We consider the U(1)-invariant Klein–Gordon equation in dimension n⩾3, self-interacting via the mean field mechanism in finitely many regions. We prove that, under certain generic assumptions, each solution converges as t→±∞ to the two-dimensional set of all “nonlinear eigenfunctions” of the form ϕ(x)e−iωt. The proof is based on the analysis of omega-limit trajectories. The Titchmarsh Convolution Theorem allows us to prove that the time spectrum of any omega-limit trajectory of each finite energy solution consists of a single point. This proves the convergence to the attractor in local sub-energy norms.
Some enzymatic properties of a new type of yeast cell ghosts are described. The ghosts were obtained from Candida utilis by the action of small basic protein molecules (protamine, cytochrome c from horse heart, bovine pancreatic ribonuclease) on a water suspension of the cells at 30 ° for 30 min. The washed ghosts were examined for enzymatic activity by adding substrates and coenzymes which do not readily penetrate into intact cells. Permeation of these substances into the ghosts permitted enzymatic reactions which were observed by analysis of the products that diffused into the surrounding medium. The ghosts resemble parcels of enzymes which are confined by the leaky membrane or the cell wall.
Early radiation injury in some species of higher vertebrates includes vascular damage that may result in circulatory stasis and death within a few hours after exposure. The chicken exhibits an early edema and hemoconcentration, and terminal events include widespread stasis and degenerative changes of the endothelium. Described in this report are the effects of protective procedures against early radiation injury to the microcirculation, studied in the extraembryonic membranes of the living, explanted, 3-day chick embryo. Early vascular damage after a lethal radiation exposure was reduced in embryos pretreated with a conditioning X-ray exposure, 4 hr before the second, or challenging, dose (a split exposure). A similar protective response was observed in irradiated embryos pretreated with the antiprotease, soybean trypsin inhibitor. These results suggest that resistive processes are active during the interval between exposures and that effects leading to vascular degeneration can be reversed or prevented at an early stage in development of the injury. The possible relation of activated or released hydrolases to the early microvascular damage is discussed.
As was done by Sinclair and Ross (1969(, we consider a cellular population that consists initially (at time zero) ofN 0 newborn cells, all with the same volumev o. It is assumed that the occurrence of cell division is determined only by a cell’s age, and not by its volume. The frequency function of interdivision times, τ, is denoted byf(τ). If cell death is negligible, the expected number of cells,N(t), will increase according to the laws of a simple age-dependent branching process. The expression forN(t) is obtained as a sum over all generations; thevth term of this sum, in turn, is a multiple convolution integral, reflecting the life history ofvth generation cells (i.e., the lengths of thev successive interdivision periods plus the age of the cell at timet). Assuming that cell volume is a given function of cell age, e.g., linear or exponential, and that cellular volume is exactly halved at each division, it is possible to calculate the volume of a cell with a given life history, and thus the average cellular volume of the whole population as a function of time. If at time zero the volumes differ from cell to cell, the final equation must be modified by averaging over initial volumes. In the case of linear volume increase with age, a very simple asymptotic expression is found for the average cellular volume ast→∞. The case of exponential volume increase with age also leads to a simple asymptotic formula, but the resulting volume distribution is unstable.
