Once-punctured Klein bottles in knot complements

AbstractWe find the family of all knots in S3 which are spanned by two essential once-punctured Klein bottles with boundary slopes at distance 4, thus settling a conjecture by K. Ichihara, M. Ohtouge, and M. Teragaito. We also address the more general question of when a knot exterior in an arbitrary 3-manifold contains two essential once-punctured Klein bottles with distinct boundary slopes

Conceptes de matemàtica abstracta adaptats a la docència secundària i batxillerat

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Jordi Font González[en] In this project we introduce, with an advanced and rigorous mathematical approach, 14 concepts and results of mathematical miscellany that have been intensively historically contextualized and chronologically organized. Moreover, we propose the design of activities and exercises suitable for ESO and Batxillerat level that, in a very intuitive and guided way, let us see these consequences, relating them with several items from the in force curriculums of Catalonia

Aprenentatge i Servei al grau de Matemàtiques

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Sergi Muria Maldonado[en] The present work is the compilation of the undertaken tasks to promote Service-Learning projects in the degree of Mathematics in the Faculty of Mathematics and Computer Science of the University of Barcelona. Firstly, a methodological approach is done within the framework of University and Mathematical Science. Afterwards, the several implementations that have been accomplished during these last months are described: a Service-Learning pilot program carried out with the Museu de Matemàtiques de Catalunya (MMACA), the incorporation of some subjects of the degree in the Compartir Idees project and the creation of links with social organizations to start Service-Learning programs in the future

A decoupled system of hyperbolic equations for linearized cosmological perturbations

A decoupled system of hyperbolic partial differential equations for linear perturbations around any spatially flat FRW universe is obtained for a wide class of perturbations. The considered perturbing energy momentum-tensors can be expressed as the sum of the perturbation of a minimally coupled scalar field plus an arbitrary (weak) energy-momentum tensor which is covariantly conserved with respect to the background. The key ingredient in obtaining the decoupling of the equations is the introduction of a new covariant gauge which plays a similar role as harmonic gauge does for perturbations around Minkowski space-time. The case of universes satysfying a linear equation of state is discussed in particular, and closed analytic expressions for the retarded Green's functions solving the de Sitter, dust and radiation dominated cases are given.Comment: 6 pages, no figures, content enlarge

Natural Matrices.

Las matrices naturales, se definen por medio de una progresión aritmética como a_(ij)= k(i−1)+ j, permiten en su estructurael uso herramientas de ubicación bidimensional, que están determinadas por los elementos de fila y columna. El presenteestudio muestra un análisis en cuanto a la suma y el producto, brindando la oportunidad de ampliar el concepto de matriznatural, al de matrices naturalmente modificada en un factor t y proponer una estructura algebraica para el producto enlo relacionado con matrices cuadradas.Natural matrices are defined by means of an arithmetic progression as a_ij=k(i −1)+j,  these matrices allow the use of two-dimensional location tools in their structure, which are determined by row and column elements. The present study shows an analysis in terms of addition and multiplication by providing the opportunity to extend the concept of natural matrix, to the naturally modified matrix in a factor t and to propose an algebraic structure for the product in relation with square matrices

Sgr A East and its surroundings observed in X-rays

We report the results of an XMM-Newton observation of Sgr A East and its surroundings. The X-ray spectrum of Sgr A East is well represented with a two-temperature plasma model with temperatures of ~1 and ~4 keV. Only the iron abundance shows clear spatial variation; it concentrates in the core of Sgr A East. The derived plasma parameters suggest that Sgr A East originated in a single supernova. Around Sgr A East, there is a broad distribution of hard X-ray emission with a superimposed soft excess component extending away from the location of Sgr A East both above and below the plane. We discuss the nature of these structures as well as the close vicinity of Sgr A*.Comment: 7 pages, 3 figures, Accepted for publication in Advances in Space Research, as a proceeding paper for the 34th COSPAR E1.4 "High Energy Studies of Supernova Remnants and Neutron stars" held at Houston, Texas, USA during 10-19 Oct 2002; also found in http://www.star.le.ac.uk/~mas/research/paper/#Sakano2003cos

Low-temperature orientational order and possible domain structures in C(_{60}) fullerite

Based on a simple model for ordering of hexagons on square planar lattice, an attempt has been made to consider possible structure of C(_{60}) fullerite in its low temperature phase. It is shown that hexagons, imitating fullerens oriented along (C_{3}) axes of \emph{sc} lattice, can be ordered into an ideal structure with four non-equivalent molecules in unit cell. Then the energy degeneracy for each hexagon rotations by (\pi /3) around its (C_{3}) axis leaves the translational and orientational order in this structure, but leads to a random distribution of (\pi /3) rotations and hence to {}``averaged{}'' unit cell with two molecules. However the most relevant structural defects are not these intrinsic \char`\"{}misorientations\char`\"{} but certain walls between the domains with different sequencies of the above-mentioned two (non-ideal) sublattices. Numeric estimates have been made for the anisotropic inter-molecular potential showing that the anisotropy is noticeably smaller for molecules in walls than in domains

Internet use in rural and remote Western Australia

Australian telecommunications universal service policy has recently been extended to include the provision of basic data services within a contestable universal service framework. In view of this fundamental policy change,infor mation about the demand for telecommunication services is critical if competition is to deliver intended outcomes. This analysis examines the demand for Internet in rural and remote communities in Western Australia. Toward this end econometric Internet subscription and use models are estimated on survey data collected for this purpose. Estimation results indicate price reduction will have a positive influence among existing Internet subscribers. A model of Internet subscription itself,however,suggests that demand for access is derivative of education and work requirements