18,295 research outputs found
Hermitian codes from higher degree places
Matthews and Michel investigated the minimum distances in certain
algebraic-geometry codes arising from a higher degree place . In terms of
the Weierstrass gap sequence at , they proved a bound that gives an
improvement on the designed minimum distance. In this paper, we consider those
of such codes which are constructed from the Hermitian function field. We
determine the Weierstrass gap sequence where is a degree 3 place,
and compute the Matthews and Michel bound with the corresponding improvement.
We show more improvements using a different approach based on geometry. We also
compare our results with the true values of the minimum distances of Hermitian
1-point codes, as well as with estimates due Xing and Chen
A two-component model for fitting light-curves of core-collapse supernovae
We present an improved version of a light curve model, which is able to
estimate the physical properties of different types of core-collapse supernovae
having double-peaked light curves, in a quick and efficient way. The model is
based on a two-component configuration consisting of a dense, inner region and
an extended, low-mass envelope. Using this configuration, we estimate the
initial parameters of the progenitor via fitting the shape of the
quasi-bolometric light curves of 10 SNe, including Type IIP and IIb events,
with model light curves. In each case we compare the fitting results with
available hydrodynamic calculations, and also match the derived expansion
velocities with the observed ones. Furthermore, we also compare our
calculations with hydrodynamic models derived by the SNEC code, and examine the
uncertainties of the estimated physical parameters caused by the assumption of
constant opacity and the inaccurate knowledge of the moment of explosion
Group-labeled light dual multinets in the projective plane (with Appendix)
In this paper we investigate light dual multinets labeled by a finite group
in the projective plane defined over a field .
We present two classes of new examples. Moreover, under some conditions on the
characteristic , we classify group-labeled light dual multinets
with lines of length least
3-nets realizing a diassociative loop in a projective plane
A \textit{-net} of order is a finite incidence structure consisting of
points and three pairwise disjoint classes of lines, each of size , such
that every point incident with two lines from distinct classes is incident with
exactly one line from each of the three classes. The current interest around
-nets (embedded) in a projective plane , defined over a field
of characteristic , arose from algebraic geometry. It is not difficult to
find -nets in as far as . However, only a few infinite
families of -nets in are known to exist whenever , or .
Under this condition, the known families are characterized as the only -nets
in which can be coordinatized by a group. In this paper we deal with
-nets in which can be coordinatized by a diassociative loop
but not by a group. We prove two structural theorems on . As a corollary, if
is commutative then every non-trivial element of has the same order,
and has exponent or . We also discuss the existence problem for such
-nets
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