The Birkhoff polytope Bn is the convex hull of all n× n permutation matrices in Rn×n. We compute the combinatorial symmetry group of the Birkhoff polytope. A representation polytope is the convex hull of some finite matrix group G 6 GL(d,R). We show that the group of permutation matrices is essentially the only finite matrix group which yields a representation polytope with the face lattice of ...

In many examples of repeating patterns in the art of various cultures, the use of symmetries to analyze those patterns does a good job of capturing the repetition intended by the artist. In other cases, however, the artist uses precise forms of repetition that are not well modeled by mathematical symmetries. The analysis of the orbits of motifs under the action of the symmetry group both reveal...

We attempt to fit observations with 5 resolution of the J=2−1 transition of CS in the directions of H ii regions A, B, and G of W49A North as well as observations with 20 resolution of the J=2−1, 3−2, 5−4, and 7−6 transitions in the directions of H ii regions A and G by using radiative transfer calculations. These calculations predict the intensity profiles resulting from several spherical clou...

MARTINS, Claudia Beatriz Monte Jorge. Technology integration into Modern Languages Courses in the state of Paraná from the teachers’ perspective: a mixed methods study. 404 f. Tese (Doutorado em Tecnologia) – Programa de PósGraduação em Tecnologia, Universidade Tecnológica Federal do Paraná. Curitiba, 2015. The objective of this study was to analyze the integration of technology, or rather CALL...

In this paper, the Lie group analysis method is applied to the geometric average Asian option pricing equation in financial problems. Firstly, the complete Lie symmetry group and infinitesimal generators of this equation are derived. Then the optimal system with one parameter for the Lie symmetry algebra are obtained, which gives the possibility to describe a complete set of invariant solutions...

There are many assumptions that have been considered when describing black liquor droplet combustion. These include assuming an isothermal particle, a constant diameter particle, inert inorganic species, and one-film diffusion model. This paper shows the effects of systematically relaxing these factors for a 1-D spherical model for black liquor combustion. The flame is described using boundary ...

We construct in a systematic way the complete Chevalley-Eilenberg cohomology at form degree two, three and four for the Galilei and Poincaré groups. The corresponding non-trivial forms belong to certain representations of the spatial rotation (Lorentz) group. In the case of two forms they give all possible central and non-central extensions of the Galilei group (and all non-central extensions o...

We have solved completely the problem of the description of quasi-linear hyperbolic differential equations in two independent variables that are invariant under three-parameter Lie groups. The problem of group classification of differential equations is one of the central problems of modern symmetry analysis of differential equations[1]. One of the important classes of hyperbolic equations. The...

The complete symmetry groups of systems of linear second order ordinary differential equations are considered in the context of the simple harmonic oscillator. One finds that in general the representation of the complete symmetry group is not unique and in the particular case of a four-dimensional system there are two distinct complete symmetry groups. The results for general second order linea...

We analyze gauge symmetry enhancements SO(16) → E8 on eight D7-branes and SO(14) × U(1) → E8 on seven D7-branes from open strings. String configurations which we present in this paper are closely related to the ones given by Gaberdiel and Zwiebach. Our construction is based on SO(8)×SO(8) decomposition and its relation to the D8-brane case via T-duality is clearer. Then we study supersymmetric ...