Search results for "Bernstein"
showing 10 items of 32 documents
A note on quarkonial systems and multilevel partition of unity methods
2013
We discuss the connection between the theory of quarkonial decompositions for function spaces developed by Hans Triebel, and the multilevel partition of unity method. The central result is an alternative approach to the stability of quarkonial decompositions in Besov spaces , s > n(1/p − 1)+, which leads to relaxed decay assumptions on the elements of a quarkonial system as the monomial degree grows.
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…
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.
A semi-parametric stochastic generator for bivariate extreme events
2017
The analysis of multiple extreme values aims to describe the stochastic behaviour of observations in the joint upper tail of a distribution function. For instance, being able to simulate multivariate extreme events is convenient for end users who need a large number of random replications of extremes as input of a given complex system to test its sensitivity. The simulation of multivariate extremes is often based on the assumption that the dependence structure, the so-called extremal dependence function, is described by a specific parametric model. We propose a simulation method for sampling bivariate extremes, under the assumption that the extremal dependence function is semiparametric. Th…
Some approximation properties by a class of bivariate operators
2019
WOS: 000503431300041
Convergence of GBS Operators
2018
In [59, 60], Bogel introduced a new concept of Bogel-continuous and Bogel-differentiable functions and also established some important theorems using these concepts. Dobrescu and Matei [80] showed the convergence of the Boolean sum of bivariate generalization of Bernstein polynomials to the B-continuous function on a bounded interval. Subsequently, Badea and Cottin [46] obtained Korovkin theorems for GBS operators.
Nonlinear systems solver in floating-point arithmetic using LP reduction
2009
This paper presents a new solver for systems of nonlinear equations. Such systems occur in Geometric Constraint Solving, e.g., when dimensioning parts in CAD-CAM, or when computing the topology of sets defined by nonlinear inequalities. The paper does not consider the problem of decomposing the system and assembling solutions of subsystems. It focuses on the numerical resolution of well-constrained systems. Instead of computing an exponential number of coefficients in the tensorial Bernstein basis, we resort to linear programming for computing range bounds of system equations or domain reductions of system variables. Linear programming is performed on a so called Bernstein polytope: though,…
Bayesian inference for the extremal dependence
2016
A simple approach for modeling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the angular measure or, alternatively, the Pickands dependence function. We propose a nonparametric Bayesian model that allows, in the bivariate case, the simultaneous estimation of both functional representations through the use of polynomials in the Bernstein form. The constraints required to provide a valid extremal dependence are addressed in a straightforward manner, by placing a prior on the coefficients of the Bernstein polynomials which gives probability one to the set of valid functions. The…
Investigation of Flow and Heat Transfer in Corrugated-Undulated Plate Heat Exchangers
2000
An experimental and numerical investigation of heat transfer and fluid flow was conducted for corrugated-undulated plate heat exchanger configurations under transitional and weakly turbulent conditions. For a given geometry of the corrugated plates the geometrical characteristics of the undulated plates, the angle formed by the latter with the main flow direction, and the Reynolds number were made to vary. Distributions of the local heat transfer coefficient were obtained by using liquid-crystal thermography, and surface-averaged values were computed; friction coefficients were measured by wall pressure tappings. Overall heat transfer and pressure drop correlations were derived. Three-dimen…
The Role of Curriculum Theory in Contemporary Higher Education Research and Practice
2017
In the light of recent debates on the possible issues in curriculum studies, formulated particularly in the field of sociology of education, this chapter discusses the role and the importance of curriculum theories in higher education. Focusing on the historical and the conceptual roots of curriculum theory approaches, the argument is that the dispute and the separation between normative and critical roles of curriculum theories are important to overcome in today’s competency-based and outcome-focused context of higher education. Basil Bernstein’s ideas on the vital role of knowledge are discussed in relation to the origins of the so-called crisis in curriculum theories. It is suggested tha…