Rearrangement thermique des adduits du tetracyanoethylene de 2H-pyrannes

The addition of tetracyanotehylene to 2H-pyrans 1 results in a mixture of two isomeric adducts 6. The thermal decomposition of the compounds 6 gives rise to both a small percentage of the retro Diels-Alder, and a new mode of evolution leading to a mixture of furans (E+Z) 7. A detailed interpretation of the ¹³C spectra of the compounds 7 was established by comparison with the ¹³C spectra of 2,5-diphenylfuran and trans-stilbene. The structure 7 is confirmed by chemical degradation.     

A study of the gold/aqueous electrolyte interphase by modulated reflection spectroscopy

The admittance and differential reflectivity of an electrode of polycrystalline gold in contact with aqueous 0.02 M NaF, KClO₄, 0.01 M Na₂SO₄ and KCl have been measured in the range of potential where the electrode is ideally polarized (?0.7 V to 0.8 V NHE). In NaF and KClO₄ evidence was obtained for the compression of the adsorbed layer of water. The increase of the number of water molecules, with respect to the number in the least original state (at?4μC cm^?2), is 3% at +8 μC cm^?2 and at?17 μC cm^?2. At the potential of zero charge the water dipoles are oriented preferentially with the oxygen towards the metal. In KCl the optical measurements confirm the existence of two types of Au?Cl^? interaction and the covalent character of the bond at the most positive charges.     

Synthesis of aromatic polythioamide-oxothioxoquinazolines from bis(1,3,4-thiadiazoline-5-thione) and aromatic bis-o-amino esters

Aromatic polythioamide-oxothioxoquinazolines were synthesized by the polycondensation of 2,2′-(m-phenylene)bis-1,3,4-thiadiazoline-5-thione with aromatic bis-o-amino esters. The polymerizations were carried out at 160°C in acidic media such as m-cresol, sulfolane, and polyphosphoric acid to produce polymers with reduced viscosities up to 0.5 dL/g. These polymers were soluble in polar aprotic solvents like N-methyl-2-pyrrolidone and some acidic media including m-cresol. The polythioamide-oxothioxoquinazolines showed relatively good thermal stability with 10% weight loss at 344–394°C in air.     

Electron spin resonance studies of the radiolysis of bi-π-cyclopentadienylalkyls of molybdenum and tungsten

Exposure of (C₅H₅)₂MO(CH₃)₂ and (C₅H₅)₂W(CH₃)₂, prepared from the corresponding dichlorides, to ²⁰Co γ-rays at 77 K gave H₂C.CML₃ carbene species characterised by their ESR spectra, together with a central feature possibly due to the parent cations. Dilute solutions in CD₃OD gave features assigned to the parent anions which were converted on bleaching with visible light into methyl radicals, and H₂C.ML₃ radicals. From the magnitude of the ¹H and ¹⁸³W hyperfine coupling constants, it is deduced that the SOMO for H₂C.WL₃ radicals is strongly localised on carbon.Dilute solutions in aqueous sulphuric acid also gave species with A(2H) = 20 G, identified as the carbene derivatives, H₂C.Ml₃. These were formed on annealing, as signals assigned to HSO₄ · radicals were lost.     

Anisotropic Hardening of Sheet Metals at Elevated Temperature: Tension-Compressions Test Development and Validation

New test equipment has been developed to measure the in-plane cyclic behavior of sheet metals at elevated temperatures. The tester has clamping dies with adjustable side force to prevent the sheet specimens from buckling during compressive loading. In addition to the room temperature experiment, cartridge type heaters are inserted in the clamping dies so that the specimen can be heated up to 400 °C during the cyclic tests. For the strain measurement, a non-contact type laser extensometer is used. In order to validate the newly developed test device, the tension-compression (and compression-tension) tests under pre-strains and various temperatures have been performed. As model materials, the aluminum alloy sheet which exhibits a large Bauschinger effect and the magnesium alloy sheet which exhibits different amounts of asymmetry under cyclic loading are used. The developed device can be well-suited to measure the cyclic material behavior, especially the anisotropic and asymmetric hardening of light-weight materials.     

Distribution of integral points on some hyperboloids of one sheet

Results of B. F. Skubenko (Izv. Akad. Nauk SSSR, Ser. Mat.,26, 721–752 (1962)) are generalized to indefinite ternary quadratic formsf(x)=f ₀(Cx), which are contained in the simplest formf ₀(x)=x ₁ x ₃–x _r ^e We prove that the integral points on the hyperboloid of one sheetf(x)=m,m<0, are uniformly distributed over area (in the sense of hyperbolic metric) and over residue classes for given modulus.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 121, pp. 83–93, 1983.     

Existence and Exponential Decay of Solutions for a Wave Equation with Integral Nonlocal Boundary Conditions of Memory Type

In this paper, we consider a wave equation with integral nonlocal boundary conditions of memory type. First, we establish two local existence theorems by using Faedo–Galerkin method and standard arguments of density. Next, we give a su?cient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical results.     

One-Step Generalized Estimating Equations With Large Cluster Sizes

Medical studies increasingly involve a large sample of independent clusters, where the cluster sizes are also large. Our motivating example from the 2010 Nationwide Inpatient Sample (NIS) has 8,001,068 patients and 1049 clusters, with average cluster size of 7627. Consistent parameter estimates can be obtained naively assuming independence, which are inefficient when the intra-cluster correlation (ICC) is high. Efficient generalized estimating equations (GEE) incorporate the ICC and sum all pairs of observations within a cluster when estimating the ICC. For the 2010 NIS, there are 92.6 billion pairs of observations, making summation of pairs computationally prohibitive. We propose a one-step GEE estimator that (1) matches the asymptotic efficiency of the fully iterated GEE; (2) uses a simpler formula to estimate the ICC that avoids summing over all pairs; and (3) completely avoids matrix multiplications and inversions. These three features make the proposed estimator much less computationally intensive, especially with large cluster sizes. A unique contribution of this article is that it expresses the GEE estimating equations incorporating the ICC as a simple sum of vectors and scalars.     

Certain properties related to well posedness of switching diffusions

This work is devoted to switching diffusions that have two components (a continuous component and a discrete component). Different from the so-called Markovian switching diffusions, in the setup, the discrete component (the switching) depends on the continuous component (the diffusion process). The objective of this paper is to provide a number of properties related to the well posedness. First, the differentiability with respect to initial data of the continuous component is established. Then, further properties including uniform continuity with respect to initial data, and smoothness of certain functionals are obtained. Moreover, Feller property is obtained under only local Lipschitz continuity. Finally, an example of Lotka–Volterra model under regime switching is provided as an illustration.