Graphes et ordonnés démontables, propriété de la clique fixe

This work extends to dismantable graphs many properties of dismantable posets dealing with products, exponentiation, existence of paths in a graph of all homomorphisms, fixed clique property, etc. We show that a poset is dismantlable in the sense of Rival if and only if its comparability graph is dismantlable, thus proving that, for posets, dismantlability is a comparability invariant. We establish the analogues for graphs of results of Duffus, Poguntke and Rival about fixed point sets and cores in posets.     

High-resolution infrared and subterahertz spectroscopy of the v2 = 1, v5 = 1, and v3 = 2 levels of CH3Cl

High-resolution Fourier-transform infrared spectra between 1235 and 1680 cm⁻¹ and subterahertz spectra between 250 and 630 GHz of monoisotopic ¹³CH₃³⁵Cl have been recorded and analyzed simultaneously, with all Coriolis, α-resonance, and l-type interactions in the polyad of the v₂ = 1, v₅ = 1, and v₃ = 2 levels taken into account. Several α-resonances (Δk = ±2, Δl = ?1) generating perturbation-allowed transitions have been assigned in the rovibrational spectra. These resonances enabled us to determine accurately and independently the ground state rotational and centrifugal distortion parameters A₀ = 5.205 746 9 (55) cm⁻¹ and . Even , which is, however, correlated to higher-order α-resonance terms, was determined. With 51 upper state parameters varied, about 5800 rovibrational wavenumbers and more than 550 rotational frequencies pertaining to the excited vibrational states were fitted within their experimental accuracy.     

Microscopic model of critical current noise in Josephson junctions

We present a simple microscopic model to show how fluctuating two-level systems in a Josephson junction tunnel barrier of thickness L can modify the potential energy of the barrier and produce critical current noise spectra. We find low frequency 1/f noise that goes as L5. Our values are in good agreement with recent experimental measurements of critical current noise in Al/AlOx/Al Josephson junctions. We also investigate the sensitivity of the noise on the nonuniformity of the tunnel barrier.     

Singular nature of nonlinear macroscale effects in high-rate flow through porous mediaNature singulière des effets macroscopiques non linéaires dans un écoulement à hautes vitesses en milieux poreux

The quadratic law of laminar flow through porous media at high Reynolds numbers, which is well confirmed by the multiple experimental data, is shown to give rise to three fundamental paradoxes. All them can be resolved by assuming the singular structure of flow. The singularity is produced by the formation of jet brunches which invade the stagnant zones and sharply loss their kinetic energy. The numerical simulation confirms this effect. To cite this article: M. Panfilov et al., C. R. Mecanique 331 (2003).     

Global Conservative Solutions of the Camassa–Holm Equation

This paper develops a new approach in the analysis of the Camassa–Holm equation. By introducing a new set of independent and dependent variables, the equation is transformed into a semilinear system, whose solutions are obtained as fixed points of a contractive transformation. These new variables resolve all singularities due to possible wave breaking. Returning to the original variables, we obtain a semigroup of global solutions, depending continuously on the initial data. Our solutions are conservative, in the sense that the total energy equals a constant, for almost every time.     

Anisotropy resolved multidimensional emission spectroscopy (ARMES): A new tool for protein analysis

Structural analysis of proteins using the emission of intrinsic fluorophores is complicated by spectral overlap. Anisotropy resolved multidimensional emission spectroscopy (ARMES) overcame the overlap problem by the use of anisotropy, with chemometric analysis, to better resolve emission from different fluorophores. Total synchronous fluorescence scan (TSFS) provided information about all the fluorophores that contributed to emission while anisotropy provided information about the environment of each fluorophore. Here the utility of ARMES was demonstrated via study of the chemical and thermal denaturation of human serum albumin (HSA).     

Aromatic Interactions in Organocatalyst Design: Augmenting Selectivity Reversal in Iminium Ion Activation

Substituting N‐methylpyrrole for N‐methyindole in secondary‐amine‐catalysed Friedel–Crafts reactions leads to a curious erosion of enantioselectivity. In extreme cases, this substrate dependence can lead to an inversion in the sense of enantioinduction. Indeed, these closely similar transformations require two structurally distinct catalysts to obtain comparable selectivities. Herein a focussed molecular editing study is disclosed to illuminate the structural features responsible for this disparity, and thus identify lead catalyst structures to further exploit this selectivity reversal. Key to effective catalyst re‐engineering was delineating the non‐covalent interactions that manifest themselves in conformation. Herein we disclose preliminary validation that intermolecular aromatic (CH–π and cation–π) interactions between the incipient iminium cation and the indole ring system is key to rationalising selectivity reversal. This is absent in the N‐methylpyrrole alkylation, thus forming the basis of two competing enantio‐induction pathways. A simple L ‐valine catalyst has been developed that significantly augments this interaction.     

Functionalization of Intramolecular Frustrated Lewis Pairs by 1,1‐Carboboration with Conjugated Enynes

The vicinal P/B frustrated Lewis pair (FLP) Mes₂PCH₂CH₂B(C₆F₅)₂ undergoes 1,1‐carboboration reactions with the Me₃Si‐substituted enynes to give ring‐enlarged functionalized C₃‐bridged P/B FLPs. These serve as active FLPs in the activation of dihydrogen to give the respective zwitterionic [P]H⁺/[B]H^? products. One such product shows activity as a metal‐free catalyst for the hydrogenation of enamines or a bulky imine. The ring‐enlarged FLPs contain dienylborane functionalities that undergo “bora‐Nazarov”‐type ring‐closing rearrangements upon photolysis. A DFT study had shown that the dienylborane cyclization of such systems itself is endothermic, but a subsequent C₆F₅ migration is very favorable. Furthermore, substituted 2,5‐dihydroborole products are derived from cyclization and C₆F₅ migration from the photolysis reaction. In the case of the six‐membered annulation product, a subsequent stereoisomerization reaction takes place and the resultant compound undergoes a P/B FLP 1,2‐addition reaction with a terminal alkyne with rearrangement.