Preliminary test results of a flight management algorithm for fuel conservative descents in a time based metered traffic environment

A flight management algorithm designed to improve the accuracy of delivering the airplane fuel efficiently to a metering fix at a time designated by air traffic control is discussed. The algorithm provides a 3-D path with time control (4-D) for a test B 737 airplane to make an idle thrust, clean configured descent to arrive at the metering fix at a predetermined time, altitude, and airspeed. The descent path is calculated for a constant Mach/airspeed schedule from linear approximations of airplane performance with considerations given for gross weight, wind, and nonstandard pressure and temperature effects. The flight management descent algorithms and the results of the flight tests are discussed

Coherence of Associativity in Categories with Multiplication

The usual coherence theorem of MacLane for categories with multiplication assumes that a certain pentagonal diagram commutes in order to conclude that associativity isomorphisms are well defined in a certain practical sense. The practical aspects include creating associativity isomorphisms from a given one by tensoring with the identity on either the right or the left. We show, by reinspecting MacLane's original arguments, that if tensoring with the identity is restricted to one side, then the well definedness of constructed isomorphisms follows from naturality only, with no need of the commutativity of the pentagonal diagram. This observation was discovered by noting the resemblance of the usual coherence theorems with certain properties of a finitely presented group known as Thompson's group F. This paper is to be taken as an advertisement for this connection.Comment: 8 pages, to appear in Journal of Pure and Applied Algebr

Cratering in low-density targets

Cratering in low density targets, and comparisons of various hypervelocity projectile-target combination

The Algebra of Strand Splitting. II. A Presentation for the Braid Group on One Strand

Presentations are computed for a braided version BV of Thompson's group V and for V itself showing that there is an Artin group/Coxeter group relation between them. The presentation for V is obtained from that for BV by declaring all that all generators are involutions.Comment: 15 page

The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V

We construct a braided version of Thompson's group V.Comment: 27 page

On small homotopies of loops

Two natural questions are answered in the negative: (1) If a space has the property that small nulhomotopic loops bound small nulhomotopies, then are loops which are limits of nulhomotopic loops themselves nulhomotopic? (2) Can adding arcs to a space cause an essential curve to become nulhomotopic? The answer to the first question clarifies the relationship between the notions of a space being homotopically Hausdorff and $\pi_1$-shape injective.Comment: 12 pages, 5 figure

Dry matter yields and quality of organic lupin/cereal mixtures for wholecrop forage

In view of climate change predictions and the general desirability of increasing the amount of home grown protein, a case exists for the investigation of lupins and lupin/cereal bicrop combinations as wholecrop forage on organic farms. A replicated randomised block trial is described which took place at the Royal Agricultural College, Cirencester, in 2005. This involved spring sown blue, white and yellow lupins, millet, wheat and triticale and lupin/cereal bi-crops. Data for dry matter yields for wholecrop silage, crude protein, MAD fi bre content and estimated ME, are presented for a single harvest. It is concluded that white lupins and white lupin bi-crops with spring wheat or triticale offer the best prospects for a viable wholecrop forage crop in an organic situation