Decompositions of complete graphs into triangles and Hamilton cycles

For all odd integers n greater than or equal to 1, let G(n) denote the complete graph of order n, and for all even integers n greater than or equal to 2 let G,, denote the complete graph of order n with the edges of a 1-factor removed. It is shown that for all non-negative integers h and t and all positive integers n, G, can be decomposed into h Hamilton cycles and t triangles if and only if nh + 3t is the number of edges in G(n). (C) 2004 Wiley Periodicals, Inc.

Storm cycles in the last millennium recorded in Yongshu Reef, southern South China Sea

Large storm-relocated Porites coral blocks are widespread on the reef flats of Nansha area, southern South China Sea. Detailed investigations of coral reef ecology, geomorphology and sedimentation on Yongshu Reef indicate that such storm-relocated blocks originated from large Porites lutea corals growing on the spurs within the reef-front living coral zone. Because the coral reef has experienced sustained subsidence and reef development during the Holocene, dead corals were continuously covered by newly growing coral colonies. For this reason, the coral blocks must have been relocated by storms from the living sites and therefore the ages of these storm-relocated corals should approximate the times when the storms occurred. Rapid emplacement of these blocks is also evidenced by the lack of coral overgrowth, encrustation or subtidal alteration. U-series dating of the storm-relocated blocks as well as of in situ reef flat corals suggests that, during the last 1000 years, at least six strong storms occurred in 1064 +/- 30, 1210 +/- 5-1201 +/- 4, 1336 +/- 9, 1443 +/- 9, 1685 +/- 8-1680 +/- 6, 1872 +/- 15 AD, respectively, with an average 160-year cycle (110-240 years). The last storm, which occurred in 1872 15 AD, also led to mortality of the reef flat corals dated at similar to 130 years ago. Thus, the storm had significant impacts on coral reef ecology and morphology. (C) 2004 Elsevier B.V. All rights reserved.

Packing lambda-fold complete multipartite graphs with 4-cycles

A maximum packing of any lambda-fold complete multipartite graph (where there are lambda edges between any two vertices in different parts) with edge-disjoint 4- cycles is obtained and the size of each minimum leave is given. Moreover, when lambda =2, maximum 4-cycle packings are found for all possible leaves.

Digenean trematodes infecting the tropical abalone Haliotis asinina have species-specific cercarial emergence patterns that follow daily or semilunar spawning cycles

Approximately 1-2% of the tropical abalone Haliotis asinina inhabiting Heron Island Reef are infected with opecoelid digeneans. These largely inhabit the haemocoel surrounding the cerebral ganglia and digestive gland-gonad complex, and infected abalone typically have significantly reduced or ablated gonads. Observations of infected abalone reveal two distinct cercarial emergence patterns, one which correlates tightly with the abalone's highly regular and synchronous fortnightly spawning cycle, and the other which occurs in a circadian pattern. The former appears to be a novel emergence strategy not previously observed in digeneans. While the cercariae in all abalone are morphologically indistinguishable, comparison of sequences from the internal transcribed spacer 2 (ITS 2) region of the ribosomal DNA reveals a 5.7% difference between cercariae displaying different emergence patterns, indicating these are two distinct species that probably belong to the same genus. The ITS 2 sequences of the species with the daily emergence pattern are identical to that of an undescribed adult opecoelid from the gut of the barramundi cod, Cromileptes altivelis. Combined molecular, morphological and emergence data suggest that while these opecoelid cercariae use the same first intermediate host and are closely related species-members of the genus Allopodocotyle-they fill different ecological niches that are likely to include different definitive hosts.

The effects of a song-singing programme on the affective speaking intonation of people with traumatic brain injury

Primary objective: To examine changes in the relationship between intonation, voice range and mood following music therapy programmes in people with traumatic brain injury. Research design: Data from four case studies were pooled and effect size, ANOVA and correlation calculations were performed to evaluate the effectiveness of treatment. Methods and procedures: Subjects sang three self-selected songs for 15 sessions. Speaking fundamental frequency, fundamental frequency variability, slope, voice range and mood were analysed pre- and post-session. Results: Immediate treatment effects were not found. Long-term improvements in affective intonation were found in three subjects, especially in fundamental frequency. Voice range improved over time and was positively correlated with the three intonation components. Mood scale data showed that immediate effects were in the negative direction whereas there weres increases in positive mood state in the longer-term. Conclusions: Findings suggest that, in the long-term, song singing can improve vocal range and mood and enhance the affective intonation styles of people with TBI.

Adjusting to change through song: Themes in songs written by clients with traumatic brain injury

The study aimed to identify themes in songs written by clients with traumatic brain injury (TBI). Lyrics (1834) from 82 songs written by 11 female and 21 male clients aged between 5 and 60 years were categorised into 8 main themes and 24 subcategories. Incidence of subcategories and themes were calculated. Self-reflections and messages were the most frequent themes portrayed within songs. Memories and reflections about significant others were also frequently communicated. It was noticeable that clients felt safer to communicate thoughts and feelings about the past and present but were less inclined to confront the future.

Stability and cycles in a cobweb model with heterogeneous expectations

We investigate the dynamics of a cobweb model with heterogeneous beliefs, generalizing the example of Brock and Hommes (1997). We examine situations where the agents form expectations by using either rational expectations, or a type of adaptive expectations with limited memory defined from the last two prices. We specify conditions that generate cycles. These conditions depend on a set of factors that includes the intensity of switching between beliefs and the adaption parameter. We show that both Flip bifurcation and Neimark-Sacker bifurcation can occur as primary bifurcation when the steady state is unstable.

ICP-MS Trace Element Analysis of Song Dynasty Porcelains from Ding, Jiexiu and Guantai kilns, North China

Bodies of Ding kiln white porcelains and their imitations from Guantai and Jiexiu kilns of the Chinese Song dynasty (960-1279 AD) were analysed for 40 trace elements by inductively coupled plasma mass spectrometry (ICP-MS). Numerous trace element compositions and ratios allow these visually similar products to be distinguished, and a Ding-style shard of uncertain origin is identified as a likely genuine Ding product. In Jiexiu kiln, Ding-style products have trace element features distinctive from blackwares of an inferior quality intended for the lower end market. Based on geochemical behaviour of these trace elements, we propose that geochemically distinctive raw materials were used for Ding-style products of a higher quality, which possibly also underwent purification by levigation prior to use. Capable of analysing over 40 elements with a typical long term precision of < 2%, this high precision ICP-MS method proves to be very powerful for grouping and characterising archaeological ceramics. Combined with geochemical interpretation, it can provide insights into the raw materials and techniques used by ancient potters. (C) 2004 Elsevier Ltd. All rights reserved.