Estimates from Below for the Spectral Function and for the Remainder in Local Weyl’s Law

We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl’s law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the Dirichlet box principle. Our results develop and extend the unpublished thesis of A. Karnaukh [Ka]. The first author was supported by NSERC, FQRNT, Alfred P. Sloan Foundation Fellowship and Dawson Fellowship. The second author was supported by NSERC and FQRNT. Received: April 2006 Revision: October 2006 Accepted: October 2006     

Statistics of travel time and intensity of two first arrivals of short pulses backscattered by a rough 3D surface

The time history of a pulse backscattered by a rough surface contains information about the position of the surface and the properties of the scatterers. This information is utilized successfully in a number of remote sensing techniques ranging from echo sounding of the ocean bottom to medical ultrasonics and satellite altimetry. In the current paper, statistical properties of backscattered waves are considered in a geometrical optics approximation. The probing pulse duration is assumed to be sufficiently short so that signals backscattered in the vicinity of individual specular points on a rough surface do not overlap in time. Theoretical results previously obtained for a 2D problem [I. M. Fuks and O. A. Godin, 2005, Waves in Random and Complex Media, 14, 539-562; M. I. Charnotskii and I. M. Fuks, 2005, Waves in Random and Complex Media, 15, 451-467] are extended to wave scattering by 3D rough surfaces by following a mathematical approach developed in stochastic geometry. Predictions of an asymptotic theory are verified against results of Monte-Carlo simulations. Probability density functions of travel times and intensities of the first and second arrivals of the backscattered wave are quantified in terms of statistical moments of roughness assuming normal distribution of elevations. It is found that, as in the 2D case, the travel time and the intensity are strongly correlated; on average, the earlier a signal arrives, the smaller is its intensity.     

Amidinoethylation—a new reaction—IV : The amidinoethylation of alcohols: a facile synthesis of 3-alkoxy-N,N'-substituted-propanamidines

The amidinoethylation of alcohols takes place by the addition of sodium alkoxides 2 (R¹ = Me, Et) to the CC double bond of a variety of N,N'-substituted-propenamidines 1 (Method A). This illustrates the activation of the CC double bond by the conjugated amidine function and provides a new class of Michael acceptors for alcohols. However, this activation is poorer than with other nucleophiles or Michael acceptors. The amidinoethylation makes available 3-alkoxy-N,N'-substituted-amidines not easily accessible by other classical methods. However, it is demonstrated that the general N,N'-substituted-amidine synthesis via the nitrilium salts can also apply to nitrile compounds having an alkoxygroup present on the molecule (method B). Since the cyanoethylation of alcohols (4) is a very fast and facile reaction the method B is the preferred strategy for the synthesis of 3-alkoxy-N,N'-substituted-propanamidines 3.     

Small-angle x-ray scattering and inhomogeneities of the electron density in polycrystalline and epitaxial PbS films

The dependence of the characteristics of the macro- and microporosity on the condensation temperature has been studied for condensation temperatures from 30 to 450°C by small-angle x-ray scattering, hydrostatic weighing, and low-temperature desorption of argon in polycrystalline and single-crystal lead sulfide films with thickness 3–5 m condensed for normal incidence of the molecular beam on polycrystalline and single-crystal substrates. The porosity of the polycrystalline films is an order of magnitude greater than in the epitaxial films. In polycrystalline condensates, the pores are elongated and are oriented along the normal to the film. The pores in the epitaxial films have a platelet form with faces along the {100} planes and are parallel to the direction of growth of the condensate. At high substrate temperature (about 400°C), more nearly equiaxial pores, with additional {110} faces are formed, as a result of the plastic deformation of the condensate by thermal macrostresses.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 46–52, August, 1979.     

Covalently Trapped Triarylamine-Based Supramolecular Polymers

C₃-Symmetric triarylamine trisamides (TATAs), decorated with three norbornene end groups, undergo supramolecular polymerization and further gelation by π–π stacking and hydrogen bonding of their TATA cores. By using subsequent ring-opening metathesis polymerization, these physical gels are permanently crosslinked into chemical gels. Detailed comparisons of the supramolecular stacks in solution, in the physical gel, and in the chemical gel states, are performed by optical spectroscopies, electronic spectroscopies, atomic force microscopy, electronic paramagnetic resonance spectroscopy, X-ray scattering, electronic transport measurements, and rheology. The results presented here clearly evidence that the core structure of the functional supramolecular polymers can be precisely retained during the covalent capture whereas the mechanical properties of the gels are concomitantly improved, with an increase of their storage modulus by two orders of magnitude.     

Labelling of peptides with <Superscript>99m</Superscript>Tc complexes through the modified C-terminal group

Easy and efficient way to modify of the C-terminus of the peptide using amino acid lysine has been proposed and experimentally verified. The synthesis yield was high (≥85%) and it was found that reactions can be carried out even with microgram amounts of the peptide. Using Fmoc-alanine (as the peptide model) with modified C-terminus the procedure of peptide labelling with monovalent and trivalent ^99mTc complexes has been elaborated.     

The effect of carbon nanotubes on epoxy matrix nanocomposites

The paper concerns thermal properties of epoxy/nanotubes composites for aircraft application. In this work, influence of carbon nanotubes on thermal stability, thermal conductivity, and crosslinking density of epoxy matrix was determined. Three kinds of nanotubes were used: non-modified with 1- and 1.5-μm length, and 1-μm length modified with amino groups. Scanning electron microscopy observations were done for examining dispersion of nanotubes in the epoxy matrix. Glass transition temperature (T _g) was readout from differential scanning calorimetry. From dynamic mechanical analysis, crosslinking density was calculated for epoxy and its composites. Also, thermogravimetric analysis was done to determine influence of nanotubes addition on thermal stability and decomposition process of composites. Activation energy was calculated from TGA curves by Flynn–Wall–Ozawa method. Thermal diffusivity was also measured. SEM images proved the uniform dispersion of carbon nanotubes without any agglomerates. It was found that nanotubes modified with amino groups lead to the increase of epoxy matrix crosslinking density. The significant increase in T _g was also observed. On the other hand, addition of carbon nanotubes leads to the decrease of thermal stability of polymer due to the increase of thermal diffusivity.     

The Michael Addition of Enamines to Propenamidines. A Convenient Synthesis of 2β-Amidinoethylcyclo-Alkanones by Amidinoethylation Reaction

A variety of propenamidines 3 have been reacted with enamines of cyclopentanone and cyclohexanone giving after hydrolysis of the Stork enamine 6, 2-β-amidinoethylcyclopentanones 8 and -hexanones 7. This reaction illustrates the electrophilic character of the C=C double bond due to the conjugated amidine function, thus providing with propenamidines 3 a new class of Michael acceptors for enamines.