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.     

Substituent effects on 15N NMR chemical shifts in selected N-alkylthiohydroxamic acids. A comparative study

The 15N NMR spectra of three N-alkyl-delta-carbomethoxyvalerothiohydroxamic acids (2) and six synthesized N-isopropylbenzothiohydroxamic acids (3) were measured and compared with appropriate spectra of structurally similar hydroxylamines (1), benzohydroxamic acids (4), benzamides (5) and thiobenzamides (6). The analysis of the chemical shifts of the thiohydroxamic acids under investigation indicates that the inductive effect of the hydroxyl group rather than steric hindrance is responsible for non-additivity of the effect of substituents. Additionally, N-hydroxyl diminishes the effect of aromatic ring substituents on the 15N chemical shifts in the thiohydroxamic acids 3 which is approximately half that in the respective thiobenzamides 6. The chemical shift values correlate best with Brown's sigma+ parameter.     

Raman study of TiO2 role in SiO2-Al2O3-MgO-TiO2-ZnO glass crystallization

Tough glass-ceramic material of special mechanical properties with nanosize crystal phases formed by appropriately controlled crystallization was studied by Raman spectroscopy. It was obtained by TiO2 activated crystallization of Mg-aluminosilicate glass of SiO2-Al2O3-MgO-TiO2-ZnO composition. Crystallization was preceded by a change in the TiO2 structural position and state, which is manifested by a changed color of glass from yellow into blue shortly before the glass transformation (Tg) temperature. Raman spectroscopy was applied to explain the mechanism of this process and to establish the role of TiO2 in the early stage of glass crystallization that precedes a complete crystal phase formation. The starting glasses were found in almost complete disorder, since all bands were weak, broad and dominated by a Bose band at about 90 cm-1. After the sample annealing all bands turned out better resolved and the Bose band practically disappeared, both confirming the amorphous structure reorganization process. A multiplet observed in the vicinity of 150 cm-1 we assigned to the anatase and other titania structures that can be considered prime centers of crystallization. Finally, in the closest neighborhood of the Rayleigh line the low frequency mode characterizing nanoparticles was observed. According to this band theory, the mean size of initial titania crystallites is about 10nm for all samples, but the size distribution varies within factor two among them.     

Nonsmooth generalized guiding functions for periodic differential inclusions

We consider the periodic problem for differential inclusions in $$ \user2{\mathbb{R}}^{\rm N} $$ with a nonconvex-valued orientor field F(t, ζ), which is lower semicontinuous in $$ \zeta \in \user2{\mathbb{R}}^{\rm N} $$ Using the notion of a nonsmooth, locally Lipschitz generalized guiding function, we prove that the inclusion has periodic solutions. We have two such existence theorems. We also study the “convex” periodic problem and prove an existence result under upper semicontinuity hypothesis on F(t, ·) and using a nonsmooth guiding function. Our work was motivated by the recent paper of Mawhin-Ward [23] and extends the single-valued results of Mawhin [19] and the multivalued results of De Blasi-Górniewicz-Pianigiani [4], where either the guiding function is C¹ or the conditions on F are more restrictive and more difficult to verify.     

Fast broadcasting and gossiping in radio networks

We establish an O(nlog²n) upper bound on the time for deterministic distributed broadcasting in multi-hop radio networks with unknown topology. This nearly matches the known lower bound of Ω(nlogn). The fastest previously known algorithm for this problem works in time O(n^3/2). Using our broadcasting algorithm, we develop an O(n^3/2log²n) algorithm for gossiping in the same network model.     

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.     

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.