5-cycle systems of K-v-F with a hole

Recently the problem of the existence of a 5-cycle system of K-v with a hole of size u was completely solved. In this paper we prove necessary and sufficient conditions on v and u for the existence of a 5-cycle system of K-v - F, with a hole of size u.

Macropore sheath: quantification of plant root and soil macropore association

Plants require roots to supply water, nutrients and oxygen for growth. The spatial distribution of roots in relation to the macropore structure of the soil in which they are growing influences how effective they are at accessing these resources. A method for quantifying root-macropore associations from horizontal soil sections is illustrated using two black vertisols from the Darling Downs, Queensland, Australia. Two-dimensional digital images were obtained of the macropore structure and root distribution for an area 55 x 55 mm at a resolution of 64 mu m. The spatial distribution of roots was quantified over a range of distances using the K-function. In all specimens, roots were shown to be clustered at short distances (1-10 mm) becoming more random at longer distances. Root location in relation to macropores was estimated using the function describing the distance of each root to the nearest macropore. From this function, a summary variable, termed the macropore sheath, was defined. The macropore sheath is the distance from macropores within which 80% of roots are located. Measured root locations were compared to random simulations of root distribution to establish if there was a preferential association between roots and macropores. More roots were found in and around macropores than expected at random.

Maximum packings of K-v-K-u with triples

We construct, for all positive integers u, and v with u less than or equal to v, a decomposition of K-v - K-u (the complete graph on v vertices with a. hole of size u) into the maximum possible number of edge disjoint triangles.

Bonding effects and the crystal structures of (NH4)(2)[Cu(H2O)(6)](SO4)(2) and its (H2O)-O-18 substituted form at 9.5 K

The crystal structures of the Tutton salts (NH4)(2)[Cu(H2O)(6)](SO4)(2), diammonium hexaaquacopper disulfate, formed with normal water and isotopically substituted (H2O)-O-18, have been determined by X-ray diffraction at 9.5 K and are very similar, with Cu-O(7) the longest of the Cu-O bonds of the Jahn-Teller distorted octahedral [Cu(H2O)(6)](2+) complex. It is known that structural differences accompany deuteration of (NH4)(2)[Cu(H2O)(6)](SO4)(2), the most dramatic of which is a switch to Cu-O(8) as the longest such bond. The present result suggests that the structural differences are associated with hydrogen-bonding effects rather than with increased mass of the water ligands affecting the Jahn-Teller coupling. The Jahn-Teller distortions and hydrogen-bonding contacts in the compounds are compared with those reported for other Tutton salts at ambient and high pressure.

Evolution of stress deficit and changing rates of seismicity in cellular automaton models of earthquake faults

We investigate the internal dynamics of two cellular automaton models with heterogeneous strength fields and differing nearest neighbour laws. One model is a crack-like automaton, transferring ail stress from a rupture zone to the surroundings. The other automaton is a partial stress drop automaton, transferring only a fraction of the stress within a rupture zone to the surroundings. To study evolution of stress, the mean spectral density. f(k(r)) of a stress deficit held is: examined prior to, and immediately following ruptures in both models. Both models display a power-law relationship between f(k(r)) and spatial wavenumber (k(r)) of the form f(k(r)) similar tok(r)(-beta). In the crack model, the evolution of stress deficit is consistent with cyclic approach to, and retreat from a critical state in which large events occur. The approach to criticality is driven by tectonic loading. Short-range stress transfer in the model does not affect the approach to criticality of broad regions in the model. The evolution of stress deficit in the partial stress drop model is consistent with small fluctuations about a mean state of high stress, behaviour indicative of a self-organised critical system. Despite statistics similar to natural earthquakes these simplified models lack a physical basis. physically motivated models of earthquakes also display dynamical complexity similar to that of a critical point system. Studies of dynamical complexity in physical models of earthquakes may lead to advancement towards a physical theory for earthquakes.

Cyanogenic polymorphism in Eucalyptus polyanthemos Schauer subsp vestita L. Johnson and K. Hill (Myrtaceae)

Plant cyanogenesis, the release of cyanide from endogenous cyanide-containing compounds, is an effective herbivore deterrent. This paper characterises cyanogenesis in the Australian tree Eucalyptus polyanthemos Schauer subsp. vestita L. Johnson and K. Hill for the first time. The cyanogenic glucoside prunasin ((R)-mandelonitrile beta-D-glucoside) was determined to be the only cyanogenic compound in E. polyanthemos foliage. Two natural populations of E. polyanthernos showed quantitative variation in foliar prumasin concentration, varying from zero (i.e. acyanogenic) to 2.07 mg CN g(-1) dry weight in one population and from 0.17 to 1.98 mg CN g(-1) dry weight in the other. No significant difference was detected between the populations with respect to the mean prunasin concentration or the degree of variation in foliar prunasin, despite significant differences in foliar nitrogen. Variation between individuals was also observed with respect to the capacity of foliage to catabolise prunasin to form cyanide. Moreover, variation in this capacity generally correlated with the amount of prunasin in the tissue, suggesting genetic linkage between prunasin and beta-glucosidase. (C) 2002 Elsevier Science Ltd. All rights reserved.

Interfacial interactions and structure of organic-inorganic nanohybrids

Understanding the interfacial interactions and structure is important to better design and application of organic-inorganic nanohybrids. This paper presents our recent molecular dynamic studies on organoclays and polymer nanocomposites, including the layering behavior of organoclays, structural and dynamic properties of dioctadecyldimethyl ammoniums in organoclays, and interfacial interactions and structure of polyurethane nanocomposites. The results demonstrate that the layering behaviors of organoclays are closely related to the chain length of quaternary alkyl ammoniums and cation exchangeable capacity of clays. In addition to typical layered structures such as monolayer, bilayer and pseudo-trilayer, a pseudo-quadrilayer structure was also observed in organoclays modified with dioctadecyldimethyl ammoniums (DODDMA). In such a structure, alkyl chains do not lie flat within a single layer but interlace, and also jump to the next layer or even the next nearest layer. Moreover, the diffusion constants of nitrogen and methylene atoms increase with the temperature and methelene towards the tail groups. For polyurethane nanocomposite, the van der Waals interaction between apolar alkyl chains and soft segments of polyurethane predominates the interactions between organoclay and polyurethane. Different from most bulk polyurethane systems, there is no distinct phase-separated structure for the polyurethane.

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.

The effect of spatial definition on the allocation of clients to screening clinics

We compared four strategies for inviting 91,456 women aged 50-69 years to one of six clinics for mammography screening and 40,142 men aged 60-79 years to one of 10 clinics for abdominal aortic aneurysm (AAA) screening. The strategies were invitation to the clinic nearest to the client and invitation to the clinic nearest to the client's area of residence defined by census small area, postcode and local government area. For each strategy we calculated the expected demand at each clinic and the travel distances for clients. We found that when women were allocated to mammography clinics on the basis of the local government area instead of their individual address, expected demand at one clinic increased by 60%, and 19% of clients were invited to attend a more remote clinic, entailing 99,000 km of additional travel. Similar results were obtained for men allocated to AAA clinics by their postcode of residence instead of their individual address: 55% difference in expected demand, 13% to a more remote clinic and 60,000 km of extra travel. Allocation on the basis of small areas did not show such great differences, except for travel distance, which was about 5% higher for each clinic type. We recommend that allocation of clients to screening clinics be made according to residential address, that assessment of the location of clinics be based on distances between residences and nearest clinic, but that planning new locations for clinics be aided with spatial analysis tools using small area demographic and social data. (C) 1997 Elsevier Science Ltd.