Mountain pass type solutions for quasilinear elliptic equations

We establish the existence of weak solutions in an Orlicz-Sobolev space to the Dirichlet problem where is a bounded domain in , , and the function is an increasing homeomorphism from onto . Under appropriate conditions on , , and the Orlicz-Sobolev conjugate of (conditions which reduce to subcriticality and superlinearity conditions in the case the functions are given by powers), we obtain the existence of nontrivial solutions which are of mountain pass type. Received April 22, 1999 / Accepted June 11, 1999 / Published online April 6, 2000     

Wave packet dynamics in different electronic states investigated by femtosecond time-resolved four-wave-mixing spectroscopy

This paper reviews results on wave packet dynamics investigated by means of femtosecond time-resolved four-wave-mixing (FWM) spectroscopy. First, it is shown that by making use of the various degrees of freedom which are offered by this technique information about molecular dynamics on different potential-energy surfaces can be accessed and separated from each other. By varying the timing, polarization, and wavelengths of the laser pulses as well as the wavelength of the detection window for the FWM signal, different dynamics are coherently excited and probed by the nonlinear spectroscopy. As a model system we use iodine in the gas phase. These techniques are then applied to more-complex molecules (gas phase: benzene, toluene, a binary mixture of benzene and toluene; solid state: polymers of diacetylene matrix-isolated in single crystals of monomer molecules). Here, ground-state dynamics are investigated first without any involvement of electronically excited states and then in electronic resonance to an absorption transition in the investigated molecules. Signal modulations result which are due to wave packet motion as well as polarization beats between modes in different molecules. Phase and intensity changes yield information about intramolecular vibrational energy redistribution, population decay (T₁), phase relaxation (T₂), and coherence times. Received: 12 October 1999 / Published online: 13 July 2000     

Double-Q magnetic structures and strong planar anisotropy in tetragonal ErRu2Ge2and ErRu2Si2

Single crystal magnetization measurements and powder neutron diffraction on tetragonal ErRu₂Ge₂ as well as anisotropy of the paramagnetic susceptibility and specific heat measurements on ErRu₂Si₂ are presented. Besides the huge crystal field contribution to the uniaxial anisotropy, which favors the basal plane, a strong in-plane anisotropy is evidenced. From these features and neutron diffraction experiments it is shown that magnetic structures of these materials are double-Q and accordingly non-colinear below their Néel temperature (5.2 and 6.0 K for Ge and Si based compounds, respectively). The magnetic structures induced during the metamagnetic processes are discussed. Received 24 December 1999     

Isotope shifts and hyperfine structure in the transitions of gadolinium

High-resolution resonance ionization mass spectrometry has been used to measure isotope shifts and hyperfine structure in all (J = 2-6) and the transitions of gadolinium (Gd I). Gadolinium atoms in an atomic beam were excited with a tunable single-frequency laser in the wavelength range of 422-429 nm. Resonant excitation was followed by photoionization with the 363.8 nm line of an argon ion laser and resulting ions were mass separated and detected with a quadrupole mass spectrometer. Isotope shifts for all stable gadolinium isotopes in these transitions have been measured for the first time. Additionally, the hyperfine structure constants of the upper states have been derived for the isotopes ^{155, 157} Gd and are compared with previous work. Using prior experimental values for the mean nuclear charge radii, derived from the combination of muonic atoms and electron scattering data, field shift and specific mass shift coefficients for the investigated transitions have been determined and nuclear charge parameters for the minor isotopes ^{152, 154} Gd have been calculated. Received 18 November 1999     

Lifetimes of metastable states in Sr II

The lifetimes of the 4d ²D _3/2,5/2 levels of Sr⁺ have been determined both experimentally and theoretically. The experiment was performed at an ion storage ring utilising collinear laser excitation. The calculation was performed by the Hartree-Fock method including relativistic effects and core polarisation. The obtained lifetimes (which are about 0.4 s) are discussed in detail and compared with earlier published results. In addition, calculated lifetimes of a large number of excited states in Sr⁺ are included. Received 15 February 2000 and Received in final form 20 March 2000     

Tetraisopropylcyclopentadienyl Chlorides of Lanthanum,Neodymium, and Ytterbium

Bis(tetraisopropylcyclopentadienyl)chlorides of lanthanum ( 1 ) or neodymium ( 2 ) can be easily obtained in good yields from the respective trichlorides and sodium tetraisopropylcyclopentadienide. Both contain one equivalent of coordinated sodium chloride, for 2 a dimer [{(C₅HR₄)₂Nd (μ‐Cl)(μ³‐Cl)Na(OEt₂)}₂] (R = CHMe₂) with a folded sheet structure has been established by X‐ray crystal structure analysis. From sodium tetraisopropylcyclopentadienide and ytterbium trichloride or upon oxidation of octaisopropylytterbocene with hexachloroethane the mono‐ring complex [(C₅HR₄)YbCl₂] ( 3 ) (R = CHMe₂) has been obtained, which could be crystallographically characterized as monomeric dimethoxyethane adduct [(C₅HR₄)YbCl₂(DME)].     

Determination of persistence lengths and mark-houwink constants of aromatic polyesters from GPC-differential viscometric coupling

The introduction of lateral substituents and/or twisted biphenylylene units increase the solubility of aromatic para-linked polyesters. Two polyesters of this type of structure were characterized by gel permeation chromatography (GPC), low angle laser light scattering (LALLS) and viscometry. From the molecular weights and limiting viscosity numbers obtained by universal calibration and LALLS/viscometry the Mark-Houwink constants and persistence lengths were determined. The values of these parameters indicated that the polyesters can be described as wormlike chains in dilute solution.     

On principal eigenvalues for quasilinear elliptic differential operators: an Orlicz-Sobolev space setting

((without abstract.)) Received January 20, 1998