By application of the Girsanov formula for measures induced by diffusion processes with constant diffusion coefficients it is possible to define the Onsager-Machlup function as the Lagrangian for the most probable tube around a differentiable function. The absolute continuity of a measure induced by a process with process depending diffusion w.r.t. a quasi translation invariant measure is investigated. The orthogonality of these measures w.r.t. quasi translation invariant measures is shown. It is concluded that the Onsager-Machlup function cannot be defined as a Lagrangian for processes with process depending diffusion coefficients.

Low-temperature specific-heat and thermal-expansion measurements on a single crystal of the heavyfermion superconductor UBe 13 reveal an anomaly in the superconducting state. The evolution of this feature is studied as a function of Th doping on several U 12x Th x Be 13 polycrystals (x # 0.03), giving rise to a new "line of anomalies," T L ͑x͒, in the T -x diagram. The anomaly at T L ͑x͒ marks the precursor of the lower of the two phase transitions at x . x cr ഠ 0.019. Implications for the interpretation of the phase diagram of superconducting U 12x Th x Be 13 are addressed. [S0031-9007(98)

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Motivated by applications to image reconstruction, in this paper we analyse a finite-difference discretisation of the Ambrosio–Tortorelli functional. Denoted by \varepsilon the elliptic-approximation parameter and by \delta the discretisation step-size, we fully describe the relative impact of \varepsilon and \delta in terms of \Gamma -limits for the corresponding discrete functionals, in the three possible scaling regimes. We show, in particular, that when \varepsilon and \delta are of the same order, the underlying lattice structure affects the \Gamma -limit which turns out to be an anisotropic free-discontinuity functional.

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