A $\Gamma$-convergence result for doubling metric measures and associated perimeters

Abstract. In this paper we study the notion of perimeter associated with doubling metric measures or strongly weights. We prove that the metric perimeter in the sense of L. Ambrosio and M. Miranda jr. coincides with the metric Minkowski content and can be obtained also as a -limit of Modica-Mortola type degenerate integral functionals. Received: 27 August 2001 / Accepted: 29 November 2001 / Published online: 10 June 2002 Investigation supported by University of Bologna, funds for selected research topics and by GNAMPA of INdAM, Italy. The authors are very grateful to Luigi Ambrosio and Francesco Serra Cassano for making their preprints available to them, for listening with patience and for many unvaluable suggestions.     

Sauna,sweat and science II – do we sweat what we drink?

ABSTRACT

Inspired by a previous ‘Sauna, sweat and science’ study [Zech et al. Isot Environ Health Stud. 2015;51(3):439–447] and out of curiosity and enthusiasm for stable isotope and sauna research we aimed at answering the question ‘do we sweat (isotopically) what we drink’? We, therefore, pulse-labelled five test persons in a sauna experiment with beverages that were ²H-enriched at about +25,600?‰. Sweat samples were collected during six sauna rounds and the hydrogen isotope composition δ²H_sweat was determined using an isotope ratio mass spectrometer. Before pulse labelling, δ²H_sweat – reflecting by approximation body water – ranged from –32 to –22?‰. This is ～35?‰ enriched compared to usual mid-European drinking water and can be explained with hydrogen-bearing food as well as with the respiratory loss of ²H-depleted vapour. The absence of a clearly detectable ²H pulse in sweat after pulse labelling and δ²H_sweat results of ≤+250?‰ due to a fast ²H equilibration with body water are moreover a clearly negative answer to our research question also in a short-term consideration. Given that the recovery of the tracer based on an isotope mass balance calculation is clearly below 100?%, we finally answer the question ‘where did the rest of the tracer go?’     

Des extensions plus petites que leurs groupes de Galois

In this article we construct some Galois extensions L∕K with finite Galois groups and such that |Gal(L∕K)|>[L:K]. Using an analog of the Noether method, we explain how to obtain, with a fixed center, such a Galois curiosity with a Galois group as large as we want.

Résumé : Dans cet article, nous construisons une extension galoisienne L∕K à groupe de Galois fini et telle que |Gal(L∕K)|>[L:K]. En utilisant un analogue non commutatif de la méthode de Noether, nous expliquons ensuite comment, à centre fixé, l’on peut construire une telle curiosité galoisienne avec un groupe aussi gros que l’on veut.

Mots clés : Corps gauches; théorie de Galois.     

Stabilization of cell-centered compressible Lagrangian methods using subzonal entropy

This work deals with the stabilization of early stages of Lagrangian calculations of compressible gas dynamics in the context of cell-centered discretization. We describe a totally conservative algorithm based on an entropy analysis of the distortion of a Lagrangian mesh. It prevents the tangling of the mesh, while remaining consistent and conservative in mass, momentum, and total energy. The method described can be applied to any cell-centered Lagrangian scheme. In this article, we detail the extension to the cell-centered Glace scheme published in Carré et al. (2009) [G. Carré, S. Del Pino, B. Després, E. Labourasse, A cell-centered Lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension, J. Comput. Phys. 228 (2009) 5160–5183]. Numerical tests are proposed to assess the accuracy and robustness.     

Eigenvalues Estimate for the Neumann Problem of a Bounded Domain

In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a domain Ω in a given complete (not compact a priori) Riemannian manifold (M,g). For this, we use test functions for the Rayleigh quotient subordinated to a family of open sets constructed in a general metric way, interesting for itself. As applications, we prove that if the Ricci curvature of (M,g) is bounded below Ric  ^g ≥−(n−1)a ², a≥0, then there exist constants A _n >0,B _n >0 only depending on the dimension, such that

Fluorescent Properties of a Hybrid Cadmium Sulfide-Dendrimer Nanocomposite and its Quenching with Nitromethane

A fluorescent hybrid cadmium sulphide quantum dots (QDs) dendrimer nanocomposite (DAB-CdS) synthesised in water and stable in aqueous solution is described. The dendrimer, DAB-G5 dendrimer (polypropylenimine tetrahexacontaamine) generation 5, a diaminobutene core with 64 amine terminal primary groups. The maximum of the excitation and emission spectra, Stokes’ shift and the emission full width of half maximum of this nanocomposite are, respectively: 351, 535, 204 and 212 nm. The fluorescence time decay was complex and a four component decay time model originated a good fit (χ = 1.20) with the following lifetimes: τ ₁ = 657 ps; τ ₂ = 10.0 ns; τ ₃ = 59.42 ns; and τ ₄ = 265 ns. The fluorescence intensity of the nanocomposite is markedly quenched by the presence of nitromethane with a dynamic Stern-Volmer constant of 25 M⁻¹. The quenching profiles show that about 81% of the CdS QDs are located in the external layer of the dendrimer accessible to the quencher. PARAFAC analysis of the excitation emission matrices (EEM) acquired as function of the nitromethane concentration showed a trilinear data structure with only one linearly independent component describing the quenching which allows robust estimation of the excitation and emission spectra and of the quenching profiles. This water soluble and fluorescent nanocomposite shows a set of favourable properties to its use in sensor applications.     

Development of Aptamer Beacons for Rapid Presumptive Detection of <Emphasis Type="Italic">Bacillus</Emphasis> Spores

A library of 92 DNA aptamer sequences was developed against Bacillus anthracis (nonpathogenic Sterne strain) spores and anthrose sugar immobilized on magnetic beads. The selected DNA sequences were studied for similarities and potential binding pockets between the B. anthracis spore and anthrose aptamers. Several recurring loop structures were identified and tested for their potential to act as aptamer beacons when labeled with TYE 665 dye on their 5′ ends and Iowa Black quencher on their 3′ ends. Of these candidate sequences, two beacons designated BAS-6F and BAS-6R emerged which gave strong fluorescence responses at high spore concentrations (greater than 30,000 spores/ml). These aptamer beacons also detect B. cereus and B. thuringiensis spores with greater fluorescence intensity, but do not strongly detect vegetative cells from an array of other bacterial species. BAS-6F and 6R are also not capable of detecting pure anthrose, thereby probably ruling that epitope out as a spore surface target for these particular beacons. While not extremely sensitive, the BAS-6F and 6R aptamer beacons are potentially valuable for rapid presumptive detection of anthrax or Bacillus spores in suspect powders or bioterrorist activity where spore concentrations are anticipated to be high. The sequence similarities of these beacons to other published Bacillus spore aptamers are also discussed.