Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements

We classify the homogeneous nilpotent orbits in certain Lie color algebras and specialize the results to the setting of a real reductive dual pair. For any member of a dual pair, we prove the bijectivity of the two Kostant-Sekiguchi maps by straightforward argument. For a dual pair we determine the correspondence of the real orbits, the correspondence of the complex orbits and explain how these two relations behave under the Kostant-Sekiguchi maps. In particular we prove that for a dual pair in the stable range there is a Kostant-Sekiguchi map such that the conjecture formulated in [6] holds. We also show that the conjecture cannot be true in general.     

Non-Singular,Vacuum, Stationary Space-Times with a Negative Cosmological Constant

We construct infinite dimensional families of non-singular stationary space times, solutions of the vacuum Einstein equations with a negative cosmological constant. Submitted: December 12, 2005. Accepted: May 22, 2006.     

Surface phenomena in the process of titanium hydride formation

Surface phenomena which occur in the course of titanium hydride TiH_x formation during the H₂ interaction with thin Ti films deposited in situ under UHV conditions were studied by means of surface potential and pressure measurements. The elementary steps of this process were distinguished and described.     

Liquid phase hydrogen transfer to cyclopentanone over MgO-I2 and MgO-RI catalysts

Instead of cyclopentanol, 2-cyclopentylidene-cyclopentanone is the main product of liquid phase hydrogen transfer from secondary alcohols to cyclopentanone in the presence of pure MgO [1]. In the present work it has been shown that a significant increase in the selectivity towards cyclopentanol has been observed for MgO treated with I₂ or alkyl iodides.     

Adsorption from solutions on patchwise heterogeneous solids

An attempt is made to develop the expression for surface excess, in adsorption of binary ideal mixtures on patchwise heterogeneous surfaces. The distribution of adsorption energies is evaluated for an adsorption system, investigated experimentally and theoretically by Sircar and Mayers.     

Segmented approximation of interference effects in atomic absorption spectrometry

A segmented approximation method is used for empirical modelling of interference effects in atomic absorption spectrometry. First- and second-degree polynomials are used in the modelling. The examples presented concern the determination of iron in presence of sodium, and calcium in the presence of strontium. In each case, the split polynomial models are more accurate and reliable than the single high-degree polynomial models.     

Sesquiterpene lactones of new stereostructural types from laser trilobum

The newly established structures of sesquiterpene lactones from Laser trilobum showed that these lactones belong among the stereostructural types of germacranolides, guaianolides, eudesmanolides and elemanolides.     

Quantum fluctuations in second-harmonic light generation

Second-harmonic light generation (SHLG) is analyzed from the viewpoint of the photon statistics of the fundamental and generated beams versus the path traversed by the two waves in the medium. The calculations lead to an anti-bunching effect for coherent incident light.     

On the invariant mass conjecture in general relativity

An asymptotic symmetries theorem is proved under certain hypotheses on the behaviour of the metric at spatial infinity. This implies that the Einstein-von Freud-ADM mass can be invariantly assigned to an asymptotically flat four dimensional end of an asymptotically empty solution of Einstein equations if the metric is a no-radiation metric or if the end is defined in terms of a collection of boost-type domains.On leave of absence from the Institute of Mathematics, Polish Academy of Sciences, Warsaw, PolandSupported in part by the Polish Ministry of Science Research Project CPBP 01.2 and by the NSF Grant PHY8503072 to Yale University