Search results for "geometri"
showing 10 items of 1091 documents
Three-page encoding and complexity theory for spatial graphs
2004
We construct a series of finitely presented semigroups. The centers of these semigroups encode uniquely up to rigid ambient isotopy in 3-space all non-oriented spatial graphs. This encoding is obtained by using three-page embeddings of graphs into the product of the line with the cone on three points. By exploiting three-page embeddings we introduce the notion of the three-page complexity for spatial graphs. This complexity satisfies the properties of finiteness and additivity under natural operations.
A discontinuous Galerkin formulation for nonlinear analysis of multilayered shells refined theories
2023
A novel pure penalty discontinuous Galerkin method is proposed for the geometrically nonlinear analysis of multilayered composite plates and shells, modelled via high-order refined theories. The approach allows to build different two-dimensional equivalent single layer structural models, which are obtained by expressing the covariant components of the displacement field through-the-thickness via Taylor’s polynomial expansion of different order. The problem governing equations are deduced starting from the geometrically nonlinear principle of virtual displacements in a total Lagrangian formulation. They are addressed with a pure penalty discontinuous Galerkin method using Legendre polynomial…
A class of nilpotent Lie algebras admitting a compact subgroup of automorphisms
2017
Abstract The realification of the ( 2 n + 1 ) -dimensional complex Heisenberg Lie algebra is a ( 4 n + 2 ) -dimensional real nilpotent Lie algebra with a 2-dimensional commutator ideal coinciding with the centre, and admitting the compact algebra sp ( n ) of derivations. We investigate, in general, whether a real nilpotent Lie algebra with 2-dimensional commutator ideal coinciding with the centre admits a compact Lie algebra of derivations. This also gives us the occasion to revisit a series of classic results, with the expressed aim of attracting the interest of a broader audience.
Geometric inequivalence of metric and Palatini formulations of General Relativity
2020
Projective invariance is a symmetry of the Palatini version of General Relativity which is not present in the metric formulation. The fact that the Riemann tensor changes nontrivially under projective transformations implies that, unlike in the usual metric approach, in the Palatini formulation this tensor is subject to a gauge freedom, which allows some ambiguities even in its scalar contractions. In this sense, we show that for the Schwarzschild solution there exists a projective gauge in which the (affine) Kretschmann scalar, K≡R R , can be set to vanish everywhere. This puts forward that the divergence of curvature scalars may, in some cases, be avoided by a gauge transformation of the …
ETP/GDOP Behavior Study for N-Sensors Arrays ina Multilateration Radar System
2009
In this paper, we evaluated the ETP (Expected Theoretical Precision) and GDOP (Geometric Dilution Of Precision) enhancement related to the number of sensors in a Multilateration radar system. An introduction about the principles of the Multilateration radar system basis operation is described, then, the formulation for evaluation the ETP/GDOP of the 3D positioning is shown. We observed that the ETP and GDOP enhance with the increase of the number of sensors. A substantial improvement was obtained until nine sensors but, for more sensors that improvement is reduced. Results for a 75km×75km area are shown, including LAM (Local Area Multilateration) and WAM (Wide Area Multilateration) settings…
A note on rank 2 diagonals
2020
<p>We solve two questions regarding spaces with a (G<sub>δ</sub>)-diagonal of rank 2. One is a question of Basile, Bella and Ridderbos about weakly Lindelöf spaces with a G<sub>δ</sub>-diagonal of rank 2 and the other is a question of Arhangel’skii and Bella asking whether every space with a diagonal of rank 2 and cellularity continuum has cardinality at most continuum.</p>
Universal infinitesimal Hilbertianity of sub-Riemannian manifolds
2019
We prove that sub-Riemannian manifolds are infinitesimally Hilbertian (i.e., the associated Sobolev space is Hilbert) when equipped with an arbitrary Radon measure. The result follows from an embedding of metric derivations into the space of square-integrable sections of the horizontal bundle, which we obtain on all weighted sub-Finsler manifolds. As an intermediate tool, of independent interest, we show that any sub-Finsler distance can be monotonically approximated from below by Finsler ones. All the results are obtained in the general setting of possibly rank-varying structures.
Using Genetic Algorithms for Optimizing the PPC in the Highway Horizontal Alignment Design.
2016
Various studies have emphasized the interesting advantages related to the use of new transition curves for improving the geometric design of highway horizontal alignments. In a previous paper, one of the writers proposed a polynomial curve, called a polynomial parametric curve (PPC), proving its efficiency in solving several design problems characterized by a very complex geometry (egg-shaped transition, transition between reversing circular curves, semidirect and inner-loop connections, and so on). The PPC also showed considerable advantages from a dynamic perspective, as evidenced by the analysis of the main dynamic variables related to motion (as well as rate of change of radial accelera…
A short proof of the infinitesimal Hilbertianity of the weighted Euclidean space
2020
We provide a quick proof of the following known result: the Sobolev space associated with the Euclidean space, endowed with the Euclidean distance and an arbitrary Radon measure, is Hilbert. Our new approach relies upon the properties of the Alberti-Marchese decomposability bundle. As a consequence of our arguments, we also prove that if the Sobolev norm is closable on compactly-supported smooth functions, then the reference measure is absolutely continuous with respect to the Lebesgue measure.
Application Of Anamorphic Systems To Directional Pseudocolor Encoding
1988
An optical nonsymmetrical imaging system composed of two anamorphic spectrum analyzers in cascade is implemented. This system can provide an undistorted final image in spite of the geometrical distortion effects in the intermediate Fourier plane. The introduction of chromatic sector filters in this plane provides a real-time technique to pseudocolor encode the spatial frequency information of a black-and-white transparency. In this way, greater discrimination is achieved in the angular orientation of object details that generate the same spatial frequencies. Experimental pseudocolored images, obtained with a symmetrical system and a nonsymmetrical system, of a black-and-white transparency a…