Concentration profiles and breakthrough curves in non-linear chromatography

The treatment of the non-linear isotherm in chromatography by one of the authors [1] is extended to other cases of practical interest. The original paper dealt with the case of an initially thin zone resulting in a Poisson distribution the asymmetry of which is a function of the plate number and the non-linearity constant. The present work shows that the same relations apply to initially thick zones and to the cases of washing and deposition leading to simple relations for breakthrough curves. For significantly non-linear isotherms other quasi-Gaussian distributions can give a better fit.     

Langmuir films of (alpha-amino) phosphorus amphiphiles on various ion-containing subphases

Monolayers of amphiphilic (alpha-amino)phosphonocarboxylic and (alpha-amino)phosphonic acids have been formed by adsorption at the air/water interface. The influence of both the ionic strength and the pH of the subphase on the stability and compactness of the monolayers have been studied. The stability and the compactness of the Langmuir films are enhanced by introduction of metallic ions such as Ca(2+) or Mg(2+) in the subphases. These effects are more pronounced with Ca(2+). These metal ions can form dimeric complexes with the phosphorus moieties of the surfactant polar heads and therefore bring the amphiphiles closer. For the less hydrophobic derivative, complexation with Ca(2+) or Mg(2+) is required to ensure the formation of a stable monomolecular film. For both phosphonocarboxylic and phosphonic compounds, models have been proposed to represent the complexation phenomenon at the air/water interface.     

On the existence of semifields of prime power order admitting free automorphism groups

The purpose of this paper is to prove the existence of semifields of order q ⁴ for any odd prime power q = p^r, q > 3, admitting a free automorphism group isomorphic to Z ₂ × Z ₂.     

Weakly nonlinear forced convection patterns in rectangular planform containers

This paper considers the structure of weakly nonlinear steady-state convection patterns in shallow rectangular planform containers heated from below. The lateral dimensions of the container are assumed to be much larger than the characteristic wavelength of convection, and the lateral boundaries are subject to forcing equivalent, for example, to imperfect thermal insulation in the Rayleigh–Benard problem. This has the effect of generating rolls parallel and perpendicular to the lateral boundaries. The resulting patterns are modelled by a coupled pair of nonlinear amplitude equations derived from a phenomenological model of convection introduced by Swift and Hohenberg [Phys. Rev. A15 (1977) 319]. These equations are applicable in the weakly nonlinear limit to a variety of pattern-forming systems such as the Rayleigh–Benard system. Solutions are found using both numerical and asymptotic methods. The boundary imperfection is shown to give rise to some novel effects, including the possibility of patterns containing square cells. More generally, patterns evolve that are dominated by rolls but with transitions to more complex bimodal forms near the edges of the container. The emergence and structure of transition lines, or grain boundaries, is analysed in detail.     

On eight-dimensional unital division algebras over finite fields

The purpose of this paper is to investigate the eight-dimensional non-associative unital division algebras {0}≠A over finite fields, admitting elementary abelian 2-group of automorphisms E≤Aut(A), of order 8, using tools from algebraic geometry.     

A fatigue-testing machine for combined bending and torsion

A testing machine is designed and developed in such a way as to be capable of exerting simultaneous cyclic bending and twisting moments, such moments being uniformly distributed along the entire gage length of the test specimen. The ratio of bending to twisting moments can be adjusted within the range 0 to 0.5, the angular deflection of specimen being controlled in the machine. Experimental results first obtained for reversed torsion show that the fatigue life is best expressed in terms of the shearstrain range or the shear-stress amplitude in potential form. Further wark on the subject is proceeding.     

The Autotopism Group of A Semifield of Order p 4, p is an Odd Prime

The aim of this article is to investigate the autotopism group of a semifield of order p ⁴, p is an odd prime, admitting a four-group of automorphisms E? Z ₂ × Z ₂ acting freely on A.     

On an investment-consumption model with transaction costs: an asymptotic analysis

In this paper we examine the Akian, Menaldi and Sulem (1996) model for the optimal management of a portfolio, when there are transaction costs which are equal to a fixed percentage of the amount transacted. We analyse this model in the realistic limit of small transaction costs. Although the full problem is a free boundary diffusion problem in as many dimensions as there are assets in the portfolio, we find explicit solutions for the optimal trading policy in this limit. This makes the solution for a realistically large number of assets a practical possibility.