5,663 research outputs found
Non-isolated Hypersurface Singularities and L\^e Cycles
In this series of lectures, I will discuss results for complex hypersurfaces
with non-isolated singularities. In Lecture 1, I will review basic definitions
and results on complex hypersurfaces, and then present classical material on
the Milnor fiber and fibration. In Lecture 2, I will present basic results from
Morse theory, and use them to prove some results about complex hypersurfaces,
including a proof of L\^e's attaching result for Milnor fibers of non-isolated
hypersurface singularities. This will include defining the relative polar
curve. Lecture 3 will begin with a discussion of intersection cycles for proper
intersections inside a complex manifold, and then move on to definitions and
basic results on L\^e cycles and L\^e numbers of non-isolated hypersurface
singularities. Lecture 4 will explain the topological importance of L\^e cycles
and numbers, and then I will explain, informally, the relationship between the
L\^e cycles and the complex of sheaves of vanishing cycles.Comment: Notes from a series of lectures from the S\~ao Carlos singularities
meeting of 2014. Revision made to Exercise 3.1 (a
Another extension of the disc algebra
We identify the complex plane C with the open unit disc D={z:|z|<1} by the
homeomorphism z --> z/(1+|z|). This leads to a compactification of C,
homeomorphic to the closed unit disc. The Euclidean metric on the closed unit
disc induces a metric d on . We identify all uniform limits of
polynomials on with respect to the metric d. The class of the above
limits is an extension of the disc algebra and it is denoted by .
We study properties of the elements of and topological properties
of the class endowed with its natural topology. The class
is different and, from the geometric point of view, richer than
the class introduced in Nestoridis (2010), Arxiv:1009.5364, on
the basis of the chordal metric.Comment: 14 page
The Massive Wolf-Rayet Binary SMC WR7
We present a study of optical spectra of the Wolf--Rayet star AzV 336a (= SMC
WR7) in the Small Magellanic Cloud. Our study is based on data obtained at
several Observatories between 1988 and 2001. We find SMC WR7 to be a double
lined WN+O6 spectroscopic binary with an orbital period of 19.56 days. The
radial velocities of the He absorption lines of the O6 component and the strong
He{\sc ii} emission at 4686\AA of the WN component describe antiphased
orbital motions. However, they show a small phase shift of 1 day. We
discuss possible explanations for this phase shift. The amplitude of the radial
velocity variations of He {\sc ii} emission is twice that of the absorption
lines. The binary components have fairly high minimum masses, 18
\modot and 34 \modot for the WN and O6 components, respectively.Comment: Accepted by MNRA
Massive runaway stars in the Small Magellanic Cloud
Using archival Spitzer Space Telescope data, we identified for the first time
a dozen runaway OB stars in the Small Magellanic Cloud (SMC) through the
detection of their bow shocks. The geometry of detected bow shocks allows us to
infer the direction of motion of the associated stars and to determine their
possible parent clusters and associations. One of the identified runaway stars,
AzV 471, was already known as a high-velocity star on the basis of its high
peculiar radial velocity, which is offset by ~40 km/s from the local systemic
velocity. We discuss implications of our findings for the problem of the origin
of field OB stars. Several of the bow shock-producing stars are found in the
confines of associations, suggesting that these may be "alien" stars
contributing to the age spread observed for some young stellar systems. We also
report the discovery of a kidney-shaped nebula attached to the early WN-type
star SMC-WR3 (AzV 60a). We interpreted this nebula as an interstellar structure
created owing to the interaction between the stellar wind and the ambient
interstellar medium.Comment: Accepted by A&
The universal order one invariant of framed knots in most S^1-bundles over orientable surfaces
It is well-known that self-linking is the only Z valued Vassiliev invariant
of framed knots in S^3. However for most 3-manifolds, in particular for the
total spaces of S^1-bundles over an orientable surface F not S^2, the space of
Z-valued order one invariants is infinite dimensional. We give an explicit
formula for the order one invariant I of framed knots in orientable total
spaces of S^1-bundles over an orientable not necessarily compact surface F not
S^2. We show that if F is not S^2 or S^1 X S^1, then I is the universal order
one invariant, i.e. it distinguishes every two framed knots that can be
distinguished by order one invariants with values in an Abelian group.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-3.abs.htm
Test of nuclear level density inputs for Hauser-Feshbach model calculations
The energy spectra of neutrons, protons, and alpha-particles have been
measured from the d+59Co and 3He+58Fe reactions leading to the same compound
nucleus, 61$Ni. The experimental cross sections have been compared to
Hauser-Feshbach model calculations using different input level density models.
None of them have been found to agree with experiment. It manifests the serious
problem with available level density parameterizations especially those based
on neutron resonance spacings and density of discrete levels. New level
densities and corresponding Fermi-gas parameters have been obtained for
reaction product nuclei such as 60Ni,60Co, and 57Fe
Charge density of a positively charged vector boson may be negative
The charge density of vector particles, for example W, may change sign. The
effect manifests itself even for a free propagation; when the energy of the
W-boson is higher than sqrt{2}m and the standing-wave is considered the charge
density oscillates in space. The charge density of W also changes sign in close
vicinity of a Coulomb center. The dependence of this effect on the g-factor for
an arbitrary vector boson, for example rho-meson, is discussed. An origin of
this surprising effect is traced to the electric quadrupole moment and
spin-orbit interaction of vector particles. Their contributions to the current
have a polarization nature. The charge density of this current, rho = -\nabla
\cdot P, where P is an effective polarization vector that depends on the
quadrupole moment and spin-orbit interaction, oscillates in space, producing
zero contribution to the total charge.Comment: 4 pages, revte
Oxygen-rich dust production in IC 10
We report the detection of oxygen-rich circumstellar envelopes in stars of
the nearby (700 kpc) starburst galaxy IC 10. The star formation history and the
chemical environment of this galaxy makes it an ideal target to observe dust
production by high-mass stars in a low-metallicity environment. The goal of
this study is to identify oxygen-rich stars in IC 10 and to constrain their
nature between asymptotic giant branch stars (AGBs), red supergiants (RSGs),
and other infrared bright sources. We examine the mass-loss rate of the stars
and compare to results obtained for the Magellanic Clouds. Our objectives are
to (1) assess whether RSGs can be significant dust producers in IC 10, and (2),
solve the discrepancy between the star formation history of IC 10 and the
relatively low number of RSGs detected in the optical. We search for silicate
dust in emission by using the spectral map observed with the Infrared
Spectrograph on board the Spitzer Space Telescope. The optical (UBVRI) and
infrared (JHK, Spitzer/IRAC and Spitzer/MIPS) photometry is used to assert the
membership of the stars to IC 10 and disentangle between AGBs and RSGs.
Radiative models are used to infer mass-loss rates and stellar luminosities.
The luminosity and colors of at least 9 silicate emission sources are
consistent with stars within IC 10. Furthermore, the photometry of 2 of these
sources is consistent with RSGs. We derive dust mass-loss rates similar to the
values found in the Magellanic Clouds. Accounting for the sample completeness,
RSGs are not important contributors to the dust mass budget in IC 10.Comment: Accepted for publication in A&
Evaluation of a Coping Kit of Items to Support Children with Developmental Disorders in the Hospital Setting
This study attempted to answer the question, Do nurses perceive coping kits to be effective at meeting the needs of hospitalized children with developmental disabilities who are at increased risk for challenging behaviors? A cross-sectional post-test survey study design was used, with a convenience sample of 24 registered nurses at a Midwestern free-standing children\u27s hospital. A coping kit with simple communication cards, social script book, and distraction items (toys) was developed to enhance communication and distract children with developmental disabilities (including autism spectrum disorder) undergoing procedures in the hospital. A modified version of Hudson\u27s (2006) intervention effectiveness survey was used to measure the nurse\u27s perception of the effectiveness of the coping kit. Nurses perceived the coping kits to be effective for decreasing their patient\u27s anxiety, calming the child\u27s behavior, and increasing cooperation during procedures. The nurse can develop a plan of care that includes a coping kit to help gain cooperation with the hospitalized child with challenging behaviors
- …