2,261,033 research outputs found
Algebra Structures on Hom(C,L)
We consider the space of linear maps from a coassociative coalgebra C into a
Lie algebra L. Unless C has a cocommutative coproduct, the usual symmetry
properties of the induced bracket on Hom(C,L) fail to hold. We define the
concept of twisted domain (TD) algebras in order to recover the symmetries and
also construct a modified Chevalley-Eilenberg complex in order to define the
cohomology of such algebras
Improved Constructions of Frameproof Codes
Frameproof codes are used to preserve the security in the context of
coalition when fingerprinting digital data. Let be the largest
cardinality of a -ary -frameproof code of length and
. It has
been determined by Blackburn that when ,
when and is even, and . In this paper, we
give a recursive construction for -frameproof codes of length with
respect to the alphabet size . As applications of this construction, we
establish the existence results for -ary -frameproof codes of length
and size for all odd when and for all
when . Furthermore, we show that
meeting the upper bound given by Blackburn, for all integers such that
is a prime power.Comment: 6 pages, to appear in Information Theory, IEEE Transactions o
Bond percolation of polymers
We study bond percolation of non-interacting Gaussian polymers of
segments on a 2D square lattice of size with reflecting boundaries. Through
simulations, we find the fraction of configurations displaying {\em no}
connected cluster which span from one edge to the opposite edge. From this
fraction, we define a critical segment density and the
associated critical fraction of occupied bonds , so that they
can be identified as the percolation threshold in the limit.
Whereas is found to decrease monotonically with for a
wide range of polymer lengths, is non-monotonic. We give
physical arguments for this intriguing behavior in terms of the competing
effects of multiple bond occupancies and polymerization.Comment: 4 pages with 6 figure
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