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.

Partitioning sets of triples into small planes

We study partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. Our partitions may contain copies of PG(2, 2) only (Fano partitions) or copies of AG(2, 3) only (affine partitions) or copies of some planes of each type (mixed partitions). We find necessary conditions for Fano or affine partitions to exist. Such partitions are already known in several cases: Fano partitions for v = 8 and affine partitions for v = 9 or 10. We construct such partitions for several sporadic orders, namely, Fano partitions for v = 14, 16, 22, 23, 28, and an affine partition for v = 18. Using these as starter partitions, we prove that Fano partitions exist for v = 7(n) + 1, 13(n) + 1, 27(n) + 1, and affine partitions for v = 8(n) + 1, 9(n) + 1, 17(n) + 1. In particular, both Fano and affine partitions exist for v = 3(6n) + 1. Using properties of 3-wise balanced designs, we extend these results to show that affine partitions also exist for v = 3(2n). Similarly, mixed partitions are shown to exist for v = 8(n), 9(n), 11(n) + 1.

Mixed partitions of sets of triples into small planes

We continue our study of partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. We develop further necessary conditions for the existence of partitions of such sets into copies of PG(2, 2) and copies of AG(2, 3), and deal with the cases v = 13, 14, 15 and 17. These partitions, together with those already known for v = 12, 16 and 18, then become starters for recursive constructions of further infinite families of partitions. (C) 2004 Elsevier B.V. All rights reserved.

The intersection problem for star designs

We determine those triples (m, II, k) of integers for which there are two m-star designs on the same n-set having exactly k stars in common.

The fine structure of (v, 3) directed triple systems: v equivalent to 2 (mod 3)

The fine structure of a directed triple system of index lambda is the vector (c(1), c(2),...,C-lambda), where c(i) is the number of directed triples appearing precisely i times in the system. We determine necessary and sufficient conditions for a vector to be the fine structure of a directed triple system of index 3 for upsilon = 2 (mod 3).

Low coral cover in a high-CO2 world

Coral reefs generally exist within a relatively narrow band of temperatures, light, and seawater aragonite saturation states. The growth of coral reefs is minimal or nonexistent outside this envelope. Climate change, through its effect on ocean temperature, has already had an impact on the world's coral reefs, with almost 30% of corals having disappeared since the beginning of the 1980s. Abnormally warm temperatures cause corals to bleach ( lose their brown dinoflagellate symbionts) and, if elevated for long enough, to die. Increasing atmospheric CO2 is also potentially affecting coral reefs by lowering the aragonite saturation state of seawater, making carbonate ions less available for calcification. The synergistic interaction of elevated temperature and CO2 is likely to produce major changes to coral reefs over the next few decades and centuries. Known tolerances of corals to projected changes to sea temperatures indicate that corals are unlikely to remain abundant on reefs and could be rare by the middle of this century if the atmospheric CO2 concentration doubles or triples. The combination of changes to sea temperature and carbonate ion availability could trigger large- scale changes in the biodiversity and function of coral reefs. The ramifications of these changes for the hundred of millions of coral reef - dependent people and industries living in a high- CO2 world have yet to be properly defined. The weight of evidence suggests, however, that projected changes will cause major shifts in the prospects for industries and societies that depend on having healthy coral reefs along their coastlines.

Steepness and deepness in the Australian macroeconomy

This study uses nonparametric tests - the triples test and the BDS test, to examine whether key Australian macroeconomic aggregates exhibit nonlinearities and important 'steepness' and 'deepness' asymmetries at the business cycle frequency. Evidence is found of nonlinearities but there is little evidence of deepness in the Australian macroeconomy. However, there is evidence of steepness, especially concerning labour market variables, as well as both the CPI and M3. The evidence suggests that unemployment (employment) rises (falls) rapidly in recessions and only recovers slowly over time. Also, positive asymmetries in M3 are reflected in similar asymmetries in the CPI but not in output, consumption or investment.

The association between auditory memory span and speech rate in children from kindergarten to sixth grade

This study reexamined the association between speech rate and memory span in children from kindergarten to sixth grade (N = 152) in order to potentially account for the inconsistencies within the published literature on this topic. Some of the inconsistencies in past research may reflect the different methods adopted in assessing speech rate. In particular, repeating word triples may itself involve memory demands, contaminating the correlation between speech rate and memory span in younger children. Analyses using composite speech rate and memory span measures showed that speech rate for word triples shared variance with memory span that was independent of speech rate for single words. Moreover, speech rate for word triples was largely redundant with age in explaining additional variation in memory span once the effects of speech rate for single words were controlled. (C) 2002 Elsevier Science.

Maximal triangle trades with foundation 5 (mod 6) - the final case

The maximum possible volume of a simple, non-Steiner (v, 3, 2) trade was determined for all v by Xhosrovshahi and Torabi (Ars Combinatoria 51 (1999), 211-223), except that in the-case v equivalent to 5 (mod 6), v >= 23, they were only able to provide an upper, bound on the volume. In this paper we construct trades with volume equal to that bound for all v equivalent to 5 (mod 6), thus completing the problem.