Search results for "Polynomials"
showing 10 items of 144 documents
MR2852326 Bekh-Ochir, C.; Rankin, S. A. Examples of associative algebras for which the T-space of central polynomials is not finitely based. Israel J…
2012
On the variety var(E^*_{(N-m, m)}. The Z-grading of M_2(E).
High-order regularization in lattice-Boltzmann equations
2017
A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order nonequilibrium moments are filtered, i.e., only the corresponding advective parts are retained afte…
Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials
2017
Abstract Many applications in risk analysis require the estimation of the dependence among multivariate maxima, especially in environmental sciences. Such dependence can be described by the Pickands dependence function of the underlying extreme-value copula. Here, a nonparametric estimator is constructed as the sample equivalent of a multivariate extension of the madogram. Shape constraints on the family of Pickands dependence functions are taken into account by means of a representation in terms of Bernstein polynomials. The large-sample theory of the estimator is developed and its finite-sample performance is evaluated with a simulation study. The approach is illustrated with a dataset of…
Extremal polynomials in stratified groups
2018
We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are used to integrate the adjoint equations.
On Pietsch measures for summing operators and dominated polynomials
2012
We relate the injectivity of the canonical map from $C(B_{E'})$ to $L_p(\mu)$, where $\mu$ is a regular Borel probability measure on the closed unit ball $B_{E'}$ of the dual $E'$ of a Banach space $E$ endowed with the weak* topology, to the existence of injective $p$-summing linear operators/$p$-dominated homogeneous polynomials defined on $E$ having $\mu$ as a Pietsch measure. As an application we fill the gap in the proofs of some results of concerning Pietsch-type factorization of dominated polynomials.
Visual acuity with computer simulated and lens-induced astigmatism
2014
[EN] The relationship between spherical and astigmatic refractive errors and their associated visual acuity is investigated in this work by means of two different approaches. In the first one, different refractive errors were induced in normal subjects by trial lenses. In the second one, defocused images were simulated numerically by the optical transfer function of a model eye and then judged by the same subjects. The amount of defocus (measured in terms of the modulus of the dioptric power vector) necessary to reduce the visual acuity to 0.1 logMAR and to 0.4 logMAR was computed with each method and then compared. We found that the visual system is clearly more tolerant to lens-induced de…
Optical quality comparison between 2 collagen copolymer posterior chamber phakic intraocular lens designs
2014
Purpose To compare the optical quality in vitro of 2 designs of the Visian Implantable Collamer Lens phakic intraocular lens (pIOL) for different powers and optical apertures. Setting University of Valencia, Valencia, Spain. Design Experimental study. Methods The Nimo TR1504 deflectometry device was used to measure the V4c pIOL, which has a smaller optic diameter, and the V5 pIOL, which has a larger optic diameter. The pIOLs were measured for −3.00 diopters (D), −6.00 D, −9.50 D, and −10.50 D at different optical apertures from 3.00 to 6.00 mm depending on the IOL power and model. The root mean square of higher-order aberrations (RMS HOAs) was analyzed. The Strehl ratio, point-spread functi…
Optical phase retrieval using four rotated versions of a single binary amplitude modulating mask
2019
In recent years, phase retrieval methods recovering the phase of an object from coded diffraction patterns have gained popularity. A numerical phase retrieval method called PhaseLift that recovers the phase of an object from a very limited number of coded diffraction patterns was recently proposed. Performance of PhaseLift has been analyzed for different types and the number of masks modulating an object. We present a unique application of PhaseLift that uses four rotations of a single mask, modulating only the amplitude of an object. In simulations, a phase screen with the root-mean-square (RMS) value 0.294 μm was used as the test object. The RMS value of the retrieved phase screen after …
Drifts in real-time partial wavefront correction and how to avoid them
2017
In visual experiments that require real-time partial correction of wavefront aberrations, small errors occur that accumulate over time and lead to drifts in Zernike coefficients of the uncorrected aberrations. A simple algorithm that does not require the inclusion of an additional optical path to obtain independent measurements of the eye's aberrations is described here, and its effectiveness in preventing these drifts is demonstrated.