On spectral minimal partitions II, the case of the rectangle

In continuation of \cite{HHOT}, we discuss the question of spectral minimal 3-partitions for the rectangle $]-\frac a2,\frac a2[\times ] -\frac b2,\frac b2[$, with $0< a\leq b$. It has been observed in \cite{HHOT} that when $0<\frac ab < \sqrt{\frac 38}$ the minimal 3-partition is obtained by the three nodal domains of the third eigenfunction corresponding to the three rectangles $]-\frac a2,\frac a2[\times ] -\frac b2,-\frac b6[$, $]-\frac a2,\frac a2[\times ] -\frac b6,\frac b6[$ and $]-\frac a2,\frac a2[\times ] \frac b6, \frac b2[$. We will describe a possible mechanism of transition for increasing $\frac ab$ between these nodal minimal 3-partitions and non nodal minimal 3-partitions at the value $\sqrt{\frac 38}$ and discuss the existence of symmetric candidates for giving minimal 3-partitions when $\sqrt{\frac 38}<\frac ab \leq 1$. Numerical analysis leads very naturally to nice questions of isospectrality which are solved by introducing Aharonov-Bohm Hamiltonians or by going on the double covering of the punctured rectangle

Stellar Populations in the Outskirts of the Small Magellanic Cloud: No Outer Edge Yet

We report the detection of intermediate-age and old stars belonging to the SMC at 6.5 kpc from the SMC center in the southern direction. We show, from the analysis of three high quality 34\arcmin $\times$ 33\arcmin CMDs, that the age composition of the stellar population is similar at galactocentric distances of $\thicksim$4.7 kpc, $\thicksim$5.6 kpc, and $\thicksim$6.5 kpc. The surface brightness profile of the SMC follows an exponential law, with no evidence of truncation, all the way out to 6.5 kpc. These results, taken together, suggest that the SMC `disk' population is dominating over a possible old Milky Way-like stellar halo, and that the SMC may be significantly larger than previously thought.Comment: Accepted for publication in ApJ Letters. High resolution figures are available at ftp://ftp.iac.es/out/noe

Efficient numerical calculation of drift and diffusion coefficients in the diffusion approximation of kinetic equations

In this paper we study the diffusion approximation of a swarming model given by a system of interacting Langevin equations with nonlinear friction. The diffusion approximation requires the calculation of the drift and diffusion coefficients that are given as averages of solutions to appropriate Poisson equations. We present a new numerical method for computing these coefficients that is based on the calculation of the eigenvalues and eigenfunctions of a Schr\"odinger operator. These theoretical results are supported by numerical simulations showcasing the efficiency of the method

Believe-type raising-to-object and raising-to-subject verbs in English and Dutch: A contrastive investigation in diachronic construction grammar

The so-called 'raising-to-subject' pattern that verbs of the type believe can occur in is usually treated as the passive alternative for the so-called 'raising-to-object' pattern. In addition to broadening the empirical basis for the opposite claim that the English and Dutch raising-to-subject (or 'nominative and infinitive') patterns have a special functionality which is different from that of the passive construction, this paper specifically examines the stronger proposition that this has always been the case. It empirically investigates whether this proposition holds equally well for English and Dutch through a comparison of the frequencies of believe-type raising-to-object and raising-to-subject patterns in two diachronic corpora. The methodology makes use of Distinctive Collexeme Analysis. © John Benjamins Publishing Company.postprin

Process intensification for the direct synthesis of adipic acid in a micro packed bed reactor

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A view through novel process windows

This mini-review discusses some of the recent work on novel process windows by the Micro Flow Chemistry and Process Technology group at the Eindhoven University of Technology, and their associates. Novel process windows consist of unconventional approaches to boost chemical production, often requiring harsh reaction conditions at short to very short time-scales. These approaches are divided into six routes: the use of high temperatures, high pressures, and high concentrations (or solvent-free), new chemical transformations, explosive conditions, and process simplification and integration. Microstructured reactors, due to their inherent safety, short time-scales, and the high degree of process control, are the means that make such extreme chemistry possible

Cadmium accumulation and interactions with zinc, copper, and manganese, analysed by ICP-MS in a long-term Caco-2 TC7 cell model

The influence of long-term exposure to cadmium (Cd) on essential minerals was investigated using a Caco-2 TC7 cells and a multi-analytical tool: microwave digestion and inductively coupled plasma mass spectrometry. Intracellular levels, effects on cadmium accumulation, distribution, and reference concentration ranges of the following elements were determined: Na, Mg, Ca, Cr, Fe, Mn, Co, Ni, Cu, Zn, Mo, and Cd. Results showed that Caco-2 TC7 cells incubated long-term with cadmium concentrations ranging from 0 to 10 lmol Cd/l for 5 weeks exhibited a significant increase in cadmium accumulation. Furthermore, this accumulation was more marked in cells exposed long-term to cadmium compared with controls, and that this exposure resulted in a significant accumulation of copper and zinc but not of the other elements measured. Interactions of Cd with three elements: zinc, copper, and manganese were particularly studied. Exposed to 30 lmol/l of the element, manganese showed the highest inhibition and copper the lowest on cadmium intracellular accumulation but Zn, Cu, and Mn behave differently in terms of their mutual competition with Cd. Indeed, increasing cadmium in the culture medium resulted in a gradual and significant increase in the accumulation of zinc. There was a significant decrease in manganese from 5 lmol Cd/l exposure, and no variation was observed with copper. Abbreviation: AAS – Atomic absorption spectrometry; CRM– Certified reference material; PBS – Phosphate buffered saline without calcium and magnesium; DMEM – Dubelcco’s modified Eagle’s medium

Modular allylation of C(sp³)-H bonds by combining decatungstate photocatalysis and HWE olefination in flow

The late-stage introduction of allyl groups provides an opportunity to synthetic organic chemists for subsequent diversification, furnishing a rapid access to new chemical space. Here, we report the development of a modular synthetic sequence for the allylation of strong aliphatic C(sp(3))–H bonds. Our sequence features the merger of two distinct steps to accomplish this goal, including a photocatalytic Hydrogen Atom Transfer and an ensuing Horner–Wadsworth–Emmons (HWE) reaction. This practical protocol enables the modular and scalable allylation of valuable building blocks and has been applied to structurally complex molecules