Hetero-Diels-Alder reaction of phosphinyl and phosphonyl nitroso alkenes with conjugated dienes: an aza-Cope rearrangement

Phosphorylated nitroso alkenes react with cyclic dienes such as cyclopentadiene or cyclohexadiene to afford hetero Diels-Alder-type cycloadducts where the nitroso alkene participates as dienophile component and the cyclic olefin acts as the 4π-electron (diene) system. Subsequent aza-Cope rearrangement affords highly functionalized 5,6-dihydro-4H-1,2-oxazines. Conversely, the reaction of TMS-substituted cyclopentadiene (dienophile) with nitroso alkenes as heterodienes leads directly to bicyclic 1,2-oxazines. Theoretical studies are in agreement with the experimental results and with the new aza-Cope rearrangement proposed.     

Reaction of N-vinylic phosphazenes with alpha,beta-unsaturated aldehydes. Azatriene-mediated synthesis of dihydropyridines and pyridines derived from beta-amino acids

Aza-Wittig reaction of N-vinylic phosphazenes (1,2 addition), derived from diphenylmethylphosphine or derived from trimethylphosphine with alpha,beta-unsaturated aldehydes, leads to the formation of 3-azatrienes through a [2 + 2]-cycloaddition-cycloreversion sequence. The presence of an alkyl substituent in position 3 of N-vinylic phosphazenes increases the steric interactions, and [4 + 2] periselectivity (1,4 addition) is observed. Reaction of azatrienes with alpha,beta-unsaturated aldehydes yields pyridines.     

Tetrapyrrole singlet excited state quenching by carotenoids in an artificial photosynthetic antenna

Two artificial photosynthetic antenna models consisting of a Si phthalocyanine (Pc) bearing two axially attached carotenoid moieties having either 9 or 10 conjugated double bonds are used to illustrate some of the function of carotenoids in photosynthetic membranes. Both models studied in toluene, methyltetrahydrofuran, and benzonitrile exhibited charge separated states of the type C*+-Pc*- confirming that the quenching of the Pc S1 state is due to photoinduced electron transfer. In hexane, the Pc S1 state of the 10 double bond carotenoid-Pc model was slightly quenched but the C*+-Pc*- transient was not spectroscopically detected. A semiclassical analysis of the data in hexane at temperatures ranging from 180 to 320 K was used to demonstrate that photoinduced electron transfer could occur. The model bearing the 10 double bond carotenoids exhibits biexponential fluorescence decay in toluene and in hexane, which is interpreted in terms of an equilibrium mixture of two isomers comprising s-cis and s-trans conformers of the carotenoid. The shorter fluorescence lifetime is associated with an s-cis carotenoid conformer where the close approach between the donor and acceptor moieties provides through-space electronic coupling in addition to the through-bond component.     

Equilibria of the three-body problem with rigid dumb-bell satellite

This paper is concerned with the orbital–rotational motion of an asymmetric dumb-bell (two masses with fixed distance among them) under the attraction of a central body. For this model, we find some equilibria and give sufficient conditions for their stability.     

Bounds for the Kirchhoff index of regular graphs via the spectra of their random walks

Using probabilistic tools, we give tight upper and lower bounds for the Kirchhoff index of any d‐regular N‐vertex graph in terms of d, N, and the spectral gap of the transition probability matrix associated to the random walk on the graph. We then use bounds of the spectral gap of more specialized graphs, available in the literature, in order to obtain upper bounds for the Kirchhoff index of these specialized graphs. As a byproduct, we obtain a closed‐form formula for the Kirchhoff index of the d‐dimensional cube in terms of the first inverse moment of a positive binomial variable. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Linguistic cost-sensitive learning of genetic fuzzy classifiers for imprecise data

Cost-sensitive classification is based on a set of weights defining the expected cost of misclassifying an object. In this paper, a Genetic Fuzzy Classifier, which is able to extract fuzzy rules from interval or fuzzy valued data, is extended to this type of classification. This extension consists in enclosing the estimation of the expected misclassification risk of a classifier, when assessed on low quality data, in an interval or a fuzzy number. A cooperative-competitive genetic algorithm searches for the knowledge base whose fitness is primal with respect to a precedence relation between the values of this interval or fuzzy valued risk. In addition to this, the numerical estimation of this risk depends on the entrywise product of cost and confusion matrices. These have been, in turn, generalized to vague data. The flexible assignment of values to the cost function is also tackled, owing to the fact that the use of linguistic terms in the definition of the misclassification cost is allowed.     

Chiral Single-Molecule Potentiometers Based on Stapled ortho- Oligo(phenylene)ethynylenes

We report on the chemical design of chiral molecular junctions with stress-dependent conductance, whose helicity is maintained during the stretching of a single molecule junction due to the stapling of both ends of the inner helix. In the reported compounds, different conductive pathways are observed, with clearly different conductance values and plateau-length distributions, attributed to different conformations of the helical structures. The large chiro-optical responses and the potential use of these molecules as unimolecular spin filters have been theoretically proved using state-of-the-art Density Functional Theory (DFT) calculations, including a fully ab-initio estimation of the CISS-originating spin polarization which is done, for the first time, for a realistic molecular system.     

Locally uniformly rotund points in convex-transitive Banach spaces

Almost transitive superreflexive Banach spaces have been considered in [C. Finet, Uniform convexity properties of norms on superreflexive Banach spaces, Israel J. Math. 53 (1986) 81–92], where it is shown that they are uniformly convex and uniformly smooth. We characterize such spaces as those convex transitive Banach spaces satisfying conditions much weaker than that of uniform convexity (for example, that of having a weakly locally uniformly rotund point). We note that, in general, the property of convex transitivity for a Banach space is weaker than that of almost transitivity.     

A moderate deflection composite helicopter rotor blade model with an improved cross-sectional analysis

The compatibility between a composite beam cross-sectional analysis based on the variational asymptotic approach, and a helicopter rotor blade model which is part of a comprehensive rotorcraft analysis code is examined. It was found that the finite element cross-sectional analysis code VABS can be combined with a moderate deflection rotor blade model in spite of the differences between the formulations. The new YF/VABS rotor blade model accounts for arbitrary cross-sectional warping, in-plane stresses, and moderate deflections. The YF/VABS composite rotor blade model was validated against experimental data and various rotor blade analyses by examining displacements and stresses under static loads, as well as aeroelastic stability of a composite rotor blade in hover, and forward flight vibratory hubloads of a four bladed composite rotor.     

Moran's genetics model via electric networks

Using the electric approach, we derive exact and asymptotic closed form formulas for hitting times in symmetric cases of the Moran's genetics model.