Universal Overconvergence of Polynomial Expansions of Harmonic Functions

For each compact subset K of ^N let (K) denote the space of functions that are harmonic on some neighbourhood of K. The space (K) is equipped with the topology of uniform convergence on K. Let Ω be an open subset of ^N such that 0Ω and ^N\Ω is connected. It is shown that there exists a series ∑H_n, where H_n is a homogeneous harmonic polynomial of degree n on ^N, such that (i) ∑H_n converges on some ball of centre 0 to a function that is continuous on Ω and harmonic on Ω, (ii) the partial sums of ∑H_n are dense in (K) for every compact subset K of ^N\Ω with connected complement. Some refinements are given and our results are compared with an analogous theorem concerning overconvergence of power series.     

Factors controlling the efficiencies of photoinduced electron-transfer reactions

The overall efficiencies of photoinduced electron transfer reactions in polar solvents are usually determined by the efficiency with which separated radical ions are formed from the initially formed geminate radical-ion pairs. These separation efficiencies are determined by the competition between retum electron transfer and separation within the geminate pairs. A method is described for determining whether variations in the quantum yields for formation of separated radical ions are due to changes in the reorganization parameters for the return electron transfer reactions, or to other factors. The use of the method is illustrated in studies of the effects of varying steric bulk and molecular size of the donors, and also in studies of the effect of using a charged sensitizer.     

Exchange reactions between oxygen and sulphur derivatives of silicon, germanium, tin and lead

The exchange of oxygen functional groups (--- OR, --- O --- and --- OCOMe) and sulphur functional groups (--- SR, --- S --- ) between R₃M (M = Si, Ge, Sn and Pb) and R₂M (M = Si, Sn) shows, in general, the heavier Group IV element to prefer sulphur. This supports the phenomenological rationalisation that the softness of the organometallic residue increase with the atomic weight of M, though germanium probably resembles silicon in its behaviour far more that it does tin.     

Quadruplex formation by a guanine-rich PNA oligomer

A guanine-rich PNA dodecamer having the sequence H-G4T4G4-Lys-NH2 (G-PNA) hybridizes with a DNA dodecamer of homologous sequence to form a four-stranded quadruplex (Datta, B.; Schmitt, C.; Armitage, B. A. J. Am. Chem. Soc. 2003, 125, 4111-4118). This report describes quadruplex formation by the PNA alone. UV melting curves and fluorescence resonance energy transfer experiments reveal formation of a multistranded structure stabilized by guanine tetrads. The ion dependency of these structures is analogous to that reported for DNA quadruplexes. Electrospray ionization mass spectrometry indicates that both dimeric and tetrameric quadruplexes are formed by G4-PNA, with the dimeric form being preferred. These results have implications for the use of G-rich PNA for homologous hybridization to G-rich targets in chromosomal DNA and suggest additional applications in assembling quadruplex structures within lipid bilayer environments.