7,490 research outputs found
Strong vortex-antivortex fluctuations in the type II superconducting film
The small size vortex-antivortex pairs proliferation in type II
superconducting film is considered for the wide interval of temperatures below
Tc. The corresponding contribution to free energy is calculated. It is shown
that these fluctuations give the main contribution to the heat capacity of the
film both at low temperatures and in the vicinity of transition
Boolean representation of manifolds and functions
It is shown that a smooth n dimensional manifold with a boundary in R^n
admits a Boolean representation in terms of closed half spaces defined by the
tangent hyperplanes at the points on its boundary. A similar result is
established for smooth functions on closed convex domains in R^n. The latter
result is considered as a form of the Legendre transformation.Comment: 6 pages, 1 figur
Discrete piecewise linear functions
The concept of permutograph is introduced and properties of integral
functions on permutographs are established. The central result characterizes
the class of integral functions that are representable as lattice polynomials.
This result is used to establish lattice polynomial representations of
piecewise linear functions on convex domains and continuous selectors on linear
orders.Comment: 17 pages, 4 figures, Fig.2.1 label correcte
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