Bi-Lipschitz geometry of complex surface singularities

We discuss the bi-Lipschitz geometry of an isolated singular point of a complex surface with particular emphasis on when it is metrically conical.      

Local Lipschitz geometry of real weighted homogeneous surfaces

We compute Hölder Complexes, i.e. the complete bi-Lipschitz invariants, for germs of real weighed homogeneous algebraic or semialgebraic surfaces.     

On the determination of the Young’s modulus of thin films using indentation tests

The main difficulty with the characterization of thin coatings using depth-sensing indentation tests is related to the determination of the contributions of the substrate and the film to the measured properties. In this study, three-dimensional numerical simulations of the Vickers hardness test are used in order to examine the influence of the elastic and plastic properties of the substrate and the film on the composite’s Young’s modulus results. The hardness of the film is equal to or higher than the substrate hardness. A study of the stress distributions and the indentation geometry of composites, film/substrate, was performed, taking into account the relative mechanical properties of the film and substrate. In addition, stress evolution during indentation was studied, in order to quantify the critical indentation depth under which the substrate is not elastically deformed. The accurate evaluation of the Young’s modulus of the films using weight functions is also examined: some of these have previously been proposed and one was introduced for this study. Two different fitting procedures were used to compare the results obtained from eight fictive film/substrate combinations using six weight functions. The first procedure, commonly used, considers the substrate’s modulus as a known parameter in the fitting process. In the second, the film and the substrate’s modulus are considered as unknown variables that are calculated simultaneously during the fitting process. The validity of the conclusions obtained using the fictive materials was checked by applying the weight functions to four real composites.     

A combined Chapman-Enskog and Grad method. III. Polyatomic gases in magnetic fields

A kinetic theory is developed for rarefied polyatomic gases of spherical and rough molecules with rotational energy in the presence of an external constant magnetic field. A method of solution of Boltzmann equation that combines features of the methods of Chapman-Enskog and Grad is used to determine transport coefficients that depend on the external magnetic field (Senftleben-Beenakker effect). Received August 4, 1997     

CAN-mediated oxidations for the synthesis of xanthones and related products

Reaction of (2,4,5-trimethoxyphenyl)(2-hydroxyphenyl)methanone with ceric ammonium nitrate furnished the xanthone, 2,3-dimethoxy-9H-xanthen-9-one. Under the same conditions the related (1,4-dimethoxynaphthalen-2-yl)(2-hydroxyphenyl)methanone resulted in the formation of 12a-methoxy-5H-benzo[c]xanthenes 5,7(12aH)-dione. Other examples of this novel transformation are also outlined.     

Integrated optical temporal Fourier transformer based on a chirped Bragg grating waveguide

We experimentally demonstrate the first integrated temporal Fourier transformer based on a linearly chirped Bragg grating waveguide written in silica glass with a femtosecond laser. The operation is based on mapping the energy spectrum of the input optical signal to the output temporal waveform by making use of first-order chromatic dispersion. The device operates in reflection, has a bandwidth of 10 nm, and can be used for incident temporal waveforms as long as 20 ps. Experimental results, obtained through both temporal oscilloscope traces and Fourier transform spectral interferometry, display a successful Fourier transformation of in-phase and out-of-phase pairs of input optical pulses, and demonstrate the correct functionality of the device for both amplitude and phase of the temporal output.     

Uniqueness of complete spacelike hypersurfaces via their higher order mean curvatures in a conformally stationary spacetime

We study complete noncompact spacelike hypersurfaces immersed into conformally stationary spacetimes, that is, Lorentzian manifolds endowed with a timelike conformal vector field V. In this setting, by using as main analytical tool a suitable maximum principle for complete noncompact Riemannian manifolds, we establish new characterizations of totally umbilical hypersurfaces in terms of their higher order mean curvatures. For instance, supposing an appropriated restriction on the norm of the tangential component of the vector field V, we are able to show that such hypersurfaces must be totally umbilical provided that either some of their higher order mean curvatures are linearly related or one of them is constant. Applications to the so‐called generalized Robertson‐Walker spacetimes are given. In particular, we extend to the Lorentzian context a classical result due to Jellett  29 .     

On the computation of all eigenvalues for the eigenvalue complementarity problem

In this paper, a parametric algorithm is introduced for computing all eigenvalues for two Eigenvalue Complementarity Problems discussed in the literature. The algorithm searches a finite number of nested intervals \([\bar{l}, \bar{u}]\) in such a way that, in each iteration, either an eigenvalue is computed in \([\bar{l}, \bar{u}]\) or a certificate of nonexistence of an eigenvalue in \([\bar{l}, \bar{u}]\) is provided. A hybrid method that combines an enumerative method [1] and a semi-smooth algorithm [2] is discussed for dealing with the Eigenvalue Complementarity Problem over an interval \([\bar{l}, \bar{u}]\) . Computational experience is presented to illustrate the efficacy and efficiency of the proposed techniques.     

'Non-covalent synthesis' of a chiral host of calix[6]arene and enantiomeric discrimination

'Non-covalent synthesis' of novel chiral hosts (calix[6]arene-chiral amine complexes) and its application to enantiomeric discrimination was investigated by (1)H NMR spectroscopy. The topology of a ternary complex was proposed for the calix[6]arene-amine-sulfoxide to rationalize the chiral recognition.