Visible Infra-red Double Extinction Measurements in Densely Laden Media,New Progress

This paper describes new progress obtained with an optical technique called V.I.D.E. (Visible Infra-red Double Extinction) which simultaneously measures mean particle size in the range of 10–120 μm and mean number density in densely laden media (up to 0.1% volume fraction). The underlying theory, taking account of multiple light scattering, is recalled. Simultaneous size and concentration measurements are obtained by simultaneously recording transmittances of the medium at two well chosen wavelengths. Experimental results for suspensions of glass particles in air, are described and discussed. The size of particles given by the technique agrees with that given by optical microscopy and Malvern diffractometry. The V.I.D.E. technique is shown to be very suitable to investigate dense media whose optical thickness is up to nine and for which other techniques fail.     

On lightlike geometry in indefinite Kenmotsu manifolds

We investigate some geometric aspects of lightlike hypersurfaces of indefinite Kenmotsu manifolds, tangent to the structure vector field, by paying attention to the geometry of leaves of integrable distributions. Theorems on parallel vector fields, Killing distribution, geodesibility of their leaves are obtained. The geometric configuration of such lightlike hypersurfaces and leaves of its screen integrable distributions are established. We show that no totally contact umbilical leaf of a screen integrable distribution of a lightlike hypersurface can be an extrinsic sphere. We also prove that the geometry of any leaf of an integrable distribution is closely related to the geometry of a normal bundle.     

Detection of Cadmium and Copper Cations Using Amorphous Nitrogenated Carbon Thin Film Electrodes

Nitrogenous amorphous carbon (a‐CN_x) thin films were deposited by radio‐frequency cathodic magnetron sputtering (13.56 MHz) on polished and etched titanium disks. While these films are cheaper to prepare than commonly reported carbon‐based electrodes, the usable electrochemical window in aqueous solution is within the same range and spans from ?1.5 to +1.8 V vs. SCE. The electrochemical reactivity was tested using the ferri‐ferrocyanide redox couple as a function of the thin films preparation parameters. The obtained electrochemical properties allow the use of these a‐CN_x thin films for stripping electroanalysis of cations in water, minimizing potential solvent reactivity. Cadmium and copper were used to test these detection abilities. Better analytical properties (notably sensitivity and linearity) were obtained as compared to a commercial boron doped diamond electrode. Preliminary competition/interaction experiments for these two cations were performed.     

The Universal Connection and Metrics on Moduli Spaces

We introduce a class of metrics on gauge theoretic moduli spaces. These metrics are made out of the universal matrix that appears in the universal connection construction of M.S. Narasimhan and S. Ramanan. As an example we construct metrics on the c₂=1 SU(2) moduli space of instantons on ⁴ for various universal matrices.Acknowledgement It is a pleasure to thank M. Blau, K. Narain, M.S. Narasimhan and T. Ramadas for many useful discussions. F. Massamba would like to thank the Abdus Salam ICTP for a fellowship. This research was supported in part by EEC contract HPRN-CT-2000-00148.     

Screen Integrable Lightlike Hypersurfaces of Indefinite Sasakian Manifolds

We investigate lightlike hypersurfaces of indefinite Sasakian manifolds, tangent to the structure vector field ξ and whose screen distribution is integrable. We prove some results on parallel vector fields and on a leaf of the integrable distribution of this class. A theorem on a geometrical configuration of the screen distribution is obtained. We show that any totally contact umbilical leaf of a screen integrable distribution of a lightlike hypersurface is an extrinsic sphere. Received: February 22, 2008., Revised: June 18, 2008., Accepted: July 10, 2008.     

Symmetries of Null Geometry in Indefinite Kenmotsu Manifolds

Null hypersurfaces have metrics with vanishing determinants and this degeneracy of these metrics leads to several difficulties. In this paper, null hypersurfaces of indefinite Kenmotsu space forms, tangent to the structure vector field, are studied with specific attention to locally symmetric, semi-symmetric and Ricci semi-symmetric null hypersurfaces. We show that locally symmetric and semi-symmetric null hypersurfaces are totally geodesic and parallel. These also hold for Ricci semi-symmetric null hypersurfaces, under a certain condition. We prove that, in null Einstein hypersurfaces of an indefinite Kenmotsu space form, tangent to the structure vector field, the local symmetry, semisymmetry and Ricci semi-symmetry notions are equivalent. For totally contact umbilical null hypersurfaces, we show that there are η-“Weyl” connections adapted to the induced structure on the null hypersurface.     

On semi-parallel lightlike hypersurfaces of indefinite Kenmotsu manifolds

We study semi-parallel lightlike hypersurfaces of an indefinite Kenmotsu manifold, tangent to the structure vector field. Some Theorems on parallel and semi-parallel vector field, geodesibility of lightlike hypersurfaces are obtained. The geometrical configuration of such lightlike hypersurfaces is established. We prove that, in totally contact umbilical lightlike hypersurfaces of an indefinite Kenmotsu manifold which has constant ${\overline{\phi}}$ -holomorphic sectional curvature c, tangent to the structure vector field and such that its distribution is parallel, the parallelism and semi-parallelism notions are equivalent.     

Lightlike Hypersurfaces in Indefinite Trans-Sasakian Manifolds

This paper deals with lightlike hypersurfaces of indefinite trans-Sasakian manifolds of type (α, β), tangent to the structure vector field. Characterization Theorems on parallel vector fields, integrable distributions, minimal distributions, Ricci-semi symmetric, geodesibility of lightlike hypersurfaces are obtained. The geometric configuration of lightlike hypersurfaces is established. We prove, under some conditions, that there are no parallel and totally contact umbilical lightlike hypersurfaces of trans-Sasakian space forms, tangent to the structure vector field. We show that there exists a totally umbilical distribution in an Einstein parallel lightlike hypersurface which does not contain the structure vector field. We characterize the normal bundle along any totally contact umbilical leaf of an integrable screen distribution. We finally prove that the geometry of any leaf of an integrable distribution is closely related to the geometry of a normal bundle and its image under ${\overline{\phi}}$ .