Search results for "Bernstein"

Bézier Solutions of the Wave Equation

2004

We study polynomial solutions in the Bezier form of the wave equation in dimensions one and two. We explicitly determine which control points of the Bezier solution at two different times fix the solution.

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…

Commentary: Concurrent Imitative Movement During Action Observation Facilitates Accuracy of Outcome Prediction in Less-Skilled Performers

2018

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…

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…

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,…

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…

Confidence Intervals for the Mean Based on Exponential Type Inequalities and Empirical Likelihood

2013

For independent observations, recently, it has been proposed to construct the confidence intervals for the mean using exponential type inequalities. Although this method requires much weaker assumptions than those required by the classical methods, the resulting intervals are usually too large. Still in special cases, one can find some advantage of using bounded and unbounded Bernstein inequalities. In this paper, we discuss the applicability of this approach for dependent data. Moreover, we propose to use the empirical likelihood method both in the case of independent and dependent observations for inference regarding the mean. The advantage of empirical likelihood is its Bartlett correcta…

Eduard Bernsteinin demokraattinen rauhanpolitiikka

2012

Tutkielmassa tarkastellaan saksalaisen työnväenliikkeen intellektuellin, journalistin ja poliitikon Eduard Bernsteinin rauhanpolitiikkaa. Tutkimuksessa kysytään, mistä näkökulmasta Bernstein lähti käsittelemään rauhankysymystä teksteissään ja valtiopäivätoiminnassaan. Mitkä olivat demokraattisen rauhanpolitiikan keskeiset piirteet? Toiseksi tutkielmassa kysytään Quentin Skinnerin inspiroimana, että mitä konventioita ja uskomuksia Bernstein lähti teksteillään haastamaan. Tutkielman otsikon käsiterauhanpolitiikka on omaksuttu historiallisen rauhantutkimuksen piiristä, mutta Bernstein puhui myös omissa teksteissään rauhanpolitiikasta. Tutkielman aineisto koostuu pääosin Bernsteinin ensimmäisen…

Sets versus trial sequences, Hausdorff versus von Mises: “Pure” mathematics prevails in the foundations of probability around 1920

2010

Abstract The paper discusses the tension which occurred between the notions of set (with measure) and (trial-) sequence (or—to a certain degree—between nondenumerable and denumerable sets) when used in the foundations of probability theory around 1920. The main mathematical point was the logical need for measures in order to describe general nondiscrete distributions, which had been tentatively introduced before (1919) based on von Mises’s notion of the “Kollektiv.” In the background there was a tension between the standpoints of pure mathematics and “real world probability” (in the words of J.L. Doob) at the time. The discussion and publication in English translation (in Appendix ) of two …