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.

Pure mathematicsComputer Science::GraphicsSeries (mathematics)Dupin cyclideBézier curveSymmetry (geometry)Barycentric coordinate systemComputational geometryTopologyBernstein polynomialMathematicsPolynomial interpolation
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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.

MapleDiscrete mathematicsModulus of smoothnesslcsh:MathematicsApplied Mathematics010102 general mathematicsApproximation theoremRegular polygonMonotonic functionFunction (mathematics)Type (model theory)engineering.materialVoronovskaja type theoremlcsh:QA1-93901 natural sciences010101 applied mathematics( p q ) $(pq)$ -Bernstein operatorsengineeringDiscrete Mathematics and Combinatorics0101 mathematics( p q ) $(pq)$ -calculusK-functionalAnalysisMathematicsDitzian-Totik first order modulus of smoothnessJournal of Inequalities and Applications
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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…

Memory Long-TermComputer scienceModels Neurological03 medical and health sciencesCellular and Molecular Neuroscience0302 clinical medicineBernstein ConferenceStatic random-access memorylcsh:QH301-705.5Auxiliary memory030304 developmental biologyNeuronsComputational Neuroscience0303 health sciencesNeuronal PlasticitySynaptic scalingConsolidation (soil)RecallLong-term memoryGeneral NeuroscienceComputational BiologyMemory Short-Termlcsh:Biology (General)SynapsesSynaptic plasticityPoster PresentationMemory consolidationMemory storage; brain; Synaptic Scaling;Neuroscience030217 neurology & neurosurgeryResearch Article
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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…

Pure mathematicsBernstein operatorModulus of smoothnessResearchApplied Mathematicslcsh:Mathematics010102 general mathematicsType (model theory)Rate of convergenceLambdalcsh:QA1-93901 natural sciences010101 applied mathematicsRate of convergenceVoronovskaja theorem41A10Discrete Mathematics and CombinatoricsKantorovich operators0101 mathematics41A2541A36AnalysisMathematicsJournal of Inequalities and Applications
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Some approximation properties by a class of bivariate operators

2019

WOS: 000503431300041

Class (set theory)Pure mathematicsGeneral MathematicsGBS-type operatorsmodulus of continuityGeneral EngineeringBernstein operatorsBivariate analysisModulus of continuityMathematics
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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…

[ INFO.INFO-NA ] Computer Science [cs]/Numerical Analysis [cs.NA]Linear programmingPolytopeBernstein polynomials01 natural sciencesSimplex algorithmApplied mathematicssimplex algorithm0101 mathematicsMathematicsDiscrete mathematicsBasis (linear algebra)Applied Mathematics010102 general mathematicssubdivision solverlinear programmingalgebraic systemsQuadratic function[INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA]Solver1991 Mathematics Subject Classification: 14Q15 14Q20 65G40Bernstein polynomialComputer Science Applications010101 applied mathematicsModeling and SimulationStandard basisGeometry and TopologyComputer Vision and Pattern RecognitionSoftwareInternational Journal of Shape Modeling
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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.

Bernstein functionsPure mathematicsTurán-type inequalitiesGeneralized inverseSeries (mathematics)General Mathematics33C99 33B99ta111Hyperbolic functionMathematics::Classical Analysis and ODEsInverseEigenfunctions of p-LaplacianEigenfunctionRamanujan's sumGeneralized trigonometric functionsymbols.namesakeDigamma functionMathematics - Classical Analysis and ODEsCompletely monotone functionsLog-convexitysymbolsTrigonometric functionsLog-concavityMathematicsFilomat
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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.

Voltaire Leibnitz Candide ou L'optimisme Candido Leonard Bernstein Lilian Hellman John Mauceri Candide musica americana teatro musicale musicalSettore L-ART/07 - Musicologia E Storia Della MusicaVoltaire Leibnitz Candide ou L'optimisme Leonard Bernstein Lilian Hellman John Mauceri Candide american music music theatre musical
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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.

Nutrition and DieteticsNTU methodChemistryMass transferHeat transferFilm temperatureHeat transfer coefficientMechanicsParametric identificationAgronomy and Crop ScienceChurchill–Bernstein equationFood ScienceBiotechnologyJournal of the Science of Food and Agriculture
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On the Complexity of the Bernstein Combinatorial Problem

2012

International audience

combinatorial complexity[ INFO.INFO-NA ] Computer Science [cs]/Numerical Analysis [cs.NA][INFO.INFO-NA] Computer Science [cs]/Numerical Analysis [cs.NA]interval arithmeticsBernstein polynomials[INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA]tensorial Bernstein basisComputingMilieux_MISCELLANEOUS
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