References of "Nicolay, Samuel"
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See detailGeneralized T_u^p spaces: On the trail of Calderón and Zygmund
Loosveldt, Laurent ULiege; Nicolay, Samuel ULiege

in Dissertationes Mathematicae (2020)

We generalize the T_u^p spaces introduced by Calderón and Zygmund and show that most of the results obtained in their study of the pointwise estimates for solutions of elliptic partial differential ... [more ▼]

We generalize the T_u^p spaces introduced by Calderón and Zygmund and show that most of the results obtained in their study of the pointwise estimates for solutions of elliptic partial differential equations and systems can be generalized in this framework with Lp-conditions. [less ▲]

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See detailA time-filling talk about fractals
Nicolay, Samuel ULiege

Conference (2019, October 03)

We presents here two applications of the multifractal formalism for functions: the first one concerns DNA sequences and the second one temperature data.

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See detailSome equivalent definitions of Besov spaces of generalized smoothness
Loosveldt, Laurent ULiege; Nicolay, Samuel ULiege

in Mathematische Nachrichten (2019), 292(10), 2262-2282

In this paper, we present some alternative definitions of Besov spaces of general-ized smoothness, defined via Littlewood–Paley-type decomposition, involving weakderivatives, polynomials, convolutions and ... [more ▼]

In this paper, we present some alternative definitions of Besov spaces of general-ized smoothness, defined via Littlewood–Paley-type decomposition, involving weakderivatives, polynomials, convolutions and generalized interpolation spaces. [less ▲]

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See detailDes maths dans l'ADN
Nicolay, Samuel ULiege

Conference given outside the academic context (2019)

Nous introduisons quelques outils mathématiques qui ont permis d'obtenir des informations structurelles et fonctionnelles concernant l'ADN des mamifères

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See detailCorrigendum to “Evidence for solar influence in a Holocene speleothem record (Père Nöel cave, SE Belgium)” (Quaternary Science Reviews (2018) 192 (249–262), (S0277379118302038) (10.1016/j.quascirev.2018.05.039))
Allan, Mohammed ULiege; Deliège, Alain ULiege; Verheyden, S. et al

in Quaternary Science Reviews (2019)

When this paper was originally published, there was an error in Fig. 7g. Indeed the curve of percentage of hematite-stained grains measured on North Atlantic MC52-VM29-191 core, published by Bond et al ... [more ▼]

When this paper was originally published, there was an error in Fig. 7g. Indeed the curve of percentage of hematite-stained grains measured on North Atlantic MC52-VM29-191 core, published by Bond et al. (2001), was inverted. Please find the correct Fig. 7 below: [Figure presented] Fig. 7 corrected: (a), (b) and (c) PN trace elements contents (Sr = red line; Ba = green line; and Mg = black line) in comparison to (d) PN Stalagmite δ 18 O (blue line), (e) δ 18 O record from Bunker Cave-W Germany (Fohlmeister et al., 2012), (f) δ 18 O record from lake Ammersee- Germany (von Grafenstein et al., 1999), (g) hematite-stained grains from the North Atlantic (Bond et al., 2001), (h) frequency of wet/dry events in the Northern Hemisphere as defined by Wanner et al. (2014). The blue horizontal bars mark cold events. In the paper, Fig. 7 allows us to compare the trace elements Ba, Sr, Mg and δ 18 O isotopes results of Père Noël (PN) stalagmite with other continental and marine records. In the figure, the blue lines underline the 6 geochemical events measured in our speleothem PN record that we attribute to cold events. As a first point, we note that most of the PN events are consistent with some of the dry events (Fig. 7h) defined by Wanner et al. (2014) for the Northern Hemisphere. The correspondence is clear for 5 intervals corresponding to the 2.6–2.8, 4.6–4.8, 6.2–6.4, 8.1–8.3 and 9.3–9.5 Wanner events (no data for the oldest event at 10.3–10.7). Second, we compare the PN record with the abundance of hematite-stained grains in core VM29-191 (Bond et al., 2001). This curve, that was used as one of the drift ice indices, represents the North Atlantic cold events. (Note the comparison with the stacked curve would lead to the same conclusion). At least the 3 PN events at 4.6–4.8, 6.2–6.4 and 9.3–9.5 ka BP occur in a time interval consistent with the Bond events 3, 4 and 6, respectively. In the manuscript, the text must be corrected (see lines 416–418):“During these three intervals (i.e., around 10.5, between 9.5 and 9.2 and between 8.4 and 8.2 ka BP), the wavelet spectrum of trace elements shows that the solar imprint is well present in the PN stalagmite (Fig. 6). Those three intervals may correspond to Bond cycles (Bond et al., 2001)”. Indeed only the 8.4-8.2 ka BP and 9.3–9.5 event may be related to Bond cycle since the 10.5 event is not covered by the Bond curve. There is no peak-to-peak correspondence between the two curves than are characterized by different age uncertainties. PN record presents an age uncertainty estimated at ±11–51 years at 2σ level for the interval 2–9.5 ka BP (see Table 1 in our manuscript). The chronology of the Bond et al. records presents an age error estimated at 50 years (1σ). Whatever the 8 Bond events display, as stated in the Fig. 2 caption of Bond et al. (2001), “a millennial-scale cycles regarded as part of the North Atlantic's 1500-year cycle”. Such millenial cyclicity was revealed in our PN trace element record by a 912–1029 yr peak in the wavelet spectral power (Fig. 6). Such periodicity may suggest some solar forcing in our PN record. The authors apologise for any inconvenience caused. © 2019 Elsevier Ltd [less ▲]

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See detailSur la notion de dimension
Nicolay, Samuel ULiege

in Quadrature: Magazine de Mathématiques Pures et Appliquées (2019), 111

Nous proposons ici quelques considérations sur la notion de dimension, inspirées par la notion physique renvoyant au nombre de degrés de liberté. L’objectif est d’introduire de manière naturelle la ... [more ▼]

Nous proposons ici quelques considérations sur la notion de dimension, inspirées par la notion physique renvoyant au nombre de degrés de liberté. L’objectif est d’introduire de manière naturelle la dimension de Hausdorff. Afin d’illustrer nos propos, nous calculons les dimensions topologique et de Hausdorff de l’ensemble triadique de Cantor. [less ▲]

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See detailGeneralized regularity spaces : toward the detection of a logarithmic correction in multi fractal analysis
Loosveldt, Laurent ULiege; Nicolay, Samuel ULiege

Conference (2018, November 07)

The aim of the talk will first be to present the notion of Hölder pointwise spaces and some functions that are studied with this notion. Then, we will introduce generalization of these spaces and explain ... [more ▼]

The aim of the talk will first be to present the notion of Hölder pointwise spaces and some functions that are studied with this notion. Then, we will introduce generalization of these spaces and explain why they give additional information about the behavior of the analyzed function. We will give some wavelets criteria to characterize generalized Hölder spaces and links with generalized Besov spaces will also be discussed. [less ▲]

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See detailOn some generalizations of the Fréchet functional equations
Molla, Arman ULiege; Nicolay, Samuel ULiege; Schneiders, Jean-Pierre ULiege

in Journal of Mathematical Analysis and Applications (2018), 466(2), 1400-1409

In this paper we study the Fréchet functional equation in the n-dimensional Euclidian space as well as in the context of distributions. We also generalizethe Cauchy functional equation for distributions ... [more ▼]

In this paper we study the Fréchet functional equation in the n-dimensional Euclidian space as well as in the context of distributions. We also generalizethe Cauchy functional equation for distributions to any natural order. [less ▲]

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See detailGeneralized regularity spaces. Part II: on the trail of Calderon and Zygmund
Loosveldt, Laurent ULiege; Nicolay, Samuel ULiege

Conference (2018, September 19)

We present a result about the regularity of the solution of an elliptic partial differentiable equation if we assume regularity condition for the coefficients of this equation.

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See detailGeneralized Regularity spaces. Part I: A wavelet-based approach
Loosveldt, Laurent ULiege; Nicolay, Samuel ULiege

Conference (2018, September 19)

The aim of this talk is to convince the audience of the interest of the generalized regularity spaces in the field of the multifractal analysis.

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See detailEvidence for solar influence in a Holocene speleothem record (Père Noël cave, SE Belgium)
Allan, Mohammed ULiege; Deliège, Adrien ULiege; Verheyden, sophie et al

in Quaternary Science Reviews (2018)

We present a decadal-centennial scale Holocene climate record based on trace elements contents from a 65cm stalagmite from Belgian Père Noël cave. “Père Noël” (PN) stalagmite covers the last 12.7 ka ... [more ▼]

We present a decadal-centennial scale Holocene climate record based on trace elements contents from a 65cm stalagmite from Belgian Père Noël cave. “Père Noël” (PN) stalagmite covers the last 12.7 ka according to U/ Th dating. High spatial resolution measurements of trace elements (Sr, Ba and Mg) were done by Laser-Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS). Trace elements profiles were interpreted as environmental and climate changes in the Han-sur-Lesse region. Power spectrum estimators and continuous wavelet transform were applied on trace elements time series to detect any statistically significant periodicities in the PN stalagmite. Spectral analyses reveal decadal to millennial periodicities (i.e., 68–75, 133–136, 198–209, 291–358, 404–602, 912–1029 and 2365–2670 yr) in the speleothem record. Results were compared to reconstructed sunspot number data to determine whether solar signal is presents in PN speleothem. The occurrence of significant solar periodicities (i.e., cycles of Gleissberg, de Vries, unnamed 500 years, Eddy and Hallstatt) supports for an impact of solar forcing on PN speleothem trace element contents. Moreover, several intervals of significant rapid winter change were detected during the Holocene at 10.3, 9.3–9.5, around 8.2, 6.4–6.2, 4.7–4.5, and around 2.7 ka BP. Those intervals are similar to the cold winter events evidenced in different natural paleoclimate archives, suggesting common climate forcing mechanisms related to changes in solar irradiance. [less ▲]

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See detailAnalyse Mathématique : Fonctions définies sur une partie de la droite réelle
Nicolay, Samuel ULiege

Book published by Ellipses (2018)

Ce livre s’adresse aux étudiants désireux d’obtenir des bases rigoureuses en analyse. L’auteur s’est donné pour objectif d’aborder la théorie des fonctions à une variable de manière complète et détaillée ... [more ▼]

Ce livre s’adresse aux étudiants désireux d’obtenir des bases rigoureuses en analyse. L’auteur s’est donné pour objectif d’aborder la théorie des fonctions à une variable de manière complète et détaillée. De nombreuses excursions théoriques, sortant des sentiers habituellement empruntés pour un tel projet, sont proposées afin de donner au lecteur une vision plus globale de la théorie. Il s’agit d’un outil de travail idéal pour aborder le programme de mathématiques du supérieur (niveau L2). Cet ouvrage est illustré par de nombreuses figures et des exemples traités en détail. Les sujets abordés sont : la logique et la théorie des ensembles, les nombres, les suites, les séries, les fonctions (continuité, dérivabilité, intégrales, primitivation, suite de fonctions, etc.) et les équations différentielles. Les fonctions élémentaires sont également rigoureusement introduites. [less ▲]

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See detailGeneralized Pointwise Hoelder Spaces Defined via Admissible Sequences
Kreit, Damien; Nicolay, Samuel ULiege

in Journal of Function Spaces (2018), 2018

We introduce in this paper a generalization of the pointwise Hölder spaces. We give alternative definitions of these spaces, look at their relationship with the wavelets, and introduce a notion of ... [more ▼]

We introduce in this paper a generalization of the pointwise Hölder spaces. We give alternative definitions of these spaces, look at their relationship with the wavelets, and introduce a notion of generalized Hölder exponent. [less ▲]

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See detailA study of histograms of wavelet coefficients of the Mars topography to determine its scaling properties
Kleyntssens, Thomas ULiege; Reynaerts, Laura ULiege; Nicolay, Samuel ULiege

Poster (2018, April 12)

Recently, the scaling properties of Mars topography have been analyzed through the Wavelet Leaders Method. The signals studied have often a few values radically different from the rest of the signal, due ... [more ▼]

Recently, the scaling properties of Mars topography have been analyzed through the Wavelet Leaders Method. The signals studied have often a few values radically different from the rest of the signal, due to the presence of crater for example. These values can disrupt the fractal study of the signals and the interpretation of the results is thus more difficult. Some new methods based on the use of histograms of wavelet coefficients allows to be more robust for the characterization of the fractal nature of signals. The main methods are the Wavelet Profile Method and the Leaders Profile Method. Moreover, a great advantage of these methods is to have a new criterion to differentiate the monofractal and the multifractal signals which is not based on the linearity of a inverse Legendre transform, as it is the case for the most of the methods of signal analysis. In this work, we show that these methods applied on Mars Orbiter Laser Altimeter (MOLA) data allows to have additional information on the topography of Mars compared to the other methods. [less ▲]

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See detailGlobal warming and natural variability
Reynaerts, Laura ULiege; Fettweis, Xavier ULiege; Nicolay, Samuel ULiege

Poster (2018, April)

In this work, we show that the lull periods of the warming episodes observed in the surface temperatures (GISS,...) can be explained through the natural variability of the climate. To do so, we use the ... [more ▼]

In this work, we show that the lull periods of the warming episodes observed in the surface temperatures (GISS,...) can be explained through the natural variability of the climate. To do so, we use the wavelet transform to extract the physical modes in the temperature data (which can be seen as am-fm components) and show that these modes induce coolings that corresponds to the lull periods empirically observed. [less ▲]

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See detailAnalysis and indication on long-term forecasting of the Oceanic Niño index with wavelet-induced components
Deliège, Adrien ULiege; Nicolay, Samuel ULiege

Poster (2018, April)

The present work provides an analysis and a long-term forecasting scheme of the Oceanic Niño Index (ONI) using the continuous wavelet transform. First, it appears that oscillatory components with main ... [more ▼]

The present work provides an analysis and a long-term forecasting scheme of the Oceanic Niño Index (ONI) using the continuous wavelet transform. First, it appears that oscillatory components with main periods of about 17, 31, 43, 61 and 140 months govern most of the variability of the signal, which is consistent with previous works. Then, this information enables us to derive a simple algorithm to model and forecast ONI. The model is based on the observation that the modes extracted from the signal are generally phased with positive or negative anomalies of ONI El Niño and La Niña events). Such a feature is exploited to generate locally stationary curves that mimic this behavior and which can be easily extrapolated to form a basic forecast. The wavelet transform is then used again to smooth out the process and finalize the predictions. The skills of the technique described in this paper are assessed through retroactive forecasts of past El Niño and La Niña events and via classic indicators computed as functions of the lead time. The main asset of the proposed model resides in its long-lead prediction skills. Consequently, this approach should prove helpful as a complement to other models for estimating the long-term trends of ONI. [less ▲]

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See detailAn algorithm for computing non-concave multifractal spectra using the Sν spaces
Kleyntssens, Thomas ULiege; Esser, Céline ULiege; Nicolay, Samuel ULiege

in Communications in Nonlinear Science and Numerical Simulation (2018), 56

We present an implementation of a multifractal formalism based on the Sν spaces and show that it effectively gives the right Hölder spectrum in numerous cases. In particular, it allows to recover non ... [more ▼]

We present an implementation of a multifractal formalism based on the Sν spaces and show that it effectively gives the right Hölder spectrum in numerous cases. In particular, it allows to recover non-concave spectra, where other multifractal formalisms only lead to the concave hull of the spectra. [less ▲]

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See detailExtracting oscillating components from nonstationary time series: A wavelet-induced method
Deliège, Adrien ULiege; Nicolay, Samuel ULiege

in Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics (2017), 96

This paper consists in the description and application of a method called wavelet-induced mode extraction (WIME) in the context of time-frequency analysis. WIME aims to extract the oscillating components ... [more ▼]

This paper consists in the description and application of a method called wavelet-induced mode extraction (WIME) in the context of time-frequency analysis. WIME aims to extract the oscillating components that build amplitude modulated-frequency modulated signals. The essence of this technique relies on the successive extractions of the dominant ridges of wavelet-based time-frequency representations of the signal under consideration. Our tests on simulated examples indicate strong decomposition and reconstruction skills, trouble-free handling of crossing trajectories in the time-frequency plane, sharp performances in frequency detection in the case of mode-mixing problems, and a natural tolerance to noise. These results are compared with those obtained with empirical mode decomposition. We also show that WIME still gives meaningful results with real-life data, namely, the Oceanic Niño Index. [less ▲]

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See detailA multifractal formalism for non-concave and non-increasing spectra: the leaders profile method
Esser, Céline ULiege; Kleyntssens, Thomas ULiege; Nicolay, Samuel ULiege

in Applied and Computational Harmonic Analysis (2017), 43(2), 269-291

We present an implementation of a multifractal formalism based on the types of histogram of wavelet leaders. This method yields non-concave spectra and is not limited to their increasing part. We show ... [more ▼]

We present an implementation of a multifractal formalism based on the types of histogram of wavelet leaders. This method yields non-concave spectra and is not limited to their increasing part. We show both from the theoretical and from the applied points of view that this approach is more e cient than the wavelet-based multifractal formalisms previously introduced. [less ▲]

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See detailDoes Belgian Holocene speleothem record solar forcing and cold events?
Allan, Mohammed ULiege; Deliège, Adrien ULiege; Nicolay, Samuel ULiege et al

in Climate of the Past Discussions (2017)

We present a decadal-centennial scale Holocene climate record based on trace elements contents from a 65 cm stalagmite (Père Noël) from Belgian Père Noël cave. Père Noël (PN) stalagmite covers the last 12 ... [more ▼]

We present a decadal-centennial scale Holocene climate record based on trace elements contents from a 65 cm stalagmite (Père Noël) from Belgian Père Noël cave. Père Noël (PN) stalagmite covers the last 12.7 ka according to U/Th dating. High spatial resolution measurements of trace elements (Sr, Ba, Mg and Al) were done by Laser-Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS). Trace elements profiles were interpreted as environmental and climate changes in the Han-sur-Lesse region. Power spectrum estimators and continuous wavelet transform were applied on trace elements time series to detect any statistically significant periodicities in the PN stalagmite. Spectral analyses reveal decadal to millennial periodicities (i.e., 68–75, 133–136, 198–209, 291–358, 404–602, 912–1029 and 2365–2670 yr) in the speleothem record. Results were compared to reconstructed sunspot number data to determine whether solar signal is presents in PN speleothem. The occurrence of significant solar periodicities (i.e., cycles of Gleissberg, de Vries, unnamed 500 years, Eddy and Hallstat) supports for an impact of solar forcing on PN speleothem trace elements contents. Moreover, several intervals of significant rapid climate change were detected during the Holocene at 10.3, 9.3–9.5, around 8.2, 6.4–6.2, 4.7–4.5, and around 2.7 ka BP. Those intervals are similar to the cold events evidenced in different natural paleoclimate archivers, suggesting common climate forcing mechanisms related to changes in solar irradiance. [less ▲]

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