The existence of global in space variables solution for non-linear subelliptic equation of floating water

The existence of global in space variables solutions for a class of non-linear subelliptic evolution operators is proved. A Cauchy problem and an initial-boundary value problem are considered using the contraction theorem and Galerkin methods.     

The performance of Hg1−x Zn x Te photodiodes

This paper considers the Hg_1–x Zn _x Te alloy system as a potential material for the fabrication of infrared photodiodes. The influence of different junction current components (diffusion, tunneling and depletion layer currents) on the R ₀ A product of n⁺-pHg_1–x Zn _x Te photodiodes is analysed. The upper theoretical limits of the R ₀ A product and detectivity are determined. Results of calculations are compared with experimental data reported by other authors and those measured in our laboratory. Preliminary results on related technology and the properties of Hg_1–x Zn _x Te prepared by the ion-etching technique are presented.     

Additive Schwarz Method for Mortar Discretization of Elliptic Problems with <Emphasis Type="Italic">P</Emphasis><Subscript>1</Subscript> Nonconforming Finite Elements

An additive Schwarz preconditioner for nonconforming mortar finite element discretization of a second order elliptic problem in two dimensions with arbitrary large jumps of the discontinuous coefficients in subdomains is described. An almost optimal estimate of the condition number of the preconditioned problem is proved. The number of preconditioned conjugate gradient iterations is independent of jumps of the coefficients and is proportional to (1+log(H/h)), where H,h are mesh sizes. AMS subject classification (2000) 65N55, 65N30, 65N22     

Weakened constraints from b-->sgamma on supersymmetry flavor mixing due to next-to-leading-order corrections

We examine the process B-->X(s)gamma in minimal supersymmetry (SUSY) with general squark flavor mix-ings. We include all relevant next-to-leading order (NLO) QCD corrections and dominant NLO SUSY effects from the gluino. We find that gluino-squark corrections to down-type quark masses induce large NLO corrections to the dominant Wilson coefficients whose size is often similar to those at LO, es-pecially at large tan(beta. For micro>0, destructive interference and suppression by the renormalization group running lead to a "focusing effect" of reducing the size of gluino corrections to the branching ratio, and also of reducing the LO sensitivity to flavor mixings among squarks. Constraints from B(B-->X(s)gamma) on the SUSY-breaking scale can become significantly weakened relative to the minimal flavor violation case, even, at large tan(beta, for small flavor mixings. The case of micro<0 also becomes allowed.     

The study of atropoisomers of meso-tetrakis[2.2]paracyclophanylporphyrin

Theoretical considerations of atropoisomers of the title compound have revealed the existence of a large number of stable isomeric species. Syntheses, carried out according to two procedures at widely separated temperatures, resulted in the formation of mixtures of atropoisomers in good yield. Two isomeric fractions have been separated and characterized. Some analytical methods have been worked out and have proved useful in separational techniques.     

5,7,12,14-Tetramethyldimethoxybenzo[b,i][1,4,8,11]tetraazacyclodecine,a new tumoricidal pseudo-porphyrin

The title compound, a mixture of two isomers differing in the position of a methoxy substituent in one benzene ring, was obtained in a Ni-templated synthesis directly as a water soluble dihydrochloride of the free base. The cyclic voltametry study indicated that in a neutral solution the reduction and oxidation are irreversible one electron processes, the latter leading to cation radical undergoing polymerization, a process followed by deposition of a film on the electrode. In 1,2-dichloroethane the cation radical is oxidized to a dication, both species being much less stable than those originating from meso-tetraphenylporphyrin. The title compoud at 2.5 × 10^?5 M in Tris buffer showed a 50% inhibition of the growth of malignant melanoma cells as compared to a 44% inhibition shown by a water soluble meso-monomethoxy-tris(N-methylpyridinium)porphyrin. The exposure to light for 30 minutes at 2.5 times smaller concentration increased the inhibition caused by the pseudo-porphyrin from 9% to 49%.     

Reduced products which are not saturated

Summary IfT is a complete theory of Boolean algebra, then we writeA ⊲_T B to denote that for every cardinal κ and every κ-regular filter over a setI such that the Boolean algebra 2 _F ^I of all subsets ofI reduced byF is a model ofT, the reduced powerA _F ^I isK ⁺-saturated wheneverB _F ^I isK ⁺-saturated. The relation ⊲_T generalizes the relation ◃ introduced by Keisler. As in the case of Keisler's ◃ it happens that ⊲_T’s are relations between complete theories, i.e. ifA≡B thenA ⊲_T B andB ⊲_T A. In this paper some examples of theories which are maximal (minimal) with respect to ⊲_T’s are provided and the relations ⊲_T are compared with each other. Presented by J. Mycielski     

Gravitational Aharonov-Bohm Effect

We study a purely gravitational Aharonov-Bohm effect. The space-time curvature is concentrated in the quasiregular singularity of a cosmic string, outside of which space-time is (locally) flat. The symmetries of this field configuration are described by the groupoid symmetries rather than by the usual group symmetries. The groupoid in question is formed by homotopy classes of piecewise smooth paths in the cosmic string region. A gravitational counterpart of the Aharonov-Bohm effect occurs if the symmetry of the system, with respect to the groupoid action, is broken down.     

Microstructure and selected properties of hot-work tool steel with PVD coatings after laser surface treatment

The paper presents the effect of HPD laser treatment on the microstructure and selected properties of the PVD CrN, (Ti,Al) and Ti(C,N) coatings deposited onto hot-work tool steel substrates. The microstructure and surface topography of the investigated samples are characteristic of the diversified morphology connected with the applied laser beam power. Employment of laser beam at 0.7 kW power to the laser treatment of samples with Ti(C,N) coatings causes clear coating adhesion growth because of the diffusive processes induced by heat release. Because of the higher value of the (Ti,Al)N absorption coefficient one can state that the observed substrate materials change and finally coatings destruction in case of those samples is the most noticeable. The moderate effect of the laser beam treatment of the hot-work tool steel with the PVD coating was observed for CrN coatings. However, for laser beam power above 0.5 kW differences in the thermal expansion coefficients of the substrate materials and coatings generate coating crackings.     

UV‐induced transformations of matrix‐isolated 1,3,4‐thiadiazole‐2‐thiones

Monomers of 5‐mercapto‐1,3,4‐thiadiazole‐2‐thione (bismuthiol) were studied using an experimental matrix‐isolation technique as well as by carrying out theoretical quantum chemical calculations. The calculations, performed using the quadratic configuration interaction method with single and double excitations (QCISD)/6‐31++G(d,p)//DFT(B3LYP)/6‐311++G(2d,p), predict that the thione–thiol tautomer of bismuthiol should be significantly (by more than 19 kJ mol^?1) more stable than other tautomeric forms. Accordingly, only the signatures of the thione–thiol tautomer were observed in the FT‐IR spectrum of bismuthiol, recorded directly after deposition of an Ar matrix. UV (λ > 320 nm) irradiation induced the conversion of the thione–thiol tautomer into the dithiol form. Analogous investigations were carried out for two related compounds: 5‐methyl‐1,3,4‐thiadiazole‐2‐thione and 5‐methylthio‐1,3,4‐thiadiazole‐2‐thione. For these two species, only the thione tautomeric forms were observed after deposition of Ar matrices. These tautomers were predicted (by QCISD calculations) to be more stable (by at least 19 kJ mol^?1) than other tautomeric forms. Upon UV irradiation, the most stable thione forms of these compounds were transformed into the corresponding thiol tautomers. Direct observation of the thione → thiol phototautomeric processes provides a clear proof that intramolecular proton transfer reaction can occur in molecules, such as bismuthiol, in spite of the increased NH···S distance, in comparison to other phototautomerizing species studied so far. All the isomers of the studied compounds (substrates and products of the photoreactions) were identified by comparison of their IR spectra with the spectra calculated at the DFT(B3LYP)/6‐311++G(2d,p) level of theory for possible isomeric structures. Copyright © 2009 John Wiley & Sons, Ltd.