Two applications of the curve lemma for orthogonal groups

We show (under some hypothesis in small dimensions) that the analytic degree of the divisor of a modular form on the orthogonal group O(2,p) is determined by its weight. Moreover, we prove that certain integrals, occurring in Arakelov intersection theory, associated with modular forms on O(2,p) converge.Comment: 16 page

Quartic Forms in Many Variables

We show that a quartic $p$-adic form with at least $3192$ variables possesses a non-trivial zero. We also prove new results on systems of cubic, quadratic and linear forms. As an example, we show that for a system comprising two cubic forms $132$ variables are sufficient.Comment: 8 page

pp-adic Zeros of Quintic Forms

It is shown that a quintic form over a p-adic field with at least 26 variables has a non-trivial zero, providing that the cardinality of the residue class field exceeds 9.Comment: Minor correction

The effect of the amido substituent on polymer molecular weight in propene homopolymerisation by titanium cyclopentadienyl-amide catalysts

In the homopolymerisation of propene by the cyclopentadienyl-amide titanium catalyst systems [η5,η1-C5H4(CH2)2NR]TiCl2/MAO and [η5,η1-C5H4(CH2)2NR]Ti(CH2Ph)2/B(C6F5)3 (R = tBu, iPr, Me), the catalyst with the smallest substituent (Me) on the amido moiety consistently gives the highest polymer molecular weight. This differs from the trend usually observed in related catalysts with tetramethylcyclopentadienyl-amide ancillary ligands, where larger amide substituents result in higher molecular weights. Based on the present information a hypothesis is formulated in which an increased cation-anion interaction for the less sterically hindered catalyst is responsible for disfavouring chain transfer relative to chain growth.