Divisor class groups of rational trinomial varieties

We give an explicit description of the divisor class groups of rational trinomial varieties. As an application, we relate the iteration of Cox rings of any rational variety with torus action of complexity one to that of a Du Val surface.Comment: 17 page

Parsec-Scale Localization of the Quasar SDSS J1536+0441A, a Candidate Binary Black Hole System

The radio-quiet quasar SDSS J1536+0441A shows two broad-line emission systems, recently interpreted as a binary black hole (BBH) system with a subparsec separation; as a double-peaked emitter; or as both types of systems. The NRAO VLBA was used to search for 8.4 GHz emission from SDSS J1536+0441A, focusing on the optical localization region for the broad-line emission, of area 5400 mas^2 (0.15 kpc^2). One source was detected, with a diameter of less than 1.63 mas (8.5 pc) and a brightness temperature T_b > 1.2 x 10^7 K. New NRAO VLA photometry at 22.5 GHz, and earlier photometry at 8.5 GHz, gives a rising spectral slope of alpha = 0.35+/-0.08. The slope implies an optically thick synchrotron source, with a radius of about 0.04 pc, and thus T_b ~ 5 x 10^10 K. The implied radio-sphere at rest frame 31.2 GHz has a radius of 800 gravitational radii, just below the size of the broad line region in this object. Observations at higher frequencies can probe whether or not the radio-sphere is as compact as expected from the coronal framework for the radio emission of radio-quiet quasars.Comment: 6 pages; 2 figures; emulateapj.cls; to appear in ApJ

On the propagation of a normal shock wave through a layer of incompressible porous material

A novel numerical formulation of the two-phase macroscopic balance equations governing the flow field in incompressible porous media is presented. The numerical model makes use of the Weighted Average Flux (WAF) method and Total Variation Diminishing (TVD) flux limiting techniques, and results in a second-order accurate scheme. A shock tube study was carried out to examine the interaction of a normal shock wave with a thin layer of porous, incompressible cellular ceramic foam. Particular attention was paid to the transmitted and reflected flow fields. The numerical model was used to simulate the experimental test cases, and their results compared with a view to validating the numerical model. A phenomenological model is proposed to explain the behaviour of the transmitted flow field

Some Algebraic and Algorithmic Problems in Acoustocerebrography

Progress in the medical diagnostic is relentlessly pushing the measurement technology as well with its intertwined mathematical models and solutions. Mathematics has applications to many problems that are vital to human health but not for all. In this article we describe how the mathematics of acoustocerebrography has become one of the most important applications of mathematics to the problems of brain monitoring as well we will show some algebraic problems which still have to be solved. Acoustocerebrography ([4, 1]) is a set of techniques of visualizing the state of (human) brain tissue and its changes with use of ultrasounds, which mainly rely on a relation between the tissue density and speed of propagation for ultrasound waves in this medium. Propagation speed or, equivalently, times of arriving for an ultrasound pulse, can be inferred from phase relations for various frequencies. Since, due to Kramers-Kronig relations,the propagation speeds depend significantly on the frequency of investigated waves, we consider multispectral wave packages of the form W (n) = ∑Hh=1 Ah · sin(2π ·fh · n/F + ψh), n = 0, . . . , N – 1 with appropriately chosen frequencies fh, h = 1, . . . ,H, amplifications Ah, h = 1, . . . ,H, start phases ψh, h = 1, . . . , H and sampling frequency F. In this paper we show some problems of algebraic and, to some extend, algorithmic nature which raise up in this topic. Like, for instance, the influence of relations between the signal length and frequency values on the error on estimated phases or on neutralizing alien frequencies. Another problem is finding appropriate initial phases for avoiding improper distributions of peaks in the resulting signal or finding a stable algorithm of phase unwinding which is resistant to sudden random disruptions