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

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

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"

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

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

THE ALLOCATION OF RESEARCH PERSONNEL: ADMINISTRATORS' RESPONSE TO EXPECTED RATES TO RETURN

Research and Development/Tech Change/Emerging Technologies,

Specifying and Executing Optimizations for Parallel Programs

Compiler optimizations, usually expressed as rewrites on program graphs, are a core part of all modern compilers. However, even production compilers have bugs, and these bugs are difficult to detect and resolve. The problem only becomes more complex when compiling parallel programs; from the choice of graph representation to the possibility of race conditions, optimization designers have a range of factors to consider that do not appear when dealing with single-threaded programs. In this paper we present PTRANS, a domain-specific language for formal specification of compiler transformations, and describe its executable semantics. The fundamental approach of PTRANS is to describe program transformations as rewrites on control flow graphs with temporal logic side conditions. The syntax of PTRANS allows cleaner, more comprehensible specification of program optimizations; its executable semantics allows these specifications to act as prototypes for the optimizations themselves, so that candidate optimizations can be tested and refined before going on to include them in a compiler. We demonstrate the use of PTRANS to state, test, and refine the specification of a redundant store elimination optimization on parallel programs.Comment: In Proceedings GRAPHITE 2014, arXiv:1407.767