Numerical method for a model of inhomogeneous muscle fibers

The numerical solution of a nonlinear and nonlocal system of integro-differential equations that models the contraction of a single heterogeneous muscle fiber is studied. The method proposed is a form of the finite difference method of characteristics. Optimal error bounds are established for the resulting approximation. © 1993 John Wiley & Sons, Inc.     

Some inequalities for partial orders

We establish some inequalities connecting natural parameters of a partial order P. For example, if every interval [a,b] contains at most maximal chains, if some antichain has cardinality v, and if there are ₁ chains whose union is cofinal and coinitial in P, then the chain decomposition number for P is ₁v (Theorem 2.2), and the inequality is sharp in a certain sense (Section 3).This paper was written while the authors were visitors at the Laboratoire d'algèbre ordinale, Département de Mathématiques, Université Claude Bernard, Lyon 1, France.Research supported by NSERC grant # A5198.     

The determination of alumina in silicates (Rocks and Refractories)

New procedures have been developed for determining the alumina contents of silicate material (rocks and refractories). The material is first taken into solution by a peroxide sinter technique, followed by dissolving the sinter in warm water and the addition of sufficient hydrochloric acid to render the solution acid to litmus. A different technique is used for silicates containing less than 5% alumina. The majority of the silica is first removed by treating with hydrofluoric-sulphuric acids and the residue is fused with potassium bisulphate. Extractions with cupferron are next employed to remove iron, titanium, zirconium etc., and the aluminium is subsequently separated from other sample constituents by precipitating as its insoluble benzoate. After filtration the aluminium benzoate is dissolved in hydrochloric acid and the aluminium concentration determined volumetrically with ethylenediaminetetraacetic acid.