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).     

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.     

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.     

Folding and unfolding of an elastinlike oligopeptide: "inverse temperature transition," reentrance, and hydrogen-bond dynamics

The temperature-dependent behavior of a solvated oligopeptide, GVG(VPGVG), is investigated. Spectroscopic measurements, thermodynamic measurements, and molecular dynamics simulations find that this elastinlike octapeptide behaves as a two-state system that undergoes an "inverse temperature" folding transition and reentrant unfolding close to the boiling point of water. A molecular picture of these processes is presented, emphasizing changes in the dynamics of hydrogen bonding at the protein/water interface and peptide backbone librational entropy.     

Detaching thiolates from copper and gold clusters: which bonds to break?

The interaction of alkanethiolates with small coinage metal clusters of copper and gold was studied based on density functional theory with a focus on the metal-thiolate junction. Calculation of fragmentation energies indicate that for Cu(n)-thiolate (n = 1,3,5,7, and 9) there is a progressive lowering in energy for the fragmentation of the S-C bond in the thiolate from a value of 2.9 eV for n = 1 to 1.4 eV for n = 9. The detailed electronic origins of this specific weakening are attributed to a polarization of electron density in the S-C bond as induced by bonding with the Cu(n) cluster. For the gold analogues, this effect is not observed and fragmentation at the S-C bond experiences only a slight 10% destabilization as n increases from 3 to 9. The relativistic origin of this difference between Cu and Au is discussed, and an analysis of bonding considerations is presented.     

Glycosidic bond formation in aqueous solution: on the oxocarbenium intermediate

The mechanism of specific acid-catalyzed glycosidic bond formation between methanol and alpha-d-glucopyranoside in aqueous solution at 300 K was studied using Car-Parrinello molecular dynamics. The reaction was found to proceed through a non-solvent equilibrated oxocarbenium cation intermediate characterized by the loss of a hydrogen-bonding interaction between the ring oxygen and solvating water. The mechanism, which was found to be D(N)A(N) in nature, is discussed in detail.