Subword complexes in Coxeter groups

Let (Π,Σ) be a Coxeter system. An ordered list of elements in Σ and an element in Π determine a subword complex, as introduced in Knutson and Miller (Ann. of Math. (2) (2003), to appear). Subword complexes are demonstrated here to be homeomorphic to balls or spheres, and their Hilbert series are shown to reflect combinatorial properties of reduced expressions in Coxeter groups. Two formulae for double Grothendieck polynomials, one of which appeared in Fomin and Kirillov (Proceedings of the Sixth Conference in Formal Power Series and Algebraic Combinatorics, DIMACS, 1994, pp. 183-190), are recovered in the context of simplicial topology for subword complexes. Some open questions related to subword complexes are presented.     

Fiber formation via solution spinning of the cellulose/ammonia/ammonium thiocyanate system

Fiber formation via the cellulose/ammonia/ammonium thiocyanate system by wet spinning has been investigated. This report presents a characterization of the structure and tensile properties of fibers spun under various coagulation conditions. Microscopic observations showed that the molecular size of coagulant was the dominant factor governing the crosssectional shape of the fibers. Density, birefringence, and crystallinity data indicated that a higher cellulose concentration and lower coagulation temperature favored development of a fiber with a denser and more oriented structure. Under optimum conditions, a welldefined fibrillar structure was obtained. Fiber tensile property measurements suggested the existence of a linear relationship between the fiber breaking tenacity and the product of the square of the Hermans' orientation factor and the infrared crystallinity index.     

The convergence rate for the strong law of large numbers: General lattice distributions

LetX ₁,X ₂, ... be a sequence of independent random variables with common lattice distribution functionF having zero mean, and let (S _n ) be the random walk of partial sums. The strong law of large numbers (SLLN) implies that for any and >0

Ultrasound treatment acceleration of solvent extraction for fumigant residues from wheat

Concerns about consumer and worker safety and the fate of fumigants have fuelled strong efforts to determine their residues in foodstuffs. Fumigants are usually extracted from commodities with solvent at room temperature (25 degrees C). In this paper, solvent extraction of methyl bromide, phosphine, carbonyl sulfide, and carbon disulfide using ultrasonic acceleration or heating was evaluated. Wheat samples plus solvent, in gas-tight bottles, were placed in an ultrasonic chamber or an oven (50 degrees C), and fumigants were released into the headspace over the solvent. Completeness of extraction was demonstrated within 2 h for ultrasonic extraction, 7-20 h for 50 degrees C heating, and 8-35 h for room temperature extraction. The rapidity of extraction was mainly due to ultrasonic vibration rather than increased temperature.