On a new class of function systems of Faber-Schauder type

In this paper, we introduce a new class of function systems generalizing the classical Faber-Schauder system. Under the condition that the generating sequence is bounded, we show that systems of such a class constitute bases in the space of continuous functions and prove some properties of series expansions of functions in these systems.     

Mg 2p shallow core-level and local atomic structure of i-ZnMgRE quasicrystals

We present a detailed analysis of the Mg 2p shallow core-levels measured on icosahedral single-grain ZnMgY, ZnMgHo, and ZnMgEr quasicrystals during a photoelectron microscopy study. The synchrotron radiation photoemission measurements were performed on in situ cleaved samples at a pressure of 10⁻¹⁰ mbar and at low temperature, typically 90-150 K. The Mg 2p photoemission lines are essentially broadened as compared to those of the Mg 2p spin-orbit doublet recorded on the Zn₂Mg crystalline Laves phase. The broadening is associated to the coordination shifts of the Mg 2p level due to the inequivalent magnesium sites in the quasicrystalline lattice. The coordination shifts are calculated on the basis of i-ZnMg(Ho, Y) atomic structure data, recently determined from the pair distribution function analysis. The coordination shifts obtained are up to 0.2 eV. The Mg 2p experimental spectral intensity is nicely reproduced by a superposition of coordination-shifted Mg 2p spin-orbit doublets.     

Deep trench etching in macroporous silicon

We present a method to create at the same time trenches and ordered macropore arrays during photo-electrochemical etching of n-type silicon. This novel method allows in situ separation of single devices with a submicrometer precision. It also enables new device structures in macroporous silicon in the areas of photonics, sensing and electronics. The limits of this new process are simulated using electrostatic models and are verified experimentally. PACS 82.45.Yz; 81.16.-c     

Electron transfer at lanthanum endohedral fullerenes

The aim of this contribution is to study lanthanum containing fullerenes produced and treated under different conditions. The work was done using solid soot extract giving poorly resolved ESR spectra or separated lanthanofullerenes in solution showing well resolved ESR spectra. ESR experiments in connection with the mass spectrometry give information on the electronic states due to the electron transfer from the endohedral metal to the fullerene cage and the influence of oxygen on endohedral lanthanofullerene. The analysis of ESR spectra indicates the presence of up to nine octets of lanthanum containing fullerenes. These species have different stabilities. Furthermore, a very narrow single ESR line in the lanthanofullerene spectrum was detected having a linewidth ΔB=0.008 mT and ag-factor 2.0025. The electron transfer to the endohedral La@C₈₂ molecule studied by voltammetry and electrochemicalin situ ESR experiments is described. The interaction of the lanthanofullerene with oxygen in solution is also studied. In different solvents the influence of oxygen on line broadening in the ESR spectra of La@C₈₂ was observed.     

Ions and atoms in superfluid helium (4He)

We review the previous conclusion [J.Y. Ryu, Y.C. Chung and S.D. Choi, Phys. Rev. B 32, 7769 (1984)] that the trace property Tr(ABC) = Tr(CAB) leads to two different cyclotron transition absorption formulae in the electron-phonon systems in the lowest order approximation. The pictorial expression and the calculated linewidths in Ge and Si show that the socalled EWC scheme is more seeming than the socalled MWC scheme. The difference is expected to disappear if we take into account all the higher order perturbation terms or start with the many body formalism in the complete scheme.