Asymptotic Correction of More Sturm–Liouville Eigenvalue Estimates

The asymptotic correction technique of Paine, de Hoog and Anderssen can dramatically improve the accuracy of finite difference or finite element eigenvalues at negligible extra cost if closed form expressions are available for the errors in a simpler related problem. This paper gives closed form expressions for the errors in the eigenvalues of certain Sturm–Liouville problems obtained by various methods, thereby increasing the range of problems for which asymptotic correction can achieve maximum efficiency. It also investigates implementation of the method for more general problems.     

Elastoplastic torsion theory for whisker crystals

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 127–134, March–April, 1991.     

A generalization of the H-theorem to steady non-equilibrium states. Part 1: A basic decomposition and the linear case

A generalized relative entropy functional is associated to the evolution of gas in a container with (generally) non-uniform boundary data. A decomposition for its rate in ‘bulk’ and in ‘boundary’ terms is given; for the linear case both have a definite sign. The relation with the strong L₁ stability is pointed out.     

Modules of piecewise polynomials and their freeness

Partially supported by NSF Grant DMS-9004123 and ARO through MSI Cornell (DAAG 29-85-C-0018)     

Asymptotics of Dirichlet Spectrum on Some Class of Noncompact Domains

We investigate the asymptotic behaviour of the counting function of Dirichlet eigenvalues on some class of noncompact manifolds. We prove that in cases when the volume or the perimeter (the volume of the boundary) of the manifold is infinite, some additional (nonclassical) terms appear in the precise asymptotics. The coefficients at the classical terms in those are regularized in some special way volume (resp. perimeter) of the manifold.     

Kinetics of Hydrogen Peroxide Decomposition in Guaiacol Solution, Catalyzed by Hexacyanoferrate(II)

The kinetics of hydrogen peroxide decomposition in a guaiacol solution, catalyzed by potassium hexacyanoferrate(II), were studied. The reaction mainly follows the pathway of guaiacol hydroxylation. The reaction order is 1 with respect to H₂O₂, 0.5 with respect to hexacyanoferrate, and from 0.4 to 0 with respect to guaiacol (the latter parameter decreases with increasing guaiacol concentration). The apparent activation energy is 105 kJ mol^{- 1}. A kinetic scheme of the process was proposed. An expression consistent with the experiment was obtained for the rate of hydrogen peroxide decomposition in the presence of guaiacol, catalyzed by hexacyanoferrate(II).