All trees are six-cordial

For any integer $k>0$, a tree $T$ is $k$-cordial if there exists a labeling of the vertices of $T$ by $\mathbb{Z}_k$, inducing a labeling on the edges with edge-weights found by summing the labels on vertices incident to a given edge modulo $k$ so that each label appears on at most one more vertex than any other and each edge-weight appears on at most one more edge than any other. We prove that all trees are six-cordial by an adjustment of the test proposed by Hovey (1991) to show all trees are $k$-cordial.Comment: 16 pages, 12 figure

Finite element model of an impact on a palmar pad from a snowboard wrist protector

Wrist injuries are the most common types of injury in snowboarding. Protectors can reduce injury risk by limiting wrist hyperextension and attenuating impact forces. There are a range of wrist protector concepts available, but it is unclear if any particular design is more effective. The aim of this study was to develop and validate a finite element model of an impact on the palmar pad from a protector. Pad material from a protector was characterised to obtain stress vs strain data, and determine whether it was rate dependent. Material data was implemented into a finite element model to predict impact behavior at 2.5 J. Four material models were investigated, with an Ogden model paired with a Prony series providing the best agreement to experimental data. Future work will build a model of a complete protector for predicting the protective levels of these products

Fuel cycle optimization of thorium and uranium fueled PWR systems

Originally presented as the first author's thesis, (Ph.D.) in the M.I.T. Dept. of Nuclear Engineering, 1978.The burnup neutronics of uniform PWR lattices are examined with respect to reduction of uranium ore requirements with an emphasis on variation of the fuel-to-moderator ratio (lattice pitch at constant fuel pin diameter) and the use of thorium. Fuel cycles using all combinations of the major fissile (U-235, U-233, Pu) and fertile (U-238, Th) species are examined. The LEOPARD code and prescriptions developed from a linear reactivity model are used to determine initial core and annual makeup fissile requirements for input into an in-house, simple, systems model, MASFLO-2, which calculates ore (and separative work) requirements per GWeyr for growing, declining, or finite-life nuclear electric systems. For low growth scenarios drier lattices are favored, and the thorium fuel cycle requires as much as 23% less ore than a comparably optimized uranium cycle with full recycle. For unmodified lattices, the thorium fuel cycle with full recycle exhibits long term uranium ore savings of 17% over the comparable uranium cycle with full recycle. For rapidly growing systems, drier lattices, and those using thorium, are less attractive because of their high startup inventories. Thus the introduction of thorium may increase ore and separative work requirements in the short term but will more than repay the ore investment in the very long term. Very little improvement was achieved by varying fuel pin diameter at a given fuel-to-moderator ratio, but itwas found to be slightly advantageous to recycle plutonium (or U-233) into dedicated reactors having individually optimized lattices: a strategy which may also be attractive for safeguards purposes.ERDA Contract no. EY-76-A-01-2295

Efficacy of Density in Predicting the Protective Properties of Padded Clothing in Rugby

World Rugby™ permits players to wear padded clothing meeting the requirements of Regulation-12, which limits density, thickness and impact performance. Due to non-uniform geometry, measuring the density of padding can be challenging and provides limited information on mechanical properties. This study investigated how well density could predict the impact performance of rugby padding, whilst reviewing compliance parameters as alternatives. Eleven samples of rugby padding, plus one control material, were tested for compliance, then impacted at energies of 4.9, 9.8 and 14.7 J using the setup as defined in Regulation-12, and finally cut to calculate density. The density and compliance parameters were correlated against peak impact accelerations using a Spearman’s rank test. Density was not significantly correlated with peak acceleration at any energy level, with compliance tests significantly correlated with impact acceleration at only 4.9 J

Design innovation for the 1990's

Statement of responsibility on title-page reads: Richard K. Lester, Michael J. Driscoll, Michael W. Golay, David D. Lanning, Lawrence M. Lidsky, Norman C. Rasmussen and Neil E. Todreas"September 1983."Includes bibliographical reference