A version of Burkholder's theorem for operator-weighted spaces

Let be an operator weight, i.e. a weight function taking values in the bounded linear operators on a Hilbert space . We prove that if the dyadic martingale transforms are uniformly bounded on for each dyadic grid in , then the Hilbert transform is bounded on as well, thus providing an analogue of Burkholder's theorem for operator-weighted -spaces. We also give a short new proof of Burkholder's theorem itself. Our proof is based on the decomposition of the Hilbert transform into ``dyadic shifts'.

     

Ueber die Verbindung der Eiweissk?rper mit Kupferoxyd

Ohne Zusammenfassung     

Carleson's counterexample and a scale of Lorentz-BMO spaces on the bitorus

We introduce a full scale of Lorentz-BMO spaces BMO _L ^p,q on the bidisk, and show that these spaces do not coincide for different values ofp andq. Our main tool is a detailed analysis of Carleson's construction in [C]. The first author gratefully acknowledges support by the LMS and Proyecto BFM2002-04013. The second author gratefully acknowledges support by EPSRC and by the Nuffield Foundation.     

Advantages of statistical analysis of giant vesicle flickering for bending elasticity measurements

We show how to greatly improve precision when determining bending elasticity of giant unilamellar vesicles. Taking advantage of the well-known quasi-spherical model of liposome flickering, we analyze the full probability distributions of the configurational fluctuations instead of limiting the analysis to the second moment measurements only as usually done in previously published works. This leads to objective criteria to reject vesicles that do not behave according to the model. As a result, the confidence in the bending elasticity determination of individual vesicles that fit the model is improved and, consequently, the reproducibility of this measurement for a given membrane system. This approach uncovers new possibilities for bending elasticity studies like detection of minute influences by solutes in the buffer or into the membrane. In the same way, we are now able to detect the inhomogeneous behavior of giant vesicle systems such as the hazardous production of peroxide in bilayers containing fluorescent dyes.     

The mann test for divisible difference sets

Generalizing a result of Jungnickel for affine difference sets, we present an existence test for arbitrary divisible difference setsD which is analogous to the well-known and powerful test of Mann for ordinary difference sets. Several applications show that this approach is of interest also in the general case.Research partially supported by NSA grant # MDA 904-87-H-2018 and by an Alexandervon-Humboldt fellowship. The author would like to thank the Mathematisches Institut der Justus-Liebig-Universität Giessen for its hospitality during the time of this research.     

On abelian difference sets with multiplier — 1

Archiv der Mathematik -     

Optical conductivity of CePd3, YPd3 and PrPd3

The optical conductivity of intermediate valence CePd₃ at 300 K exhibits a maximum near 16 meV, which is absent in the reference materials YPd₃ and PrPd₃. Using a modified Drude model with a memory function ansatz this anomaly has been identified as a resonant electron-electron scattering process of conduction electrons at the localized 4f states near the Fermi level E_F. The model fit gives estimates of the width of the 4f states, of their separation from E_F and of the f-d hybridization energy. Intra-4f transitions of CePd₃ are stronger compared to those of PrPd₃ due to the stronger f-d hybirdization. 4d→4f transition energies of CePd₃ are reduced due to an electron-hole Coulomb binding energy.     

Thermal expansion and specific heat of intermediate valent YbCuAl

The specific heat, thermal expansion and resistivity was measured for the intermediate valence compound YbCuAl and its reference compound LuCuAl between 1.5 and 400 K. All quantities show strong anomalies. The entropy of the specific heat anomaly is found to be nearR·ln9, the value expected for the entropy of a high temperature mixture of Yb-ions in the ratio dictated by the degeneracies of the Hund's rule groundstates of 4f ¹⁴ and 4f ¹³. TheT ³ coefficient of the low temperature specific heat of YbCuAl contains a large electronic contribution. The integrated thermal expansion anomaly indicates a shift of the valence by at least 3.5% towards 3⁺ between 1.5 and 310 K.     

Thermal expansion of La3S4 at low temperatures

The thermal expansion of the superconductor La₃S₄ has been investigated on a single crystal by a capacitive method between 1.6 and 14 K. The relative length change shows a well pronounced second order phase transformation near 8.05 K, which is caused by the superconducting transition. From the calculated linear thermal expansion coefficient we determine the pressure coefficient of the transition temperature and of the thermodynamic critical field as well as the thermodynamic critical field itself. Furthermore we estimate the electronic, phononic and total Grüneisen parameters. These parameters have been used to discuss on the basis of the McMillan equation the reason for the increase of the transition temperature under pressure.     

Luminescence of Mn ions in ordered and disordered LiAl5O8

The phosphorescence and excitation spectra of Mn ions in the ordered and disordered phases of LiAl₅O₈ have been measured. In both phases Mn²⁺ ions substitute for Al³⁺ ions in two different tetrahedral sites of the LiAl₅O₈ lattice. In both sites in the ordered phase, sharp zero-phonon transitions have been observed in the low temperature phosphorescence and excitation spectra - these transitions were considerably broadened in the disordered phase due to crystal field inhomogeneity in that phase. The deviation from neutrality caused by the Mn²⁺ ions in the ordered phase is largely compensated by Mn⁴⁺ ions occupying octahedral Al³⁺ sites. On disordering, a large proportion of Mn⁴⁺ is reduced to Mn²⁺, while the remainder takes up a site with a higher proportion of Li⁺ ions as next nearest neighbours. This leads to an increase in the ionicity of the Mn⁴⁺ site in the disordered phase and hence to a larger value of the Racah parameter B.