Some Diophantine equations associated to seminormal Cohen-Kaplansky domains

15 pagesInternational audienceA Cohen-Kaplansky domain (CK domain) R is an integral domain where every nonzero nonunit element of R is a ¯nite product of irreducible elements and such that R has only ¯nitely many nonassociate irreducible elements. In this paper, we investigate seminormal CK domains and obtain the form of their irreducible elements. The solutions of a system of diophantine equations allow us to give a formula for the number of distinct factorizations of a nonzero nonunit element of R, with an asymptotic formula for this number

Enabling Gaia observations of naked-eye stars

The ESA Gaia space astrometry mission will perform an all-sky survey of stellar objects complete in the nominal magnitude range G = [6.0 - 20.0]. The stars with G lower than 6.0, i.e. those visible to the unaided human eye, would thus not be observed by Gaia. We present an algorithm configuration for the Gaia on-board autonomous object observation system that makes it possible to observe very bright stars with G = [2.0-6.0). Its performance has been tested during the in-orbit commissioning phase achieving an observation completeness of ~94% at G = 3 - 5.7 and ~75% at G = 2 - 3. Furthermore, two targeted observation techniques for data acquisition of stars brighter than G = 2.0 were tested. The capabilities of these two techniques and the results of the in-flight tests are presented. Although the astrometric performance for stars with G lower than 6.0 has yet to be established, it is clear that several science cases will benefit from the results of the work presented here.Comment: 12 pages, 5 figures. To appear in the proceedings of the SPIE 9143, 2014 Astronomical Instrumentation and Telescopes conferenc

Using porous boron nitride in adsorption-based processes: investigation of material challenges and opportunities

In 2016, industrial separation processes accounted for 10-15% of the global energy consumption. This striking figure has urged the scientific community to continue developing new materials and technologies to significantly reduce global emissions in industry, for example in the field of adsorption processes. In light of this, porous boron nitride (BN) has gradually appeared as a promising adsorbent owing to its tunable chemistry and porosity, which a priori make it adaptable for various applications. However, research on porous BN remains at laboratory scale due to a lack of understanding of its formation mechanism. Furthermore, the material has displayed hydrolytic instability, which is an issue due to the presence of moisture in most industrial settings. Finally, the use of porous BN has mainly been focusing on molecular separations, but little is known about its potential for other adsorption-based applications, such as thermal energy storage. In this thesis, I first investigated the formation mechanism of porous BN to shed light on the critical steps of its synthesis. Considering a wide range of separations, I then searched new ways of enhancing its hydrolytic stability via surface functionalization. I developed two methods involving organosilane grafting, which produced porous BN adsorbents with enhanced moisture resistance and adequate CO2/N2 selectivity in the context of CO2 capture. Finally, I expanded the range of possible applications using porous BN and researched its potential for thermochemical energy storage, which has recently emerged as a key technology to mitigate CO2 emissions. I prepared BN-based adsorbents with various structural and thermal properties, allowing to understand how material properties affect the performance in thermochemical energy storage via adsorption. Overall, this thesis presents new knowledge on porous BN and explores the opportunities and challenges associated with its unique properties in the context of adsorption-based applications, in particular CO2/N2 separation and thermochemical energy storage.Open Acces

Distributive FCP extensions

We are dealing with extensions of commutative rings $R\subseteq S$ whose chains of the poset $[R,S]$ of their subextensions are finite ({\em i.e.} $R\subseteq S$ has the FCP property) and such that $[R,S]$ is a distributive lattice, that we call distributive FCP extensions. Note that the lattice $[R,S]$ of a distributive FCP extension is finite. This paper is the continuation of our earlier papers where we studied catenarian and Boolean extensions. Actually, for an FCP extension, the following implications hold: Boolean $\Rightarrow$ distributive $\Rightarrow$ catenarian. A comprehensive characterization of distributive FCP extensions actually remains a challenge, essentially because the same problem for field extensions is not completely solved. Nevertheless, we are able to exhibit a lot of positive results for some classes of extensions. A main result is that an FCP extension $R\subseteq S$ is distributive if and only if $R\subseteq\overline R$ is distributive, where $\overline R$ is the integral closure of $R$ in $S$. A special attention is paid to distributive field extensions

Computing the closure of a support

When $E$ is an $R$-module over a commutative unital ring $R$, the Zariski closure of its support is of the form $\mathrm V(\mathcal O(E))$ where $\mathcal O(E)$ is a unique radical ideal. We give an explicit form of $\mathcal O(E)$ and study its behavior under various operations of algebra. Applications are given, in particular for ring extensions of commutative unital rings whose supports are closed. We provide some applications to crucial and critical ideals of ring extensions