255,683 research outputs found
On Theta-palindromic Richness
In this paper we study generalization of the reversal mapping realized by an
arbitrary involutory antimorphism . It generalizes the notion of a
palindrome into a -palindrome -- a word invariant under . For
languages closed under we give the relation between
-palindromic complexity and factor complexity. We generalize the notion
of richness to -richness and we prove analogous characterizations of
words that are -rich, especially in the case of set of factors
invariant under . A criterion for -richness of
-episturmian words is given together with other examples of
-rich words.Comment: 14 page
Parametric CR-umbilical Locus of Ellipsoids in
For every real numbers , with , the curve parametrized by valued in
with components: has
image contained in the CR-umbilical locus: of the
ellipsoid of equation
Finitely-Generated Projective Modules over the Theta-deformed 4-sphere
We investigate the "theta-deformed spheres" C(S^{3}_{theta}) and
C(S^{4}_{theta}), where theta is any real number. We show that all
finitely-generated projective modules over C(S^{3}_{theta}) are free, and that
C(S^{4}_{theta}) has the cancellation property. We classify and construct all
finitely-generated projective modules over C(S^{4}_{\theta}) up to isomorphism.
An interesting feature is that if theta is irrational then there are nontrivial
"rank-1" modules over C(S^{4}_{\theta}). In that case, every finitely-generated
projective module over C(S^{4}_{\theta}) is a sum of a rank-1 module and a free
module. If theta is rational, the situation mirrors that for the commutative
case theta=0.Comment: 34 page
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