Leading-Order Dynamics of Gravity-Driven Flows in?Free-Standing Soap Films

We derive the leading-order equations that govern the dynamics of the flow in a falling, free-standing soap film. Starting with the incompressible Navier?CStokes equations, we carry out an asymptotic analysis using parameters that correspond to a common experimental setup. We account for the effects of inertia, surface elasticity, pressure, viscous stresses, gravity, and air drag. We find that the dynamics of the flow is dominated by the effects of inertia, surface elasticity, gravity, and air drag. We solve the leading-order equations to compute the steady-state profiles of velocity, thickness, and pressure in an experiment in which the film is in the Marangoni elasticity regime. The computational results, which include a Marangoni shock, are in good accord with the experimental measurements.     

On the K-stability of complete intersections in polarized manifolds

We consider the problem of existence of constant scalar curvature Kähler metrics on complete intersections of sections of vector bundles. In particular we give general formulas relating the Futaki invariant of such a manifold to the weight of sections defining it and to the Futaki invariant of the ambient manifold. As applications we give a new Mukai–Umemura–Tian like example of Fano 5-fold admitting no Kähler–Einstein metric, and a strong evidence of K-stability of complete intersections in Grassmannians.     

Synthesis of uracil derivatives by oxidation of Fischer tungsten-carbene uracil complexes

A study on the oxidation of Fischer tungsten-carbene uracil complexes has been carried out. Several commonly used oxidants gave results strongly influenced by the presence of substituent on nitrogen atoms. In particular, usual oxidants failed in the oxidation of 3-alkyl uracil carbene complexes. Finally, we showed that t-butyl hydroperoxide is able to oxidize successfully also 3-alkyl uracil carbene complexes and can be used as a good alternative to the other methods.     

Characterization of disk media

It has been shown that the scalar properties of recording media can be characterized by a moving model that includes reversible and irreversible magnetizing processes. A test of this model for various media is reported in this paper. It is found that the model is capable of calculating accurate major and minor loops.     

Optical characterization of pigments by reflectance spectroscopy in support of UV laser cleaning treatments

The study of optical properties of artwork materials is of fundamental importance for laser-based restoration techniques. In this work, reflectance spectroscopic measurements and colorimetric analyses of painted wooden models were performed to discriminate between pigments on the basis of their spectral features. In particular, the spectral reflection factors of different white pigments were recorded with a fibre optics reflectance spectroscopy module, both before and after excimer laser (248 nm) irradiation. Colour data were obtained and monitored with an integrating sphere spectrophotometer and expressed with the CIE L^*a^*b^* colour coordinates. Moreover, the laser-induced morphological changes of the samples were investigated by scanning electron microscopy. PACS  42.62-b; 61.80.Ba; 07.60.Dq     

A converse result for approximation by a weighted Szász-Mirakyan operator

We prove that the weighted error of approximation by the Szász-Mirakyan-type operator introduced in [1] is equivalent to the modulus of smoothness of the function. This result is analogous to previous results for Bernstein-type operators obtained by Ditzian-Ivanov and Szabados. Research supported by Hungarian Scientific Research Fund (OTKA), Grant No. T-049196.