23,190 research outputs found
Generating sequences and Poincar\'e series for a finite set of plane divisorial valuations
Let be a finite set of divisorial valuations centered at a 2-dimensional
regular local ring . In this paper we study its structure by means of the
semigroup of values, , and the multi-index graded algebra defined by ,
\gr_V R. We prove that is finitely generated and we compute its minimal
set of generators following the study of reduced curve singularities. Moreover,
we prove a unique decomposition theorem for the elements of the semigroup.
The comparison between valuations in , the approximation of a reduced
plane curve singularity by families of sets of divisorial
valuations, and the relationship between the value semigroup of and the
semigroups of the sets , allow us to obtain the (finite) minimal
generating sequences for as well as for .
We also analyze the structure of the homogeneous components of \gr_V R. The
study of their dimensions allows us to relate the Poincar\'e series for and
for a general curve of . Since the last series coincides with the
Alexander polynomial of the singularity, we can deduce a formula of A'Campo
type for the Poincar\'e series of . Moreover, the Poincar\'e series of
could be seen as the limit of the series of ,
Dirac Triplet Extension of the MSSM
In this paper we explore extensions of the Minimal Supersymmetric Standard
Model involving two triplet chiral superfields that share a
superpotential Dirac mass yet only one of which couples to the Higgs fields.
This choice is motivated by recent work using two singlet superfields with the
same superpotential requirements. We find that, as in the singlet case, the
Higgs mass in the triplet extension can easily be raised to
without introducing large fine-tuning. For triplets that carry hypercharge, the
regions of least fine tuning are characterized by small contributions to the
parameter, and light stop squarks, ; the latter is a result of the dependence of
the triplet contribution to the Higgs mass. Despite such light stop masses,
these models are viable provided the stop-electroweakino spectrum is
sufficiently compressed.Comment: 26 pages, 4 figure
The stellar content of the Local Group dwarf galaxy Phoenix
We present new deep ground-based photometry of the Local Group dwarf
galaxy Phoenix. Our results confirm that this galaxy is mainly dominated by red
stars, with some blue plume stars indicating recent (100 Myr old) star
formation in the central part of the galaxy. We have performed an analysis of
the structural parameters of Phoenix based on an ESO/SRC scanned plate, in
order to search for differentiated component. The results were then used to
obtain the color-magnitude diagrams for three different regions of Phoenix in
order to study the variation of the properties of its stellar population. The
young population located in the central component of Phoenix shows a clear
asymmetry in its distribution, that could indicate a propagation of star
formation across the central component. The HI cloud found at 6 arcmin
Southwest by Young & Lo (1997) could have been involved in this process.
We also find the presence of a substantial intermediate-age population in the
central region of Phoenix that would be less abundant or absent in its outer
regions. This result is also consistent with the gradient found in the number
of horizontal branch stars, whose frequency relative to red giant branch stars
increases towards the outer part of the galaxy. These results, together with
those of our morphological study, suggest the existence of an old, metal-poor
population with a spheroidal distribution surrounding the younger inner
component of Phoenix. This two-component structure may resemble the halo-disk
structure observed in spirals, although more data, in particular on kinematics,
are necessary to confirm this.Comment: 46 pages, 21 figures, 9 Tables, to be published in AJ, August 9
Authoring courses with rich adaptive sequencing for IMS learning design
This paper describes the process of translating an adaptive sequencing strategy designed using Sequencing Graphs to the semantics of IMS Learning Design. The relevance of this contribution is twofold. First, it combines the expressive power and ïŹexibility of Sequencing Graphs, and the interoperability capabilities of IMS. Second, it shows some important limitations of IMS speciïŹcations (focusing on Learning Design) for the sequencing of learning activities
Semiquantitative theory of electronic Raman scattering from medium-size quantum dots
A consistent semiquantitative theoretical analysis of electronic Raman
scattering from many-electron quantum dots under resonance excitation
conditions has been performed. The theory is based on
random-phase-approximation-like wave functions, with the Coulomb interactions
treated exactly, and hole valence-band mixing accounted for within the
Kohn-Luttinger Hamiltonian framework. The widths of intermediate and final
states in the scattering process, although treated phenomenologically, play a
significant role in the calculations, particularly for well above band gap
excitation. The calculated polarized and unpolarized Raman spectra reveal a
great complexity of features and details when the incident light energy is
swept from below, through, and above the quantum dot band gap. Incoming and
outgoing resonances dramatically modify the Raman intensities of the single
particle, charge density, and spin density excitations. The theoretical results
are presented in detail and discussed with regard to experimental observations.Comment: Submitted to Phys. Rev.
Equivariant Poincar\'e series of filtrations and topology
Earlier, for an action of a finite group on a germ of an analytic
variety, an equivariant -Poincar\'e series of a multi-index filtration in
the ring of germs of functions on the variety was defined as an element of the
Grothendieck ring of -sets with an additional structure. We discuss to which
extend the -Poincar\'e series of a filtration defined by a set of curve or
divisorial valuations on the ring of germs of analytic functions in two
variables determines the (equivariant) topology of the curve or of the set of
divisors
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