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Finite nilpotent semigroups of small coclass
The parameter coclass has been used successfully in the study of nilpotent
algebraic objects of different kinds. In this paper a definition of coclass for
nilpotent semigroups is introduced and semigroups of coclass 0, 1, and 2 are
classified. Presentations for all such semigroups and formulae for their
numbers are obtained. The classification is provided up to isomorphism as well
as up to isomorphism or anti-isomorphism. Commutative and self-dual semigroups
are identified within the classification.Comment: 11 page
Spectral Properties of Grain Boundaries at Small Angles of Rotation
We study some spectral properties of a simple two-dimensional model for small
angle defects in crystals and alloys. Starting from a periodic potential , we let in the right half-plane
and in the left half-plane , where is the usual matrix describing
rotation of the coordinates in by an angle . As a main result,
it is shown that spectral gaps of the periodic Schr\"odinger operator fill with spectrum of as . Moreover, we obtain upper and lower bounds for a quantity
pertaining to an integrated density of states measure for the surface states.Comment: 22 pages, 3 figure
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