The functional integral with unconditional Wiener measure for anharmonic oscillator

In this article we propose the calculation of the unconditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. In such a case we can profit from the representation of the integral in question by the parabolic cylinder functions. We show that in such a case the series expansions are uniformly convergent and we find recurrence relations for the Wiener functional integral in the $N$ - dimensional approximation. In continuum limit we find that the generalized Gelfand - Yaglom differential equation with solution yields the desired functional integral (similarly as the standard Gelfand - Yaglom differential equation yields the functional integral for linear harmonic oscillator).Comment: Source file which we sent to journa

A philosophical context for methods to estimate origin-destination trip matrices using link counts.

This paper creates a philosophical structure for classifying methods which estimate origin-destination matrices using link counts. It is claimed that the motivation for doing so is to help real-life transport planners use matrix estimation methods effectively, especially in terms of trading-off observational data with prior subjective input (typically referred to as 'professional judgement'). The paper lists a number of applications that require such methods, differentiating between relatively simple and highly complex applications. It is argued that a sound philosophical perspective is particularly important for estimating trip matrices in the latter type of application. As a result of this argument, a classification structure is built up through using concepts of realism, subjectivity, empiricism and rationalism. Emphasis is put on the fact that, in typical transport planning applications, none of these concepts is useful in its extreme form. The structure is then used to make a review of methods for estimating trip matrices using link counts, covering material published over the past 30 years. The paper concludes by making recommendations, both philosophical and methodological, concerning both practical applications and further research

Radio Emission from the Composite Supernova Remnant G326.3-1.8 (MSH15-56)

High resolution radio observations of the composite supernova remnant (SNR) G326.3-1.8 or MSH 15-56 with the Australia Telescope Compact Array show details of both the shell and the bright plerion which is offset about 1/3 of the distance from the center of the SNR to the shell. The shell appears to be composed of thin filaments, typical of older shell SNRs. The central part of the elongated plerion is composed of a bundle of parallel ridges which bulge out at the ends and form a distinct ring structure on the northwestern end. The magnetic field with a strength of order 45 microGauss, is directed along the axis of the ridges but circles around the northwestern ring. This plerion is large and bright in the radio but is not detected in x-ray or optical wavelengths. There is, however, a faint hard x-ray feature closer to the shell outside the plerion. Perhaps if the supernova explosion left a rapidly moving magnetar with large energy input but initially rapid decay of both relativistic particles and magnetic field, the observed differences with wavelength could be explained.Comment: 15 pages, 10 figures, accepted by Ap

Ultraviolet Diversity of Type Ia Supernovae

Ultraviolet (UV) observations of Type Ia supernovae (SNe Ia) probe the outermost layers of the explosion, and UV spectra of SNe Ia are expected to be extremely sensitive to differences in progenitor composition and the details of the explosion. Here we present the first study of a sample of high signal-to-noise ratio SN Ia spectra that extend blueward of 2900 A. We focus on spectra taken within 5 days of maximum brightness. Our sample of ten SNe Ia spans the majority of the parameter space of SN Ia optical diversity. We find that SNe Ia have significantly more diversity in the UV than in the optical, with the spectral variance continuing to increase with decreasing wavelengths until at least 1800 A (the limit of our data). The majority of the UV variance correlates with optical light-curve shape, while there are no obvious and unique correlations between spectral shape and either ejecta velocity or host-galaxy morphology. Using light-curve shape as the primary variable, we create a UV spectral model for SNe Ia at peak brightness. With the model, we can examine how individual SNe vary relative to expectations based on only their light-curve shape. Doing this, we confirm an excess of flux for SN 2011fe at short wavelengths, consistent with its progenitor having a subsolar metallicity. While most other SNe Ia do not show large deviations from the model, ASASSN-14lp has a deficit of flux at short wavelengths, suggesting that its progenitor was relatively metal rich.Comment: 9 pages, 6 figures, submitted to MNRA

Vortex Images and q-Elementary Functions

In the present paper problem of vortex images in annular domain between two coaxial cylinders is solved by the q-elementary functions. We show that all images are determined completely as poles of the q-logarithmic function, where dimensionless parameter $q = r^2_2/r^2_1$ is given by square ratio of the cylinder radii. Resulting solution for the complex potential is represented in terms of the Jackson q-exponential function. By composing pairs of q-exponents to the first Jacobi theta function and conformal mapping to a rectangular domain we link our solution with result of Johnson and McDonald. We found that one vortex cannot remain at rest except at the geometric mean distance, but must orbit the cylinders with constant angular velocity related to q-harmonic series. Vortex images in two particular geometries in the $q \to \infty$ limit are studied.Comment: 17 page

On the non-abelian Brumer-Stark conjecture and the equivariant Iwasawa main conjecture

We show that for an odd prime p, the p-primary parts of refinements of the (imprimitive) non-abelian Brumer and Brumer-Stark conjectures are implied by the equivariant Iwasawa main conjecture (EIMC) for totally real fields. Crucially, this result does not depend on the vanishing of the relevant Iwasawa mu-invariant. In combination with the authors' previous work on the EIMC, this leads to unconditional proofs of the non-abelian Brumer and Brumer-Stark conjectures in many new cases.Comment: 33 pages; to appear in Mathematische Zeitschrift; v3 many minor updates including new title; v2 some cohomological arguments simplified; v1 is a revised version of the second half of arXiv:1408.4934v

The Robotic Super-LOTIS Telescope: Results & Future Plans

We provide an overview of the robotic Super-LOTIS (Livermore Optical Transient Imaging System) telescope and present results from gamma-ray burst (GRB) afterglow observations using Super-LOTIS and other Steward Observatory telescopes. The 0.6-m Super-LOTIS telescope is a fully robotic system dedicated to the measurement of prompt and early time optical emission from GRBs. The system began routine operations from its Steward Observatory site atop Kitt Peak in April 2000 and currently operates every clear night. The telescope is instrumented with an optical CCD camera and a four position filter wheel. It is capable of observing Swift Burst Alert Telescope (BAT) error boxes as early or earlier than the Swift UV/Optical Telescope (UVOT). Super-LOTIS complements the UVOT observations by providing early R- and I-band imaging. We also use the suite of Steward Observatory telescopes including the 1.6-m Kuiper, the 2.3-m Bok, the 6.5-m MMT, and the 8.4-m Large Binocular Telescope to perform follow-up optical and near infrared observations of GRB afterglows. These follow-up observations have traditionally required human intervention but we are currently working to automate the 1.6-m Kuiper telescope to minimize its response time

Second order perturbations of a zero-pressure cosmological medium: Proofs of the relativistic-Newtonian correspondence

The dynamic world model and its linear perturbations were first studied in Einstein's gravity. In the system without pressure the relativistic equations coincide exactly with the later known ones in Newton's gravity. Here we prove that, except for the gravitational wave contribution, even to the second-order perturbations, equations for the relativistic irrotational zero-pressure fluid in a flat Friedmann background coincide exactly with the previously known Newtonian equations. Thus, to the second order, we correctly identify the relativistic density and velocity perturbation variables, and we expand the range of applicability of the Newtonian medium without pressure to all cosmological scales including the super-horizon scale. In the relativistic analyses, however, we do not have a relativistic variable which corresponds to the Newtonian potential to the second order. Mixed usage of different gauge conditions is useful to make such proofs and to examine the result with perspective. We also present the gravitational wave equation to the second order. Since our correspondence includes the cosmological constant, our results are relevant to currently favoured cosmology. Our result has an important practical implication that one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near horizon.Comment: 10 pages, no figur