171 research outputs found
On some invariants in numerical semigroups and estimations of the order bound
We study suitable parameters and relations in a numerical semigroup S. When S
is the Weierstrass semigroup at a rational point P of a projective curve C, we
evaluate the Feng-Rao order bound of the associated family of Goppa codes.
Further we conjecture that the order bound is always greater than a fixed value
easily deduced from the parameters of the semigroup: we also prove this
inequality in several cases
On semigroup rings with decreasing Hilbert function
In this paper we study the Hilbert function HR of one-dimensional semigroup
rings R = k[[S]]. For some classes of semigroups, by means of the notion of
support of the elements in S, we give conditions on the generators of S in
order to have decreasing HR. When the embedding dimension v and the
multiplicity e verify v + 3 ? e ? v + 4, the decrease of HR gives explicit
description of the Apery set of S. In particular for e = v+3, we classify the
semigroups with e = 13 and HR decreasing, further we show that HR is
non-decreasing if e < 12. Finally we deduce that HR is non-decreasing for every
Gorenstein semigroup ring with e ? v + 4
One-dimensional Gorenstein local rings with decreasing Hilbert function
In this paper we solve a problem posed by M.E. Rossi: {\it Is the Hilbert
function of a Gorenstein local ring of dimension one not decreasing? } More
precisely, for any integer , $h \notin\{14+22k, \, 35+46k \ | \
k\in\mathbb{N} \}h$; moreover we prove that there are no
bounds to the decrease of the Hilbert function. The key tools are numerical
semigroup theory, especially some necessary conditions to obtain decreasing
Hilbert functions found by the first and the third author, and a construction
developed by V. Barucci, M. D'Anna and the second author, that gives a family
of quotients of the Rees algebra. Many examples are included
On the minimum distance of AG codes, on Weierstrass semigroups and the smoothability of certain monomial curves in 4-Space
In this paper we treat several topics regarding numerical Weierstrass
semigroups and the theory of Algebraic Geometric Codes associated to a pair
, where is a projective curve defined over the algebraic closure of
the finite field and P is a -rational point of . First we show
how to evaluate the Feng-Rao Order Bound, which is a good estimation for the
minimum distance of such codes. This bound is related to the classical
Weierstrass semigroup of the curve at . Further we focus our attention
on the question to recognize the Weierstrass semigroups over fields of
characteristic 0. After surveying the main tools (deformations and
smoothability of monomial curves) we prove that the semigroups of embedding
dimension four generated by an arithmetic sequence are Weierstrass.Comment: 30 pages, presented at CAAG 2010 (Bangalore, India
Morphological Segregation in the Surroundings of Cosmic Voids
We explore the morphology of galaxies living in the proximity of cosmic
voids, using a sample of voids identified in the Sloan Digital Sky Survey Data
Release 7. At all stellar masses, void galaxies exhibit morphologies of a later
type than galaxies in a control sample, which represent galaxies in an average
density environment. We interpret this trend as a pure environmental effect,
independent of the mass bias, due to a slower galaxy build-up in the rarefied
regions of voids. We confirm previous findings about a clear segregation in
galaxy morphology, with galaxies of a later type being found at smaller
void-centric distances with respect to the early-type galaxies. We also show,
for the first time, that the radius of the void has an impact on the
evolutionary history of the galaxies that live within it or in its
surroundings. In fact, an enhanced fraction of late-type galaxies is found in
the proximity of voids larger than the median void radius. Likewise, an excess
of early-type galaxies is observed within or around voids of a smaller size. A
significant difference in galaxy properties in voids of different sizes is
observed up to 2 Rvoid, which we define as the region of influence of voids.
The significance of this difference is greater than 3sigma for all the
volume-complete samples considered here. The fraction of star-forming galaxies
shows the same behavior as the late-type galaxies, but no significant
difference in stellar mass is observed in the proximity of voids of different
sizes.Comment: Published in ApJ
Evaluation of the capture efficiency and size selectivity of four pot types in the prospective fishery for North Pacific giant octopus (Enteroctopus dofleini)
Over 230 metric tons of octopus is harvested as bycatch annually in Alaskan trawl, long-line, and pot fisheries. An expanding market has fostered interest in the development
of a directed fishery for North Pacific giant octopus (Enteroctopus dofleini). To investigate the potential for fishery development we examined the efficacy of four different pot types for capture of this species. During two
surveys in Kachemak Bay, Alaska, strings of 16 –20 sablefish, Korean hair crab, shrimp, and Kodiak wooden
lair pots were set at depths ranging between 62 and 390 meters. Catch per-unit-of-ef for t estimates were highest for sablefish and lair pots. Sablefish pots caught significantly heavier North Pacific giant octopuses but also produced the highest bycatch of commercially important species, such as halibut (Hippoglossus stenolepis),
Pacific cod (Gadus macrocephalus), and Tanner crab (Chionoecetes bairdi)
Syzygies of GS monomial curves and Weierstrass property.
We find a resolution for the coordinate ring R of an algebraic monomial curve associated to a G numerical semigroup (i.e. generated by a generalized arithmetic sequence), by extending a previous paper (Gimenez, Sengupta, Srinivasan) on arithmetic sequences . A consequence is the determinantal description of the first syzygy module of R. By this fact, via suitable deformations of the defining matrices, we can prove the smoothability of the curves associated to a large class of semigroups generated by arithmetic sequences, that is the Weierstrass property for such semigroups
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