Investigation of multicomponent fluoride optical materials in the UV spectral region: I. Single crystals of Ca1−x R xF2+x (R = Sc, Y, La, Yb, Lu) solid solutions

Crystalline materials that are transparent in the vacuum UV spectral region and currently used have been reviewed. Transmission of crystals of solid solutions with the fluorite structure Ca_1?x R _xF_2+x (R = Sc, Y, La, Yb, Lu) in the UV and vacuum UV spectral regions has been investigated. It is shown that application of different methods of purification of fluorides from some impurities can significantly improve the optical quality of fluoride multicomponent crystals in the short-wavelength spectral region.     

Localization and the integer-quantized Hall effect: Diffusion constant for high Landau levels and white noise potential

The diffusion constant and the diagonal conductivity for non-interacting electrons in a two-dimensional, disordered system are studied. A homogeneous magnetic field perpendicular to the electron system is assumed. For weak short-range random potentials and high fields the Landau quantum numbern can be used as expansion parameter. In the limit of high Landau levels the system shows metallic behaviour. Corrections for finiten decrease the conductivity and indicate localized states in the whole energy band. A breakdown of the expansion and stronger localization are observed only for the lowest Landau levels if the typical experimental length scale of the quantized Hall effect is used.     

Vascular morphology by three-dimensional magnetic resonance imaging

A three-dimensional examination of blood vessels is provided using MR data from seven cases. The vascular surfaces are constructed with an algorithm that automatically follows the selected artery or vein and generates a projected three-dimensional gradient shaded image. Fast 3DFT pulse sequences were optimized to enhance the time-of-flight contrast of the intravascular region. By increasing the surface threshold value in a three-dimensional head study, the flesh of a patient's face was peeled away to demonstrate the superfacial temporal artery. Gated cardiac images show the great vessels and cardiac chambers. A three-dimensional view of the aorta shows an irregular surface in the vicinity of an adrenal tumor. 3D MR exams provide a non-invasive technique for assessing vascular morphology in a clinical setting.     

Mathematical modelling of the oxidation of nickel titanium alloys

A one-dimensional bulk reaction model for the oxidation of nickeltitanium is formulated, with preferential oxidation of titaniumbeing included. The modelling is directed at the better understandingof the dominant mechanisms involved in the oxidation processand their significance for the biocompatibility of the alloy.Two different regimes for the relative diffusivities of oxygenand the metals are investigated. By assuming fast bulk reactions,different asymptotic structures emerge in different parameterregimes and the resulting models take the form of moving boundaryproblems. Different profiles of nickel concentration are obtained:in particular a nickel-rich layer (observed in practice) ispresent below the oxide/metal interface for the case when oxygenand the metals diffuse at comparable rates.     

Universal Models For Real Submanifolds

In previous papers by the present author, a machinery for calculating automorphisms, constructing invariants, and classifying real submanifolds of a complex manifold was developed. The main step in this machinery is the construction of a “nice” model surface. The nice model surface can be treated as an analog of the osculating paraboloid in classical differential geometry. Model surfaces suggested earlier possess a complete list of the desired properties only if some upper estimate for the codimension of the submanifold is satisfied. If this estimate fails, then the surfaces lose the universality property (that is, the ability to touch any germ in an appropriate way), which restricts their applicability. In the present paper, we get rid of this restriction: for an arbitrary type (n,K) (where n is the dimension of the complex tangent plane, and K is the real codimension), we construct a nice model surface. In particular, we solve the problem of constructing a nondegenerate germ of a real analytic submanifold of a complex manifold of arbitrary given type (n,K) with the richest possible group of holomorphic automorphisms in the given class.