzendenzgrad der reellen Zahlen über bestimmten mengentheoretischen Teilkörpern.Paradoxical sets appear in many areas of mathematics. These are sets that are constructed using the Axiom of Choice and exhibit counterintuitive properties, examples include the Vitali set and the Banach-Tarski paradox. The central question of this thesis is whether certain fragments of the Axiom of Choice can be recovered from the existence of specific paradoxical sets. We provide several negative answers to this question. In particular, we show that there exist models of ZFC without a well-ordering of the reals that still contain a partition of three-dimensional Euclidean space into unit circles. Furthermore, we develop a general framework for constructing similar models for other paradoxical sets, under certain conditions of extendability and amalgamation. We also include some results on the transcendence degree of the reals over certain set theoretical subfields
Geometría del plano hiperbólico
Get PDFTesis (Lic. en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2019.En este trabajo estudiamos la geometría del plano hiperbólico siguiendo un esquema axiomático similar al de la geometría euclídea. Ambas geometrías coinciden en sus bases, salvo por reemplazar el Axioma de las paralelas o Postulado V de Euclides. Este cambio genera una geometría muy rica, que abre un nuevo mundo en donde los triángulos tienen suma de ángulos interiores menor que 180°, existen rectas paralelas asintóticas y hay pentágonos con todos sus ángulos rectos. Usamos el modelo del semiplano superior para desarrollar los elementos básicos: distancia, trigonometría, área y circunferencias. A lo largo del trabajo, estuvimos guiados por las siguientes preguntas: ¿Cuáles teoremas conocidos se siguen cumpliendo? ¿Hay resultados completamente diferentes a los de la geometría euclídea? Para concluir, haremos una breve mención a los hexaframes, que son una generalización de los hexágonos rectangulares en el espacio hiperbólico.In the present work we study the hyperbolic plane geometry. We follow an axiomatic approach, similar to the one used in euclidean geometry. Both geometries share their bases with the exception of the parallel postulate, also called Euclid’s fifth postulate. This change generates a really rich geometry. It opens up a world of possibilities, where the sum of the angles of a triangle is always strictly less than 180°, there exist asymptotic parallel lines, and there are right-angled pentagons. We use the Poincaré half-plane model to develop the basic elements in geometry: distance, trigonometry, area and circles. Throughout this work, the following questions have been guiding us: Which well known theorems are still true? Is there any result completely different from the ones in euclidean geometry? To conclude, we will briefly mention the hexaframes, a generalization of the right-angled hexagons in the hyperbolic space
Enseñanza de ecuaciones a través de diferentes representaciones
Get PDFInforme Final (Profesorado en Matemática)--Universidad Nacional de Córdoba. Facultad de Matemática Astronomía, Física y Computación, 2017.El presente escrito narra nuestra experiencia durante las prácticas de matemática en un primer año de una institución privada de la provincia de Córdoba. El tema que se trabajó fue ecuaciones lineales de una incógnita en el conjunto de los números enteros. Para esto utilizamos distintas formas de representación moviéndonos desde lo tangible hacia lo abstracto: realizamos actividades con balanzas de platillos para introducirlas como representación de las ecuaciones y desde allí comenzamos a trabajar con lápiz y papel, continuando con un trabajo con tablas, realizadas en hojas de cálculo en computadora. En este informe presentamos la información recabada en el período de observaciones (Capítulo 1), la planificación y las actividades que efectivamente se pusieron en práctica (Capítulo 2), el análisis teórico de una problemática que surgió durante la etapa de prácticas (Capítulo 3), y reflexiones finales (Capítulo 4)
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
koamabayili/VECTRON-author-checklist: VECTRON author checklist
No full textWe have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
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