Théorie tannakienne non commutative

Inspired by a recent paper by Deligne [2], we extend the Tannaka-Krein duility results (over a field) to the non-commutative situation. To be precise, we establish a 1-1 corresponde:ice between ‘tensorial autonomous categories’ equipped with a ‘fibre functor’ (i. e. tannakian categories without the commutativity condition on the tensor product), and ‘quantum groupoids’ (as defined by Maltsiniotis, [9]) which are ‘transitive’ (7.1.). When the base field is perfect, a quantum groupoid over Spec B is transitive iff it is projective and faithfully fiat over B? _k B. Moreover, the fibre functor is unique up to ‘quantum isomorphism’ (7.6.). Actually, we show Tannaka-Krein duality results in the more general setting where there is no monoidal structure on the category (and the functor); the algebraic object corresponding to such a category is a ‘semi-transitive’ coalgebroid (5.2. and 5.8.).     

Fluorescent Microcrystals Obtained from Coumarin 6 Using the Reprecipitation Method

The reprecipitation method was applied to Coumarin 6. A concentrated solution of the dye in acetone was mixed at room temperature with a large volume of water, and microcrystals rapidly appeared in the medium. Their size and shape were visualized by fluorescence microscopy, as well as by transmission electron microscopy. The absorption and fluorescence properties were studied on the suspensions and compared with those of the dissolved dye. This study is aimed at clarifying the influence of the reprecipitation process upon the fluorescence properties of the dye in the solid state.     

Carbonylation of C−N Bonds in Tertiary Amines Catalyzed by Low‐Valent Iron Catalysts

The first iron catalysts able to promote the formal insertion of CO into the C?N bond of amines are reported. Using low‐valent iron complexes, including K₂[Fe(CO)₄], amides are formed from aromatic and aliphatic amines, in the presence of an iodoalkane promoter. Inorganic Lewis acids, such as AlCl₃ and Nd(OTf)₃, have a positive influence on the catalytic activity of the iron salts, enabling the carbonylation at a low pressure of CO (6 to 8 bars).     

Correction to: EQRAIN: uranium and plutonium interlaboratory exercises from 1997 to 2016—comparison to ITVs-2010

Journal of Radioanalytical and Nuclear Chemistry - In the original publication of the article, the values of u(s), u(r) and ITV for HKED were published incorrectly in Table 6.     

On the Uniqueness for the Spatially Homogeneous Boltzmann Equation with a Strong Angular Singularity

We prove an inequality on the Wasserstein distance with quadratic cost between two solutions of the spatially homogeneous Boltzmann equation without angular cutoff, from which we deduce some uniqueness results. In particular, we obtain a local (in time) well-posedness result in the case of (possibly very) soft potentials. A global well-posedness result is shown for all regularized hard and soft potentials without angular cutoff. Our uniqueness result seems to be the first one applying to a strong angular singularity, except in the special case of Maxwell molecules. Our proof relies on the ideas of Tanaka (Z. Wahrscheinlichkeitstheor. Verwandte. Geb. 46(1):67–105, [1978]) we give a probabilistic interpretation of the Boltzmann equation in terms of a stochastic process. Then we show how to couple two such processes started with two different initial conditions, in such a way that they almost surely remain close to each other.     

Transient adaptivity applied to two-phase incompressible flows

An anisotropic adaptation process is applied to a three-dimensional incompressible two-phase flow solver. The solver uses a level set/finite element method on unstructured tetrahedral meshes. We show how the level set function can be used to build an anisotropic mesh with good properties. Some computations with a strong transient character and large densities ratios (1/1000) are presented. We show that the efficiency of the computations can be deeply enhanced by mesh adaptations.     

Stabilization of the misfit layer compound (PbS)1.13TaS2 by metal cross substitution

Photoemission microspectroscopy on the layered misfit compound (PbS)1.13TaS2 provides direct evidence for Ta substitution into PbS layers as well as for Pb substitution into TaS2 layers. This metal cross substitution alters the charge balance between alternating layers and can explain the remarkable stability of (PbS)1.13TaS2 and, possibly, of analogous misfit compounds. It is suggested that even formally stoichiometric misfit compounds can be stabilized by this mechanism.     

The crack tip: a nanolab for studying confined liquids

We study the equilibrium properties of a liquid phase condensed at the nanoscale between the surfaces of a sharp crack in fused silica in a moist controlled atmosphere. The extension of the condensed phase along the fracture is measured by in situ atomic force microscopy phase imaging and it is shown to be determined by a critical distance between the opposite crack surfaces, which is an increasing function of humidity. The present technique is very promising for measuring the properties of confined liquids at the nanoscale as well as for modeling the physics and chemistry of slow crack propagation in glasses.     

Bimodality: a sign of critical behavior in nuclear reactions

The recently discovered coexistence of multifragmentation and residue production for the same total transverse energy of light charged particles, which has been dubbed bimodality like it has been introduced in the framework of equilibrium thermodynamics, can be well reproduced in numerical simulations of heavy ion reactions. A detailed analysis shows that fluctuations (introduced by elementary nucleon-nucleon collisions) determine which of the exit states is realized. Thus, we can identify bifurcation in heavy ion reactions as a critical phenomenon. Also the scaling of the coexistence region with beam energy is well reproduced in these results from the quantum molecular dynamics simulation program.