4,625 research outputs found
Importance of interlinguistic similarity and stable bilingualism when two languages compete
In order to analyze the dynamics of two languages in competition, one
approach is to fit historical data on their numbers of speakers with a
mathematical model in which the parameters are interpreted as the similarity
between those languages and their relative status. Within this approach, we
show here, on the basis of a detailed analysis and extensive calculations, the
outcomes that can emerge for given values of these parameters. Contrary to
previous results, it is possible that in the long term both languages coexist
and survive. This happens only when there is a stable bilingual group, and this
is possible only if the competing languages are sufficiently similar, in which
case its occurrence is favoured by both similarity and status symmetry.Comment: to appear in New Journal of Physic
Level structures on the Weierstrass family of cubics
Let W -> A^2 be the universal Weierstrass family of cubic curves over C. For
each N >= 2, we construct surfaces parametrizing the three standard kinds of
level N structures on the smooth fibers of W. We then complete these surfaces
to finite covers of A^2. Since W -> A^2 is the versal deformation space of a
cusp singularity, these surfaces convey information about the level structure
on any family of curves of genus g degenerating to a cuspidal curve. Our goal
in this note is to determine for which values of N these surfaces are smooth
over (0,0). From a topological perspective, the results determine the
homeomorphism type of certain branched covers of S^3 with monodromy in
SL_2(Z/N).Comment: LaTeX, 12 pages; added section giving a topological interpretation of
the result
On one-sided division infinite-dimensional normed real algebras
In this note we introduce the concept of Cayley homomorphism which is closely related with those of composition algebra and normalized orthogonal multiplication. The key result shows the existente of certain types of Cayley homomorphisms for infinite dimension. As an application we prove the existente of left division infinite-dimensional complete normed real algebras with left unity
- …