W-superalgebras as truncation of super-Yangians

We show that some finite W-superalgebras based on gl(M|N) are truncation of the super-Yangian Y(gl(M|N)). In the same way, we prove that finite W-superalgebras based on osp(M|2n) are truncation of the twisted super-Yangians Y(gl(M|2n))^{+}. Using this homomorphism, we present these W-superalgebras in an R-matrix formalism, and we classify their finite-dimensional irreducible representations.Comment: Latex, 32 page

Phase mapping of aging process in InN nanostructures: oxygen incorporation and the role of the zincblende phase

Uncapped InN nanostructures undergo a deleterious natural aging process at ambient conditions by oxygen incorporation. The phases involved in this process and their localization is mapped by Transmission Electron Microscopy (TEM) related techniques. The parent wurtzite InN (InN-w) phase disappears from the surface and gradually forms a highly textured cubic layer that completely wraps up a InN-w nucleus which still remains from original single-crystalline quantum dots. The good reticular relationships between the different crystals generate low misfit strains and explain the apparent easiness for phase transformations at room temperature and pressure conditions, but also disable the classical methods to identify phases and grains from TEM images. The application of the geometrical phase algorithm in order to form numerical moire mappings, and RGB multilayered image reconstructions allows to discern among the different phases and grains formed inside these nanostructures. Samples aged for shorter times reveal the presence of metastable InN:O zincblende (zb) volumes, which acts as the intermediate phase between the initial InN-w and the most stable cubic In2O3 end phase. These cubic phases are highly twinned with a proportion of 50:50 between both orientations. We suggest that the existence of the intermediate InN:O-zb phase should be seriously considered to understand the reason of the widely scattered reported fundamental properties of thought to be InN-w, as its bandgap or superconductivity.Comment: 18 pages 7 figure

Soliton surfaces associated with symmetries of ODEs written in Lax representation

The main aim of this paper is to discuss recent results on the adaptation of the Fokas-Gel'fand procedure for constructing soliton surfaces in Lie algebras, which was originally derived for PDEs [Grundland, Post 2011], to the case of integrable ODEs admitting Lax representations. We give explicit forms of the \g-valued immersion functions based on conformal symmetries involving the spectral parameter, a gauge transformation of the wave function and generalized symmetries of the linear spectral problem. The procedure is applied to a symmetry reduction of the static $\phi^4$-field equations leading to the Jacobian elliptic equation. As examples, we obtain diverse types of surfaces for different choices of Jacobian elliptic functions for a range of values of parameters.Comment: 14 Pages, 2 figures Conference Proceedings for QST7 Pragu

Estimation of translation and rotation by Fourier transform

In the research area of vision-aided motion sensors, the rotation parameters can be computed from the motion in the picture . Th e properties of translation and rotation in the frequency domain of the Fourier transform are used here . This study is restricted to rigid-body transformations, but other application domains, such as matching of rigidly misaligned images, also exist .Dans l'idée de compléter les capteurs mécaniques de mouvement par des techniques à base de vision, nous analysons le déplacement d'une image pour en déduire les paramètres de rotation de la caméra. L'approche choisie est celle de la transformation de Fourier dont on utilise les propriétés d'invariance par rotation et de déphasage par translation. L'application, réduite pour cette étude aux rotations de caméra, peut s'étendre à tous les domaines liés au recalage d'images

Detection and construction of an elliptic solution to the complex cubic-quintic Ginzburg-Landau equation

In evolution equations for a complex amplitude, the phase obeys a much more intricate equation than the amplitude. Nevertheless, general methods should be applicable to both variables. On the example of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation (CGL5), we explain how to overcome the difficulties arising in two such methods: (i) the criterium that the sum of residues of an elliptic solution should be zero, (ii) the construction of a first order differential equation admitting the given equation as a differential consequence (subequation method).Comment: 12 pages, no figure, to appear, Theoretical and Mathematical Physic

Failure mechanism of AlN nanocaps used to protect rare earth-implanted GaN during high temperature annealing

The structural properties of nanometric AlN caps, grown on GaN to prevent dissociation during high temperature annealing after Eu implantation, have been characterized by scanning electron microscopy and electron probe microanalysis. The caps provide good protection up to annealing temperatures of at least 1300 degrees C, but show localized failure in the form of irregularly shaped holes with a lateral size of 1-2 µm which extend through the cap into the GaN layer beneath. Compositional micrographs, obtained using wavelength dispersive x-ray analysis, suggest that these holes form when GaN dissociates and ejects through cracks already present in the as-grown AlN caps due to the large lattice mismatch between the two materials. Implantation damage enhances the formation of the holes during annealing. Simultaneous room temperature cathodoluminescence mapping showed that the Eu luminescence is reduced in N-poor regions. Hence, exposed GaN dissociates first by outdiffusion of nitrogen through AlN cracks, thereby opening a hole in the cap through which Ga subsequently evaporates

Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equation

We look for singlevalued solutions of the squared modulus M of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation. Using Clunie's lemma, we first prove that any meromorphic solution M is necessarily elliptic or degenerate elliptic. We then give the two canonical decompositions of the new elliptic solution recently obtained by the subequation method.Comment: 14 pages, no figure, to appear, Acta Applicandae Mathematica

Surfaces immersed in Lie algebras associated with elliptic integrals

The main aim of this paper is to study soliton surfaces immersed in Lie algebras associated with ordinary differential equations (ODE's) for elliptic functions. That is, given a linear spectral problem for such an ODE in matrix Lax representation, we search for the most general solution of the wave function which satisfies the linear spectral problem. These solutions allow for the explicit construction of soliton surfaces by the Fokas-Gel'fand formula for immersion, as formulated in (Grundland and Post 2011) which is based on the formalism of generalized vector fields and their prolongation structures. The problem has been reduced to examining three types of symmetries, namely, a conformal symmetry in the spectral parameter (known as the Sym-Tafel formula), gauge transformations of the wave function and generalized symmetries of the associated integrable ODE. The paper contains a detailed explanation of the immersion theory of surfaces in Lie algebras in connection with ODE's as well as an exposition of the main tools used to study their geometric characteristics. Several examples of the Jacobian and P-Weierstrass elliptic functions are included as illustrations of the theoretical results.Comment: 22 pages, 3 sets of figures. Keywords: Generalized symmetries, integrable models, surfaces immersed in Lie algebra

Discovery of the optical counterpart to the X-ray pulsar SAX J2103.5+4545

We report optical and infrared photometric and spectroscopic observations that identify the counterpart to the 358.6-s X-ray transient pulsar SAX J2103.5+4545 with a moderately reddened V=14.2 B0Ve star. This identification makes SAX J2103.5+4545 the Be/X-ray binary with the shortest orbital period known, Porb= 12.7 days. The amount of absorption to the system has been estimated to be Av=4.2+-0.3, which for such an early-type star implies a distance of about 6.5 kpc. The optical spectra reveal major and rapid changes in the strength and shape of the Halpha line. The Halpha line was initially observed as a double peak profile with the ratio of the intensities of the blue over the red peak greater than one (V/R > 1). Two weeks later this ratio reversed (V/R< 1). Subsequently, in less than a month, the emission ceased and Halpha appeared in absorption. This fast spectral variability is interpreted within the viscous decretion disc model and demonstrates the significant role of the neutron star on the evolution of the circumstellar disc around the Be star. The implications of the small orbit and moderate eccentricity on the spin period of the neutron star are discussed.Comment: 9 pages, 6 figures, accepted for publication in A&