Reactivity of the triple ion and separated ion pair of tris(trimethylsilyl)methyllithium with aldehydes: a RINMR study

Low-temperature rapid-injection NMR (RINMR) experiments were performed on tris(trimethylsilyl)methyllithium. In THF/Me2O solutions, the separated ion (1S) reacted faster than can be measured at -130 degrees C with MeI and substituted benzaldehydes (k >/= 2 s -1), whereas the contact ion (1C) dissociated to 1S before reacting. Unexpectedly, the triple ion reacted faster with electron-rich benzaldehydes relative to electron-deficient ones. The addition of HMPA had no effect on the rate of reaction of the triple ion with p-diethylaminobenzaldehyde, and the immediate product of the reaction was the HMPA-solvated separated ion 1S, with the Peterson product forming only slowly. Thus, the aldehyde is catalyzing the dissociation of the triple ion. HMPA greatly decelerated the reaction of 1S (<10 -10), providing an estimate of the Lewis acid activating effect of a THF-solvated lithium cation in an organolithium addition to an aldehyde.     

Structures and solution dynamics of pseudorotaxanes mediated by alkali-metal cations

Kinetic stability studies of a series of pseudorotaxanes formed from electron-rich crown ethers (hosts and ) and naphthalene diimide (guest ) in the presence of alkali salt templates MX (where M(+) = Li(+) and Na(+), and X(-) = Cl(-), Br(-), I(-), NO(3)(-) and CF(3)SO(3)(-)) were performed by (1)H NMR. The switching between the (bound) host and its linkage isomer host (free) was monitored in solution in the presence and absence of alkali salts, to establish the relative thermodynamic stabilities in the series. We also report here six new crystal structures, for pseudorotaxanes of type: [.], [M(2)..](2+) and [M(2)..](2+). Their solution-phase structures are in good agreement with the solid-state structures determined by X-ray crystallography.     

The Littlewood-Gowers problem

The paper has two main parts. To begin with, suppose that G is a compact abelian group. Chang’s Theorem can be viewed as a structural refinement of Bessel’s inequality for functions ƒ ∈ L ²(G). We prove an analogous result for functions ƒ ∈ A(G), where A(G) is the space endowed with the norm , and generalize this to the approximate Fourier transform on Bohr sets. As an application of the first part of the paper, we improve a recent result of Green and Konyagin. Suppose that p is a prime number and A ⊂ ℤ/pℤ has density bounded away from 0 and 1 by an absolute constant. Green and Konyagin have shown that ‖χ _A ‖ _A(ℤ/pℤ) ≫ ɛ (log p)^1/3−ɛ; we improve this to ‖χ _A ‖ _A(ℤ/pℤ) ≫ ɛ (log p)^1/2−ɛ. To put this in context, it is easy to see that if A is an arithmetic progression, then ‖χ _A ‖ _A(ℤ/pℤ) ≪ log p.     

On spanning trees and walks of low maximum degree

This article uses the discharging method to obtain the best possible results that a 3‐connected graph embeddable on a surface of Euler characteristic χ ≤ −46 has a spanning tree of maximum degree at most and a closed, spanning walk meetting each vertex at most times. Each of these results is shown to be best possible. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 67–74, 2001     

Metalloporphyrin Dendrimers with Folding Arms

Rigid and flexible linkers are combined in the new dendrimer shown schematically in the picture, which contains nine metalloporphyrin units (Porph). The construction is such that the four “arms” of the dendrimer can fold in a cooperative and predetermined manner in response to added 1,4-diazabicyclo[2.2.2]octane (DABCO).