Pointwise construction of Lipschitz aggregation operators

This paper establishes tight upper and lower bounds on Lipschitz aggregation operators considering their diagonal, opposite diagonal and marginal sections. Also we provide explicit formulae to determine the bounds. These are useful for construction of these type of aggregation operators, especially using interpolation schemata.

Good global governance : custom, the cosmopolitan and international law

International law has both less and more to offer to the cosmopolitan project than one might think. As currently understood, international law presages a global system of obligations comprising the convergent systems of universal customary international laws and near-universal conventional instruments (treaties), both of which legal forms are characterised by natural law tendencies. From the point of view of a pluralistic cosmopolitanism, this is a dead end. Thinking beyond these formulae requires that international law be treated as a species of general law rather than state-centred law.

Mechanical properties of titanium foam for biomedical applications

Understanding the mechanical behaviour of pure titanium (Ti) foam is crucial for the design and development of Ti foam-based load-bearing implants. In this work, pure titanium foam is fabricated by a powder metallurgical process using the space-holder technique with a spacer size of 500 to 800 µm. Experimental data from static compression testing on the Ti foam are presented. The application of theoretical formulae to predict Young's modulus and yield strength of titanium foams is also discussed. A foam with 63% porosity, 87 ± 5 MPa yield strength, and 6.5 ± 1.3 GPa Young's modulus is found to be appropriate for a number of dental and orthopaedic applications.

What can student-generated diagrams tell us about their understanding of chemical equations?

Chemical equations are representations that use symbols to summarise the net changes occurring in a reaction whereas depictions such as drawings of the submicroscopic level provide representations of the chemical transformations. While the ability to balance and interpret chemical equations is key to understanding many concepts in chemistry, many undergraduate chemistry students struggle to master these skills. The equations contain a great deal of implicit information and novices may not be able to make the connection between the equation and the actual chemical transformations that are occurring. This paper reports on a study which used submicroscopic diagrams to probe students' understanding of chemical equations. Assessment tasks required students to interpret diagrams, construct diagrams and to relate diagrams to symbolic representations. The analysis showed that some students have misconceptions about the molecular nature and chemical formulae and could not distinguish between coefficients and subscripts when representing chemical formulae. While students were generally able to balance a chemical equation presented as a set of diagrams, a significant number could not generate the balanced equation based on a diagram of the progress of a reaction, The study has demonstrated the use of student-generated diagrams to provide insight into students' understandings of chemical equations.

Student-generated submicro diagrams : a useful tool for teaching and learning chemical equations and stoichiometry

This paper reports on a pedagogical approach to the teaching of chemical equations introduced to first year university students with little previous chemical knowledge. During the instruction period students had to interpret and construct diagrams of reactions at the submicro level, and relate them to chemical equations at the symbolic level with the aim of improving their conceptual understanding of chemical equations and stoichiometry. Students received instruction in symbol conventions, practice through graded tutorial tasks, and feedback on their efforts over the semester. Analysis of the student responses to formative test and summative exam items over consecutive years indicates that there was a consistent improvement in the abilities of the various cohorts to answer stoichiometry questions correctly. The responses provide evidence for diagrams of the submicro level being used as tools for reasoning in solving chemical problems, to recognise misconceptions of chemical formulae and to recognise the value of using various multiple representations of chemical reactions connecting the submicro and symbolic levels of representation. The student-generated submicro diagrams serve as a visualisation tool for teaching and learning abstract concepts in solving stoichiometric problems. We argue that the use of diagrams of the submicro level provides a more complete picture of the reaction, rather than a net summary of a chemical equation, leading to a deeper conceptual understanding.

Teaching secondary school mathematics : research and practice for the 21st century

For the last decade or so, educational policy makers and researchers in many countries have been calling for significant changes to the way mathematics is taught in secondary schools. Australian mathematics curriculum documents now promote learning goals that go beyond mastery of a pre-determined body of knowledge and procedures - the traditional emphasis on facts, skills, formulae - to include mathematical reasoning and problem solving, communication, and real world applications. There is also pressure to move away from over-reliance on teacher-centred practices such as exposition and individual seatwork, towards activities that promote learners' involvement in constructing, applying, and evaluating mathematical ideas. Further impetus for reform comes from research recommending that if learners are to develop mathematically powerful forms of thinking and habits of mind, then classrooms should immerse them in the authentic practices of the discipline by supporting a culture of collaboration and sense-making. Teaching Secondary School Mathematics - incorporates recent developments in research and practice and applications to teaching mathematics in Australian secondary schools. Covering such areas as curriculum, pedagogy and assessment; teaching mathematical content; equity and diversity in the classroom; and professional and community engagement, it is an invaluable resource for all practising and pre-service mathematics teachers.

Request mitigating devices in Australian English and Iraqi Arabic : a comparative study

Speech acts realization in everyday interaction is seen as an important field to explore the impact of linguistic and cultural variations on cross-cultural communication and second language acquisition. The reported study investigates the use of request mitigating devices in Australian English and Iraqi Arabic. It explores the internal and external devices that speakers of the two languages use to mitigate the imposition force of requests and the impact of the linguistic and cultural parameters on this use. Request samples were collected from 14 native speakers of Australian English and 14 native speakers of Iraqi Arabic by means of eight role-play interviews. The mitigating devices were identified and classified according to a modified categorization scheme based on Blum-Kulka et al. (1989). Additional categories of mitigating devices were added to this scheme to meet the requirements of data analysis. These include consultative device (Blum-Kulka & Olshtain, 1984), questions (Trosborg, 1995), apology (Economidou-Kogetsidis, 2008), alerter (Schauer, 2007), closing (Al-Ali & Alawneh, 2010), and new categories: wish/hope statement and verbal incentive. The results showed that internal mitigating devices were more frequent in Australian English requests than in Iraqi Arabic requests, while external mitigating devices were equally pervasive in both groups. The two groups also used different semantic formulae of some mitigating devices in specific situations. The pervasive occurrence of external mitigators in both groups‟ requests is discussed in terms of volubility as a politeness strategy. It is suggested that the divergence between the two groups in their utilization of request mitigations is related to linguistic and cultural variations between the Australian and Iraqi languages and cultures.

Request mitigating devices in Australian English and Iraqi Arabic : a comparative study

Significant issues, especially miscommunication in a cross-cultural setting and pragmatic failure in second language (L2) acquisition, stem from the linguistic and cultural differences between social groups. The investigation of speech acts realization in everyday situations is deemed as an important field to explore the impact of linguistic and cultural variations on cross-cultural communication and L2 acquisition. This paper examines the internal and external mitigating devices that Australian English native speakers (AENSs) and Iraqi Arabic native speakers (IANSs) use to soften the force of request speech acts in everyday situations. It aims to explore request mitigating devices employed in Australian English and Iraqi Arabic in terms of semantic formulae and frequencies in everyday interaction. Request samples were collected from native speakers of Australian English and Iraqi Arabic by means of role-play interviews. The mitigating devices found in requests were identified and classified. The results showed that internal mitigating devices were more frequent in AENSs’ requests than in IANSs’ requests, while external mitigating devices were pervasive in both groups. The two groups also used different semantic formulae of some mitigating devices in some situations. The pervasive occurrence of external mitigators in both groups’ requests is explained in terms of the notion of volubility as a politeness strategy. It is also suggested that the divergence between the two groups in their utilization of request mitigations is related to linguistic and cultural variations between the Australian and Iraqi cultures.

The descent of Morgan in Australia: kinship representation from the Australian colonies

Morgan had two extraordinary disciples in Lorimer Fison and Alfred Howitt in Australia. They were inspired by Morgan’s kinship schedule and were profoundly engaged in the method and theory of the collection of kinship data and its interpretation. Fison began using the schedule in Fiji in 1869. Soon after his first contact with Howitt, in 1873, they changed the method of collection of kinship terminologies. This paper traces the shift from tabulated kinship lists to family trees and the use of sticks to represent relationships (nearly twenty years before Rivers’ celebrated ‘genealogical method’), as well as efforts to find new means of representing kinship through experimentation with ‘ graphic formulae’ inspired by chemical equations. These innovations first occurred through the gathering of kinship data about the Kŭnai of Gippsland, Victoria, and crucially involved close collaboration between Howitt and his Kŭnai consultant Tulaba. What was revealed in this process was an indigenous kinship system quite different from that found in other parts of colonial Australia known at the time. Fison and Howitt explained this system as transitional between two stages in terms of Morgan’s evolutionary scheme, but at the same time challenged the assumption that the general scheme could be applied to Australia. While the details of Morgan’s evolutionary stages have faded from view, the methods of collection, representation, transmission, comparison and interpretation of kinship data are still live issues in anthropology today. The kind of kinship system discovered in Gippsland involved neutralisation of the cross-parallel distinctions, distinctions that are otherwise typical of Australia. Such neutralisation can now be shown to occur elsewhere in Australia. There does indeed seem to have been a transition from a Dravidianate system with cross-parallel distinctions to ‘overlays’ of cross-parallel neutralisation, and finally a complete loss in some generations of such distinctions in the terminology. These discoveries open up possibilities of rebuilding a diachronic theory of kinship change and evolution, incorporating some of the insights of Fison and Howitt, though without their specific hypotheses, either of local developments in Gippsland or the grand scheme of Morgan.

Prolonged and flexible primary moult overlaps extensively with breeding in beach-nesting Hooded Plovers Thinornis rubricollis

We present the first report of complete overlap of breeding and moult in a shorebird. In southeastern Australia, Hooded Plovers Thinornis rubricollis spend their entire lives on oceanic beaches, where they exhibit biparental care. Population moult encompassed the 6-month breeding season. Moult timing was estimated using the Underhill-Zucchini method for Type 2 data with a power transformation to accommodate sexual differences in rates of moult progression in the early and late stages of moult. Average moult durations were long in females (170.3 ± 14.2 days), and even longer in males (210.3 ± 13.5 days). Breeding status was known for most birds in our samples, and many active breeders (especially males) were also growing primaries. Females delayed the onset of primary moult but were able to increase the speed of moult and continue breeding, completing moult at about the same time as males. The mechanism by which this was achieved appeared to be flexibility in moult sequence. All moult formulae fell on one of two linked moult sequences, one faster than the other. The slower sequence had fewer feathers growing concurrently and also had formulae indicating suspended moults. Switching between sequences via common formulae is possible at many points during the moult cycle, and three of 12 recaptures were confirmed to have switched sequences in the same moult season. Hooded Plovers thus have a prolonged primary moult with the flexibility to change their rate of moult; this may facilitate high levels of replacement clutches that are associated with passive nest defence and low reproductive success. © 2014 British Ornithologists' Union.

Describing human finger flexibility via reachable subspaces

In recent years, the reachable space concept has attracted the attention of many researchers as a mean of describing finger flexibility. Existing approaches such as exhaustive scanning or Monte Carlo methods to obtain the reachable space are resource-hungry techniques. In this paper, we introduce a novel approach to determine and quantify the reachable space of the finger. The approach was developed around a set of formulae determining the boundary of the reachable space. The Monte Carlo simulation is proposed to estimate the capacity of the reachable space. Using the new technique, reachable spaces can be visualised and quantified in order to effectively compare the functionality of different subjects and their therapeutic status. The performance of the proposed method was evaluated against the kinematic feed-forward approach. The computational cost to obtain the reachable space is significantly less than the standard kinematic feed-forward approach due to exclusive description of the reachable space boundary, unique to the proposed approach.

Hydrothermal synthesis of dioctahedral smectites: The Al-Fe3+chemical series. Part II: crystal-chemistry

The crystal-chemistry of a series of synthetic Al-Fe3+ smectites was studied in detail using near and mid infrared spectroscopy. Chemical and NIR data indicated a quite complete range of octahedral Al for Fe3+ substitution, and therefore, the solid-solution between beidellite and nontronite end-members was continuous and complete. The wavenumbers of several infrared absorption bands were correlated with the chemistry of the synthetic smectites, providing a useful tool to constrain their structural formulae and also for assisting in assignments of similar bands in natural smectites. The Al and Fe3+ cations were shown to be randomly distributed in the octahedral sheet of synthesized smectites. Despite the high availability of iron during synthesis, generally only a small amount of tetrahedral Fe3+ was observed.