States in Łukasiewicz logic correspond to probabilities of rational polyhedra

It will be shown that probabilities of infinite-valued events represented by formulas in ?ukasiewicz propositional logic are in one-to-one correspondence with tight probability measures over rational polyhedra in the unit hypercube. This result generalizes a recent work on rational measures of polyhedra and provides an elementary geometric approach to reasoning under uncertainty with states in ?ukasiewicz logic.     

Theoretical analysis of discrete contact problems with Coulomb friction

A discrete model of the two-dimensional Signorini problem with Coulomb friction and a coefficient of friction F depending on the spatial variable is analysed. It is shown that a solution exists for any F and is globally unique if F is sufficiently small. The Lipschitz continuity of this unique solution as a function of F as well as a function of the load vector f is obtained. Furthermore, local uniqueness of solutions for arbitrary F > 0 is studied. The question of existence of locally Lipschitz-continuous branches of solutions with respect to the coefficient F is converted to the question of existence of locally Lipschitz-continuous branches of solutions with respect to the load vector f. A condition guaranteeing the existence of locally Lipschitz-continuous branches of solutions in the latter case and results for determining their directional derivatives are given. Finally, the general approach is illustrated on an elementary example, whose solutions are calculated exactly.     

PHOTOSENSITIZING PROPERTIES OF BACTERIOCHLOROPHYLLIN a and BACTERIOCHLORIN a, TWO DERIVATIVES OF BACTERIOCHLOROPHYLL a

Abstract The photosensitizing properties of two water soluble derivatives of bacteriochlorophyll a , bacteriochlorophyllin a and bacteriochlorin a (lacking the central Mg-ion) were investigated and compared to those of hematoporphyrin derivatives. At physiological pH the oxygen consumption rate of histidine, tryptophan, dithiothreitol and guanosine upon illumination was 3 to 4 times higher when bacteriochlorin a was used as photosensitizer than when hematoporphyrin derivatives were used. Especially bacteriochlorin a proved to be an effective sensitizer for the killing of L929 cells. Because bacteriochlorin a has an absorption maximum at 765 nm in phosphate buffered saline (allowing a light penetration in tissue about ten times larger than at 630 nm) and a high molar absorption coefficient (32 000 M cm⁻¹) it has promising possibilities for the application in photodynamic therapy.     

Vibration-inversion-rotation spectra of ammonia: Centrifugal distortion, Coriolis interactions, and force field in NH3, NH3, ND3, and NT3

An effective inversion-rotation Hamiltonian has been developed for NH₃ which avoids the necessity of having to include high powers of the inversion motion coordinate in the Taylor expansions of the potential energy and the inverse moment of inertia tensor. This nonrigid bender Hamiltonian describes the centrifugal distortion and the Coriolis interactions in the ground and excited inversion states. It also describes the inversion doublings in the ground and excited vibration-inversion states of ammonia. A least-squares procedure that includes the numerical integration of the Schrödinger wave equation has been used to determine the harmonic force field and the double-minimum inversion potential function for (¹⁴NH₃, ¹⁵NH₃) and for (¹⁴ND₃ and ¹⁴NT₃).The anomalous rotational dependence of the inversion doublings in the (±l) components of the v₄ = 1 state of ¹⁴NH₃ has been explained by the Coriolis interactions between v₂=1, v₄ = 1, v₂ = 2, v₂ = 1, v₄ = 1, and v₂ = 3 vibration-inversion states.     

Pullback attractors for non-autonomous 2D-Navier–Stokes equations in some unbounded domains

In this Note we first introduce the concept of pullback asymptotic compactness. Next, we establish a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets. Finally, we prove the existence of a pullback attractor for a non-autonomous 2D Navier–Stokes model in an unbounded domain, a case in which the theory of uniform attractors does not work since the non-autonomous term is quite general. To cite this article: T. Caraballo et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Two-step synthesis of high aspect ratio gold nanorods

We describe a very simple, two-step synthetic method to prepare gold nanorods with extremely high aspect ratios (> 20) and average lengths of more than 1000 nm. The method is based on a seed-mediated growth in presence of the surfactant cetyltrimethylammonium bromide. The length and aspect ratios of the nanorods can be manipulated by varying the surfactant concentration.     

Asymmetric synthesis and applications of beta-amino Weinreb amides: asymmetric synthesis of (S)-coniine

Conjugate addition of lithium (S)-N-benzyl-N-alpha-methylbenzylamide to a range of alpha, beta-unsaturated Weinreb amides proceeds with high levels of diastereoselectivity (>95% de). The beta-amino Weinreb amide products may be transformed into beta-amino ketones via reactions with Grignard reagents, while treatment with DIBAL-H furnishes beta-amino aldehydes. Trapping of the aldehyde via Wadsworth-Emmons reaction and subsequent manipulation offers an efficient route to homochiral delta-amino acid derivatives and 2-substituted piperidines. The application of this methodology for the synthesis of (S)-coniine is demonstrated.     

Rh2(II)-catalyzed intramolecular aliphatic C-H bond amination reactions using aryl azides as the N-atom source

Rhodium(II) dicarboxylate complexes were discovered to catalyze the intramolecular amination of unactivated primary, secondary, or tertiary aliphatic C-H bonds using aryl azides as the N-atom precursor. While a strong electron-withdrawing group on the nitrogen atom is typically required to achieve this reaction, we found that both electron-rich and electron-poor aryl azides are efficient sources for the metal nitrene reactive intermediate.