On almost hyperHermitian structures on Riemannian manifolds and tangent bundles

Some results concerning almost hyperHermitian structures are considered, using the notions of the canonical connection and the second fundamental tensor field h of a structure on a Riemannian manifold which were introduced by the second author. With the help of any metric connection on an almost Hermitian manifold M an almost hyperHermitian structure can be constructed in the defined way on the tangent bundle TM. A similar construction was considered in [6], [7]. This structure includes two basic anticommutative almost Hermitian structures for which the second fundamental tensor fields h ¹ and h ² are computed. It allows us to consider various classes of almost hyperHermitian structures on TM. In particular, there exists an infinite-dimensional set of almost hyperHermitian structures on TTM where M is any Riemannian manifold.     

A non-conforming finite element method with anisotropic mesh grading for the Stokes problem in domains with edges

The solution of the Stokes problem in three-dimensional domainswith edges has anisotropic singular behaviour which is treatednumerically by using anisotropic finite element meshes. Thevelocity is approximated by Crouzeix–Raviart (nonconformingP₁ ) elements and the pressure by piecewise constants. Thismethod is stable for general meshes (without minimal or maximalangle condition). Denoting by N_e the number of elements in themesh, the interpolation and consistency errors are of the optimalorder h N_e^–1/3 which is proved for tensor product meshes.As a by-product, we analyse also nonconforming prismatic elementswith P₁ [oplus ] span {x₃²} as the local space for the velocitywhere x₃ is the direction of the edge.     

Some test statistics for the structural coefficients of the multivariate linear functional relationship model

Summary For the testing problem concerning the coefficients of the multivariate linear functional relationship model, the distribution of a statistic previously proposed by A. P. Basu depends on the unknown covariance matrixV of errors, so limiting its applicability. This article proposes new test statistics with sampling distributions which are independent of the unknown parameters for the cases whereV is either unknown or known only up to a proportionality factor. The exact distributions of the test statistics are also discussed.     

In situ FTIR study of oxygen adsorption on nanostructured RuO2 thin-film electrode

In situ Fourier transform spectroscopy (FTIR) was used to study interactions of nanostructured ruthenium oxide (RuO₂) thin-film sensing electrode with O₂ at room temperature. RuO₂ nanostructures were pretreated at 1,000 °C for 1 h in order to obtain good crystallinity of amorphous RuO₂ nanoparticles. Morphology and properties of nanostructured RuO₂ were characterized by X-ray diffraction, thermo-gravimetric/differential thermal analysis, scanning electron microscopy, and FTIR. It was shown that pretreated RuO₂ is quite active for O₂ ⁻, O₂ ²⁻, and O²⁻ adsorption with clear 722 cm⁻¹ band for superoxide ions (O₂ ⁻) adsorption for the different oxygen concentrations. The results of in situ FTIR measurements revealed that the active sites for oxygen adsorption are not limited to the triple boundaries, but extended to surfaces of RuO₂ electrodes. Fundamental vibration frequencies of ruthenium–oxygen bond at a temperature of 23 °C as well as region above fundamental frequencies for the nanostructured RuO₂ were identified.     

Coumarin 314 free radical cation: formation, properties, and reactivity toward phenolic antioxidants

We have explored the photogeneration of the coumarin 314 radical cation by using nanosecond laser excitation at wavelengths longer than 400 nm in benzene, acetonitrile, dichloromethane, and aqueous media. In addition, time-resolved absorption spectroscopy measurements allowed detection of the triplet excited state of coumarin 314 (C(314)) with a maximum absorption at 550 nm in benzene. The triplet excited state has a lifetime of 90 μs in benzene. It is readily quenched by oxygen (k(q) = 5.0 × 10(9) M(-1) s(-1)). From triplet-triplet energy transfer quenching experiments, it is shown that the energy of this triplet excited state is higher than 35 kcal/mol, in accord with the relatively large singlet oxygen quantum yield (Φ(Δ) = 0.25). However, in aqueous media, the coumarin triplet was no longer observed, and instead of that, a long-lived (160 μs in air-equilibrated solutions) free radical cation with a maximum absorbance at 370 nm was detected. The free radical cation generation, which has a quantum yield of 0.2, occurs by electron photoejection. Moreover, density functional theory (DFT) calculations indicate that at least 40% of the electronic density is placed on the nitrogen atom in aqueous media, which explains its lack of reactivity toward oxygen. On the other hand, rate constant values close to the diffusion rate limit in water (>10(9) M(-1) s(-1)) were found for the quenching of the C(314) free radical cation by phenolic antioxidants. The results have been interpreted by an electron-transfer reaction between the phenolic antioxidant and the radical cation where ion pair formation could be involved.     

A new approach on improving the fire resistance of polyamide 11 by incorporating sulfur‐based flame retardant

In this work, a novel sulfur‐based flame retardant (SA‐M) was synthesized by the self‐assembly of melamine and sulfamic acid. The chemical structure of SA‐M was fully characterized. SA‐M, in company with Al₂O₃, was then introduced into polyamide 11 (PA 11) by melt compounding in order to improve the fire resistance of the polymer substrate. The observation by scanning electron microscopy (SEM) and electron probe microanalysis (EPMA) indicated the well dispersion of SA‐M in PA 11 matrix. The fire performance of PA 11 composites was evaluated by limiting oxygen index (LOI), vertical burning (UL‐94), and cone calorimeter tests, respectively. The results showed that the presence of 17.5% SA‐M and 2.5% Al₂O₃ increased the LOI value from 22.4% to 30.9%, upgraded the UL‐94 rating from no rating to V‐0, significantly eliminated the melt dripping, and decreased the peak heat release rate from 1024 to 603 kW/m². The thermal behaviors were investigated by thermogravimeric analysis (TGA) and TGA‐Fourier transform infrared spectroscopy (FTIR). It was suggested that SA‐M took effects mainly in gas phase by diluting the combustible fuel, leading to the improvement of the fire resistance of PA 11.     

Total synthesis of (+)-cassaine via transannular Diels-Alder reaction

A full account of the total synthesis of (+)-cassaine ( 1) using the transannular Diels-Alder (TADA) reaction as the pivotal construction is described. The strategy began from Evans' oxazolidine 8, the only chiral source used for the total stereochemical outcome of the target molecule. The key intermediate 3 was obtained from 8 in 10 steps in 40% overall yield. Following extensive optimization, the coupling of 3 on both ends with another densely functional partner 2 followed by TADA reaction on macrocycle 4 cleanly furnished the tricycle 5. The stereochemical outcome in 5 was expected via a least-energetic transition state T4. A stereoselective reduction, hydroboration, and methyl cuprate 1,4-addition along with a few other functional interconversions transformed 5 into the key intermediate 37. Final tethering of dimethylaminoethyloxycarbonyl along with epimerization at C8 and alcohol deprotection at C3 yielded the natural product 1.     

The quantum Weyl group and the universal quantumR-matrix for affine lie algebraA1(1)

The universal quantumR-matrix is obtained in the case of the affine Kac-Moody Lie algebra sl(2).     

Public debates driven by incomplete scientific data: The cases of evolution theory, global warming and H1N1 pandemic influenza

Public debates driven by incomplete scientific data where nobody can claim absolute certainty, due to the current state of scientific knowledge, are studied. The cases of evolution theory, global warming and H1N1 pandemic influenza are investigated. The first two are of controversial impact while the third is more neutral and resolved. To adopt a cautious balanced attitude based on clear but inconclusive data appears to be a lose-out strategy. In contrast overstating arguments with incorrect claims which cannot be scientifically refuted appears to be necessary but not sufficient to eventually win a public debate. The underlying key mechanisms of these puzzling and unfortunate conclusions are identified using the Galam sequential probabilistic model of opinion dynamics (Galam, 2002 [4], Galam, 2005 [18], Galam and Jacobs, 2007 [19]). It reveals that the existence of inflexible agents and their respective proportions are the instrumental parameters to determine the faith of incomplete scientific data in public debates. Acting on one’s own inflexible proportion modifies the topology of the flow diagram, which in turn can make irrelevant initial supports. On the contrary focusing on open-minded agents may be useless given some topologies. When the evidence is not as strong as claimed, the inflexibles rather than the data are found to drive the opinion of the population. The results shed a new but disturbing light on designing adequate strategies to win a public debate.