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Physical Sciences and Mathematics

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Selected Works

1984

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Guage Invariant De Gennes Model, Anthony Day, T. Lubensky Jun 1984

Guage Invariant De Gennes Model, Anthony Day, T. Lubensky

Anthony Roy Day

A gauge-invariant formulation of the de Gennes model for the nematic—to—smectic-A transition is presented. In this formulation the energy associated with the gauge field A⃗ reduces to the Frank elastic energy with the application of the constraint n⃗0·A⃗=0 where n⃗0 is the uniform equilibrium director and A⃗ is to be identified with deviations δn⃗ of the director from equilibrium. It is shown that thermodynamic quantities and renormalization-group recursion relations are gauge invariant. All gauge dependence appears in the exponent η describing order-parameter correlations. The gauge invariance of a negative dielectric anisotropy smectic-A in an external electric field is also studied.

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Small Area Statistics: Large Statistical Problems, Paula Diehr Mar 1984

Small Area Statistics: Large Statistical Problems, Paula Diehr

Paula Diehr

No abstract provided.

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An Artin Relation (Mod 2) For Finite Group Actions On Spheres, Ronald M. Dotzel Jan 1984

An Artin Relation (Mod 2) For Finite Group Actions On Spheres, Ronald M. Dotzel

Ronald Dotzel

Recently it has been shown that whenever a finite group G (not a /7-group) acts on a homotopy sphere there is no general numerical relation which holds between the various formal dimensions of the fixed sets of ^-subgroups (p dividing the order of (7). However, if G is dihedral of order 2q (q an odd prime power) there is a numerical relation which holds (mod 2). In this paper, actions of groups G which are extensions of an odd order /?-group by a cyclic 2-group are considered and a numerical relation (mod 2) is found to be satisfied (for such …

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Maximal Functions Measuring Smoothness, Ronald A. Devore, Robert C. Sharpley Dec 1983

Maximal Functions Measuring Smoothness, Ronald A. Devore, Robert C. Sharpley

Robert Sharpley

Maximal functions which measure the smoothness of a function are introduced and studied from the point of view of their relationship to classical smoothness and their use in proving embedding theorems, extension theorems and various results on differentiation. New spaces of functions which generalize Sobolev spaces are introduced.

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