Two-player envy-free multi-cake division

We introduce a generalized cake-cutting problem in which we seek to divide multiple cakes so that two players may get their most-preferred piece selections: a choice of one piece from each cake, allowing for the possibility of linked preferences over the cakes. For two players, we show that disjoint envy-free piece selections may not exist for two cakes cut into two pieces each, and they may not exist for three cakes cut into three pieces each. However, there do exist such divisions for two cakes cut into three pieces each, and for three cakes cut into four pieces each. The resulting allocations of pieces to players are Pareto-optimal with respect to the division. We use a generalization of Sperner's lemma on the polytope of divisions to locate solutions to our generalized cake-cutting problem.Comment: 15 pages, 7 figures, see related work at http://www.math.hmc.edu/~su/papers.htm

Comparison of dose estimates using the buildup-factor method and a Baryon transport code (BRYNTRN) with Monte Carlo results

Continuing efforts toward validating the buildup factor method and the BRYNTRN code, which use the deterministic approach in solving radiation transport problems and are the candidate engineering tools in space radiation shielding analyses, are presented. A simplified theory of proton buildup factors assuming no neutron coupling is derived to verify a previously chosen form for parameterizing the dose conversion factor that includes the secondary particle buildup effect. Estimates of dose in tissue made by the two deterministic approaches and the Monte Carlo method are intercompared for cases with various thicknesses of shields and various types of proton spectra. The results are found to be in reasonable agreement but with some overestimation by the buildup factor method when the effect of neutron production in the shield is significant. Future improvement to include neutron coupling in the buildup factor theory is suggested to alleviate this shortcoming. Impressive agreement for individual components of doses, such as those from the secondaries and heavy particle recoils, are obtained between BRYNTRN and Monte Carlo results

Cryogenic Scan Mechanism for Fourier Transform Spectrometer

A compact and lightweight mechanism has been developed to accurately move a Fourier transform spectrometer (FTS) scan mirror (a cube corner) in a near-linear fashion with near constant speed at cryogenic temperatures. This innovation includes a slide mechanism to restrict motion to one dimension, an actuator to drive the motion, and a linear velocity transducer (LVT) to measure the speed. The cube corner mirror is double-passed in one arm of the FTS; double-passing is required to compensate for optical beam shear resulting from tilting of the moving cube corner. The slide, actuator, and LVT are off-the-shelf components that are capable of cryogenic vacuum operation. The actuator drives the slide for the required travel of 2.5 cm. The LVT measures translation speed. A proportional feedback loop compares the LVT voltage with the set voltage (speed) to derive an error signal to drive the actuator and achieve near constant speed. When the end of the scan is reached, a personal computer reverses the set voltage. The actuator and LVT have no moving parts in contact, and have magnetic properties consistent with cryogenic operation. The unlubricated slide restricts motion to linear travel, using crossed roller bearings consistent with 100-million- stroke operation. The mechanism tilts several arc seconds during transport of the FTS mirror, which would compromise optical fringe efficiency when using a flat mirror. Consequently, a cube corner mirror is used, which converts a tilt into a shear. The sheared beam strikes (at normal incidence) a flat mirror at the end of the FTS arm with the moving mechanism, thereby returning upon itself and compensating for the shea

Application rates to undergraduate programs in Information Technology in Australian universities

Over the past decade, there has been much discussion regarding both the supply and the current and potential demand for information technology-oriented graduates in Australia with numerous surveys and market analyses being undertaken. Some surveys have focussed on the supply of graduates from the tertiary and VET sectors and their demand in Australian industry, while others discuss enrolment statistics into IT based University and VET sector courses. Few, however, investigate application rates to IT courses. At the same time, there has been a general, and in some cases significant, decline in the application rates for some science and engineering courses prompting universities to review their awards with a view to making them more attractive to students and industry. Although this study takes advantage of the centralised admissions systems used in Australia, data available elsewhere shows that the results may be applicable more broadly

An analysis of application rates to programs in information technology, science, and engineering

A shift away from generic undergraduate degrees toward an emphasis on vocationally oriented qualifications has been evident in the awards offered by higher education institutions in Australia over the past few years. This has included those in information technology, science and engineering, where the growth in the number of, and variation in, awards has been particularly evident. The past few years have also seen a general, and in some cases significant, decline in the application rates for some forms of science and engineering. This has prompted many institutions to look at their awards with a view to making them more attractive, both to students and industry, often through the development of more highly specialized awards. In this paper, the authors investigate application trends for information technology, science and engineering awards from a number of perspectives, including the market perceptions of the institution offering the degree. Although the paper focuses on three broad categories of awards - information technology, science and engineering - some lessons may be appropriate for other disciplines. Moreover, although this study takes advantage of the centralized admissions systems used in Australia, available indicators show that the results may well be applicable in the United States and the U.K. and possibly elsewhere

Green's function methods in heavy ion shielding

An analytic solution to the heavy ion transport in terms of Green's function is used to generate a highly efficient computer code for space applications. The efficiency of the computer code is accomplished by a nonperturbative technique extending Green's function over the solution domain. The computer code can also be applied to accelerator boundary conditions to allow code validation in laboratory experiments

Effects of fragmentation parameter variations on estimates of galactic cosmic ray exposure: Dose sensitivity studies for aluminum shields

Initial studies of the sensitivities of estimates of particle fluence, absorbed dose, and dose equivalent to fragmentation parameter variations are undertaken by using the LaRC galactic cosmic ray transport code (HZETRN). The new results, presented as a function of aluminum shield thickness, include upper and lower bounds on dose/dose equivalent corresponding to the physically realistic extremes of the fragmentation process and the percentage of variation of the dose/dose equivalent as a function of fragmentation parameter variation

Improved model for solar cosmic ray exposure in manned Earth orbital flights

A calculational model is derived for use in estimating Solar cosmic ray exposure to critical body organs in low-Earth orbit at the center of a large spherical shield of fixed thickness. The effects of the Earth's geomagnetic field and the astronauts' self-shielding are evaluated explicitly. The geomagnetic field model is an approximate tilted eccentric dipole with geomagnetic storms represented as a uniform-impressed field. The storm field is related to the planetary geomagnetic index K(sub p). The code is applied to the Shuttle geometry using the Shuttle mass distribution surrounding two locations on the flight deck. The Shuttle is treated as pure aluminum and the astronaut as soft tissue. Short-term, average fluence over a single orbit is calculated as a function of the location of the lines of nodes or long-term averages over all lines of nodes for a fixed inclination

School sport and academic achievement

ABSTRACT BACKGROUND: Physical Education and School Sport (PESS) is an integral part of the school curriculum in Ireland. Historically the Healthy Body, Healthy Mind philosophy has promoted the inclusion of PESS alongside more cognitive school subjects and research suggests that PESS can promote cognitive function and provide educational benefits. However there is little research on how the choice of school sport influences academic achievement. This case study aims to investigate how participation in school sport influences the Leaving Certificate points score in an Irish secondary school. In particular, the study will investigate how the particular sport chosen by students participating in school sport during their Leaving Certificate years influences their Leaving Certificate results. METHODS: The study recorded the Leaving Certificate scores and sporting participation from 402 school children graduating from an all-boys secondary school in the Republic of Ireland during the period 2008-2011. Sports participation was assigned one of four categories: Rugby; Rowing; Soccer; No Sport. RESULTS: Participation in a sport during the Leaving Certificate years conferred a 25.4 point benefit to the final Leaving Certificate score. However, participation in Rowing, the only individual sport available in the study, resulted in significantly higher Leaving Certificate scores than Rugby, Soccer and No Sport (p < .05), conferring an additional 73.4 point benefit over the next highest group, Rugby. CONCLUSION: Promoting participation in school sport and providing access to a range of team and individual sports throughout the secondary school years may be a beneficial way to improve students Leaving Certificate results

Simplified model for solar cosmic ray exposure in manned Earth orbital flights

A simple calculational model is derived for use in estimating solar cosmic ray exposure to critical body organs in low-Earth orbit at the center of a large spherical shield of fixed thickness. The effects of the Earth's geomagnetic field, including storm conditions and the astronauts' self-shielding, are evaluated explicitly. The magnetic storm model is keyed to the planetary index K(sub p)