Search results for "Bernstein"
showing 10 items of 32 documents
Conversion of Dupin Cyclide Patches into Rational Biquadratic Bézier Form
2005
This paper uses the symmetry properties of circles and Bernstein polynomials to establish a series of interesting barycentric properties of rational biquadratic Bezier patches. A robust algorithm is presented, based on these properties, for the conversion of Dupin cyclide patches into Bezier form. A set of conversion examples illustrates the use of this algorithm.
Some approximation properties of ( p , q ) $(p,q)$ -Bernstein operators
2016
This paper is concerned with the $(p,q)$ -analog of Bernstein operators. It is proved that, when the function is convex, the $(p,q)$ -Bernstein operators are monotonic decreasing, as in the classical case. Also, some numerical examples based on Maple algorithms that verify these properties are considered. A global approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem are proved.
Synaptic Scaling Enables Dynamically Distinct Short- and Long-Term Memory Formation
2013
Memory storage in the brain relies on mechanisms acting on time scales from minutes, for long-term synaptic potentiation, to days, for memory consolidation. During such processes, neural circuits distinguish synapses relevant for forming a long-term storage, which are consolidated, from synapses of short-term storage, which fade. How time scale integration and synaptic differentiation is simultaneously achieved remains unclear. Here we show that synaptic scaling – a slow process usually associated with the maintenance of activity homeostasis – combined with synaptic plasticity may simultaneously achieve both, thereby providing a natural separation of short- from long-term storage. The inter…
Approximation properties of λ-Kantorovich operators
2018
In the present paper, we study a new type of Bernstein operators depending on the parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lambda\in[-1,1]$\end{document}λ∈[−1,1]. The Kantorovich modification of these sequences of linear positive operators will be considered. A quantitative Voronovskaja type theorem by means of Ditzian–Totik modulus of smoothness is proved. Also, a Grüss–Voronovskaja type theorem for λ-Kantorovich operators is provided. Some numerical examples which show the relevance of the res…
Some approximation properties by a class of bivariate operators
2019
WOS: 000503431300041
OPTIMIZATIONS FOR TENSORIAL BERNSTEIN–BASED SOLVERS BY USING POLYHEDRAL BOUNDS
2010
The tensorial Bernstein basis for multivariate polynomials in n variables has a number 3n of functions for degree 2. Consequently, computing the representation of a multivariate polynomial in the tensorial Bernstein basis is an exponential time algorithm, which makes tensorial Bernstein-based solvers impractical for systems with more than n = 6 or 7 variables. This article describes a polytope (Bernstein polytope) with a number of faces, which allows to bound a sparse, multivariate polynomial expressed in the canonical basis by solving several linear programming problems. We compare the performance of a subdivision solver using domain reductions by linear programming with a solver using a c…
Turán type inequalities for generalized inverse trigonometric functions
2013
In this paper we study the inverse of the eigenfunction $\sin_p$ of the one-dimensional $p$-Laplace operator and its dependence on the parameter $p$, and we present a Tur\'an type inequality for this function. Similar inequalities are given also for other generalized inverse trigonometric and hyperbolic functions. In particular, we deduce a Tur\'an type inequality for a series considered by Ramanujan, involving the digamma function.
Il "Candide" da Voltaire e Bernstein
2015
Il saggio ricostruisce la genesi del "Candide" di Leonard Bernstein, e la storia delle sue tante stesure e riprese: dal primo progetto teatrale del 1953-54 sino cosiddetta "Scottish Opera Version, curata da John Mauceri, del 1988. Il percorso drammaturgico dello spettacolo viene messo a confronto con le narrazioni del romanzo di Voltaire e nella seconda parte del saggio vengono affrontati anche gli aspetti musicali e compositivi dell'opera.
A method for the calculation of the heat transfer coefficient in potato drying
1993
A method for the determination of the heat transfer coefficient was proposed for the first falling drying period of potato cubes. During this period, heat and mass transfer were considered as coupled phenomena. Temperature calculation inside the sample was performed using the macroscopic heat transfer balance. The heat transfer coefficient was computed by means of parametric identification, using the Gauss–Newton method. The figure obtained for the heat transfer coefficient shows good agreement with other sources.
On the Complexity of the Bernstein Combinatorial Problem
2012
International audience