On the proximity relation between two surface-melted clusters involved in inter-cluster mass-transfer

We explore the way free particles produced by dissociating ``particle-hole pairs'' on a surface-melted cluster can be transferred to a second, nearby surface-melted cluster. This mass transport is based on an inter-cluster direct transfer mechanism of the particles. We found that in this particular case one cluster may grow at the expense of another, obeying a temporal power law with the exponent 1/2 for the average radius R = const t^{1/2}. The change from the expected universal power law R = const t^{1/3} is a consequence of the proximity relation between these two clusters which lead to enhance the effective transport rates.Comment: 8 pages, 1 fig., Eur. Phys. J. D - to appea

Vanishing of second cohomology for tensor products of typeII1_1 von Neumann algebras

We show that the second cohomology group $H^2(M\overline\otimes N, M\overline\otimes N)$ is always zero for arbitrary type II$_1$ von Neumann algebras $M$ and $N$.Comment: 13 page

On the optimal dividend problem for a spectrally negative L\'{e}vy process

In this paper we consider the optimal dividend problem for an insurance company whose risk process evolves as a spectrally negative L\'{e}vy process in the absence of dividend payments. The classical dividend problem for an insurance company consists in finding a dividend payment policy that maximizes the total expected discounted dividends. Related is the problem where we impose the restriction that ruin be prevented: the beneficiaries of the dividends must then keep the insurance company solvent by bail-out loans. Drawing on the fluctuation theory of spectrally negative L\'{e}vy processes we give an explicit analytical description of the optimal strategy in the set of barrier strategies and the corresponding value function, for either of the problems. Subsequently we investigate when the dividend policy that is optimal among all admissible ones takes the form of a barrier strategy.Comment: Published at http://dx.doi.org/10.1214/105051606000000709 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

N-doped TiO2 coatings grown by atmospheric pressure MOCVD for visible light-induced photocatalytic activity

N-doped TiO2 films were deposited by atmospheric pressure CVD from titanium tetra-isopropoxide (TTIP) and N2H4 as reactive gas in the temperature range 400–500 °C on various substrates. The films grown at 400 °C are amorphous and exhibit a compact structure and a smooth surface morphology. Increasing the deposition temperature first leads to the crystallization in the anatase structure (temperature range 410–450 °C) and then to the formation of rutile, so that an anatase-rutile mixture is observed in the temperature range 450–500 °C. Correlation between the structure, the morphology, optical properties, hydrophilicity and photocatalytic activity of the thin films both under UVand VIS light are presented and discussed in relation with deposition conditions

Effect of H2 on the microstructure and properties of TiO2 films grown by atmospheric pressure MOCVD on steel substrates

TiO2 thin films were deposited under atmospheric pressure by MOCVD in the range 400-600 °C on various steel substrates under hydrogen ambiance. It is unusual to study the growth of functional oxide layers under H2 partial pressure, i.e. a reactive gas generally used as reductive atmosphere in CVD. Titanium tetra-isopropoxide was used as single source precursor of Ti and O. The growth rate of TiO2 layers grown under nitrogen increases with the temperature and reaches a maximum in the range 500-550 °C. At these temperatures the diffusion of substrate ions enhances the formation of rutile leading to a lower UV photocatalytic activity. Addition of H2 in the input gas phase during the deposition (i) reduces the formation of interface oxide layer, (ii) prevents the diffusion of cations from the steel substrate toward the TiO2 layer and (iii) favors the growth of anatase. This leads to an increase of photocatalytic efficiency under UV irradiation

Growth of TiO2 thin films by AP-MOCVD on stainless steel substrates for photocatalytic applications

TiO2 thin films were deposited under atmospheric pressure by MOCVD in the temperature range 400–600 °C on stainless steel and Si(100) substrates. Titanium tetraisopropoxide (TTIP) was used as Ti and O source. Single-phased anatase and bi-phased (anatase/rutile) coatings with controlled composition have been deposited depending on the temperature and the TTIP mole fraction. The films grown on stainless steel at low temperature (b420 °C) and low TTIP mole fraction (b10−4) are constituted of pure anatase and they exhibit a high photocatalytic activity under UV light and a high hydrophilicity. In the temperature range 430–600 °C the rutile starts growing leading to anatase/rutile mixtures and subsequently to a progressive decrease of both photocatalytic activity and wettability. Correlations between functional properties and microstructure of the films are discussed

Exit problem of a two-dimensional risk process from the quadrant: Exact and asymptotic results

Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem considered is that of the corresponding two-dimensional risk process first leaving the positive quadrant; another is that of entering the negative quadrant. When the claims arrive according to a Poisson process, we obtain a closed form expression for the ultimate ruin probability. In the general case, we analyze the asymptotics of the ruin probability when the initial reserves of both companies tend to infinity under a Cram\'{e}r light-tail assumption on the claim size distribution.Comment: Published in at http://dx.doi.org/10.1214/08-AAP529 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Supersymmetric Canonical Commutation Relations

We present unitarily represented supersymmetric canonical commutation relations which are subsequently used to canonically quantize massive and massless chiral,antichiral and vector fields. The massless fields, especially the vector one, show new facets which do not appear in the non superymmetric case. Our tool is the supersymmetric positivity induced by the Hilbert-Krein structure of the superspace.Comment: 14 page