Hilbert重级数定理的一个改进

The object of this note is to prove the followingTheorem Let{a_n}and{b_n}be sequences of real numbers such that0<∑∑a_n~2<+∞and0<∑b_n~2<+∞.Then we have the inequalitysum from m=1 to∞sum from n=1 to∞a_mb_n/m+n<{sum from n=1 to∞(π-θ/n~(1/2)a_n~2}~1/2{sum from n=1 to∞(π-θ/n~(1/2)b_n~2}~1/2 (1)whereθ=3/2~(1/2)-1=1.121320343.     

Inclusion of carbon nanotubes in a TiO2 sol-gel matrix

We report here the successful inclusion of carbon nanotubes (CNs) into a TiO₂ matrix prepared by a sol-gel method. The presence of CNs in the sol-gel matrix and the structure of the film were analyzed principally by transmission electron microscopy. Complementary information about the behavior of embedded carbon nanotubes versus heat treatment and ion irradiation were obtained by X-ray photoelectron spectroscopy. The elaboration of an inorganic matrix containing embedded carbon nanotubes leads to a new nanocomposite. The possible applications of this nanocomposite are discussed.     

Numerical solutions of the shallow water equations with discontinuous bed topography

A simple scheme is developed for treatment of vertical bed topography in shallow water flows. The effect of the vertical step on flows is modelled with the shallow water equations including local energy loss terms. The bed elevation is denoted with z_b^‐ for the left and z_b⁺ for the right values at each grid point, hence exactly representing a discontinuity in the bed topography. The surface gradient method (SGM) is generalized to reconstruct water depths at cell interfaces involving a vertical step so that the fluxes at the cell interfaces can accurately be calculated with a Riemann solver. The scheme is verified by predicting a surge crossing a step, a tidal flow over a step and dam‐break flows on wet/dry beds. The results have shown good agreements compared with analytical solutions and available experimental data. The scheme is efficient, robust, and may be used for practical flow calculations. Copyright © 2002 John Wiley & Sons, Ltd.     

Three-dimensional Schwarzschild spacetimes

In the following we find all of the three-dimensional flat spacetimes which are static and rotationally symmetric.     

Estimating a reduced rank regression model for non-normal variables

A method using third order moments for estimating the regression coefficients as well as the latent state scores of the reduced-rank regression model when the latent variable(s) are non-normally distributed is presented in this paper. It is shown that the factor analysis type indeterminacy of the regression coefficient matrices is eliminated. A real life example of the proposed method is presented. Differences of this solution with the reduced-rank regression eigen solution are discussed.     

Study of the reaction238U (α, α′f) atE α=480 MeV

The excitation function of the fission probability P _E E _x) for²³⁸U has been measured in the reaction²³⁸U(α, α′ f) at 480 MeV bombarding energy. The reaction mechanism of this reaction is discussed for excitation energies belowB _nf , the threshold for second chance fission, and aboveB _nf up toE _x =37 MeV. In comparing with results from fission induced by photons and by particle transfer reactions the (α, α′f) reaction gives too low values for the fission probabilityP _f at excitation energies well aboveB _nE . The role of the quasi-elastic knock-out process in this reaction is discussed.     

Electrical properties and Schottky diodes using N-N′diphenyl-1-4phenylenediamine

Thin films of, N-N′diphenyl 1-4phenylene-diamineane are prepared using vacuum sublimation technique. The electrical conductivity from room temperature down to 127 K is studied. It is found that the conduction of charge carriers obeys T^−1/2 dependence on temperature. The average hopping distance, hopping energy, density of states and their variation due to post-deposition heat treatment are studied. Schottky diodes are fabricated with gold as ohmic contact and aluminium as Schottky contact. From the observed current voltage characteristics the saturation current density, diode ideality factor and the barrier height are determined. Their variation with air annealing is also investigated.