Prolactin significantly increased the rate of fatty acid synthesis in explants of mid-pregnant rat mammary gland cultured for 96 h with insulin plus corticosterone. Under these conditions, prolactin increased the specific activity of total acetyl-CoA carboxylase in nuclear-free homogenates of explants by 2·6, and increased the proportion of the enzyme in the active polymeric form from 0·44 to 0·89. Removal of prolactin after 48 h in culture decreased the specific activity of the total enzyme by about half, and decreased the proportion as polymer to 0·52. The results show that prolactin plays a major role in mid-pregnant rat mammary gland in the polymerization which accompanies increased activity of the total enzyme and increased rate of fatty acid synthesis.

The polydisperse coagulation equation models irreversible aggregation of particles with varying masses. This paper uses a one-parameter family of discrete-time continuous multitype branching processes to solve the polydisperse coagulation equation when

The critical time tc when diverges corresponds to a critical branching process, while post-critical times t> tc correspond to supercritical branching processes.

The concept of relaxing a Markov process is introduced; this is the creation of additional transitions between ergodic classes of the process in such a way as to conserve the existing equilibrium distribution within ergodic classes. The ‘open' version of a ‘closed' model of migration, polymerisation etc. often has this character. As further examples, generalized versions of Jackson networks and networks with clustering nodes are given.

The susceptibility of rocks to weathering into soils and the subsequent weathering of the solum itself are important both with respect to sediment formation and to agriculture. Residual soils developed on some rock types representative of the major soil associations of NE Scotland have consequently been examined in detail in an attempt to assess the weatherability of both the rocks and the derived soils. Methods based on chemical composition have been supplemented by potential methods related to the production of poorly-ordered aluminosilicate material and to depolymerisation of the silicate framework in the minerals present. In general, there is, as would be expected on the basis of increasing energy supply and increasing entropy, an increase in the amount of monomeric silica towards the surface and this appears to be closely related to the amount and nature of the poorly-ordered aluminosilicate. The results suggest that only the purely chemical methods can currently enable a reasonable assessment to be made of the susceptibility of a rock or soil to further weathering.

We consider a polymerisation process stratified in that space is divided into regions, between which migration occurs, but with bonding occurring only within a region. In the case of a process whose specification is spatially homogeneous, criticality (gelation) is then easily detectable as the point at which statistical equidistribution over regions becomes unstable. Stratification does import a new feature, however, in that the equipartition solution can become metastable below criticality; local fluctuations of density can induce ‘gelational collapse’ at a density below the critical value. We derive also detailed results for the inhomogeneous case, both below and above criticality. Statistics of polymer size and structure are also easily determined in the stratified case, although one can locate the critical point without recourse to these. Finally, one can to a large extent treat the case in which inter- and intrapolymer reaction rates differ, and show that such difference affects the onset of metastability rather than of instability.

The solution for the multitype version of the polymerisation process treated in earlier papers is examined, and found to present several new features, because of the necessarily complex integration path, and because of the greater number and variety of potential singularities. Cases of ‘Poisson interaction’ are particularly amenable to treatment, however, and we examine two particular cases of interest in Sections 5 and 6. One is a version of the Ising model, which shows phase transition and its character very simply. The other is a version of the farmer–trader model considered previously, which now manifests a number of features, including a discontinuous transition between agrarian and mercantile economies. A stratified Poisson-interaction model is examined in Section 7. The roles of the various singularities are clarified, and a behaviour analogous to that of the single-type case confirmed.

We study clustering (‘polymerisation’) processes under the assumptions that new bonds may or may not form within an existing cluster. We show that both models exhibit criticality (‘gelation’) at the same point, and investigate statistics of polymer size and structure beyond criticality in the first case. Gelation may or may not be accompanied by critical effects at unit level; we examine a prototype of each case: the cosh model and the Poisson model.