Multivariate Markov-switching ARMA processes with regularly varying noise

The tail behaviour of stationary R^d-valued Markov-switching ARMA (MS-ARMA) processes driven by a regularly varying noise is analysed. It is shown that under appropriate summability conditions the MS-ARMA process is again regularly varying as a sequence. Moreover, it is established that these summability conditions are satisfied if the sum of the norms of the autoregressive parameters is less than one for all possible values of the parameter chain, which leads to feasible sufficient conditions.Our results complement in particular those of Saporta [Tail of the stationary solution of the stochastic equation Y_n+1=a_nY_n+b_n with Markovian coefficients, Stochastic Process. Appl. 115 (2005) 1954-1978.] where regularly varying tails of one-dimensional MS-AR(1) processes coming from consecutive large values of the parameter chain were studied.     

Structure and rheology of model side-chain liquid crystalline polymers with varying mesogen length

We probed the structural transitions and rheological properties of norbornene-based polymeric liquid crystals with attached side mesogenic groups of varying length. Whereas the short side chain liquid crystals (C5) formed a nematic mesophase, the long ones (C9) formed a smectic-A solid. The degree of polymerization of the main backbone affected the isotropic-mesophase transition temperatures, but did not influence the change of the mesophase dynamics from the isotropic to the anisotropic state. The temperature dependence of the shift factors obtained from the time-temperature superposition were divided into three regions, namely isotropic, mesophase, and transition, all exhibiting Arrhenius behavior except for the nematic fluid, which followed a WLF dependence. A remarkable strain hardening observed in both nematic and smectic samples was attributed to the dynamic coupling of the main chain and the mesogenic side groups. By applying large amplitude oscillatory shear, macroscopic alignment was achieved; the long recovery times upon flow cessation suggested a very slow structural reorganization, which was much longer in the smectics compared to the nematics, possibly due to the involvement of smaller length scales in the former case. Received: 26 December 2000/Accepted: 26 February 2001     

Moments of charge distributions in the reaction92Mo+92Mo at 14.7 MeV/u

First and second moments of primary charge distributions were determined as a function of the total kinetic energy loss in the reaction⁹²Mo+⁹²Mo at an incident energy of 14.7 MeV/u. Up to energy losses of 200 MeV no significant drift of the first moments is observed. The second moments are in agreement with predictions of a stochastic model derived at lower bombarding energies.     

Kinetik des Abbaues von 1,4-Polybutadien durch Olefin-Metathese

Ohne Zusammenfassung     

Stationarity and geometric ergodicity of BEKK multivariate GARCH models

Conditions for the existence of strictly stationary multivariate GARCH processes in the so-called BEKK parametrisation, which is the most general form of multivariate GARCH processes typically used in applications, and for their geometric ergodicity are obtained. The conditions are that the driving noise is absolutely continuous with respect to the Lebesgue measure and zero is in the interior of its support and that a certain matrix built from the GARCH coefficients has spectral radius smaller than one.To establish the results, semi-polynomial Markov chains are defined and analysed using algebraic geometry.     

Nonradiative deactivation of europium(III) luminescence as a detection scheme for moisture

The nonradiative deactivation of the excited state of europium(III)-based phosphors via OH-vibrations in the presence of water allows the detection of moisture in nitrogen at concentration levels down to at least 25 ppm (0.09% RH).     

Anisotropic Optical and Transport Properties of Trans-(Ch)X

We have produced fully oriented highly crystal 1ine trans-(CH)_X films, which exhibit dramatic polarization effects for light polarized parallel or perpendicular to the oriented (CH)_X-chains. The polarization behavior in the vicinity of the bandgap and of the characteristic IR-modes, including those which are introduced as a result of doping with ASF5 is presented. DC-conductivity measurements allow to deduce the conductivity anisotropy of δ_‖/δ_⊥ ～ 100 for undoped and I₂-doped trans-(CH)_x at 300 K.