Arne Magnus

Size exclusion at the external surfaces of spherical packing used in high-performance liquid chromatography

Experimental observations from several laboratories, including our own, have demonstrated that the elution volume of very large macromolecules or particles shows a small dependence on size even when the packing gels are impermeable to these substances. We call this process “external size exclusion”, but it has also been termed “hydrodynamic chromatography/rd. We have derived a quantitative expression for the phenomenon based on an equilibrium process in which spherical macromolecules of radius r pass through a column filled with uniform spheres of radius R in hexagonal close packing. The final expression gives the ratio of the elution volume Ve of a sphere of radius r to the total volume of the column Vt. The range of practical usefulness is 0.01 < r/R < 0.1. “Premature” elution of aggregated tobacco mosaic virus is explained by the use of this equation.

Computation of poles of two-point Padé approximants and their limits

Abstract Algorithms are developed to compute simultaneously the poles of functions represented by continued fractions whose approximants lie on the main diagonal of two-point Pade tables. The algorithms are based on equations recently developed by McCabe and Murphy for producing continued fraction expansions of a pair of power series. Sufficient conditions are given to ensure that the computations can be carried out and that the resulting approximations converge geometrically to the desired poles. As a by-product, an algorithm is obtained for computing zeros of polynomials. The theory and methods are illustrated by means of numerical examples.

On the non-normal two-point Pade´ table

Abstract The M -table for two power series expansions, one about the origin and the other about infinity, is generalized to the non-normal case. It is shown that equal entries appear in square blocks, quadrants or half planes. In addition, the continued fractions whose convergents are diagonal or horizontal sequences are constructed. The results are based on a transformation that reduces the study of the two-point table to that of the Pade table.

PC-Fractions and orthogonal laurent polynomials for log-normal distributions

Abstract Log-normal distributions have received considerable recent attention partly through their applications to several branches of science, economics, and business and partly in their relation to orthogonal Laurent polynomials (L-polynomials), Pade approximants, and continued fractions. This paper investigates PC-fractions and orthogonal L-polynomials associated with log-normal distributions. Our main results include: (a) explicit expressions for the continued fractions and their approximants, and the L-polynomials; (b) proofs of the existence of the limits of subsequences of approximants and of L-polynomials; (c) closed form expressions for the limits of these subsequences; and (d) identities between related approximants and related L-polynomials. Several of the limit functions are seen to be essentially theta funcions.

Para-orthogonal Laurent polynomials and associated sequences of rational functions

AbstractOn the space, Л, of Laurent polynomials (L-polynomials) we consider a linear functional ℒ which is positive definite on (0, ∞) and is defined in terms of a given bisequence, {μk}−∞∞. Two sequences of orthogonal L-polynomials, {Qn(z)0∞ and

General t-fraction expansions for ratios of hypergeometric functions

\{ \hat Q_n (z)\} _0^\infty

Continued fractions for Satisfying

, are constructed which span Λ in the order {1,z−1,z,z−2,z2,...} and {1,z,z−1,z2,z−2,...} respectively. Associated sequences of L-polynomials {Pn(z)0∞, and