The number of connected sparsely edged graphs. II. Smooth graphs and blocks

A smooth graph is a connected graph without endpoints; f(n, q) is the number of connected graphs, v(n, q) is the number of smooth graphs, and u(n, q) is the number of blocks on n labeled points and q edges: W_k, V_k, and U_k are the exponential generating functions of f(n, n + k), v(n, n + k), and u(n, n + k), respectively. For any k ? 1, our reduction method shows that V_k can be deduced at once from W_k, which was found for successive k by the computer method described in our previous paper. Again the reduction method shows that U_k must be a sum of powers (mostly negative) of 1 - X and, given this information, we develop a recurrence method well suited to calculate U_k for successive k. Exact formulas for v(n, n + k) and u(n, n + k) for general n follow at once.     

Metal-non-metal transition in the lead-argon system

A sharp metal-non-metal transition as the composition of Pb-Ar samples is varied at about 4K has been observed at 50 at.% Pb and is described.     

The fast atom bombardment mass spectra of xanthane dyes

The Fast Atom Bombardment mass spectra of a number of xanthane dyes are reported. These dyes are insufficiently volatile to give spectra by conventional electron impact ionization. Fragmentation pathways have been determined by metastable linked scan techniques and accurate masses obtained by peak matching. The xanthane dyes may be readily identified from their FAB spectra by the presence of characteristic ions.     

The massless Thirring model: Positivity of Klaiber'sn-point functions

We present a simple solution to the problem of proving positivity of Klaiber'sn-point functions for the massless Thirring model. The corresponding fields are obtained as strong limits of explicitly given approximate fields, obviating reconstruction. By invoking recent results on the boson-fermion correspondence it is shown how the model can be formulated on the charged fermion Fock space. It is pointed out that the question of cyclicity of the vacuum is open, and that an affirmative answer is necessary to confirm the superselection sector picture of the model.     

High-frequency measurements of blast wave propagation

Blast wave propagation measurements were conducted to investigate nonlinear propagation effects on blast waveform evolution with distance. Measurements were made with a wide-bandwidth capacitor microphone for comparison with conventional 3.175-mm (1/8-in.) microphones with and without baffles. It was found that the 3.175-mm microphone did not have sufficient high-frequency response to capture the actual rise times in some regions. For a source of 0.57 kg (1.25 lb) of C-4 plastic explosive, the trend observed is that nonlinear effects steepened the waveform, thereby decreasing the shock rise time, up to a range of 50 m. At 100 m, the rise times had increased slightly.     

The synthesis of new weakly coordinating diborate anions: anion stability as a function of linker structure and steric bulk

The successive addition of KCN and Ph3CCl to B(C6F4-C6F5-2)3 (PBB) affords triphenylmethyl salts of the [NC-PBB]- anion. By contrast, the analogous reaction with sodium dicyanamide followed by treatment with Ph(3)CCl leads to the zwitterionic aminoborane H2NB(C12F9)2C12F8, via nucleophilic attack on an o-F atom, together with CPh3[F-PBB]. Whereas treatment of [NC-PBB]- with either PBB or B(C6F5)3 fails to give isolable cyano-bridged diborates, the reaction of Me3SiNC-B(C6F5)3 with PBB in the presence of Ph3CCl affords [Ph3C][PBB-NC-B(C6F5)3]. Due to steric hindrance this anion is prone to borane dissociation. The longer linking group N(CN)2- gives the very voluminous anions [N[CNB(C6F5)3]2]- and [N(CN-PBB)2]-. A comparison of propylene polymerisations with rac-Me2Si(Ind)2ZrMe2 activated with the various boranes or trityl borates gives an anion-dependent activity sequence, in the order [NC-PBB]- < [MeB(C6F5)3]- < [MePBB]- approximately [PBB-NCB(C6F5)3]- approximately [N[CNB(C6F5)3]2]- < [F-PBB]-< [B(C6F5)4]- < [N(CN-PBB)2]-. The anion [N(CN-PBB)2]- gives a catalyst productivity about 2500 times higher than that of [NC-PBB]- and exceeds that of [B(C6F5)4]- based catalysts. The van der Waals volumes and surface areas of the anions have been calculated and provide a rationale for the observed reactivity trends in polymerisation reactions.