The structure of fluids confined by planar walls is studied using density functional theory. The density functional used is a generalized form of the hypernetted chain (HNC) functional which contains a term third order in the density. This term is chosen to ensure that the modified density functional gives the correct bulk pressure. The proposed density functional applied to a Lennard-Jones...

A theory of third order extended regular variation is developed, somewhat similar to the corresponding theories of first and second order.

In recent work, Schweber [7] introduces a framework for reverse mathematics in a third order setting and investigates several natural principles of transfinite recursion. The main result of that paper is a proof, using the method of forcing, that in the context of two-person perfect information games with moves in R, open determinacy (Σ1 -DET) is not implied by clopen determinacy (∆ R 1 -DET). ...

SUMMARY For a variable and parameter of the same dimension, the tangent exponential model (Fraser, 1988) approximates an asymptotic model to third order in a rst derivative neighbourhood of the data point and to second order otherwise. For the more usual case of a variable of larger dimension than the parameter, we obtain a unique expression for the third order ancillary distribution as project...