Search results for "Parabola"

New approaches based on modified Gaussian models for the prediction of chromatographic peaks

2012

Abstract The description of skewed chromatographic peaks has been discussed extensively and many functions have been proposed. Among these, the Polynomially Modified Gaussian (PMG) models interpret the deviations from ideality as a change in the standard deviation with time. This approach has shown a high accuracy in the fitting to tailing and fronting peaks. However, it has the drawback of the uncontrolled growth of the predicted signal outside the elution region, which departs from the experimental baseline. To solve this problem, the Parabolic-Lorentzian Modified Gaussian (PLMG) model was developed. This combines a parabola that describes the variance change in the peak region, and a Lor…

Functional Type Error Control for Stabilised Space-Time IgA Approximations to Parabolic Problems

2018

The paper is concerned with reliable space-time IgA schemes for parabolic initial-boundary value problems. We deduce a posteriori error estimates and investigate their applicability to space-time IgA approximations. Since the derivation is based on purely functional arguments, the estimates do not contain mesh dependent constants and are valid for any approximation from the admissible (energy) class. In particular, they imply estimates for discrete norms associated with stabilised space-time IgA approximations. Finally, we illustrate the reliability and efficiency of presented error estimates for the approximate solutions recovered with IgA techniques on a model example.

Analītiskā ģeometrija plaknē

1947

Half-width plots, a simple tool to predict peak shape, reveal column kinetics and characterise chromatographic columns in liquid chromatography: Stat…

2013

Peak profiles in chromatography are characterised by their height, position, width and asymmetry; the two latter depend on the values of the left and right peak half-widths. Simple correlations have been found between the peak half-widths and the retention times. The representation of such correlations has been called half-width plots. For isocratic elution, the plots are parabolic, although often, the parabolas can be approximated to straight-lines. The plots can be obtained with the half-widths/retention time data for a set of solutes experiencing the same kinetics, eluted with a mobile phase at fixed or varying composition. When the analysed solutes experience different resistance to mas…

Motor strategies and adiabatic invariants: The case of rhythmic motion in parabolic flights

2021

The role of gravity in human motor control is at the same time obvious and difficult to isolate. It can be assessed by performing experiments in variable gravity. We propose that adiabatic invariant theory may be used to reveal nearly-conserved quantities in human voluntary rhythmic motion, an individual being seen as a complex time-dependent dynamical system with bounded motion in phase-space. We study an explicit realization of our proposal: An experiment in which we asked participants to perform $\infty-$ shaped motion of their right arm during a parabolic flight, either at self-selected pace or at a metronome's given pace. Gravity varied between $0$ and $1.8$ $g$ during a parabola. We c…

A relation between the curvature ellipse and the curvature parabola

2019

Abstract At each point in an immersed surface in ℝ4 there is a curvature ellipse in the normal plane which codifies all the local second order geometry of the surface. Recently, at the singular point of a corank 1 singular surface in ℝ3, a curvature parabola in the normal plane which codifies all the local second order geometry has been defined. When projecting a regular surface in ℝ4 to ℝ3 in a tangent direction, corank 1 singularities appear generically. The projection has a cross-cap singularity unless the direction of projection is asymptotic, where more degenerate singularities can appear. In this paper we relate the geometry of an immersed surface in ℝ4 at a certain point to the geome…

Optic disc positioning and blood vessels extraction on eye fundus

2009

This paper presents two methods aimed to the optic disc positioning on the retinal images. The first is based on a template of the entire image, while the second is based on the retinal vascularisation. For this second task, also a vessel extraction method is provided. Both the algorithm have been tested on test images of the Drive Database.

"Ludzka krotochwila" na scenie teatru świata w twórczości Mikołaja Reja i Marcina Bielskiego

2019

Artykuł jest próbą interpretacji dzieł Mikołaja Reja i Marcina Bielskiego w kategoriach encyklopedycznego teatru. Taka konstrukcja stanowi odwzorowanie obrazu ówczesnego świata. Można mówić o zgodności między uczonymi treściami a wielką machiną theatrum mundi, którego struktury, relacje i zakres sprawnie funkcjonują w zamkniętym dyskursie literackich utworów. „Krotochwila ludzka” staje się więc miejscem zmagań człowieka z własnymi słabościami i losem. Staropolscy pisarze, aby zilustrować tę walkę, posłużyli się popularnym w renesansie mitem o bogini Kirke i jej ofiarach zamienionych w zwierzęta. Maski faunistyczne stanowiły znakomite alegorie występków ludzkich, chociaż mogły również przeds…