A finite element method based on time dependent basis functions is presented for solving a two phase Stefan problem for heat equation in one space dimension. The stability and the convergence of the method are studied, and a numerical example is given.

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We study the fixed point algebra \mathfrak{A}^α of a UHF algebra \mathfrak{A} under a periodic automorphism α of product type. We show an example of \mathfrak{A}^α which is simple and has more than two tracial states and we characterize the case where \mathfrak{A}^α had only one tracial state. Next we show that \mathfrak{A}^α is a UHF algebra if and only if \mathfrak{A} is generated by an infinite family of mutually commuting α-invariant type I_p subfactors whose fixed point algebras are abelian and by a UHF subalgebra of \mathfrak{A}^α which commutes with the former (where P denotes the period of α).

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