This paper describes the first-order logical environment FOLE. Institutions
in general, and logical environments in particular, give equivalent
heterogeneous and homogeneous representations for logical systems. As such,
they offer a rigorous and principled approach to distributed interoperable
We have both full and
Reduced crossed products, and each has a coaction of G. We investigate "exotic"
Coactions in between, that are determined by certain ideals E of the
Fourier-Stieltjes algebra B(G) -- an approach that is inspired by recent work
Of Brown and Guentner on new C*-group algebra compl...
The cone-volume measure of a polytope with centroid at the origin is proved
to satisfy the subspace concentration condition. As a consequence a conjectured
(a dozen years ago) fundamental sharp affine isoperimetric inequality for the
U-functional is completely established -- along with it's equalit...
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