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On a zero equation model of turbulence

In this paper we study a widely used zero equation model of turbulence. The governing equations are derived by applying to the incompressible Navier-Stokes equations the Reynolds time averaging procedure. We achieve closure by employing the eddy viscosity concept. Using the Implicit Function Theorem we obtain an existence and uniquencess result. We also discuss the existence of nonsingular solutions. Finally, we present an algorithm for solving the modeled equations.     

The preparation,phase relationships,and Eu-151 Mössbauer spectroscopy of europium tungsten bronzes and related phases

Crystal chemistry and phase relations for the bronze-forming region of the EuWO system have been investigated. A bronze Eu_xWO₃ is stable up to 1000°C when x ? 0.125 and in the region 0.085 ? x ? 0.125 the symmetry is cubic. A tetragonal bronze exists at x = 0.05, and an orthorhombic bronze with a structure closely related to the orthorhombic form of WO₃ exists below x = 0.01. Mössbauer spectra at room temperature and at 80 K indicate that in all these phases the europium is highly ionized as Eu(III) with no electron localization to give (EuII) even at low values for x. The decomposition products of the bronzes have been established, and the Mössbauer parameters for the highly nonstoichiometric tungstates Eu_xWO₄ were determined. Both Eu(II) and Eu(III) resonances were obtained, and a cation vacancy model for Eu_xWO₄ was found to fit the data best. In conformity with the foregoing data, a sample of composition “Eu₂W₂O₇” was found not be be a pyrochlore but to comprise a mixture of Eu₆WO₁₂, Eu_xWO₄, and W. The phase relationships for the europium bronze system Eu_xWO₃ are compared with those of other ionic bronzes Na_xWO₃, Li_xWO₃, and Al_xWO₃.     

Radiative lifetimes of ions measured with the photoelectron spectrometer

Using a modified photoelectron spectrometer the radiative lifetimes of some electronically excited diatomic and triatomic molecular ions have been determined. The method is based on measuring the time delay between the ejection of a photoelectron from a molecule and the emission of a photon from the resulting ion.     

Syntheses of 3,7-dimethylpentadecan-2-ols from intermediates formed from co-oligomerisation reactions of butadiene with diethyl malonate and acetaldehyde

The products of the reaction of butadiene with diethyl malonate catalysed by a palladium complex and of butadiene with acetaldehyde catalysed by a nickel(0) complex have been used in two syntheses of 3,7-dimethylpentadecan-2-ol.     

Spectra and structure of organogermanes: Part XX. Infrared and Raman spectra of (CH3)3GeNCO and (CH3)3GeNCS

The infrared and Raman spectra of gaseous and solid (CH₃)₃ GeNCO and solid (CH₃)₃GeNCS have been recorded over the frequency range 20–4000 cm^?1 . The Raman spectra of the liquids have also been recorded. Assignments of the normal modes have been made on the bases of band types, Raman depolarization values, and characteristic frequencies. Spectral data indicate that (CH₃)₃ GeNCO is non-linear in all phases and that (CH₃)₃GeNCS has a linear or quasi-linear heavy atom skeleton in the fluid phases.