Traces on Noncommutative Homogeneous Spaces

We study properties of C*-algebraic deformations of homogeneous spaces G/Γ which are equivariant in the sense that they preserve the natural action of G by left translation. The center is shown to be isomorphic to C(G/G⁰_ρ) for a certain subgroup G⁰_ρ of G, and there is a 1-1 correspondence between normalised traces and probability measures on G/G⁰_ρ. This makes it possible to represent the deformed algebra as operators over L²(G/Γ). Applications to K-theory are also mentioned.     

Combined confocal and magnetic resonance microscopy

Confocal fluorescence optical microscopy and magnetic resonance microscopy are each used to study live cells in a minimally invasive way. Both techniques provide complementary information. Therefore, by examining cells simultaneously with both methodologies, more detailed information is obtained than is possible with each microscope individually. In this paper two configurations of a combined confocal and magnetic resonance microscope are described. The first configuration is capable of studying large single cells or three-dimensional cell agglomerates, whereas the second configuration is designed for the investigation of monolayers of mammalian cells. In both cases the sample compartment is part of a temperature regulated perfusion system. Images obtained with the combined system are shown forXenopus laevis oocytes, model JB6 tumor spheroids, and a single layer of Chinese hamster ovary cells. Finally, potential applications of the combined microscope are discussed.     

Cryostat attachment for IR spectrometers

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 50, No. 1, pp. 158–162, January, 1989.     

Eigenvalues of Two Parameter Polynomial Operator Pencils of Waveguide Type

The spectral structure of two parameter unbounded operator pencils of waveguide type is studied. Theorems on discreteness of the spectrum for a fixed parameter are proved. Variational principles for real eigenvalues in some parts of the root zones are established. In the case of n = 1 (quadratic pencils) domains containing the spectrum are described (see Fig. 1–3). Conditions in the definition of the pencils of waveguide type arise naturally from physical problems and each of them has a physical meaning. In particular a connection between the energetic stability condition and a perturbation problem for the coefficients is given.     

Interpolation and extrapolation of gamma detection efficiency curve as a function of distance

Summary The paper deals with the common mistake of interpolating calculation of the efficiency of gamma-detectors by the inverse square law of the distance of the source from the detector cap and suggests the use of the distance from the virtual point detector instead.     

A two-fraction model for the calculation of the resonance spectra of the complex permittivity of ice in the far infrared

A two-fraction model that makes it possible to calculate analytically the complex dielectric permittivity of ice in the far infrared and submillimeter wavelength ranges is proposed. The librational and vibrational fractions are considered. The first fraction, consisting of rigid dipoles executing anharmonic reorientations in defects of the structure, gives rise to the librational band of ice at 800 cm^?1. The second fraction consists of elastically vibrating oppositely charged H-bonded molecules. This fraction describes two bands of ice in the range 100–300 cm^?1, and the nonresonant background of dielectric losses in the submillimeter wavelength range. The dielectric permittivity spectra of ice calculated for the temperature of ?7°C are consistent with the experimental spectra. The spectra of ice at the temperature ?30°C are predicted.     

On the model of divacancies in germanium

A model of a divacancy which explains a number of experimental facts for Ge exposed to a flow of accelerated electrons at temperature T=77 K is proposed. The model explains the absence of photoconduction associated with photoexcitation of infrared absorption bands at 0.44 and 0.52 eV corresponding to divacancies; the difference in the values of activation energy for divacancy energy levels determined by optical and electrical methods; and the existence of the limiting position of the Fermi level in the forbidden gap in the case of irradiation with large radiation fluxes.     

Well-posed absorbing layer for hyperbolic problems

Summary. The perfectly matched layer (PML) is an efficient tool to simulate propagation phenomena in free space on unbounded domain. In this paper we consider a new type of absorbing layer for Maxwell's equations and the linearized Euler equations which is also valid for several classes of first order hyperbolic systems. The definition of this layer appears as a slight modification of the PML technique. We show that the associated Cauchy problem is well-posed in suitable spaces. This theory is finally illustrated by some numerical results. It must be underlined that the discretization of this layer leads to a new discretization of the classical PML formulation. Received May 5, 2000 / Published online November 15, 2001