On Topological Properties of Min-Max Functions

We examine the topological structure of the upper-level set M ^max given by a min-max function φ. It is motivated by recent progress in Generalized Semi-Infinite Programming (GSIP). Generically, M ^max is proven to be the topological closure of the GSIP feasible set (see Guerra-Vázquez et al. 2009; Günzel et al., Cent Eur J Oper Res 15(3):271–280, 2007). We formulate two assumptions (Compactness Condition CC and Sym-MFCQ) which imply that M ^max is a Lipschitz manifold (with boundary). The Compactness Condition is shown to be stable under C ⁰-perturbations of the defining functions of φ. Sym-MFCQ can be seen as a constraint qualification in terms of Clarke’s subdifferential of the min-max function φ. Moreover, Sym-MFCQ is proven to be generic and stable under C ¹-perturbations of the defining functions which fulfill the Compactness Condition. Finally we apply our results to GSIP and conclude that generically the closure of the GSIP feasible set is a Lipschitz manifold (with boundary).     

Microscopic phonon theory of Si/Ge nanocrystals

Microscopic phonon theory of semiconductor nanocrystals (NCs) is reviewed in this paper. Phonon modes of Si and Ge NCs with various sizes of up to 7 nm are investigated by valence force field theory. Phonon modes in spherical SiGe alloy NCs approximately 3.6 nm (containing 1147 atoms) in size have been investigated as a function of the Si concentration. Phonon density-of-states, quantum confinement effects, as well as Raman intensities are discussed.      

Synthesis of a highly enantiomerically enriched silyllithium compound

The highly enantiomerically enriched silyllithium compound lithiomethylphenyl(1-piperidinylmethyl)silane (4) reacts stereospecifically with chlorosilanes, but over a period of several hours slow racemization in solution at room temperature occurs, which can be suppressed by a transmetalation reaction with MgBr2(thf)4.     

Characterization and quantification of metallothionein isoforms by capillary electrophoresis–inductively coupled plasma–isotope-dilution mass spectrometry

In a new approach to the characterization and quantification of metallothionein isoforms an on-line isotope-dilution method in combination with the coupling of capillary electrophoresis (CE) to an inductively coupled plasma-sector field mass spectrometer (ICP-SFMS) is reported. Metallothionein (MT) isoforms are separated by CE and the elements Cu, Zn, Cd, and S are detected simultaneously by use of ICP-SFMS in the medium resolution mode. On-line isotope dilution is performed by continuous introduction of an isotopically enriched, species-unspecific spike solution after the separation step. MT from rabbit liver and a further purified MT-1 isoform were quantified by determination of sulfur, and the stoichiometric compositions of the metalloprotein complexes are characterized by determination of their sulfur-to-metal ratios.     

Helfrich repulsion and dynamical phase separation of multicomponent lipid bilayers

Thermal fluctuations of surfactant bilayers in an aqueous solution produce an effective, long-range repulsion that can lead to a continuous unbinding transition. We report on an optical interferometry study of the thermal fluctuations of multicomponent bilayers close to the unbinding transition. We find that, in contrast to the case of single-component bilayers, the thermal fluctuation spectrum of multicomponent bilayers does not agree with a continuous unbinding transition but instead indicates the proximity of an unbinding tricritical point.     

8-phenyl-10,10a-dihydropyrido

Base treatment of the pyridinium bromides 11a-e gives rise to the formation of the dihydropyridoazepines 14a-e as the only monomolecular products. The reaction takes place by initial deprotonation to the ylides 12, which undergo 8pi-electrocyclization affording the seven-membered-ring systems; no products of a dipolar 6pi-cyclization were detected. On the basis of quantum mechanical calculations a rationalization of the periselectivity of the electrocyclization process is given.     

Femtosecond holography in lithium niobate crystals

Spatial gratings are recorded holographically by two femtosecond pump pulses at 388 nm in lithium niobate (LiNbO3) crystals and read out by a Bragg-matched, temporally delayed probe pulse at 776 nm. We claim, to our knowledge, the first holographic pump-probe experiments with subpicosecond temporal resolution for LiNbO3. An instantaneous grating that is due mostly to the Kerr effect as well as a long-lasting grating that results mainly from the absorption caused by photoexcited carriers was observed. The Kerr coefficient of LiNbO3 for our experimental conditions, i.e., pumped and probed at different wavelengths, was approximately 1.0 x 10(-5) cm2/GW.