Search results for "Affine"
showing 10 items of 183 documents
Modified Operators Interpolating at Endpoints
2021
Some classical operators (e.g., Bernstein) preserve the affine functions and consequently interpolate at the endpoints. Other classical operators (e.g., Bernstein–Durrmeyer) have been modified in order to preserve the affine functions. We propose a simpler modification with the effect that the new operators interpolate at endpoints although they do not preserve the affine functions. We investigate the properties of these modified operators and obtain results concerning iterates and their limits, Voronovskaja-type results and estimates of several differences.
COMPLEX STRUCTURES ON INDECOMPOSABLE 6-DIMENSIONAL NILPOTENT REAL LIE ALGEBRAS
2007
We compute all complex structures on indecomposable 6-dimensional real Lie algebras and their equivalence classes. We also give for each of them a global holomorphic chart on the connected simply connected Lie group associated to the real Lie algebra and write down the multiplication in that chart.
On invariant measures of finite affine type tilings
2006
In this paper, we consider tilings of the hyperbolic 2-space, built with a finite number of polygonal tiles, up to affine transformation. To such a tiling T, we associate a space of tilings: the continuous hull Omega(T) on which the affine group acts. This space Omega(T) inherits a solenoid structure whose leaves correspond to the orbits of the affine group. First we prove the finite harmonic measures of this laminated space correspond to finite invariant measures for the affine group action. Then we give a complete combinatorial description of these finite invariant measures. Finally we give examples with an arbitrary number of ergodic invariant probability measures.
Structure function as a tool in AE and Dst time series analysis
1995
A new method to analyse the structure function (SF) has been constructed and used in the analysis of the AE time series for the years 1978-85 and Dst time series for 1957-84. It is shown that this SF analysis makes a clear distinction between affine and periodicity dominated time series, and it displays the essential periodicities of the series in a range relevant to its characteristic time scale. The AE time series is found to be affine such that the scaling exponent changes at a time scale of 113 (±9) minutes. On the other hand, in the SF function analysis, the Dst data are dominated by the 24-hour and 27-day periods. The 27-day period is modulated by the annual variation.
Mapping nonlinear gravity into General Relativity with nonlinear electrodynamics
2018
We show that families of nonlinear gravity theories formulated in a metric-affine approach and coupled to a nonlinear theory of electrodynamics can be mapped into General Relativity (GR) coupled to another nonlinear theory of electrodynamics. This allows to generate solutions of the former from those of the latter using purely algebraic transformations. This correspondence is explicitly illustrated with the Eddington-inspired Born-Infeld theory of gravity, for which we consider a family of nonlinear electrodynamics and show that, under the map, preserve their algebraic structure. For the particular case of Maxwell electrodynamics coupled to Born-Infeld gravity we find, via this corresponden…
A hybrid framework of multiple active appearance models and global registration for 3D prostate segmentation in MRI.
2012
International audience; Real-time fusion of Magnetic Resonance (MR) and Trans Rectal Ultra Sound (TRUS) images aid in the localization of malignant tissues in TRUS guided prostate biopsy. Registration performed on segmented contours of the prostate reduces computational complexity and improves the multimodal registration accuracy. However, accurate and computationally efficient 3D segmentation of the prostate in MR images could be a challenging task due to inter-patient shape and intensity variability of the prostate gland. In this work, we propose to use multiple statistical shape and appearance models to segment the prostate in 2D and a global registration framework to impose shape restri…
Formal Group Laws for Affine Kac-Moody groups and group quantization
1987
We describe a method for obtaining Formal Group Laws from the structure constants of Affine Kac-Moody groups and then apply a group manifold quantization procedure which permits construction of physical representations by using only canonical structures on the group. As an intermediate step we get an explicit expression for two-cocycles on Loop Groups. The programme is applied to the AffineSU(2) group.
Absorption by black hole remnants in metric-affine gravity
2019
Using numerical methods, we investigate the absorption properties of a family of nonsingular solutions {which arise in different metric-affine theories, such as quadratic and Born-Infeld gravity.} These solutions continuously interpolate between Schwarzschild black holes and naked solitons with wormhole topology. The resulting spectrum is characterized by a series of quasibound states excitations, associated with the existence of a stable photonsphere.
ON THE DEFORMATION QUANTIZATION OF AFFINE ALGEBRAIC VARIETIES
2004
We compute an explicit algebraic deformation quantization for an affine Poisson variety described by an ideal in a polynomial ring, and inheriting its Poisson structure from the ambient space.
Quantum and Braided Integrals
2001
We give a pedagogical introduction to integration techniques appropriate for non-commutative spaces while presenting some new results as well. A rather detailed discussion outlines the motivation for adopting the Hopf algebra language. We then present some trace formulas for the integral on Hopf algebras and show how to treat the $\int 1=0$ case. We extend the discussion to braided Hopf algebras relying on diagrammatic techniques. The use of the general formulas is illustrated by explicitly worked out examples.