Search results for "Polynomial"
showing 10 items of 566 documents
Group Actions and Asymptotic Behavior of Graded Polynomial Identities
2002
Periodic Polynomial Splines
2018
In this chapter, the spaces of periodic polynomial splines and the Spline Harmonic Analysis (SHA) in these spaces are briefly outlined. The stuff of this chapter is used for the design of periodic discrete-time splines and discrete-time-spline-based wavelets and wavelet packets. For a detailed description of the subject we refer to (Averbuch, Neittaanmaki and Zheludev, Spline and Spline Wavelet Methods with Applications to Signal and Image Processing, Springer, Berlin, 2014) [1]. Periodic polynomial splines provide an example of mixed discrete-continuous circular convolution.
Sur les feuilletages alg�briques de Rolle
1997
L'objet de ce travail est l'etude des feuilletages algebriques de Rolle dans \( \Bbb {R}^n \). On montre que leur restriction au complementaire d'un nombre fini de feuilles possede une structure de produit. On precise aussi la topologie de certaines de leurs feuilles.
The Bernstein Basis and its applications in solving geometric constraint systems
2012
International audience; This article reviews the properties of Tensorial Bernstein Basis (TBB) and its usage, with interval analysis, for solving systems of nonlinear, univariate or multivariate equations resulting from geometric constraints. TBB are routinely used in computerized geometry for geometric modelling in CAD-CAM, or in computer graphics. They provide sharp enclosures of polynomials and their derivatives. They are used to reduce domains while preserving roots of polynomial systems, to prove that domains do not contain roots, and to make existence and uniqueness tests. They are compatible with standard preconditioning methods and fit linear program- ming techniques. However, curre…
Arbitrarily shaped plates analysis via Line Element-Less Method (LEM)
2018
Abstract An innovative procedure is introduced for the analysis of arbitrarily shaped thin plates with various boundary conditions and under generic transverse loading conditions. Framed into Line Element-less Method, a truly meshfree method, this novel approach yields the solution in terms of the deflection function in a straightforward manner, without resorting to any discretization, neither in the domain nor on the boundary. Specifically, expressing the deflection function through a series expansion in terms of harmonic polynomials, it is shown that the proposed method requires only the evaluation of line integrals along the boundary parametric equation. Further, minimization of appropri…
New Objective Refraction Metric Based on Sphere Fitting to the Wavefront
2017
Purpose. To develop an objective refraction formula based on the ocular wavefront error (WFE) expressed in terms of Zernike coefficients and pupil radius, which would be an accurate predictor of subjective spherical equivalent (SE) for different pupil sizes.Methods. A sphere is fitted to the ocular wavefront at the center and at a variable distance,t. The optimal fitting distance,topt, is obtained empirically from a dataset of 308 eyes as a function of objective refraction pupil radius,r0, and used to define the formula of a new wavefront refraction metric (MTR). The metric is tested in another, independent dataset of 200 eyes.Results. For pupil radiir0≤2 mm, the new metric predicts the equ…
Semi-Supervised Support Vector Biophysical Parameter Estimation
2008
Two kernel-based methods for semi-supervised regression are presented. The methods rely on building a graph or hypergraph Laplacian with both the labeled and unlabeled data, which is further used to deform the training kernel matrix. The deformed kernel is then used for support vector regression (SVR). The semi-supervised SVR methods are sucessfully tested in LAI estimation and ocean chlorophyll concentration prediction from remotely sensed images.
Reflectance-based surface saliency
2017
In this paper, we propose an original methodology allowing the computation of the saliency maps for high dimensional RTI data (Reflectance Transformation Imaging). Unlike most of the classical methods, our approach aims at devising an intrinsic visual saliency of the surface, independent of the sensor (image) and the geometry of the scene (light-object-camera). From RTI data, we use the DMD (Discrete Modal Decomposition) technique for the angular reflectance reconstruction, which we extend by a new transformation on the modal basis enabling a rotation-invariant representation of reconstructed reflectances. This orientation-invariance of the resulting reflectance shapes fosters a robust esti…
Integration of a Dirac comb and the Bernoulli polynomials
2016
Abstract For any positive integer n , we consider the ordinary differential equations of the form y ( n ) = 1 − Ш + F where Ш denotes the Dirac comb distribution and F is a piecewise- C ∞ periodic function with null average integral. We prove the existence and uniqueness of periodic solutions of maximal regularity. Above all, these solutions are given by means of finite explicit formulae involving a minimal number of Bernoulli polynomials. We generalize this approach to a larger class of differential equations for which the computation of periodic solutions is also sharp, finite and effective.
Splittings of Toric Ideals
2019
Let $I \subseteq R = \mathbb{K}[x_1,\ldots,x_n]$ be a toric ideal, i.e., a binomial prime ideal. We investigate when the ideal $I$ can be "split" into the sum of two smaller toric ideals. For a general toric ideal $I$, we give a sufficient condition for this splitting in terms of the integer matrix that defines $I$. When $I = I_G$ is the toric ideal of a finite simple graph $G$, we give additional splittings of $I_G$ related to subgraphs of $G$. When there exists a splitting $I = I_1+I_2$ of the toric ideal, we show that in some cases we can describe the (multi-)graded Betti numbers of $I$ in terms of the (multi-)graded Betti numbers of $I_1$ and $I_2$.