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.     

On Cullen numbers which are both Riesel and Sierpiński numbers

We describe an algorithm to determine whether or not a given system of congruences is satisfied by Cullen numbers. We use this algorithm to prove that there are infinitely many Cullen numbers which are both Riesel and Sierpiński. (Such numbers should be discarded if you are searching prime numbers with Proth?s theorem.)