Letters to the Editor

The mathematical intelligencer encourages comments about the material in this issue. letters to the editor should be sent to either of the editors-in-chief, chandler davis or Marjorie Senechal.     

Optical parametric oscillator with a pulse repetition rate of 39 GHz and 2.1-W signal average output power in the spectral region near 1.5 microm

We present a singly resonant, synchronously pumped optical parametric oscillator with a record-high repetition rate of 39 GHz. The transform-limited 2.2-ps pulses at 1570 nm have as much as 2.1-W average output power. The all-solid-state pump source is based on a diode-pumped passively mode-locked 39-GHz Nd:YVO4 laser and an efficient ytterbium-doped fiber amplifier.     

Exponential decay of derivatives of covariance operators on the lattice

We prove exponential decay for derivatives of covariance operators on the lattice. This result is obtained by using random walk methods on the v-dimensional lattice and a certain estimate on the generating function of the one-dimensional random walk. The result is useful in the frame of the cluster and mean field expansion of continuous spin models on the lattice.     

NHC→SiCl4: An Ambivalent Carbene‐Transfer Reagent

The addition of BCl₃ to the carbene‐transfer reagent NHC→SiCl₄ (NHC=1,3‐dimethylimidazolidin‐2‐ylidene) gave the tetra‐ and pentacoordinate trichlorosilicon(IV) cations [(NHC)SiCl₃]⁺ and [(NHC)₂SiCl₃]⁺ with tetrachloroborate as counterion. This is in contrast to previous reactions, in which NHC→SiCl₄ served as a transfer reagent for the NHC ligand. The addition of BF₃ ? OEt₂, on the other hand, gave NHC→BF₃ as the product of NHC transfer. In addition, the highly Lewis acidic bis(pentafluoroethyl)silane (C₂F₅)₂SiCl₂ was treated with NHC→SiCl₄. In acetonitrile, the cationic silicon(IV) complexes [(NHC)SiCl₃]⁺ and [(NHC)₂SiCl₃]⁺ were detected with [(C₂F₅)SiCl₃]^? as counterion. A similar result was already reported for the reaction of NHC→SiCl₄ with (C₂F₅)₂SiH₂, which gave [(NHC)₂SiCl₂H][(C₂F₅)SiCl₃]. If the reaction medium was changed to dichloromethane, the products of carbene transfer, NHC→Si(C₂F₅)₂Cl₂ and NHC→Si(C₂F₅)₂ClH, respectively, were obtained instead. The formation of the latter species is a result of chloride/hydride metathesis. These compounds may serve as valuable precursors for electron‐poor silylenes. Furthermore, the reactivity of NHC→SiCl₄ towards phosphines is discussed. The carbene complex NHC→PCl₃ shows similar reactivity to NHC→SiCl₄, and may even serve as a carbene‐transfer reagent as well.