Summation and transformation formulas for elliptic hypergeometric series

Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating, balanced, very-well-poised, elliptic hypergeometric series.Comment: 21 pages, AMS-LaTe

Geometric Laws of Vortex Quantum Tunneling

In the semiclassical domain the exponent of vortex quantum tunneling is dominated by a volume which is associated with the path the vortex line traces out during its escape from the metastable well. We explicitly show the influence of geometrical quantities on this volume by describing point vortex motion in the presence of an ellipse. It is argued that for the semiclassical description to hold the introduction of an additional geometric constraint, the distance of closest approach, is required. This constraint implies that the semiclassical description of vortex nucleation by tunneling at a boundary is in general not possible. Geometry dependence of the tunneling volume provides a means to verify experimental observation of vortex quantum tunneling in the superfluid Helium II.Comment: 4 pages, 2 figures, revised version to appear in Phys. Rev.

A high-resolution radio survey of the Vela supernova remnant

This paper presents a high-resolution radio continuum (843 MHz) survey of the Vela supernova remnant. The contrast between the structures in the central pulsar-powered nebula of the remnant and the synchrotron radiation shell allows the remnant to be identified morphologically as a member of the composite class. The data are the first of a composite remnant at spatial scales comparable with those available for the Cygnus Loop and the Crab Nebula, and make possible a comparison of radio, optical and soft X-ray emission from the resolved shell filaments. The survey, made with the Molonglo Observatory Synthesis Telescope, covers an area of 50 square degrees at a resolution of 43'' x 60'', while imaging structures on scales up to 30'.Comment: 18 pages, 7 jpg figures (version with ps figures at http://astro.berkeley.edu/~dbock/papers/); AJ, in pres

Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN 1006

A joint spectral analysis of some Chandra ACIS X-ray data and Molonglo Observatory Synthesis Telescope radio data was performed for 13 small regions along the bright northeastern rim of the supernova remnant SN 1006. These data were fitted with a synchrotron radiation model. The nonthermal electron spectrum used to compute the photon emission spectra is the traditional exponentially cut off power law, with one notable difference: The power-law index is not a constant. It is a linear function of the logarithm of the momentum. This functional form enables us to show, for the first time, that the synchrotron spectrum of SN 1006 seems to flatten with increasing energy. The effective power-law index of the electron spectrum is 2.2 at 1 GeV (i.e., radio synchrotron-emitting momenta) and 2.0 at about 10 TeV (i.e., X-ray synchrotron-emitting momenta). This amount of change in the index is qualitatively consistent with theoretical models of the amount of curvature in the proton spectrum of the remnant. The evidence of spectral curvature implies that cosmic rays are dynamically important instead of being "test" particles. The spectral analysis also provides a means of determining the critical frequency of the synchrotron spectrum associated with the highest-energy electrons. The critical frequency seems to vary along the northeastern rim, with a maximum value of 1.1e17 (0.6e17 - 2.1e17) Hz. This value implies that the electron diffusion coefficient can be no larger than a factor of ~4.5-21 times the Bohm diffusion coefficient if the velocity of the forward shock is in the range 2300-5000 km/s. Since the coefficient is close to the Bohm limit, electrons are accelerated nearly as fast as possible in the regions where the critical frequency is about 1.0e17 Hz.Comment: 41 pages, 8 figures, accepted by Ap

Radio Observations of the Supernova Remnant Candidate G312.5-3.0

The radio images from the Parkes-MIT-NRAO (PMN) Southern Sky Survey at 4850 MHz have revealed a number of previously unknown radio sources. One such source, G312.5-3.0 (PMN J1421-6415), has been observed using the multi-frequency capabilities of the Australia Telescope Compact Array (ATCA) at frequencies of 1380 MHz and 2378 MHz. Further observations of the source were made using the Molonglo Observatory Synthesis Telescope (MOST) at a frequency of 843 MHz. The source has an angular size of 18 arcmin and has a distinct shell structure. We present the reduced multi-frequency observations of this source and provide a brief argument for its possible identification as a supernova remnant.Comment: 5 pages, 5 figures, Accepted for publication in MNRA

PSR J1016-5857: a young radio pulsar with possible supernova remnant, X-ray, and gamma-ray associations

We report the discovery of a young and energetic pulsar in the Parkes multibeam survey of the Galactic plane. PSR J1016-5857 has a rotation period of 107 ms and period derivative of 8e-14, implying a characteristic age of 21 kyr and spin-down luminosity of 2.6e36 erg/s. The pulsar is located just outside, and possibly interacting with, the shell supernova remnant G284.3-1.8. Archival X-ray data show a source near the pulsar position which is consistent with emission from a pulsar wind nebula. The pulsar is also located inside the error box of the unidentified EGRET source 3EG J1013-5915, for which it represents a plausible counterpart.Comment: 5 pages, 3 included figures, accepted for publication by ApJ Letter

Vector Theory of Gravity

We proposed a gravitation theory based on an analogy with electrodynamics on the basis of a vector field. For the first time, to calculate the basic gravitational effects in the framework of a vector theory of gravity, we use a Lagrangian written with gravitational radiation neglected and generalized to the case of ultra-relativistic speeds. This allows us to accurately calculate the values of all three major gravity experiments: the values of the perihelion shift of Mercury, the light deflection angle in the gravity field of the Sun and the value of radar echo delay. The calculated values coincide with the observed ones. It is shown that, in this theory, there exists a model of an expanding Universe.Comment: 9 page

Dynamics of bacterial blight disease in resistant and susceptible rice varieties

Bacterial blight (X. oryzae pv. oryzae) is a serious disease in rice across the world. To better control the disease, it is important to understand its epidemiology and how key aspects of this (e.g. infection efficiency, and spatial spread) change according to environment (e.g. local site conditions and season), management, and in particular, variety resistance. To explore this, we analysed data on the disease progress on resistant and susceptible varieties of rice grown at four sites in the Philippines across five seasons using a combination of mechanistic modelling and statistical analysis. Disease incidence was generally lower in the resistant variety. However, we found no evidence that the primary infection efficiency was lower in resistant varieties, suggesting that differences were largely due to reduced secondary spread. Despite secondary spread being attributed to splash dispersal which is exacerbated by wind and rain, the wetter sites of Pila and Victoria in south Luzon tended to have lower infection rates than the drier sites in central Luzon. Likewise, we found spread in the dry season can be substantial and should therefore not be ignored. In fact, we found site to be a greater determinant of the number of infection attempts suggesting that other environmental and management factors had greater effect on the disease than climate. Primary infection was characterised by spatially-random observations of disease incidence. As the season progressed, we observed an emerging short-range (1.6 m–4 m) spatial structure suggesting secondary spread was predominantly short-range, particularly where the resistant variety was grown

Third order perturbations of a zero-pressure cosmological medium: Pure general relativistic nonlinear effects

We consider a general relativistic zero-pressure irrotational cosmological medium perturbed to the third order. We assume a flat Friedmann background but include the cosmological constant. We ignore the rotational perturbation which decays in expanding phase. In our previous studies we discovered that, to the second-order perturbation, except for the gravitational wave contributions, the relativistic equations coincide exactly with the previously known Newtonian ones. Since the Newtonian second-order equations are fully nonlinear, any nonvanishing third and higher order terms in the relativistic analyses are supposed to be pure relativistic corrections. In this work we derive such correction terms appearing in the third order. Continuing our success in the second-order perturbations we take the comoving gauge. We discover that the third-order correction terms are of $\phi_v$-order higher than the second-order terms where $\phi_v$ is a gauge-invariant combination related to the three-space curvature perturbation in the comoving gauge; compared with the Newtonian potential we have $\delta \Phi \sim {3 \over 5} \phi_v$ to the linear order. Therefore, the pure general relativistic effects are of $varphi_v$-order higher than the Newtonian ones. The corrections terms are independent of the horizon scale and depend only on the linear order gravitational potential perturbation strength. From the temperature anisotropy of cosmic microwave background we have ${\delta T \over T} \sim {1 \over 3} \delta \Phi \sim {1 \over 5} \phi_v \sim 10^{-5}$. Therefore, our present result reinforces our previous important practical implication that near current era one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near the horizon.Comment: 9 pages, no figur