Stabilizer rigidity in irreducible group actions

We consider irreducible actions of locally compact product groups, and of higher rank semi-simple Lie groups. Using the intermediate factor theorems of Bader–Shalom and Nevo–Zimmer, we show that the action stabilizers, and all irreducible invariant random subgroups, are co-amenable in their normal closure. As a consequence, we derive rigidity results on irreducible actions that generalize and strengthen the results of Bader–Shalom and Stuck–Zimmer.     

A theoretical investigation of structural,mechanical, electronic and thermoelectric properties of orthorhombic CH<Subscript>3</Subscript>NH<Subscript>3</Subscript>PbI<Subscript>3</Subscript>

The structural, mechanical, electronic and thermoelectric properties of the low temperature orthorhombic perovskite phase of CH₃NH₃PbI₃ have been investigated using density functional theory (DFT). Elastic parameters bulk modulus B, Young’s modulus E, shear modulus G, Poisson’s ratio ν and anisotropy value A have been calculated by the Voigt–Reuss–Hill averaging scheme. Phonon dispersions of the structure were investigated using a finite displacement method. The relaxed system is dynamically stable, and the equilibrium elastic constants satisfy all the mechanical stability criteria for orthorhombic crystals, showing stability against the influence of external forces. The lattice thermal conductivity was calculated within the single-mode relaxation-time approximation of the Boltzmann equation from first-principles anharmonic lattice dynamics calculations. Our results show that lattice thermal conductivity is anisotropic, and the corresponding lattice thermal conductivity at 150 K was found to be 0.189, 0.138, and 0.530 Wm^?1K^?1 in the a, b, and c directions. Electronic structure calculations demonstrate that this compound has a DFT direct band gap at the gamma point of about 1.57 eV. The electronic transport properties have been calculated by solving the semiclassical Boltzmann transport equation on top of DFT calculations, within the constant relaxation time approximation. The Seebeck coefficient S is almost constant from 50 to 150 K. At temperatures 100 and 150 K, the maximal figure of merit is found to be 0.06 and 0.122 in the direction of the c-axis, respectively.     

On the Number of Bases of Bicircular Matroids

Let t(G) be the number of spanning trees of a connected graph G, and let b(G) be the number of bases of the bicircular matroid B(G). In this paper we obtain bounds relating b(G) and t(G), and study in detail the case where G is a complete graph K_n or a complete bipartite graph K_n,m.Received April 25, 2003     

Development of a rapid and convenient method to separate eight ginsenosides from Panax ginseng by high-speed counter-current chromatography coupled with evaporative light scattering detection

Ginsenosides exhibit diverse biological activities and are major well-known components isolated from the radix of Panax ginseng C.A. Meyer. In the present work, a rapid and facile method for the separation and purification of eight ginsenosides from P. ginseng by high-speed counter-current chromatography coupled with evaporative light scattering detector (HSCCC-ELSD) was successfully developed. The crude samples for HSCCC separation were first purified from ginseng extract using a macroporous resin; the extract was loaded onto a Diaion-HP20 column and fractionated by methanol and water gradient elution. The ginsenosides-protopanaxadiol (PPD) and protopanaxatriol (PPT) fractions were subsequently eluted with 65 and 80% methanol and water gradient elution, respectively. Furthermore, these two fractions were separated by HSCCC-ELSD. The two-phase solvent system used for separation was composed of chloroform/methanol/water/isopropanol at a volume ratio of 4:3:2:1. Each fraction obtained was collected and dried, yielding the following eight ginsenosides: Rg(1), Re, Rf, Rh(1), Rb(1), Rc Rb(2) and Rd. The purity of these ginsenosides was greater than 97% as assessed by HPLC-ELSD, and their structures were characterized by electrospray-ionization mass spectrometry (ESI-MS) and nuclear magnetic resonance spectroscopy. This is the first report regarding the separation of the ginsenosides Rh(1), Rb(2) and Rc from P. ginseng by HSCCC.     

Modeling of claim exceedances over random thresholds for related insurance portfolios

Large claims in an actuarial risk process are of special importance for the actuarial decision making about several issues like pricing of risks, determination of retention treaties and capital requirements for solvency. This paper presents a model about claim occurrences in an insurance portfolio that exceed the largest claim of another portfolio providing the same sort of insurance coverages. Two cases are taken into consideration: independent and identically distributed claims and exchangeable dependent claims in each of the portfolios. Copulas are used to model the dependence situations. Several theorems and examples are presented for the distributional properties and expected values of the critical quantities under concern.     

Computer simulation of the formation of polymer networks

Complex crosslinked polymer structures can be quite easily modeled with the aid of computers. BTOSYM's implementation of an algorithm that has been developed by Eichinger and his co-workers over the last few years is described. This algorithm allows us to model both random (as in sulfur-cured rubber) and site-specific (as in end-linked silicones) crosslinking reactions. The simulation method provides detailed information on gel points, cycle rank, modulus of elasticity and other characteristics of the networks as they are formed. Illustrative results obtained with the program are presented.