A Survey of Hydroxyl Toward Supernova Remnants: Evidence for Extended 1720 MHz Maser Emission

We present the results of GBT observations of all four ground-state hydroxyl (OH) transitions toward 15 supernova remnants (SNRs) which show OH(1720 MHz) maser emission. This species of maser is well established as an excellent tracer of an ongoing interaction between the SNR and dense molecular material. For the majority of these objects we detect significantly higher flux densities with a single dish than has been reported with interferometric observations. We infer that spatially extended, low level maser emission is a common phenomenon that traces the large-scale interaction in maser-emitting SNRs. Additionally we use a collisional pumping model to fit the physical conditions under which OH is excited behind the SNR shock front. We find the observed OH gas associated with the SNR interaction having columns less than approximately 10^17 per square cm, temperatures of 20 to 125 K, and densities 10^5 per cubic cm.Comment: 24 pages, 23 figures, Accepted to ApJ, March 26, 2008; v2 - added Figure 6, minor clarifications to text in Sections 3 and

Multiwavelength observations of the supernova remnant G349.7+02 interacting with a molecular cloud

We present molecular-line observations at millimetre, centimetre and infrared wavelengths of the region containing OH(1720 MHz) masers in the supernova remnant (SNR) G349.7+0.2, using the Australia Telescope (AT) Mopra antenna, the Swedish-ESO Submillimeter Telescope, the AT Compact Array and the UNSW Infrared Fabry-Perot narrow-band filter installed on the Anglo-Australian Telescope. Several molecular transitions were observed between 1.6 and 3 mm to constrain the physical parameters of the molecular cloud interacting with the SNR and to investigate the effects of the SNR shock on the gas chemistry. We detected shock-excited near-infrared H2 emission towards the centre of the SNR, revealing highly clumped molecular gas and a good correlation with published mid-infrared images from the Spitzer Space Telescope. An excellent correlation between the H2 clumps and OH(1720 MHz) maser positions supports the shock excitation of the OH(1720 MHz) maser emission. Furthermore, we detected OH absorption at 1665 and 1667 MHz which shows a good correlation with the shocked H2 emission and the masers. We found maser emission at 1665 MHz near the OH(1720 MHz) masers in this SNR, which is found to be associated with a GLIMPSE source SSTGLMC G349.7294+00.1747. We also detected 1665 and 1667 MHz OH masers, and weak 4.8 GHz H2CO absorption towards the ultracompact HII region IRAS 17147-3725 located to the southeast of the SNR. We found no 4.7- or 6-GHz excited-state OH masers or 6-GHz CH3OH maser towards either the SNR or the HII region.Comment: 25 pages, 13 figures, published in MNRA

A λ\lambda20cm Survey of the Galactic Center Region I: Detection of Numerous Linear Filaments

We present a sensitive $\lambda$20cm VLA continuum survey of the Galactic center region using new and archival data based on multi-configuration observations taken with relatively uniform {\it uv} coverage. The high dynamic range images cover the regions within $-2^\circ < l < 5^\circ$ and $-40' < b < 40'$ with a spatial resolution of $\approx30''$ and 10$''$. The wide field imaging technique is used to construct a low-resolution mosaic of 40 overlapping pointings. The mosaic image includes the Effelsburg observations filling the low spatial frequency {\it uv} data. We also present high resolution images of twenty three overlapping fields using DnC and CnB array configurations. The survey has resulted in a catalog of 345 discrete sources as well as 140 images revealing structural details of HII regions, SNRs, pulsar wind nebulae and more than 80 linear filaments distributed toward the complex region of the Galactic center. These observations show the evidence for an order of magnitude increase in the number of faint linear filaments with typical lengths of few arcminutes. Many of the filaments show morphological characteristics similar to the Galactic center nonthermal radio filaments (NRFs). The linear filaments are not isolated but are generally clustered in star forming regions where prominent NRFs had been detected previously. The extensions of many of these linear filaments appear to terminate at either a compact source or a resolved shell-like thermal source. A relationship between the filaments, the compact and extended thermal sources as well as a lack of preferred orientation for many RFs should constrain models that are proposed to explain the origin of nonthermal radio filaments in the Galactic center.Comment: 48 pages. The complete version of the paper with 140 figures and four tables can be found in the ApJ preprint website: http://www.journals.uchicago.edu/ApJ/future.htm

Reducing the Risk of Adeno-Associated Virus (AAV) Vector Mobilization with AAV Type 5 Vectors

Current adeno-associated virus (AAV) gene therapy vectors package a transgene flanked by the terminal repeats (TRs) of AAV type 2 (AAV2). Although these vectors are replication deficient, wild-type (wt) AAV2 prevalent in the human population could lead to replication and packaging of a type 2 TR (TR2)-flanked transgene in trans during superinfection by a helper virus, leading to “mobilization” of the vector genome from treated cells. More importantly, it appears likely that the majority of currently characterized AAV serotypes as well as the majority of new novel isolates are capable of rescuing and replicating AAV2 vector templates. To investigate this possibility, we flanked a green fluorescent protein transgene with type 2 and, the most divergent AAV serotype, type 5 TRs (TR2 or TR5). Consistent with AAV clades, AAV5 specifically replicated TR5 vectors, while AAV2 and AAV6 replicated TR2-flanked vectors. To exploit this specificity, we created a TR5 vector production system for Cap1 to Cap5. Next, we showed that persisting recombinant AAV genomes flanked by TR2s or TR5s were mobilized in vitro after addition of the cognate AAV Rep (as well as Rep6 for TR2) and adenoviral helper. Finally, we showed that a cell line containing a stably integrated wt AAV2 genome resulted in mobilization of a TR2-flanked vector but not a TR5-flanked vector upon adenoviral superinfection. Based on these data and the relative prevalence of wt AAV serotypes in the population, we propose that TR5 vectors have a significantly lower risk of mobilization and should be considered for clinical use

A Cauchy-Dirac delta function

The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal definition of delta.Comment: 24 pages, 2 figures; Foundations of Science, 201

Postglacial expansion of the arctic keystone copepod calanus glacialis

Calanus glacialis, a major contributor to zooplankton biomass in the Arctic shelf seas, is a key link between primary production and higher trophic levels that may be sensitive to climate warming. The aim of this study was to explore genetic variation in contemporary populations of this species to infer possible changes during the Quaternary period, and to assess its population structure in both space and time. Calanus glacialis was sampled in the fjords of Spitsbergen (Hornsund and Kongsfjorden) in 2003, 2004, 2006, 2009 and 2012. The sequence of a mitochondrial marker, belonging to the ND5 gene, selected for the study was 1249 base pairs long and distinguished 75 unique haplotypes among 140 individuals that formed three main clades. There was no detectable pattern in the distribution of haplotypes by geographic distance or over time. Interestingly, a Bayesian skyline plot suggested that a 1000-fold increase in population size occurred approximately 10,000 years before present, suggesting a species expansion after the Last Glacial Maximum.GAME from the National Science Centre, the Polish Ministry of Science and Higher Education Iuventus Plus [IP2014 050573]; FCT-PT [CCMAR/Multi/04326/2013]; [2011/03/B/NZ8/02876

Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite-Difference Scheme

We discuss the numerical solution of nonlinear parabolic partial differential equations, exhibiting finite speed of propagation, via a strongly implicit finite-difference scheme with formal truncation error $\mathcal{O}\left[(\Delta x)^2 + (\Delta t)^2 \right]$. Our application of interest is the spreading of viscous gravity currents in the study of which these type of differential equations arise. Viscous gravity currents are low Reynolds number (viscous forces dominate inertial forces) flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. The fluids may be confined by the sidewalls of a channel or propagate in an unconfined two-dimensional (or axisymmetric three-dimensional) geometry. Under the lubrication approximation, the mathematical description of the spreading of these fluids reduces to solving the so-called thin-film equation for the current's shape $h(x,t)$. To solve such nonlinear parabolic equations we propose a finite-difference scheme based on the Crank--Nicolson idea. We implement the scheme for problems involving a single spatial coordinate (i.e., two-dimensional, axisymmetric or spherically-symmetric three-dimensional currents) on an equispaced but staggered grid. We benchmark the scheme against analytical solutions and highlight its strong numerical stability by specifically considering the spreading of non-Newtonian power-law fluids in a variable-width confined channel-like geometry (a "Hele-Shaw cell") subject to a given mass conservation/balance constraint. We show that this constraint can be implemented by re-expressing it as nonlinear flux boundary conditions on the domain's endpoints. Then, we show numerically that the scheme achieves its full second-order accuracy in space and time. We also highlight through numerical simulations how the proposed scheme accurately respects the mass conservation/balance constraint.Comment: 36 pages, 9 figures, Springer book class; v2 includes improvements and corrections; to appear as a contribution in "Applied Wave Mathematics II

Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545

Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond

Many historians of the calculus deny significant continuity between infinitesimal calculus of the 17th century and 20th century developments such as Robinson's theory. Robinson's hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, Robinson regards Berkeley's criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning with historical infinitesimal magnitudes. We argue that Robinson, among others, overestimates the force of Berkeley's criticisms, by underestimating the mathematical and philosophical resources available to Leibniz. Leibniz's infinitesimals are fictions, not logical fictions, as Ishiguro proposed, but rather pure fictions, like imaginaries, which are not eliminable by some syncategorematic paraphrase. We argue that Leibniz's defense of infinitesimals is more firmly grounded than Berkeley's criticism thereof. We show, moreover, that Leibniz's system for differential calculus was free of logical fallacies. Our argument strengthens the conception of modern infinitesimals as a development of Leibniz's strategy of relating inassignable to assignable quantities by means of his transcendental law of homogeneity.Comment: 69 pages, 3 figure