Eigenfunctions on symmetric spaces with distribution-valued boundary forms

A characterization is given for those eigenfunctions of invariant differential operators on symmetric spaces of noncompact type which are representable as generalized Poisson integrals of distributions on the boundary, the criterion being that the function grow no faster than some power of the exponential of the distance from the origin. For symmetric spaces of arbitrary rank, the result is proved in one direction only, namely, that the Poisson integral of a distribution satisfies the growth condition; however, for rank one symmetric spaces, the converse is also shown to be true.     

Stress bounds for bars in torsion

Upper bounds for the maximum shear stress in the St. Venant torsion problem are derived with the aid of the theory of subharmonic functions. The main result is a bound that is determined in a simple manner by the magnitude of the applied twisting moment and two parameters peculiar to the cross section: the radius of the largest circle contained in it and the minimum curvature of the curve that bounds it.

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Zusammenfassung Mit Hilfe subharmonischer Funktionen werden obere Grenzen in dem Torsionsproblem von St. Venant erhalten. Das Hauptergebnis ist eine Grenze, die auf einfache Weise vom Drehmoment und zwei nur vom Querschnitt abhängigen Parametern bestimmt ist, und zwar von dem Radius des grössten eingeschriebenen Kreises und von der Minimalkrümmung der Begrenzungskurve des Querschnitts.

     

Desymmetrization of glycerol derivatives with peptide-based acylation catalysts

[reaction: see text] Nucleophile-loaded peptides have been evaluated as catalysts for the desymmetrization of glycerol derivatives through an enantioselective acylation process. Enantiomeric excesses of up to 97% have been obtained for the monoacylated products. A range of other substrates have been examined that shed light on the mechanistic basis of the desymmetrizations.     

Origins of blinking in single-molecule Raman spectroscopy

We observe spectral and intensity fluctuations in Raman scattering from single molecules of 4-mercaptopyridine (4-Mpy) adsorbed on textured silver surfaces. We present evidence that the root cause of these fluctuations is thermal. Analysis of the spectra shows that in some cases the spectral changes are associated with molecular reorientation and in others with chemical reactions of the 4-Mpy. Analogous surfaces fully covered with 4-Mpy exhibit similar behavior, indicating that monolayer Raman spectra are dominated by a few molecules at most.     

Thomson-scattering study of the subharmonic decay of ion-acoustic waves driven by the Brillouin instability

Thomson scattering (TS) has been used to investigate the two-ion decay instability of ion acoustic waves generated by stimulated Brillouin scattering in an underdense CH plasma. Two complementary TS diagnostics, spectrally and spatially resolved, demonstrate the occurrence of the subharmonic decay of the primary ion acoustic wave into two secondary waves. The study of the laser intensity dependence shows that the secondary ion acoustic waves are correlated with the SBS reflectivity saturation, at a level of a few percent.     

Arrays for the combinatorial exploration of cell adhesion

A new method for the fabrication of arrays of self-assembled monolayers (SAMs) of alkane thiols (ATs) on gold to combinatorially assay surfaces for cell adhesion is reported. A fluorous SAM, which is both cytophobic and solvophobic, was used as the background between the array features. The resulting solvophobic background permits the application of an assembly after conjugation strategy for fabrication. SAMs containing mixtures of ATs and peptide-terminated ATs were generated. Multiple cell types demonstrated differential and specific binding to these surfaces. Additionally, pluripotent human embryonic stem cells proliferated on surfaces generated by this method.