Transferring estimates for zonal convolution operators

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Truncation error bounds for modified continued fractions with applications to special functions

Much recent work has been done to investigate convergence of modified continued fractions (MCF's), following the proof by Thron and Waadeland [35] in 1980 that a limit-periodic MCFK(a _n , 1;x ₁), with andnth approximant

N-α-Benzyloxyacetyl derivatives of (S)-4-benzyl-5,5-dimethyloxazolidin-2-one for the asymmetric synthesis of differentially protected α,β-dihydroxyaldehydes

α-Dibenzylamino- and α-benzyloxy- derivatives of N-acetyl-(S)-4-benzyl-5,5-dimethyloxazolidin-2-one readily undergo highly stereoselective boron mediated syn-aldol reactions with a range of aromatic and aliphatic aldehydes, generating the syn-aldol products in good to excellent yields as single diastereoisomers after purification. In the α-dibenzylamino series, deprotection of the functionalised aldol fragments to the corresponding α-amino-β-hydroxy methyl ester or α-amino-β-hydroxyaldehyde proved problematic, with a range of N- and O-protecting groups giving mixtures of products arising from endocyclic and exocyclic cleavage pathways. However, in the α-benzyloxy series, O-silyl protection of the aldol products, and subsequent DIBAL reduction gives stereoselectively the corresponding N-1′-hydroxyalkyloxazolidin-2-ones, which undergo base promoted fragmentation to the desired highly functionalised and differentially protected α,β-dihydroxyaldehydes in good yields and without loss of stereochemical integrity.     

Energetic ion bombardment of Ag surfaces by C<Stack><Subscript>60</Subscript><Superscript>+</Superscript></Stack> and Ga<Superscript>+</Superscript> projectiles

The ion bombardment-induced release of particles from a metal surface is investigated using energetic fullerene cluster ions as projectiles. The total sputter yield as well as partial yields of neutral and charged monomers and clusters leaving the surface are measured and compared with corresponding data obtained with atomic projectile ions of similar impact kinetic energy. It is found that all yields are enhanced by about one order of magnitude under bombardment with the C60+ cluster projectiles compared with Ga+ ions. In contrast, the electronic excitation processes determining the secondary ion formation probability are unaffected. The kinetic energy spectra of sputtered particles exhibit characteristic differences which reflect the largely different nature of the sputtering process for both types of projectiles. In particular, it is found that under C60+ impact (1) the energy spectrum of sputtered atoms peaks at significantly lower kinetic energies than for Ga+ bombardment and (2) the velocity spectra of monomers and dimers are virtually identical, a finding which is in pronounced contrast to all published data obtained for atomic projectiles. The experimental findings are in reasonable agreement with recent molecular dynamics simulations.     

The crystal and molecular structure of 1,1,1,3,3,3-hexaphenyl-1,3-disilapropane

Crystals of the title compound H₂C(SiPh₃)₂ are triclinic, space group P$\text{1}$, with a = 9.290(2), b = 12.128(4), c = 16.882(4) Å, α = 62.08(1), β = 106.88(1), γ = 117.28(2)° and Z = 2. The central skeletal angle SiCSi is 128.8(7)°. The structures of the molecules H₂C(SiR₃)₂ (R = H, CH₃, and Ph) are compared and discussed: a simple model for the skeletal geometry of species H₂C(MR₃)₂ is proposed, and tested against experimental data and theoretical calculations.     

Solvent dependence of the 2-naphthyl(carbomethoxy)carbene singlet-triplet energy gap

The solvent dependence of the 2-naphthyl(carbomethoxy)carbene (2) singlet-triplet energy gap has been examined by time-resolved infrared (TRIR) and computational methods. The ground state of 2 changes from the triplet state in hexane to the singlet state in acetonitrile. Preferential stabilization of the singlet carbene is the result of its increased dipole moment in polar solvents. Variable-temperature TRIR experiments provide measurements of the enthalpic and entropic differences between (1)2 and (3)2 and suggest that solvent and geometry effects on the entropy of singlet and triplet carbenes can offset differences arising from spin multiplicity. B3LYP calculations using the polarizable continuum solvation model (PCM) reproduce the general trends in enthalpic differences seen experimentally.