Repeating patterns : strategies to assist young students to generalise the mathematical structure

This paper focuses on very young students' ability to engage in repeating pattern tasks and identifying strategies that assist them to ascertain the structure of the pattern. It describes results of a study which is part of the Early Years Generalising Project (EYGP) and involves Australian students in Years 1 to 4 (ages 5-10). This paper reports on the results from the early years' cohort (Year 1 and 2 students). Clinical interviews were used to collect data concerning students' ability to determine elements in different positions when two units of a repeating pattern were shown. This meant that students were required to identify the multiplicative structure of the pattern. Results indicate there are particular strategies that assist students to predict these elements, and there appears to be a hierarchy of pattern activities that help students to understand the structure of repeating patterns.

Mathematical modelling of controlled drug release from polymer micro-spheres : incorporating the effects of swelling, diffusion and dissolution via moving boundary problems

Controlled drug delivery is a key topic in modern pharmacotherapy, where controlled drug delivery devices are required to prolong the period of release, maintain a constant release rate, or release the drug with a predetermined release profile. In the pharmaceutical industry, the development process of a controlled drug delivery device may be facilitated enormously by the mathematical modelling of drug release mechanisms, directly decreasing the number of necessary experiments. Such mathematical modelling is difficult because several mechanisms are involved during the drug release process. The main drug release mechanisms of a controlled release device are based on the device’s physiochemical properties, and include diffusion, swelling and erosion. In this thesis, four controlled drug delivery models are investigated. These four models selectively involve the solvent penetration into the polymeric device, the swelling of the polymer, the polymer erosion and the drug diffusion out of the device but all share two common key features. The first is that the solvent penetration into the polymer causes the transition of the polymer from a glassy state into a rubbery state. The interface between the two states of the polymer is modelled as a moving boundary and the speed of this interface is governed by a kinetic law. The second feature is that drug diffusion only happens in the rubbery region of the polymer, with a nonlinear diffusion coefficient which is dependent on the concentration of solvent. These models are analysed by using both formal asymptotics and numerical computation, where front-fixing methods and the method of lines with finite difference approximations are used to solve these models numerically. This numerical scheme is conservative, accurate and easily implemented to the moving boundary problems and is thoroughly explained in Section 3.2. From the small time asymptotic analysis in Sections 5.3.1, 6.3.1 and 7.2.1, these models exhibit the non-Fickian behaviour referred to as Case II diffusion, and an initial constant rate of drug release which is appealing to the pharmaceutical industry because this indicates zeroorder release. The numerical results of the models qualitatively confirms the experimental behaviour identified in the literature. The knowledge obtained from investigating these models can help to develop more complex multi-layered drug delivery devices in order to achieve sophisticated drug release profiles. A multi-layer matrix tablet, which consists of a number of polymer layers designed to provide sustainable and constant drug release or bimodal drug release, is also discussed in this research. The moving boundary problem describing the solvent penetration into the polymer also arises in melting and freezing problems which have been modelled as the classical onephase Stefan problem. The classical one-phase Stefan problem has unrealistic singularities existed in the problem at the complete melting time. Hence we investigate the effect of including the kinetic undercooling to the melting problem and this problem is called the one-phase Stefan problem with kinetic undercooling. Interestingly we discover the unrealistic singularities existed in the classical one-phase Stefan problem at the complete melting time are regularised and also find out the small time behaviour of the one-phase Stefan problem with kinetic undercooling is different to the classical one-phase Stefan problem from the small time asymptotic analysis in Section 3.3. In the case of melting very small particles, it is known that surface tension effects are important. The effect of including the surface tension to the melting problem for nanoparticles (no kinetic undercooling) has been investigated in the past, however the one-phase Stefan problem with surface tension exhibits finite-time blow-up. Therefore we investigate the effect of including both the surface tension and kinetic undercooling to the melting problem for nanoparticles and find out the the solution continues to exist until complete melting. The investigation of including kinetic undercooling and surface tension to the melting problems reveals more insight into the regularisations of unphysical singularities in the classical one-phase Stefan problem. This investigation gives a better understanding of melting a particle, and contributes to the current body of knowledge related to melting and freezing due to heat conduction.

Footprint-based estimates of arch structure are confounded by body composition in adults

Previous research employing indirect measures of arch structure, such as those derived from footprints, have indicated that obesity results in a “flatter” foot type. In the absence of radiographic measures, however, definitive conclusions regarding the osseous alignment of the foot cannot be made. We determined the effect of body mass index (BMI) on radiographic and footprint‐based measures of arch structure. The research was a cross‐sectional study in which radiographic and footprint‐based measures of foot structure were made in 30 subjects (10 males, 20 female) in addition to standard anthropometric measures of height, weight, and BMI. Multiple (univariate) regression analysis demonstrated that both BMI ( β  = 0.39, t 26  = 2.12, p  = 0.04) and radiographic arch alignment ( β  = 0.51, t 26  = 3.32, p  < 0.01) were significant predictors of footprint‐based measures of arch height after controlling for all variables in the model ( R 2  = 0.59, F 3,26  = 12.3, p  < 0.01). In contrast, radiographic arch alignment was not significantly associated with BMI ( β  = −0.03, t 26  = −0.13, p  = 0.89) when Arch Index and age were held constant ( R 2  = 0.52, F 3,26  = 9.3, p  < 0.01). Adult obesity does not influence osseous alignment of the medial longitudinal arch, but selectively distorts footprint‐based measures of arch structure. Footprint‐based measures of arch structure should be interpreted with caution when comparing groups of varying body composition.

Vision based control for micro aerial vehicles : Application to sense and avoid

This work presents a collision avoidance approach based on omnidirectional cameras that does not require the estimation of range between two platforms to resolve a collision encounter. Our method achieves minimum separation between the two vehicles involved by maximising the view-angle given by the omnidirectional sensor. Only visual information is used to achieve avoidance under a bearing- only visual servoing approach. We provide theoretical problem formulation, as well as results from real flights using small quadrotors

Understanding the operational structure of Southeast Asian drug trafficking groups in Australia

This thesis examined the operational structure of Southeast Asian drug trafficking groups operating on the eastern seaboard of Australia by testing the validity and application of organised crime and drug trafficking typologies using data obtained from 159 drug trafficking cases in three Australian states: New South Wales; Queensland; and Victoria. Key findings indicated that the usefulness of typologies is limited when classifying and analysing organised crime groups. In particular, Southeast Asian drug trafficking groups operated largely in small, informal, family-based hierarchies or groups that were better conceptualised using theoretical perspectives from network and cultural studies. The study recommended that replicating previous empirical research in the field is an effective approach that will contribute towards building a cumulative body of knowledge on organised crime structures.

Micro-credit is not sufficient for the success of micro-enterprises at the bottom of the pyramid

This study examines the factors affecting the successful provision of micro-credit to people at the bottom of the pyramid and discusses the activities required to support entrepreneurial activities in a peri-urban African setting. The findings enable us to better understand why micro-credit, though useful, is only part of the solution, in a setting characterized by extreme resource constraints with an institutional fabric lacking the infrastructure that assists market development. We depict the crafting of new entrepreneurial activity as an ongoing process and present an emerging research agenda for future developments.

The molecular structure of the phosphate mineral väyrynenite : a vibrational spectroscopic study

We have studied the mineral väyrynenite from the Viitaniemi pegmatite, located in the Eräjärvi area, Finland using a combination of electron microscopy electron microprobe and vibrational spectroscopic techniques. Chemical analysis shows the formula of the mineral to be (Mn0.88,Fe0.08,Mg0.01)∑0.97Be1.02(PO4)1.00(OH)1.02. Vibrational spectroscopy enables an assessment of the molecular structure of väyrynenite to be assessed. An intense Raman band at 1004 cm−1 is to the ν1 symmetric stretching mode. The observation of multiple bands in the phosphate stretching region, offers support for the concept of different phosphate units in the väyrynenite structure. Infrared spectroscopy confirms this multiplicity of vibrational bands. Multiple bands are observed in the phosphate bending region.

Vibrational spectroscopy of the mineral meyerhofferite CaB3O3(OH)5·H2O – An assessment of the molecular structure

Meyerhofferite is a calcium hydrated borate mineral with ideal formula: CaB3O3(OH)5�H2O and occurs as white complex acicular to crude crystals with length up to �4 cm, in fibrous divergent, radiating aggregates or reticulated and is often found in sedimentary or lake-bed borate deposits. The Raman spectrum of meyerhofferite is dominated by intense sharp band at 880 cm�1 assigned to the symmetric stretching mode of trigonal boron. Broad Raman bands at 1046, 1110, 1135 and 1201 cm�1 are attributed to BOH in-plane bending modes. Raman bands in the 900–1000 cm�1 spectral region are assigned to the antisymmetric stretching of tetrahedral boron. Distinct OH stretching Raman bands are observed at 3400, 3483 and 3608 cm�1. The mineral meyerhofferite has a distinct Raman spectrum which is different from the spectrum of other borate minerals, making Raman spectroscopy a very useful tool for the detection of meyerhofferite in sedimentary and lake bed deposits.

The molecular structure of the phosphate mineral senegalite Al2(PO4)(OH)3⋅3H2O – A vibrational spectroscopic study

We have studied the mineral senagalite, a hydrated hydroxy phosphate of aluminium with formula Al2(PO4)(OH)3⋅3H2O using a combination of electron microscopy and vibrational spectroscopy. Senegalite crystal aggregates shows tabular to prismatic habitus and orthorhombic form. The Raman spectrum is dominated by an intense band at 1029 cm−1 assigned to the PO43- ν1 symmetric stretching mode. Intense Raman bands are found at 1071 and 1154 cm−1 with bands of lesser intensity at 1110, 1179 and 1206 cm−1 and are attributed to the PO43- ν3 antisymmetric stretching vibrations. The infrared spectrum shows complexity with a series overlapping bands. A comparison is made with spectra of other aluminium containing phosphate minerals such as augelite and turquoise. Multiple bands are observed for the phosphate bending modes giving support for the reduction of symmetry of the phosphate anion. Vibrational spectroscopy offers a means for the assessment of the structure of senagalite.

First-principle studies of electronic structure and C-doping effect in boron nitride nanoribbon

Structural and electronic properties have been studied for Boron Nitride nanoribbons (BNNR) with both zigzag and armchair shaped edge (Z-BNNR and A-BNNR) by first-principle spin-polarized total energy calculations. We found that the energy band gap of Z-BNNR is indirect and decreases monotonically with the increasing ribbon width, whereas direct energy band gap oscillation was observed for A-BNNRs. Additionally, C-substitution at either single boron or nitrogen atom site in BNNRs could induce spontaneous magnetization. Our results could be potentially useful to design magnetic nano-devices based on BNNRs.

Structure character in small-carbon-cluster deposition on diamond surface

Experimentally, hydrogen-free diamond-like carbon (DLC) films were assembled by means of pulsed laser deposition (PLD), where energetic small-carbon-clusters were deposited on the substrate. In this paper, the chemisorption of energetic C2 and C10 clusters on diamond (001)-( 2×1) surface was investigated by molecular dynamics simulation. The influence of cluster size and the impact energy on the structure character of the deposited clusters is mainly addressed. The impact energy was varied from a few tens eV to 100 eV. The chemisorption of C10 was found to occur only when its incident energy is above a threshold value ( E th). While, the C2 cluster was easily to adsorb on the surface even at much lower incident energy. With increasing the impact energy, the structures of the deposited C2 and C10 are different from the free clusters. Finally, the growth of films synthesized by energetic C2 and C10 clusters were simulated. The statistics indicate the C2 cluster has high probability of adsorption and films assembled of C2 present slightly higher SP3 fraction than that of C10-films, especially at higher impact energy and lower substrate temperature. Our result supports the experimental findings. Moreover, the simulation underlines the deposition mechanism at atomic scale.

Some extensions to representation and encoding of structure in models of distributional semantics

This thesis makes several contributions towards improved methods for encoding structure in computational models of word meaning. New methods are proposed and evaluated which address the requirement of being able to easily encode linguistic structural features within a computational representation while retaining the ability to scale to large volumes of textual data. Various methods are implemented and evaluated on a range of evaluation tasks to demonstrate the effectiveness of the proposed methods.

The architecture of children’s use of language and tools when problem solving collaboratively with robotics

This paper demonstrates, following Vygotsky, that language and tool use has a critical role in the collaborative problem-solving behaviour of school-age children. It reports original ethnographic classroom research examining the convergence of speech and practical activity in children’s collaborative problem solving with robotics programming tasks. The researchers analysed children’s interactions during a series of problem solving experiments in which Lego Mindstorms toolsets were used by teachers to create robotics design challenges among 24 students in a Year 4 Australian classroom (students aged 8.5–9.5 years). The design challenges were incrementally difficult, beginning with basic programming of straight line movement, and progressing to more complex challenges involving programming of the robots to raise Lego figures from conduit pipes using robots as pulleys with string and recycled materials. Data collection involved micro-genetic analysis of students’ speech interactions with tools, peers, and other experts, teacher interviews, and student focus group data. Coding the repeated patterns in the transcripts, the authors outline the structure of the children’s social speech in joint problem solving, demonstrating the patterns of speech and interaction that play an important role in the socialisation of the school-age child’s practical intellect.

Infrared and Raman spectroscopic characterization of the borate mineral colemanite – CaB3O4(OH)3·H2O – implications for the molecular structure

Colemanite CaB3O4(OH)3 H2O is a secondary borate mineral formed from borax and ulexite in evaporate deposits of alkaline lacustrine sediments. The basic structure of colemanite contains endless chains of interlocking BO2(OH) triangles and BO3(OH) tetrahedrons with the calcium, water and extra hydroxide units interspersed between these chains. The Raman spectra of colemanite is characterized by an intense band at 3605 cm-1 assigned to the stretching vibration of OH units and a series of bands at 3182, 3300, 3389 and 3534 cm-1 assigned to water stretching vibrations. Infrared bands are observed in similar positions. The BO stretching vibrations of the trigonal and tetrahedral boron are characterized by Raman bands at 876, 1065 and 1084 cm-1. The OBO bending mode is defined by the Raman band at 611 cm-1. It is important to characterize the very wide range of borate minerals including colemanite because of the very wide range of applications of boron containing minerals.

Quantifying spatial structure in experimental observations and agent-based simulations using pair-correlation functions

We define a pair-correlation function that can be used to characterize spatiotemporal patterning in experimental images and snapshots from discrete simulations. Unlike previous pair-correlation functions, the pair-correlation functions developed here depend on the location and size of objects. The pair-correlation function can be used to indicate complete spatial randomness, aggregation or segregation over a range of length scales, and quantifies spatial structures such as the shape, size and distribution of clusters. Comparing pair-correlation data for various experimental and simulation images illustrates their potential use as a summary statistic for calibrating discrete models of various physical processes.