A heated triangular cylinder is suddenly cooled in a constant temperature bath. The transient heat conduction problem is transformed to the Helmholtz equation related to the vibration of membranes. Using the membrane analogy, exact analytic solutions for the transient heat conduction problem for three triangular cross sections are found.

Pyramidal elements are often used to connect tetrahedral and hexahedral elements in the finite element method. In this paper we derive three new higher order numerical cubature formulae for pyramidal elements.

We investigate a class of triangular UHF algebras which have the special property that there exists a sequence of unital multiplicative contractive finite-rank conditional expectations of the algebra into itself, which converges strongly to the identity, whose ranges form an increasing chain with dense union. A partial classification is given in terms of a local finiteness property, and a delimiting counterexample is obtained. Associated inverse limit algebras are considered, and a characterization of residually finite dimensional triangular AF algebras is obtained.

1991 Mathematics Subject Classification: 47D25, 46J35.