Lambda-fold 3-perfect 9-cycle systems

The spectrum for the decomposition of lambda K-v into 3-perfect 9-cycles is found for all lambda > 1. (The case lambda = 1 was dealt with in an earlier paper by the authors and Lindner.) The necessary conditions for the existence of a suitable decomposition turn out to be sufficient.

d-cube decompositions of K-n/K-m

Necessary conditions on n, m and d are given for the existence of an edge-disjoint decomposition of K-n\K-m into copies of the graph of a d-dimensional cube. Sufficiency is shown when d = 3 and, in some cases, when d = 2(t). We settle the problem of embedding 3-cube decompositions of K-m into 3-cube decompositions of K-n; where n greater than or equal to m.

Ca2+-activated K+ channels in rat otic ganglion cells: Role of Ca2+ entry via Ca2+ channels and nicotinic receptors

1. Intracellular recordings were made from neurones in the rat otic ganglion in vitro in order to investigate their morphological, physiological and synaptic properties. We took advantage of the simple structure of these cells to test for a possible role of calcium influx via nicotinic acetylcholine receptors during synaptic transmission. 2. Cells filled with biocytin comprised a homogeneous population with ovoid somata and sparse dendritic trees. Neurones had resting membrane potentials of -53 +/- 0.7 mV (n = 69), input resistances of 112 + 7 M Omega, and membrane time constants of 14 +/- 0.9 ms (n = 60). Upon depolarization, all cells fired overshooting action potentials which mere followed by an apamin-sensitive after-hyperpolarization (AHP). In response to a prolonged current injection, all neurones fired tonically. 3. The repolarization phase of action potentials had a calcium component which was mediated by N-type calcium channels. Application of omega-conotoxin abolished both the repolarizing hump and the after-hgrperpolarization suggesting that calcium influx via N-type channels activates SK-type calcium-activated potassium channels which underlie the AHP. 4. The majority (70%) of neurones received innervation from a single preganglionic fibre which generated a suprathreshold excitatory postsynaptic potential mediated by nicotinic acetylcholine receptors. The other 30% of neurones also had one or more subthreshold nicotinic inputs. 5. Calcium influx via synaptic nicotinic receptors contributed to the AHP current, indicating that this calcium has access to the calcium-activated potassium channels and therefore plays a role in regulating cell excitability.