Bogomolov restriction theorem for Higgs bundles

Let (E,θ) be a stable Higgs bundle of rank r on a smooth complex projective surface X equipped with a polarization H. Let C⊂X be a smooth complete curve with [C]=n⋅H. If where , then we prove that the restriction of (E,θ) to C is a stable Higgs bundle. This is a Higgs bundle analog of Bogomolov's restriction theorem for stable vector bundles.     

Broadband dielectric relaxation study on a diluted solution of a ferroelectric liquid crystal by time domain reflectometry

In this work, complex permittivity measurements on a diluted solution of the ferroelectric liquid crystal, 4-[(S,S)-2,3-epoxyhexyloxy]-phenyl 4-(decyloxy)-benzoate, which shows ferroelectric smectic C phase (S*_C), have been performed. Using time domain reflectometry, at frequencies between 10 MHz and 10 GHz, in the temperature range from 50°C down to 10°C for every 10°C, at 5, 10 and 30 wt.% in benzene we observe two independent relaxation processes around 150 MHz and 2 GHz. It is shown that the high frequency process is due to the internal molecular reorientations while the low frequency one is due to molecular orientation around the long molecular axis. It is concluded that the reorientation around the long axis is hindered and leads to a resultant macroscopic polarization.     

The galilean group in 2+1 space-times and its central extension

The problem of constructing the central extensions, by the circle group, of the group of Galilean transformations in two spatial dimensions; as well as that of its universal covering group, is solved. Also solved is the problem of the central extension of the corresponding Lie algebra. We find that the Lie algebra has a three parameter family of central extensions, as does the simply-connected group corresponding to the Lie algebra. The Galilean group itself has a two parameter family of central extensions. A corollary of our result is the impossibility of the appearance of non-integer-valued angular momentum for systems possessing Galilean invariance.     

Novel nitration of estrone by metal nitrates

Nitration of estrone has been investigated with different types of metal salts in the presence of solid surfaces under various conditions.     

Exact Controllability and Boundary Stabilization of Torsional Vibrations of an Internally Damped Flexible Space Structure

In this paper, we study the exact controllability and boundary stabilization of the torsional vibrations of a flexible space structure (such as a solar cell array) modeled by a rectangular panel, incorporating the material damping of the structure. The panel is hoisted at one end by a rigid hub and the other end is totally free. For the attachment of this hub on one side of the panel, the hub dynamics leads to a nonstandard boundary condition. To incorporate internal damping of the material, we assume Voigt-type viscoelasticity of the structure. Exact controllability theory is established using the Hilbert uniqueness method by means of a control torque applied only on the rigid hub of the panel. At the same time, uniform exponential energy decay rate is obtained directly for the solution of this problem.     

A fluctuations limit for scaled age distributions and weighted Sobolev spaces

It is shown that under the central-limit scaling, the fluctuations of the space—time renormalized age distributions of particles (whose development is controlled by critical linear birth and death processes) around the law-of-large-numbers limit converge in a Hilbert space (containing the class of signed Radon measures with finite moment generating functionals) to a continuous Gaussian process satisfying a Langevin equation. So far, the space of rapidly decreasing functions has been considered to be the natural state space for the kind of limit theorem considered here. However, the space of rapidly decreasing functions is not suitable in the present context and we are led to define an appropriate family of Sobolev spaces. In fact, we construct a scale of Hilbert spaces based on the eigenfunctions expansions of an elliptic operator defined on a weightedL ²-space.This research was partially supported by an NSERC of Canada grant.     

Thermal quenching of luminescence in erbium doped semiconductors

The nature of the temperature dependence of luminescence intensity from Er⁺ ions in GaInAsP, Si, InP, GaAs, AlGaAs, ZnTe, as observed by Favennecet al [1] has been examined in terms of a double exponential model. The smaller activation energy is found to be 58–100 meV, characteristic of a localized energy barrier at the Er⁺ centre while the higher activation energy is approximately 0.8E _g attributed to an Auger non-radiative process of carrier excitation into bands. This model has been found to describe the observed temperature dependences with reasonably good agreement.     

Order–disorder transition in nanocrystalline Ni3Al prepared by a chemical route

Ni₃Al alloys of nanometer dimensions in the range 10–38 nm could be synthesized by reaction sintering of sol–gel-derived Ni/SiO₂ nanocomposite and commercially available micrometer-sized aluminum powder. The sintering was carried out at a temperature of 923 K and a pressure of 2.4 MPa. By a suitable choice of sintering conditions a disordered phase of Ni₃Al was stabilized. The disordered phase could be converted to an ordered one by an increase of heat treatment temperature.     

Transition metal complexes of furfural and benzil schiff bases derived from S-benzyldithiocarbazate

New nickel(II), copper(II), cobalt(III) and rohdium(III) complexes of two Schiff base ligands formed by condensation of furfural and benzil with S-benzyldithiocarbazate have been synthesized and characterized by elemental analysis and magnetic and spectroscopic measurements. The nickel(II) complexes, Ni(NS)₂ and Ni(ONS)₂ (NS and ONS stand for the uninegatively charged furfural and benzil Schiff bases, respectively) are square-planar and octahedral, respectively. The Cu(NS)Cl complex is paramagnetic with a magnetic moment fo 1.73 B.M. A halogen-bridged dimeric structure is proposed for this complex. The copper(II) complex, Cu(ONS)Cl is diamagnetic, suggesting strong antiferromagnetic interactions between a pair of copper(II) ions in a thiolo sulphur-bridged dimeric or polymeric structure. Cobalt(II) ions are oxidized in the presence of the Schiff bases with the concomitant formation of cobalt(III) complexes of empirical formulae, Co(NS)₃, Co(ONS)₂ClO₄ and Co(ONS)₂Cl, respectively, which are spin-paired and octahedral. The rhodium(III) complex of the furfural Schiff base, Rh(NS)₂Cl is tentatively assigned a halogen-bridged dimeric structre.