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 $\bar{C}$ of C, homeomorphic to the closed unit disc. The Euclidean metric on the closed unit disc induces a metric d on $\bar{C}$. We identify all uniform limits of polynomials on $\bar{D}$ with respect to the metric d. The class of the above limits is an extension of the disc algebra and it is denoted by $\bar{A}(D)$. We study properties of the elements of $\bar{A}(D)$ and topological properties of the class $\bar{A}(D)$ endowed with its natural topology. The class $\bar{A}(D)$ is different and, from the geometric point of view, richer than the class $\tilde{A}(D)$ 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 $\lambda$4686\AA of the WN component describe antiphased orbital motions. However, they show a small phase shift of $\sim$ 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, $\sim$ 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

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

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

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