The diophantine problem Y² - X³ = A in a polynomial ring

Let C[z] be the ring of polynomials in z with complex coefficients; we consider the equation Y² — X³ = A, with A[is an element of]C[z] given, and seek solutions of this with X, Y[is an element of]C[z] i.e. we treat the equation as a "polynomial diophantine" problem. We show that when A is of degree 5 or 6 and has no multiple roots, then there are exactly 240 solutions (X, Y) to the problem with deg X ≤ 2 and deg Y ≤ 3

A Modern Look at Freedman's Box Model

This paper revisits the box model, a metaphor developed by David Freedman to explain sampling distributions and  statistical inference to introductory statistics students. The basic idea is to represent all random phenomena in terms of drawing tickets at random from a box. In this way, random sampling from a population can be described in the same way as everyday phenomena, like coin tossing and card dealing. For Freedman, box models were merely a thought experiment; calculations were still done using normal approximations. In this paper, we propose a more modern view that treats the box model as a practical simulation framework for conducting inference. We show how concepts in introductory statistics and probability classes can be motivated by simulating from a box model. To facilitate this simulation-based approach to teaching box models, we developed an online, open-source "box model simulator"

Nozzle fabrication technique

This invention relates to techniques for fabricating hour glass throat or convergent divergent nozzle shapes, and more particularly to new and improved techniques for forming rocket nozzles from electrically conductive material and forming cooling channels in the wall thereof. The concept of positioning a block of electrically conductive material so that its axis is set at a predetermined skew angle with relation to a travelling electron discharge machine electrode and thereafter revolving the body about its own axis to generate a hyperbolic surface of revolution, either internal or external is novel. The method will generate a rocket nozzle which may be provided with cooling channels using the same control and positioning system. The configuration of the cooling channels so produced are unique and novel. Also the method is adaptable to nonmetallic material using analogous cutting tools, such as, water jet, laser, abrasive wire and hot wire

Exploring the Revenue Mix of Nonprofit Organizations -- Does it Relate to Publicness

Nonprofit organizations offer a wide range of goods and services and seek funding from a variety of revenue sources. Our working theory n this paper is that the sources of funding are related to the services a nonprofit provides - specifically whether services are public, private, or mixed in the nature of their benefits. Using multiple subfields from three major fields in the National Taxonomy of Exempt Entities (NTEE), this study divides nonprofits according to service type, and estimates the impact of service character on particular revenue streams and overall level of revenue diversification. Generally, the proportion of revenues generated by program fees is lowest for the category deemed public, highest for those with mostly private benefits, and midway for "mixed" services which are private in character but entail substantial public benefits. Similarly, the more public a nonprofit's services, the greater the proportion of revenues it generates through donations. However, we also identify some puzzling results that suggest the need for continued investigation of the determinants of the sources and mixes of nonprofit income. Working Paper 07-3

Spectroscopy of Ultra-diffuse Galaxies in the Coma Cluster

We present spectra of 5 ultra-diffuse galaxies (UDGs) in the vicinity of the Coma Cluster obtained with the Multi-Object Double Spectrograph on the Large Binocular Telescope. We confirm 4 of these as members of the cluster, quintupling the number of spectroscopically confirmed systems. Like the previously confirmed large (projected half light radius $>$ 4.6 kpc) UDG, DF44, the systems we targeted all have projected half light radii $> 2.9$ kpc. As such, we spectroscopically confirm a population of physically large UDGs in the Coma cluster. The remaining UDG is located in the field, about $45$ Mpc behind the cluster. We observe Balmer and Ca II H \& K absorption lines in all of our UDG spectra. By comparing the stacked UDG spectrum against stellar population synthesis models, we conclude that, on average, these UDGs are composed of metal-poor stars ([Fe/H] $\lesssim -1.5$). We also discover the first UDG with [OII] and [OIII] emission lines within a clustered environment, demonstrating that not all cluster UDGs are devoid of gas and sources of ionizing radiation.Comment: 5 pages, 4 figure

Optical instrumentation data evaluation of the SA-204/LM-1 Saturn 1B launch vehicle

Optical instrumentation data evaluation of SA- 204 /LM-1/ Saturn 1B launch vehicl