Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function

We develop an analog of classical oscillation theory for Sturm-Liouville operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing zeros of solutions of one operator by weighted zeros of Wronskians of solutions of two different operators. In particular, we show that a Sturm-type comparison theorem still holds in this situation and demonstrate how this can be used to investigate the finiteness of eigenvalues in essential spectral gaps. Furthermore, the connection with Krein's spectral shift function is established.Comment: 26 page

On the Global Existence of Bohmian Mechanics

We show that the particle motion in Bohmian mechanics, given by the solution of an ordinary differential equation, exists globally: For a large class of potentials the singularities of the velocity field and infinity will not be reached in finite time for typical initial values. A substantial part of the analysis is based on the probabilistic significance of the quantum flux. We elucidate the connection between the conditions necessary for global existence and the self-adjointness of the Schr\"odinger Hamiltonian.Comment: 35 pages, LaTe

The Dirac system on the Anti-de Sitter Universe

We investigate the global solutions of the Dirac equation on the Anti-de-Sitter Universe. Since this space is not globally hyperbolic, the Cauchy problem is not, {\it a priori}, well-posed. Nevertheless we can prove that there exists unitary dynamics, but its uniqueness crucially depends on the ratio beween the mass $M$ of the field and the cosmological constant $\Lambda>0$ : it appears a critical value, $\Lambda/12$, which plays a role similar to the Breitenlohner-Freedman bound for the scalar fields. When $M^2\geq \Lambda/12$ there exists a unique unitary dynamics. In opposite, for the light fermions satisfying $M^2<\Lambda/12$, we construct several asymptotic conditions at infinity, such that the problem becomes well-posed. In all the cases, the spectrum of the hamiltonian is discrete. We also prove a result of equipartition of the energy.Comment: 33 page

Atom capture by nanotube and scaling anomaly

The existence of bound state of the polarizable neutral atom in the inverse square potential created by the electric field of single walled charged carbon nanotube (SWNT) is shown to be theoretically possible. The consideration of inequivalent boundary conditions due to self-adjoint extensions lead to this nontrivial bound state solution. It is also shown that the scaling anomaly is responsible for the existence of bound state. Binding of the polarizable atoms in the coupling constant interval \eta^2\in[0,1) may be responsible for the smearing of the edge of steps in quantized conductance, which has not been considered so far in literature.Comment: Accepted in Int.J.Theor.Phy

Bessel Process and Conformal Quantum Mechanics

Different aspects of the connection between the Bessel process and the conformal quantum mechanics (CQM) are discussed. The meaning of the possible generalizations of both models is investigated with respect to the other model, including self adjoint extension of the CQM. Some other generalizations such as the Bessel process in the wide sense and radial Ornstein- Uhlenbeck process are discussed with respect to the underlying conformal group structure.Comment: 28 Page

The 3D Structure of N132D in the LMC: A Late-Stage Young Supernova Remnant

We have used the Wide Field Spectrograph (WiFeS) on the 2.3m telescope at Siding Spring Observatory to map the [O III] 5007{\AA} dynamics of the young oxygen-rich supernova remnant N132D in the Large Magellanic Cloud. From the resultant data cube, we have been able to reconstruct the full 3D structure of the system of [O III] filaments. The majority of the ejecta form a ring of ~12pc in diameter inclined at an angle of 25 degrees to the line of sight. We conclude that SNR N132D is approaching the end of the reverse shock phase before entering the fully thermalized Sedov phase of evolution. We speculate that the ring of oxygen-rich material comes from ejecta in the equatorial plane of a bipolar explosion, and that the overall shape of the SNR is strongly influenced by the pre-supernova mass loss from the progenitor star. We find tantalizing evidence of a polar jet associated with a very fast oxygen-rich knot, and clear evidence that the central star has interacted with one or more dense clouds in the surrounding ISM.Comment: Accepted for Publication in Astrophysics & Space Science, 18pp, 8 figure

Diagnostic applications of molecular and serological assays for bluetongue and African horse sickness

The availability of rapid, highly sensitive and specific molecular and serologic diagnostic assays, such as competitive enzyme-linked immunosorbent assay (cELISA), has expedited the diagnosis of emerging transboundary animal diseases, including bluetongue (BT) and African horse sickness (AHS), and facilitated more thorough characterisation of their epidemiology. The development of assays based on real-time, reverse-transcription polymerase chain reaction (RT-PCR) to detect and identify the numerous serotypes of BT virus (BTV) and AHS virus (AHSV) has aided in-depth studies of the epidemiology of BTV infection in California and AHSV infection in South Africa. The subsequent evaluation of pan-serotype, real-time, RT-PCR-positive samples through the use of serotype-specific RT-PCR assays allows the rapid identification of virus serotypes, reducing the need for expensive and time-consuming conventional methods, such as virus isolation and serotype-specific virus neutralisation assays. These molecular assays and cELISA platforms provide tools that have enhanced epidemiologic surveillance strategies and improved our understanding of potentially altered Culicoides midge behaviour when infected with BTV. They have also supported the detection of subclinical AHSV infection of vaccinated horses in South Africa. Moreover, in conjunction with whole genome sequence analysis, these tests have clarified that the mechanism behind recent outbreaks of AHS in the AHS-controlled area of South Africa was the result of the reversion to virulence and/or genome reassortment of live attenuated vaccine viruses. This review focuses on the use of contemporary molecular diagnostic assays in the context of recent epidemiologic studies and explores their advantages over historic virus isolation and serologic techniques.https://www.woah.org/en/what-we-do/publications/scientific-and-technical-reviewVeterinary Tropical Disease

Influence of Grain Boundary Character on Creep Void Formation in Alloy 617

Alloy 617, a high temperature creep-resistant, nickel-based alloy, is being considered for the primary heat exchanger for the Next Generation Nuclear Plant (NGNP) which will operate at temperatures exceeding 760oC. Orientation imaging microscopy (OIM) is used to characterize the grain boundaries in the vicinity of creep voids that develop during high temperature creep tests (800-1000oC at creep stresses ranging from 20-85 MPa) terminated at creep strains ranging from 5-40%. Observations using optical microscopy indicate creep rate does not significantly influence the creep void fraction at a given creep strain. Preliminary analysis of the OIM data indicates voids tend to form on grain boundaries parallel, perpendicular or 45o to the tensile axis, while few voids are found at intermediate inclinations to the tensile axis. Random grain boundaries intersect most voids while CSL-related grain boundaries did not appear to be consistently associated with void development

Horizontal Branch Stars: The Interplay between Observations and Theory, and Insights into the Formation of the Galaxy

We review HB stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters (GCs) in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC. A rediscussion of the second-parameter problem is presented. A technique is proposed to estimate the HB types of extragalactic GCs on the basis of integrated far-UV photometry. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyrae, is also revisited, giving a distance modulus to the LMC of (m-M)_0 = 18.44+/-0.11. RR Lyrae period change rates are studied. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are investigated. [ABRIDGED]Comment: 56 pages, 22 figures. Invited review, to appear in Astrophysics and Space Scienc