On a vector-valued Hopf-Dunford-Schwartz lemma

In this paper, we state as a conjecture a vector-valued Hopf-Dunford-Schwartz lemma and give a partial answer to it. As an application of this powerful result, we prove some Fe fferman-Stein inequalities in the setting of Dunkl analysis where the classical tools of real analysis cannot be applied

Parametric channel estimation for massive MIMO

Channel state information is crucial to achieving the capacity of multi-antenna (MIMO) wireless communication systems. It requires estimating the channel matrix. This estimation task is studied, considering a sparse channel model particularly suited to millimeter wave propagation, as well as a general measurement model taking into account hybrid architectures. The contribution is twofold. First, the Cram{\'e}r-Rao bound in this context is derived. Second, interpretation of the Fisher Information Matrix structure allows to assess the role of system parameters, as well as to propose asymptotically optimal and computationally efficient estimation algorithms

A one-dimensional Chandrasekhar-mass delayed-detonation model for the broad-lined Type Ia supernova 2002bo

We present 1D non-local thermodynamic equilibrium (non-LTE) time-dependent radiative-transfer simulations of a Chandrasekhar-mass delayed-detonation model which synthesizes 0.51 Msun of 56Ni, and confront our results to the Type Ia supernova (SN Ia) 2002bo over the first 100 days of its evolution. Assuming only homologous expansion, this same model reproduces the bolometric and multi-band light curves, the secondary near-infrared (NIR) maxima, and the optical and NIR spectra. The chemical stratification of our model qualitatively agrees with previous inferences by Stehle et al., but reveals significant quantitative differences for both iron-group and intermediate-mass elements. We show that +/-0.1 Msun (i.e., +/-20 per cent) variations in 56Ni mass have a modest impact on the bolometric and colour evolution of our model. One notable exception is the U-band, where a larger abundance of iron-group elements results in less opaque ejecta through ionization effects, our model with more 56Ni displaying a higher near-UV flux level. In the NIR range, such variations in 56Ni mass affect the timing of the secondary maxima but not their magnitude, in agreement with observational results. Moreover, the variation in the I, J, and K_s magnitudes is less than 0.1 mag within ~10 days from bolometric maximum, confirming the potential of NIR photometry of SNe Ia for cosmology. Overall, the delayed-detonation mechanism in single Chandrasekhar-mass white dwarf progenitors seems well suited for SN 2002bo and similar SNe Ia displaying a broad Si II 6355 A line. Whatever multidimensional processes are at play during the explosion leading to these events, they must conspire to produce an ejecta comparable to our spherically-symmetric model.Comment: Accepted for publication in MNRAS. The hydrodynamical input and synthetic spectra are available at https://www-n.oca.eu/supernova/home.html . Minor changes from v1: corrected several typos and updated acknowledgement

Evidence for sub-Chandrasekhar-mass progenitors of Type Ia supernovae at the faint end of the width-luminosity relation

The faster light-curve evolution of low-luminosity Type Ia supernovae (SNe Ia) suggests that they could result from the explosion of white dwarf (WD) progenitors below the Chandrasekhar mass ($M_{\rm Ch}$). Here we present 1D non-LTE time-dependent radiative transfer simulations of pure central detonations of carbon-oxygen WDs with a mass (M_\rm{tot}) between 0.88 M$_{\odot}$ and 1.15 M$_{\odot}$, and a $^{56}\rm{Ni}$ yield between 0.08 M$_{\odot}$ and 0.84 M$_{\odot}$. Their lower ejecta density compared to $M_{\rm Ch}$ models results in a more rapid increase of the luminosity at early times and an enhanced $\gamma$-ray escape fraction past maximum light. Consequently, their bolometric light curves display shorter rise times and larger post-maximum decline rates. Moreover, the higher M(^{56}\rm{Ni})/M_\rm{tot} ratio at a given $^{56}\rm{Ni}$ mass enhances the temperature and ionization level in the spectrum-formation region for the less luminous models, giving rise to bluer colours at maximum light and a faster post-maximum evolution of the $B-V$ colour. For sub-$M_{\rm Ch}$ models fainter than $M_B\approx -18.5$ mag at peak, the greater bolometric decline and faster colour evolution lead to a larger $B$-band post-maximum decline rate, $\Delta M_{15}(B)$. In particular, all of our previously-published $M_{\rm Ch}$ models (standard and pulsational delayed detonations) are confined to $\Delta M_{15}(B) < 1.4$ mag, while the sub-$M_{\rm Ch}$ models with M_\rm{tot}\lesssim 1 M$_{\odot}$ extend beyond this limit to $\Delta M_{15}(B)\approx 1.65$ mag for a peak $M_B\approx -17$ mag, in better agreement with the observed width-luminosity relation (WLR). Regardless of the precise ignition mechanism, these simulations suggest that fast-declining SNe Ia at the faint end of the WLR could result from the explosion of WDs whose mass is significantly below the Chandrasekhar limit.Comment: 10 pages, 6 figures. Accepted for publication in MNRA

Étude de certains déterminants des incendies volontaires à Montréal

Research into the determining factors in arson cases has traditionally focused on factors linked to the characteristics of the burned building. One of our basic hypotheses is that deliberately set fires also have an underlying economic motivation.In this case, the present study confirms the hypothesis that there appears to be an indisputable link between the unemployment rate and mortgage burdens and arson rates, regardless of the phase of the economic cycle in which the arson occurs.Moreover, the study corroborates the idea that increased surveillance is necessary in areas presenting a higher risk of fraud and having a specific socioeconomic and financial profile. A lower incidence of arson and the improvement of insurers ' ability to predict losses due to arson could lead to a significant reduction in the number of claims, and consequently, in the amount of premiums.By looking more specifically at the economic motivations influencing arson throughout the different phases of the economic cycle, this study evokes the establisment of a forecasting system that would allow insurance companies to identify the areas of Montreal that present a higher risk level for arson, thus allowing them to establish their rates in a more equitable manner