Uniform convergence of samples of Lebesgue integrals

Generalizations of a theorem of Halkin on themultiple balayage of vector integrals are deduced from a result of Adams and Morse.     

Proof of character-valued index theorems

A character-valued index is a generalization of the ordinary Dirac index to manifolds with nontrivial automorphism groups. A simple proof of the corresponding fixed-point theorem is presented which uses the techniques of supersymmetric quantum mechanics. This theorem relates the character-valued index to a topological integral of curvature forms on the fixed-point space of the automorphism in question.     

The single-step synthesis of a DNA tetrahedron

A tetrahedral nanostructure whose edges are DNA double helices self-assembles spontaneously when four appropriately designed oligonucleotides are annealed together in solution; the ease of synthesis, rigidity, and adaptability of this construct make it a promising candidate as a cage for other large molecules and as a building block for more complicated nanostructures.     

Surfactant layering on mixed monolayer-protected gold clusters

Positively-charged monolayer protected gold clusters (MMPCs) were mixed with sodium dodecyl sulfate (SDS). At lower SDS concentration, the initially water-soluble particles became organic-soluble while remaining discrete. Upon further addition of SDS, the particles aggregate and become water-soluble. NaCN decomposition, TEM, and DLS characterization reveal the morphology and properties of these encapsulated assemblies.     

A promising enantioselective Diels–Alder dienophile by computer-assisted rational design: 2,5-diphenyl-1-vinyl-borolane

Several chiral vinylboranes have been theoretically evaluated as enantioselective Diels-Alder dienophiles. Theoretical results suggest that optically pure 2,5-diphenyl-1-vinyl-borolane should be the reagent of choice for performing such transformations efficiently.     

Rapid and localized electron internal-transport-barrier formation during shear inversion in fully noninductive TCV discharges

Clear evidence is reported for the first time of a rapid localized reduction of core electron energy diffusivity during the formation of an electron internal-transport barrier. The transition occurs rapidly (approximately = 3 ms), during a slow (approximately = 200 ms) self-inductive evolution of the magnetic shear. This crucial observation, and the correlation of the transition with the time and location of the magnetic shear reversal, lend support to models attributing the reduced transport to the local properties of a zero-shear region, in contrast to models predicting a gradual reduction due to a weak or negative shear.