Search results for "Homogeneous space"
showing 10 items of 142 documents
A tool for a first analysis of architectural façades
1997
Abstract This work presents a tool for analysing the figurative structure of architectural facades. The procedure begins by singling out the elementary shapes which make up the facade image; it detects and identifies them as “area objects”, even if present in combination in virtual or mental form and groups them into classes of equal objects. A second step is the analysis of the inner structure of the classes: equidistant, arithmetical and geometrical sequences, or alternate distances are distinguished. The procedure ends by singling out the symmetries which structure the facade image and displaying them, pointing out their implied hierarchy through a thickness differentiation.
Spin–orbit coupling effects on the electronic properties of the pressure-induced superconductor CrAs
2019
We present the effects of spin-orbit coupling on the low-energy bands and Fermi surface of the recently discovered pressure-induced superconductor CrAs. We apply the L\"owdin down-folding procedure to a tight-binding hamiltonian that includes the intrinsic spin-orbit interaction, originating from the Cr 3d electrons as well as from As 4p ones. Our results indicate that As contributions have negligible effects, whereas the modifications to the band structure and the Fermi surface can be mainly ascribed to the Cr contribution. We show that the inclusion of the spin-orbit interaction allows for a selective removal of the band degeneracy due to the crystal symmetries, along specific high symmet…
Robust semi-Dirac points and unconventional topological phase transitions in doped superconducting Sr2IrO4 tunnel coupled to t2g electron systems
2017
Semi-Dirac fermions are known to exist at the critical points of topological phase transitions requiring fine-tuning of the parameters. We show that robust semi-Dirac points can appear in a heterostructure consisting of superconducting Sr2IrO4 and a t2g electron system (t2g-ES) without fine-tuning. They are topologically stable in the presence of the symmetries of the model, metallic t2g-ES and a single active band in Sr2IrO4. If the t2g metal is coupled to two different layers of Sr2IrO4 (effectively a multiband superconductor) in a three-layer-structure the semi-Dirac points can split into two stable Dirac points with opposite chiralities. A similar transition can be achieved if the t2g-E…
Soft Pyramid Symmetry Transforms
2005
Pyramid computation is a natural paradigm of computation in planning strategies and multi-resolution image analysis. This paper introduces a new paradigm that is based on the concept of soft-hierarchical operators implemented in a pyramid architecture to retrieve global versus local symmetries. The concept of symmetry is mathematically well defined in geometry whenever patterns are crisp images (two levels). Necessity for a soft approach occurs whenever images are multi-levels and the separation between object and background is subjective or not well defined. The paper describes a new pyramid operator to detect symmetries and shows some experiments supporting the approach. This work has bee…
Symmetries and solvable models for evaporating 2D black holes
1997
We study the evaporation process of a 2D black hole in thermal equilibrium when the ingoing radiation is suddenly switched off. We also introduce global symmetries of generic 2D dilaton gravity models which generalize the extra symmetry of the CGHS model. © Elsevier Science B.V
Vacuum type I spacetimes and aligned Papapetrou fields: symmetries
2003
We analyze type I vacuum solutions admitting an isometry whose Killing 2--form is aligned with a principal bivector of the Weyl tensor, and we show that these solutions belong to a family of type I metrics which admit a group $G_3$ of isometries. We give a classification of this family and we study the Bianchi type for each class. The classes compatible with an aligned Killing 2--form are also determined. The Szekeres-Brans theorem is extended to non vacuum spacetimes with vanishing Cotton tensor.
On cyclic branched coverings of prime knots
2007
We prove that a prime knot K is not determined by its p-fold cyclic branched cover for at most two odd primes p. Moreover, we show that for a given odd prime p, the p-fold cyclic branched cover of a prime knot K is the p-fold cyclic branched cover of at most one more knot K' non equivalent to K. To prove the main theorem, a result concerning the symmetries of knots is also obtained. This latter result can be interpreted as a characterisation of the trivial knot.
Symmetry operators in computer vision
1996
Abstract Symmetry plays a remarkable role in perception problems. For example, peaks of brain activity are measured in correspondence with visual patterns showing symmetry . Relevance of symmetry in vision was already noted by Koler in 1929. Here, properties of a symmetry operator are reported and a new algorithm to measure local symmetries is proposed. Its performance is tested on segmentation of complex visual patterns and the classification of sparse images.
Networked Analysis of a Teaching Unit for Primary School Symmetries in the Form of an E-Book
2021
In mathematics education, technology offers many opportunities to enrich curricular contents. Plane symmetries is a topic often skipped by primary teachers. However, it is important and may be worked in attractive ways in dynamic geometry software environments. In any regular classroom there are students with different levels of mathematical attainment, some needing easy tasks while others, particularly mathematically-gifted students, need challenging problems. We present a teaching unit for plane symmetries, adequate for upper primary school grades, implemented in a fully interactive electronic book, with most activities solved in GeoGebra apps. The book allows student to choose which itin…
homogeneous embeddings of SL2(C) modulo a finite sub-group.
2000
L'objet de ce travail est l'étude des variétés algébriques normales complexes munies d'une action algébrique de $SL_{2}$ et qui contiennent $SL_{2}/H$ comme orbite ouverte, $H$ étant un sous-groupe fini de $SL_{2}$.Plus précisément on définit un plongement homogène de $SL_{2}/H$ comme la donnée d'une $SL_{2}$-variété irréductible $X$ (quasi-projective ou non) contenant $SL_{2}/H$ comme orbite ouverte et d'un morphisme $SL_{2}$-équivariant de $SL_{2}$ dans $X$.Les plongements homogènes lisses ainsi que les plongements minimaux (plongements lisses et complets qui ne sont pas des éclatements d'un autre plongement lisse complet) de $SL_{2}/\{Id\}$ et de $SL_{2}/\{\pm Id\}$ ont été déterminés pa…