Attractors for 2D-Navier-Stokes models with delays

The existence of an attractor for a 2D-Navier-Stokes system with delay is proved. The theory of pullback attractors is successfully applied to obtain the results since the abstract functional framework considered turns out to be nonautonomous. However, on some occasions, the attractors may attract not only in the pullback sense but in the forward one as well. Also, this formulation allows to treat, in a unified way, terms containing various classes of delay features (constant, variable, distributed delays, etc.). As a consequence, some results for the autonomous model are deduced as particular cases of our general formulation.     

Diffusion Structural Analysis Study of Titania Films Deposited by Sol-Gel Technique on Silica Glass

The diffusion structural analysis (DSA) was used to characterize microstructure changes of hydrous titania gel films under in situ conditions of heating. TG and DTA were used in order to elucidate the processes controlling the formation of anatase film during heating of hydrous titania gel film. The annealing of porosity and near surface structure defects of the dehydrated titania films was indicated by DSA in the temperature range 255–700°C as the decrease of radon release rate. It was demonstrated that the annealing was enhanced on heating in oxygen in comparison with heating in argon. The DSA experimental results were compared with model curves describing the radon diffusion mobility and the annealing of radon diffusion paths.     

Essay: Supersymmetry, the Cosmological Constant, and a Theory of Quantum Gravity in Our Universe

There are many theories of quantum gravity, depending on asymptotic boundary conditions, and the amount of supersymmetry. The cosmological constant is one of the fundamental parameters that characterizes different theories. If it is positive, supersymmetry must be broken. A heuristic calculation shows that a cosmological constant of the observed size predicts superpartners in the TeV range. This mechanism for SUSY breaking also puts important constraints on low energy particle physics models.     

Investigating buyer and seller strategies in online auctions

The annual turnover of online auctions is already in tens of billions of dollars and this amount is predicted to grow substantially over the next few years. Hence, it is important to know how buyers and sellers can influence their chances of success. Therefore, data were collected from eBay auctions for three different categories of collectible items, namely those with a published guide price, those with a rough guide price and those having no easily obtainable guide price. The options available to buyers and sellers of items were then analysed. It was found that it was hard for the seller to influence an item's achieved price significantly, apart from items with no guide price where the starting price could have an effect. Most bidders bid close to the current value and so there were insufficient data to determine the consequences of timing on the placing of high bids. For low bids, delaying a bid was found to improve significantly the chances of winning for one of the data sets.     

Estimate for the Best Approximation of Summable Functions of Several Variables with a Certain Symmetry of Fourier Coefficients

An upper bound for the best approximation of summable functions of several variables by trigonometric polynomials in the metric of L is determined in terms of Fourier coefficients. We consider functions representable by trigonometric series with certain symmetry of coefficients satisfying a multiple analog of the Sidon–Telyakovskii conditions.     

On Coercive Estimates for Solutions of Linear Systems of Hydrodynamic Type

Local and nonlocal coercive estimates in Lebesgue, Hölder, and Morrey–Campanato spaces are proved for solutions of linear stationary systems of hydrodynamic type. For this purpose, the technique proposed by Italian mathematicians for the study of solutions to equations and systems of elliptic and parabolic types is developed. Bibliography: 14 titles.     

Rovibrational matrix elements of polarizability of HD, HT and DT molecules

Fresh computations of rovibrational matrix elements of the polarizability α[=(α_||+2α_⊥)/3] and the polarizability anisotropy γ(=α_||−α_⊥) of the heteronuclear isotopomers, HD, HT, and DT, of the hydrogen molecule are presented. The computations combine the most accurate polarizability functions α(R) and γ(R) (R being the bond distance) on the one hand and the most accurate adiabatic potential on the other. The calculations are extended to the product operators xα and xγ where x is the centre of mass to centre of charge separation in the heteronuclear species. The latter matrix elements are needed, additionally, for elucidating the absorption intensities of some of the zero-phonon rovibrational transitions peculiar to the heteronuclear species in the crystalline phase.     

Scattering of excited atoms due to ion bombardment of metals

The spectrum and the spatial distribution of the emission of scattered particles upon bombardment of Be, Ti, Ta, and W with H and He ions were studied. The quantum yield and the velocity and angular distributions of the scattered excited particles were measured. Computer simulation of the scattering of H ions and He ions from the metals under study was performed with the use of the program TRIM-95. Agreement is observed between the calculated and experimentally measured angular distributions of the scattered particles.