Cycloaddition of Thiourea to Tri(1-propenyl)amine

Russian Journal of General Chemistry -     

Random matrix theory and non-parametric model of random uncertainties in vibration analysis

Recently, a new approach, called a non-parametric model of random uncertainties, has been introduced for modelling random uncertainties in linear and non-linear elastodynamics in the low-frequency range. This non-parametric approach differs from the parametric methods for random uncertainties modelling and has been developed in introducing a new ensemble of random matrices constituted of symmetric positive-definite real random matrices. This ensemble differs from the Gaussian orthogonal ensemble (GOE) and from the other known ensembles of the random matrix theory. The present paper has three main objectives. The first one is to study the statistics of the random eigenvalues of random matrices belonging to this new ensemble and to compare with the GOE. The second one is to compare this new ensemble of random matrices with the GOE in the context of the non-parametric approach of random uncertainties in structural dynamics for the low-frequency range. The last objective is to give a new validation for the non-parametric model of random uncertainties in structural dynamics in comparing, in the low-frequency range, the dynamical response of a simple system having random uncertainties modelled by the parametric and the non-parametric methods. These three objectives will allow us to conclude about the validity of the different theories.     

Viscoelastic properties of nanostructured natural rubber/polystyrene interpenetrating polymer networks

The effects of the blend ratio and initiating system on the viscoelastic properties of nanostructured natural rubber/polystyrene‐based interpenetrating polymer networks (IPNs) were investigated in the temperature range of ?80 to 150 °C. The studies were carried out at different frequencies (100, 50, 10, 1, and 0.1 Hz), and their effects on the damping and storage and loss moduli were analyzed. In all cases, tan δ and the storage and loss moduli showed two distinct transitions corresponding to natural rubber and polystyrene phases, which indicated that the system was not miscible on the molecular level. However, a slight inward shift was observed in the IPNs, with respect to the glass‐transition temperatures (T_g's) of the virgin polymers, showing a certain degree of miscibility or intermixing between the two phases. When the frequency increased from 0.1 to 100 Hz, the T_g values showed a positive shift in all cases. In a comparison of the three initiating systems (dicumyl peroxide, benzoyl peroxide, and azobisisobutyronitrile), the dicumyl peroxide system showed the highest modulus. The morphology of the IPNs was analyzed with transmission electron microscopy. The micrographs indicated that the system was nanostructured. An attempt was made to relate the viscoelastic behavior to the morphology of the IPNs. Various models, such as the series, parallel, Halpin–Tsai, Kerner, Coran, Takayanagi, and Davies models, were used to model the viscoelastic data. The area under the linear loss modulus curve was larger than that obtained by group contribution analysis; this showed that the damping was influenced by the phase morphology, dual‐phase continuity, and crosslinking of the phases. Finally, the homogeneity of the system was further evaluated with Cole–Cole analysis. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1680–1696, 2003     

Norm Series in High-Dimensional Local Fields

In the present paper, the notion of norm series with respect to the norm residue symbol is generalized to high-dimensional local fields. Necessary and sufficient conditions for the existence of norm series are obtained. Bibliography: 12 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 305, 2003, pp. 60–83.     

L2 -cohomology of manifolds with flat ends

Geometric and Functional Analysis - We give a topological interpretation of the spaces of L2 -harmonic forms on manifolds with flat ends. We also prove a Chern-Gauss-Bonnet formula for the L2...     

Crack path instabilities in DCDC experiments in the low speed regime

We studied the low speed fracture regime (10⁻⁴-10⁻⁹ m s⁻¹) in different glassy materials (soda-lime glass, glass ceramics) with variable but controlled length scale of heterogeneity. The chosen mechanical system enabled us to work in pure mode I (tensile) and at a fixed load on double cleavage drilled compression specimen. The internal residual stresses of studied samples were carefully relaxed by appropriate thermal treatment. By means of optical and atomic force microscopy techniques fracture surfaces have been examined. We have shown for the first time that the crack front line underwent an out-of-plane oscillating behavior as a result of a reproducible sequence of instabilities. The wavelength of such a phenomenon is in the micrometer range and its amplitude in the nanometer range. These features were observed for different glassy materials providing that a typical length scale characterizing internal heterogeneities was lower than a threshold limit estimated to few nanometers. This effect is the first clear experimental evidence of crack path instabilities in the low speed regime in a uniaxial loading experiment. This phenomenon has been interpreted by referring to the stability criterion for a straight crack propagation as presented by Adda-Bedia et al. [Phys. Rev. Lett. 76 (1996) 1497].     

Synthesis and characterization of isotopically enriched methylmercury (CH3201Hg+)

A simple procedure for the synthesis of an important standard, isotopically enriched methylmercury, which is not commercially available, has been established successfully. The isotopically enriched standard synthesized is utilized in conventional isotope dilution mass spectrometry (IDMS), as well as in speciated IDMS (SIDMS), for determination of the true concentration of methylmercury in environmental samples. The CH₃²⁰¹Hg⁺ standard has been synthesized from commercially available ²⁰¹HgO and tetramethyltin. The synthesis time required is 1 h at 60°C. The product is highly pure, yielding more than 90% as ²⁰¹Hg in CH₃²⁰¹Hg⁺. Hazardous dimethylmercury does not occur during this synthesis procedure. The product synthesized was analyzed using high‐performance liquid chromatography coupled with inductively coupled plasma mass spectrometry (ICP‐MS) and ICP‐MS alone in order to determine its concentration, isotopic composition and purity. The stability of the product was also evaluated for over 6 months and found to be stable at 4°C in the dark. The isotopically enriched methylmercury synthesized can be used in SIDMS and IDMS analyses as a standard. Copyright © 2003 John Wiley & Sons, Ltd.