Search results for "Geometry"

Arc routing problems: A review of the past, present, and future

2020

[EN] Arc routing problems (ARPs) are defined and introduced. Following a brief history of developments in this area of research, different types of ARPs are described that are currently relevant for study. In addition, particular features of ARPs that are important from a theoretical or practical point of view are discussed. A section on applications describes some of the changes that have occurred from early applications of ARP models to the present day and points the way to emerging topics for study. A final section provides information on libraries and instance repositories for ARPs. The review concludes with some perspectives on future research developments and opportunities for emergin…

Solving the length constrained K-drones rural postman problem

2021

[EN] In this paper we address the Length Constrained K-Drones Rural Postman Problem (LC K-DRPP). This is a continuous optimization problem where a fleet of homogeneous drones have to jointly service (traverse) a set of (curved or straight) lines of a network. Unlike the vehicles in classical arc routing problems, a drone can enter a line through any of its points, service a portion of that line, exit through another of its points, then travel directly to any point on another line, and so on. Moreover, since the range of the drones is restricted, the length of each route is limited by a maximum distance. Some applications for drone arc routing problems include inspection of pipelines, railwa…

Documenting carved stones by 3D modelling – Example of Mongolian deer stones

2018

Rock art studies are facing major technical challenges for extensive documentation. Nowadays, recording is essentially obtained from time-consuming tracing and rubbing, techniques that also require a high level of expertise. Recent advances in 3D modelling of natural objects and computational treatment of the modelled surfaces may provide an alternative, and reduce the current documentation bottleneck. The aim of this study is to examine the extent to which such treatments can be applied. The case study presented here concerns the famous deer stones erected by ancient Mongolian nomad populations. The 3D acquisition workflow is based on structure-from-motion, a versatile photogrammetric tech…

The limits of freely-available tree-ring chronologies

2020

Documenting carved stones from 3D models. Part II - Ambient occlusion to reveal carved parts.

2021

10 pages; International audience; Revealing carved parts in rock art is of primary importance and remains a major challenge for archaeological documentation. Computational geometry applied to 3D imaging provides a unique opportunity to document rock art. This study evaluates five algorithms and derivatives used to compute ambient occlusion and sky visibility on 3D models of Mongolian stelae, also known as deer stones. By contrast with the previous companion work, models are processed directly in 3D, without preliminary projection. Volumetric obscurance gives the best results for the identification of carved figures. The effects of model resolution and parameters specific to ambient occlusio…

Study of the performance of a resolution criterion to characterise complex chromatograms with unknowns or without standards

2017

The search for best conditions in liquid chromatography is routinely carried out with information provided by chemical standards. However, sometimes there are samples with insufficient knowledge about their chemical composition. In other cases, identities of the components are known, but there are no standards available, and in other cases the identities of peaks in chromatograms taken under different conditions are ambiguous. Most resolution criteria used to measure separation performance cannot be applied to these samples. In this work, a global resolution function valid for all situations was developed based on automatic measurements of peak prominences (area fraction exceeding the line …

Cardinal invariants of cellular Lindelof spaces

2018

A space X is said to be cellular-Lindelof if for every cellular family $$\mathcal {U}$$ there is a Lindelof subspace L of X which meets every element of $$\mathcal {U}$$ . Cellular-Lindelof spaces generalize both Lindelof spaces and spaces with the countable chain condition. Solving questions of Xuan and Song, we prove that every cellular-Lindelof monotonically normal space is Lindelof and that every cellular-Lindelof space with a regular $$G_\delta $$ -diagonal has cardinality at most $$2^\mathfrak {c}$$ . We also prove that every normal cellular-Lindelof first-countable space has cardinality at most continuum under $$2^{<\mathfrak {c}}=\mathfrak {c}$$ and that every normal cellular-Lindel…

Mononuclear and tetranuclear Fe(III) complexes with two different types of N, O donor Schiff base ligands

2013

Abstract A mononuclear Fe(III) complex of a tetradentate N 2 O 2 donor Schiff base ligand derived from 3-ethoxysalicaldehyde and ethylenediamine has been reported. In addition two tetranuclear Fe(III) complexes with discrete Fe 4 III (μ 4 -O) cores have been synthesized and characterized using two Schiff base ligands (H 2 L 1–2 ) derived from two different aromatic acid hydrazides and diacetyl monoxime. The mononuclear Fe(III) and one of the tetranuclear Fe(III) complexes have been structurally characterized by single-crystal X-ray crystallography. The mononuclear complex has a highly distorted octahedral geometry. The tetranuclear Fe(III) complexes are found to be rare examples with discre…

Mössbauer relaxation spectra in arbitrarily ordered absorbers—Line shape analysis for an iron(II) spincrossover complex in the presence of texture

1989

The stochastic theory of Mossbauer line shapes is formulated in a fashion which allows the evaluation of the spectral shapes for absorbers of arbitrary thickness, texture, and an anisotropic Lamb—Mossbauer factor. The results are specialized to a two-state-relaxation model of fluctuating electric hyperfine interaction in the case of an absorber of axially symmetric texture. The formalism is applied to the line shape analysis of Mossbauer spectra of a textured sample of the spin-crossover complex [Fe(mtz)6] (PF6)2 (mtz=1-methyltetrazole). It is found that between 185 and 240 K the rate constants for the HS→LS conversion are temperature independent, whereas an Arrhenius behaviour is found for…

Dynamics of spin state conversion processes in the solid state

1989

High spin (HS) ⇌ low spin (LS) conversions in transition metal complexes are nonradiative transitions between spin states. In this contribution, we present a study of the temperature and pressure dependence of the HS ⇌ LS intersystem crossing dynamics. For some iron(II) spin-crossover complexes, the rate constants were determined by line shape analysis of57Fe Mossbauer spectra. Their temperature dependence is described by an Arrhenius equation, their pressure dependence is interpreted within absolute rate theory. HS → LS conversion rates at low temperatures were determined from the relaxation of light-induced formation of HS states, monitored by optical spectroscopy. Deviations from a simpl…