Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

Hydrodynamic and hydromagnetic stability

ing journals. At the head of each abstract is the name of the author and the title of the paper, although not its date or origin, and also a pair of numbers. The reader is able to find by trial that one of these numbers is the serial number of the same paper as entered in the bibliographical list, the other being a new serial number for the paper in the sequence of abstracts. At the end of the volume are three lists. The first, a short one, is of numbers entitled ‘List of the entries included in bibliography no. 1’; bibliography no. 1 is apparently what this bibliography used to be when it was issued informally by AGARD in February 1960. The second is an index to authors, which presumably serves to identify the number of a paper written by a known author who is one of several joint authors and not the first named, the latter alone being used in the bibliographical list. The last is a subject-index, in which there are seven main divisions, like ‘magnetohydrodynamics ’ and ‘magneto-gas-dynamics ),with afew sub-divisions for each. The value of the subject index will be limited by the fact that the subheading ‘ General’ swallows up about half the entries in four of the main divisions. It is obviously useful to prepare and disseminate an up-to-date and ordered list of papers on this important subject, and the initiative and work contributed by AGARD have been widely appreciated. But why print a second time, publish, and sell at a substantial price, a bibliography which pays little attention to the ordinary principles of fact-gathering and indexing? As well as being rather wasteful, the book does not maintain accepted standards in scientific publications. G. K. BATCHELOR

An Introduction to Magneto-Fluid Mechanics. By V. C. A. Fekrabo and C. Plumpton. Pp. 181. 25s. 1961. (Oxford University Press)

This study complements existing literature by investigating how the advancement in information and communication technology affects the formal economic participation of women. The focus is on 48 African countries for the period 1990-2014. The empirical evidence is based on Ordinary Least Squares, Fixed Effects and the Generalized Method of Moments regressions. The results show that improving communication technology increases female economic participation with the following consistent order of increasing magnitude: mobile phone penetration; internet penetration, and fixed broadband subscriptions. The findings are robust to the control for heterogeneities across countries. Policy implications are discussed.

Female Economic Participation with Information and Communication Technology Advancement: Evidence from Sub-Saharan Africa

Stability analysis of double-diffusive convection of Maxwell fluid in a porous medium heated from below

The linear and non-linear stability of a horizontal layer of a binary fluid mixture in a porous medium heated and salted from below is studied, in the Oberbeck–Boussinesq–Darcy scheme, through the Lyapunov direct method. This is an interesting geophysical case because the salt gradient is stabilizing while heating from below provides a destabilizing effect. The competing effects make an instability analysis difficult. Unconditional non-linear exponential stability is found in the case where the normalized porosity ϵ is equal to one. For other values of ϵ a conditional stability theorem is proved. In both cases we demonstrate the optimum result that the linear and non-linear critical stability parameters are the same whenever the Principle of Exchange of Stabilities holds. Copyright © 2001 John Wiley & Sons, Ltd.

Non-linear stability in the Bénard problem for a double-diffusive mixture in a porous medium

The nonlinear stability of the conduction-diffusion solution of a fluid mixture heated and salted from below (and of a homogeneous fluid heated from below) and saturating a porous medium is studied with the Lyapunov direct method. Both Darcy and Brinkman models have been used. The porous medium is bounded by two horizontal parallel planes and is rotating about a vertical axis. Necessary and sufficient conditions of unconditional stability are proved (i.e., the critical linear and nonlinear stability Rayleigh numbers coincide). Our results generalize those given by Straughan [21] for a homogeneous fluid in the Darcy regime. In the case of a mixture two stabilizing effects act: that of the rotation and of the concentration of the solute.

S. Lombardo

Papers

Non-linear stability in the Bénard problem for a double-diffusive mixture in a porous medium

Necessary and sufficient conditions of global nonlinear stability for rotating double-diffusive convection in a porous medium

Mathematical models of innovation diffusion with stage structure

Nonlinear stability in reaction–diffusion systems via optimal Lyapunov functions

Global Nonlinear Exponential Stability of the Conduction-Diffusion Solution for Schmidt Numbers Greater than Prandtl Numbers