On spectral sets of integers

Based on tiles and on the Coven-Meyerowitz property, we present some examples and some general constructions of spectral subsets of integers

Sums of random polynomials with differing degrees

Let $\mu$ and $\nu$ be probability measures in the complex plane, and let $p$ and $q$ be independent random polynomials of degree $n$, whose roots are chosen independently from $\mu$ and $\nu$, respectively. Under assumptions on the measures $\mu$ and $\nu$, the limiting distribution for the zeros of the sum $p+q$ was by computed by Reddy and the third author [J. Math. Anal. Appl. 495 (2021) 124719] as $n \to \infty$. In this paper, we generalize and extend this result to the case where $p$ and $q$ have different degrees. In this case, the logarithmic potential of the limiting distribution is given by the pointwise maximum of the logarithmic potentials of $\mu$ and $\nu$, scaled by the limiting ratio of the degrees of $p$ and $q$. Additionally, our approach provides a complete description of the limiting distribution for the zeros of $p + q$ for any pair of measures $\mu$ and $\nu$, with different limiting behavior shown in the case when at least one of the measures fails to have a logarithmic moment.Comment: 30 pages, 2 figures. Major update containing new methods and improved result

Scaling of Spectra of Cantor-Type Measures and Some Number Theoretic Considerations

We investigate some relations between number theory and spectral measures related to the harmonic analysis of a Cantor set. Specifically, we explore ways to determine when an odd natural number m generates a complete or incomplete Fourier basis for a Cantor-type measure with scale g

Early Results from VLT-SPHERE: Long-Slit Spectroscopy of 2MASS 0122-2439B, a Young Companion Near the Deuterium Burning Limit

We present 0.95-1.80 $\mu$m spectroscopy of the $\sim$12-27 $M_{\rm Jup}$ companion orbiting the faint ($R$$\sim$13.6), young ($\sim$120 Myr) M-dwarf 2MASS J01225093--2439505 ("2M0122--2439 B") at 1.5 arcsecond separation (50 AU). Our coronagraphic long-slit spectroscopy was obtained with the new high contrast imaging platform VLT-SPHERE during Science Verification. The unique long-slit capability of SPHERE enables spectral resolution an order of magnitude higher than other extreme AO exoplanet imaging instruments. With a low mass, cool temperature, and very red colors, 2M0122-2439 B occupies a particularly important region of the substellar color-magnitude diagram by bridging the warm directly imaged hot planets with late-M/early-L spectral types (e.g. $\beta$ Pic b and ROXs 42Bb) and the cooler, dusty objects near the L/T transition (e.g. HR 8799bcde and 2MASS 1207b). We fit BT-Settl atmospheric models to our $R$$\approx$350 spectrum and find $T_{\rm eff}$=1600$\pm$100 K and $\log(g)$=4.5$\pm$0.5 dex. Visual analysis of our 2M0122-2439 B spectrum suggests a spectral type L3-L4, and we resolve shallow $J$-band alkali lines, confirming its low gravity and youth. Specifically, we use the Allers & Liu (2013) spectral indices to quantitatively measure the strength of the FeH, VO, KI, spectral features, as well as the overall $H$-band shape. Using these indices, along with the visual spectral type analysis, we classify 2M0122-2439 B as an intermediate gravity (INT-G) object with spectral type L3.7$\pm$1.0.Comment: Accepted to ApJ Letters, 8 pages, 4 figures, some minor typographical issues were fixe

Rethinking the anti-FGM zero-tolerance policy: From intellectual concerns to empirical challenges

Abstract Purpose of Review Based on the discussions of a symposium co-organized by the Université Libre de Bruxelles (ULB) and the University of Lausanne (UNIL) in Brussels in 2019, this paper critically reflects upon the zero-tolerance strategy on “Female Genital Mutilation” (FGM) and its socio-political, legal and moral repercussions. We ask whether the strategy is effective given the empirical challenges highlighted during the symposium, and also whether it is credible. Recent Findings The anti-FGM zero-tolerance policy, first launched in 2003, aims to eliminate all types of “female genital mutilation” worldwide. The FGM definition of the World Health Organization condemns all forms of genital cutting (FGC) on the basis that they are harmful and degrading to women and infringe upon their rights to physical integrity. Yet, the zero-tolerance policy only applies to traditional and customary forms of genital cutting and not to cosmetic alterations of the female genitalia. Recent publications have shown that various popular forms of cosmetic genital surgery remove the same tissue as some forms of “FGM”. In response to the zero-tolerance policy, national laws banning traditional forms of FGC are enforced and increasingly scrutinize the performance of FGC as well as non-invasive rituals that are culturally meaningful to migrants. At the same time, cosmetic procedures such as labiaplasty have become more popular than ever before and are increasingly performed on adolescents. Summary This review shows that the socio-legal and ethical inconsistencies between “FGM” and cosmetic genital modification pose concrete dilemmas for professionals in the field that need to be addressed and researched

Polar Smectic Films

We report on a new experimental procedure for forming and studying polar smectic liquid crystal films. A free standing smectic film is put in contact with a liquid drop, so that the film has one liquid crystal/liquid interface and one liquid crystal/air interface. This polar environment results in changes in the textures observed in the film, including a boojum texture and a previously unobserved spiral texture in which the winding direction of the spiral reverses at a finite radius from its center. Some aspects of these textures are explained by the presence of a Ksb term in the bulk elastic free energy density that favors a combination of splay and bend deformations.Comment: 4 pages, REVTeX, 3 figures, submitted to PR

Preparation and deep characterization of composite/hybrid multi-scale and multi-domain polymeric microparticles

Polymeric microparticles were produced following a three-step procedure involving (i) the production of an aqueous nanoemulsion of tri and monofunctional acrylate-based monomers droplets by an elongational-flow microemulsifier, (ii) the production of a nanosuspension upon the continuous-flow UV-initiated miniemulsion polymerization of the above nanoemulsion and (iii) the production of core-shell polymeric microparticles by means of a microfluidic capillaries-based double droplets generator; the core phase was composed of the above nanosuspension admixed with a water-soluble monomer and gold salt, the shell phase comprised a trifunctional monomer, diethylene glycol and a silver salt; both phases were photopolymerized on-the-fly upon droplet formation. Resulting microparticles were extensively analyzed by energy dispersive X-rays spectrometry and scanning electron microscopy to reveal the core-shell morphology, the presence of silver nanoparticles in the shell, organic nanoparticles in the core but failed to reveal the presence of the gold nanoparticles in the core presumably due to their too small size (c.a. 2.5 nm). Nevertheless, the reddish appearance of the as such prepared polymer microparticles emphasized that this three-step procedure allowed the easy elaboration of composite/hybrid multi-scale and multi-domain polymeric microparticles

Assessment of Confounding Factors Affecting the Tumor Markers SMRP, CA125, and CYFRA21-1 in Serum

The purpose of this analysis was to evaluate if serum levels of potential tumor markers for the diagnosis of malignant mesothelioma and lung cancer are affected by confounding factors in a surveillance cohort of workers formerly exposed to asbestos. SMRP, CA125, and CYFRA21-1 concentrations were determined in about 1,700 serum samples from 627 workers formerly exposed to asbestos. The impact of factors that could modify the concentrations of the tumor markers was examined with linear mixed models. SMRP values increased with age 1.02-fold (95% CI 1.01–1.03) and serum creatinine concentration 1.32-fold (95% CI 1.20–1.45). Levels differed by study centers and were higher after 40 years of asbestos exposure. CA125 levels increased with longer storage of the samples. CYFRA21-1 values correlated with age 1.02-fold (95% CI 1.01–1.02), serum creatinine 1.21-fold (95% CI 1.14–1.30) and varied by study centers due to differences in sample handling. Tumor marker concentrations are influenced by subject-related factors, sample handling, and storage. These factors need to be taken into account in screening routine