A novel polyimide forming reaction is reported. Pyromellitic dianhydride undergoes a condensation polymerization with diphenylmethane diisocyanate in solution or under melt‐fusion conditions to give polydiphenylmethanepyromellitimide (II) and carbon dioxide. Polymer II was characterized by inherent viscosity, infrared spectrum, and thermogravimetric analysis. An intermediate Polymer I was isolated which appeared to contain seven‐membered rings in the backbone. It is postulated that these rings eliminate carbon dioxide to form polyimide II.

We study not necessarily self-similar Dirichlet forms on the Sierpiński gasket that can be described as limits of compatible resistance networks on the sequence of graphs approximating the gasket. We describe the compatibility conditions in detail, and we also present an alternative description, based on just 3 conductance values and the 3-dimensional space of harmonic functions. In addition, we show how to parameterize all the Dirichlet forms by a set of independent variables.

Let M be a complete Riemannian manifold and D ⊂ M a smoothly bounded domain with compact closure. We use Brownian motion and the classic results on the Stieltjes moment problem to study the relationship between the Dirichlet spectrum of D and the heat content asymptotics of D. Central to our investigation is a sequence of invariants associated to D defined using exit time moments. We prove that our invariants determine that part of the spectrum corresponding to eigenspaces which are not orthogonal to constant functions, that our invariants determine the heat content asymptotics associated to the manifold, and that when the manifold is a generic domain in Euclidean space, the invariants determine the Dirichlet spectrum.1991 Mathematics Subject Classification. 58J50, 58J65.

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