Diophantine equations as a context for technology-enhanced training in conjecturing and proving

Solving indeterminate algebraic equations in integers is a classic topic in the mathematics curricula across grades. At the undergraduate level, the study of solutions of non-linear equations of this kind can be motivated by the use of technology. This article shows how the unity of geometric contextualization and spreadsheet-based amplification of this topic can provide a discovery experience for prospective secondary teachers and information technology students. Such experience can be extended to include a transition from a computationally driven conjecturing to a formal proof based on a number of simple yet useful techniques.

Intervertebral staple grading system with micro-CT

Introduction Intervertebral stapling is a leading method of fusionless scoliosis treatment which attempts to control growth by applying pressure to the convex side of a scoliotic curve in accordance with the Hueter-Volkmann principle. In addition to that, staples have the potential to damage surrounding bone during insertion and subsequent loading. The aim of this study was to assess the extent of bony structural damage including epiphyseal injury as a result of intervertebral stapling using an in vitro bovine model. Materials and Methods Thoracic spines from 6-8 week old calves were dissected and divided into motion segments including levels T4-T11 (n=14). Each segment was potted in polymethylemethacrylate. An Instron Biaxial materials testing machine with a custom made jig was used for testing. The segments were tested in flexion/extension, lateral bending and axial rotation at 37⁰C and 100% humidity, using moment control to a maximum 1.75 Nm with a loading rate of 0.3 Nm per second for 10 cycles. The segments were initially tested uninstrumented with data collected from the tenth load cycle. Next an anterolateral 4-prong Shape Memory Alloy (SMA) staple (Medtronic Sofamor Danek, USA) was inserted into each segment. Biomechanical testing was repeated as before. The staples were cut in half with a diamond saw and carefully removed. Micro-CT scans were performed and sagittal, transverse and coronal reformatted images were produced using ImageJ (NIH, USA).The specimens were divided into 3 grades (0, 1 and 2) according to the number of epiphyses damaged by the staple prongs. Results: There were 9 (65%) segments with grade 1 staple insertions and 5 (35%) segments with grade 2 insertions. There were no grade 0 staples. Grade 2 spines had a higher stiffness level than grade 1 spines, in all axes of movement, by 28% (p=0.004). This was most noted in flexion/extension with an increase of 49% (p=0.042), followed by non-significant change in lateral bending 19% (p=0.129) and axial rotation 8% (p=0.456) stiffness. The cross sectional area of bone destruction from the prongs was only 0.4% larger in the grade 2 group compared to the grade 1 group (p=0.961). Conclusion Intervertebral staples cause epiphyseal damage. There is a difference in stiffness between grade 1 and grade 2 staple insertion segments in flexion/extension only. There is no difference in the cross section of bone destruction as a result of prong insertion and segment motion.

Experimental investigation of post-fire mechanical properties of cold-formed steels

Cold-formed steel members are widely used in residential, industrial and commercial buildings as primary load-bearing elements. During fire events, they will be exposed to elevated temperatures. If the general appearance of the structure is satisfactory after a fire event then the question that has to be answered is how the load bearing capacity of cold-formed steel members in these buildings has been affected. Hence after such fire events there is a need to evaluate the residual strength of these members. However, the post-fire behaviour of cold-formed steel members has not been investigated in the past. This means conservative decisions are likely to be made in relation to fire exposed cold-formed steel buildings. Therefore an experimental study was undertaken to investigate the post-fire mechanical properties of cold-formed steels. Tensile coupons taken from cold-formed steel sheets of three different steel grades and thicknesses were exposed to different elevated temperatures up to 800 oC, and were then allowed to cool down to ambient temperature before they were tested to failure. Tensile coupon tests were conducted to obtain their post-fire stress-strain curves and associated mechanical properties (yield stress, Young’s modulus, ultimate strength and ductility). It was found that the post-fire mechanical properties of cold-formed steels are reduced below the original ambient temperature mechanical properties if they had been exposed to temperatures exceeding 300 oC. Hence a new set of equations is proposed to predict the post-fire mechanical properties of cold-formed steels. Such post-fire mechanical property assessments allow structural and fire engineers to make an accurate prediction of the safety of fire exposed cold-formed steel buildings. This paper presents the details of this experimental study and the results of post-fire mechanical properties of cold-formed steels. It also includes the results of a post-fire evaluation of cold-formed steel walls.

Sibling bullying perpetration: Associations with gender, grade, peer perpetration, trait anger, and moral disengagement

This study investigated bullying amongst siblings in both traditional and cyber forms, and the associations of gender, grade, peer bullying perpetration, trait anger and moral disengagement. The participants were 455 children in grades 5 to 12 (262 girls and 177 boys with 16 unknown gender) who had a sibling. As the number of siblings who only bullied by technology was low, these associations were not able to be calculated. However, the findings showed that the percentage of sibling traditional bullying perpetration (31.6%) was higher than peer bullying perpetration (9.8%). Sibling bullies reported engaging in complex behaviours of perpetration and victimisation in both the physical and in cyber settings, although the number was small. Gender, trait anger, moral disengagement and bullying peers at school (but not grade) were all significantly associated with sibling traditional bullying perpetration. The implications of the findings are discussed for bullying intervention and prevention programs to understand childhood bullying in diverse contexts.

An integrated modeling and risk analysis tool for mine water interactions

Poor mine water management can lead to corporate, environmental and social risks. These risks become more pronounced as mining operations move into areas of water scarcity and/or increase climatic variability while also managing increased demand, lower ore grades and increased strip ratios. Therefore, it is vital that mine sites better understand these risks in order to implement management practices to address them. Systems models provide an effective approach to understand complex networks, particularly across multiple scales. Previous work has represented mine water interactions using systems model on a mine site scale. Here, we expand on that work by present an integrated tool that uses a systems modeling approach to represent mine water interactions on a site and regional scale and then analyses the risks associated with events stemming from those interactions. A case study is presented to represent three indicative corporate, environmental and social risks associated with a mine site that exists in a water scarce region. The tool is generic and flexible, and can be used in many scenarios to provide significant potential utility to the mining industry.

UNICEF, Jakarta, Indonesia : Review of Satap Schools

A. Background and context 1. Education, particularly basic education (grades1-9), has been considered critical to promoting national economic growth and social well being1. Three factors that con-tribute to the above are: (i) Education increases human capital inherent in a labor force and thus increases productivity. It also increases capacity for working with others and builds community consensus to support national development. (ii) Education can in-crease the innovative capacity of a community to support social and economic growth—use of new technologies, products and services to promote growth and wellbeing. (iii) Education can facilitate knowledge transfer needed to understand the social and eco-nomic innovations and new processes, practices and values. Cognizant of the above benefits of education, the Millennium Development Goals (MDG) and the Education for All (EFA) declarations advocating universal basic education were formulated and ratified by UN member countries. 2. Achieving universal primary education (grade 6) may not be sufficient to maxim-ize the above noted socio-economic and cultural benefits. There is general consensus that basic literacy and numeracy up to grade 9 are essential foundational blocks for any good education system to support national development. Basic Education provides an educational achievement threshold that ensures the learning is retained. To achieve this, the donor partner led interventions and the UN declarations such as the MDG goals have sought universal access to basic education (grades 1-9). As many countries progress towards achieving the universal access targets, recent research evidence suggests that we need more than just access to basic education to impact on the na-tional development. Measuring basic education completion cycle, gross enrolment rate (GER) and participation rate etc., has to now include a focus on quality and relevance of the education2. 3. While the above research finding is generally accepted by the Government of In-donesia (GoI), unlike many other developing countries, Indonesia is geographically and linguistically complex and has the fourth largest education sector in the world. It has over 3000 islands, 17,000 ethnic groups and it takes as long as 7 hours to travel from east to west of the country and has multiple time differences. The education system has six years of primary education (grades 1-6), 3 years of junior secondary education (grades 7-9) and three years of senior secondary education (grades 10-12). Therefore, applying the findings of the above cited research in a country like Indonesia is a chal-lenge. Nevertheless, since the adoption of the National Education Law (2003)3 the GoI has made significant progress in improving access to and quality of basic education (grades 1-9). The 2011/12 national education statistics show the primary education (grades 1-6) completion rate was 99.3%, the net enrolment rate (NER) was 95.4% and the GER was 115.4%. This is a significant achievement considering the complexities faced within Indonesia. This increase in the primary education sub-sector, however, has not flowed onto the Junior Secondary School (JSS) education. The transition from pri-mary to JSS is still short of the GoI targets. In 2012, there were 146,826 primary schools feeding into 33,668 junior secondary schools. The transition rate from primary to secondary in 2011/12 was 78%. When considering district or sub-district level data the transition in poor districts could be less than the aggregated national rate. Poverty and lack of parents’ education, confounded by opportunity cost, are major obstacles to transitioning to JSS4. 4. Table 1 presents a summary of GoI initiatives to accelerate the transition to JSS. GoI, with assistance from the donor community, has built 2465 new regular JSS, mak-ing the total number of regular JSS 33,668. In addition, 57,825 new classrooms have been added to existing regular JSS. Also, in rural and remote areas 4136 Satu-Atap5 (SATAP) schools were built to increase access to JSS. These SATAP schools are the focus of this study as they provide education opportunities to the most marginalized, ru-ral, remote children who otherwise would not have access to JSS and consequently not complete basic education.

Experimental and numerical studies of fire exposed lipped channel columns subject to distortional buckling

Cold-formed steel sections are commonly used in low-rise commercial and residential buildings. During fire events, cold-formed steel structural elements in these buildings are exposed to elevated temperatures. Hence after such events there is a need to determine the residual strength of these structural elements. However, only limited information is available in relation to the residual strength of fire exposed cold-formed steel members. This research is aimed at investigating the residual distortional buckling capacities of fire exposed cold-formed steel lipped channel sections. A series of compression tests of fire exposed, short lipped channel columns made of varying steel grades and thicknesses was undertaken in this research. Test columns were exposed to different elevated temperatures up to 800 oC. They were then allowed to cool down at ambient temperature before they were tested to failure. Suitable finite element models of tested columns were also developed and validated using test results. The residual compression capacities of tested columns were predicted using the ambient temperature cold-formed steel design rules (AS/NZS 4600, AISI S100 and Direct Strength Method). Post-fire mechanical properties obtained from a previous study were used in this study. Comparison of results showed that ambient temperature design rules for compression members can be used to predict the residual compression capacities of fire exposed short or laterally restrained cold-formed steel columns provided the maximum temperature experienced by the columns can be estimated after a fire event. Such residual capacity assessments will allow structural and fire engineers to make an accurate prediction of the safety of buildings after fire events. This paper presents the details of these experimental and numerical studies and the results.

Fire performance and design of cold-formed steel wall systems

Traditionally, the fire resistance rating of Light gauge steel frame (LSF) wall systems is based on approximate prescriptive methods developed using limited fire tests. These fire tests are conducted using standard fire time-temperature curve given in ISO 834. However, in recent times fire has become a major disaster in buildings due to the increase in fire loads as a result of modern furniture and lightweight construction, which make use of thermoplastics materials, synthetic foams and fabrics. Therefore a detailed research study into the performance of load bearing LSF wall systems under both standard and realistic design fires on one side was undertaken to develop improved fire design rules. This study included both full scale fire tests and numerical studies of eight different LSF wall systems conducted for both the standard fire curve and the recently developed realistic design fire curves. The use of previous fire design rules developed for LSF walls subjected to non-uniform elevated temperature distributions based on AISI design manual and Eurocode 3 Parts 1.2 and 1.3 was investigated first. New simplified fire design rules based on AS/NZS 4600, North American Specification and Eurocode 3 Part 1.3 were then proposed with suitable allowances for the interaction effects of compression and bending actions. The importance of considering thermal bowing, magnified thermal bowing and neutral axis shift in the fire design was also investigated and their effects were included. A spread sheet based design tool was developed based on the new design rules to predict the failure load ratio versus time and temperature curves for varying LSF wall configurations. The accuracy of the proposed design rules was verified using the fire test and finite element analysis results for various wall configurations, steel grades, thicknesses and load ratios under both standard and realistic design fire conditions. A simplified method was also proposed to predict the fire resistance rating of LSF walls based on two sets of equations developed for the load ratio-hot flange temperature and the time-temperature relationships. This paper presents the details of this study on LSF wall systems under fire conditions and the results.

Fire performance of LSF wall panels using numerical parametric studies

Light Gauge Steel Framing (LSF) walls made of cold-formed and thin-walled steel lipped channel studs with plasterboard linings on both sides are commonly used in commercial, industrial and residential buildings. However, there is limited data about their structural and thermal performances under fire conditions. Recent research at the Queensland University of Technology has investigated the structural and thermal behaviour of load bearing LSF wall systems. In this research a series of full scale fire tests was conducted first to evaluate the performance of LSF wall systems with eight different wall configurations under standard fire conditions. Finite element models of LSF walls were then developed, analysed under transient and steady state conditions, and validated using full scale fire tests. This paper presents the details of an investigation into the fire performance of LSF wall panels based on an extensive finite element analysis based parametric study. The LSF wall panels with eight different plasterboard-insulation configurations were considered under standard fire conditions. Effects of varying steel grades, steel thicknesses, screw spacing, plasterboard restraint, insulation materials and load ratio on the fire performance of LSF walls were investigated and the results of extensive fire performance data are presented in the form of load ratio versus time and critical hot flange (failure) temperature curves.

Post-fire mechanical properties of cold-formed steels

Cold-formed steel members have been widely used in residential, industrial and commercial buildings as primary load-bearing and non-load bearing structural elements. These buildings must be properly evaluated after a fire event to assess the nature and extent of structural damage. If the general appearance of the structure is satisfactory after a fire event then the question that has to be answered is how the structural capacity of cold-formed steel members in these buildings has been affected. Elevated temperatures during a fire event affect the structural performance of cold-formed steel members even after cooling down to ambient temperature due to the possible detrimental changes in their mechanical properties. However, the post-fire behaviour of cold-formed steel members has not been investigated in the past and hence there is a need to investigate the post-fire mechanical properties of cold-formed steels. Therefore an experimental study was undertaken at the Queensland University of Technology to understand the residual mechanical properties of cold-formed steels after fire events. Tensile coupon tests were conducted on three different steel grades and thicknesses to obtain their stress-strain curves and relevant mechanical properties after cooling them down from different elevated temperatures. It was found that the post-fire mechanical properties of cold-formed steels are different to the original ambient temperature mechanical properties. Hence a new set of equations is proposed to predict the reduced mechanical properties of cold-formed steels after a fire event.

Design of cold-formed steel columns at elevated temperatures subject to flexural-torsional buckling

Cold-formed steel members are often subject to axial compression loads in a range of applications. These thin-walled members can be subject to various types of buckling modes, including flexural-torsional buckling. Design standards provide guidelines for columns subject to flexural-torsional buckling modes at ambient temperature. However, there are no specific design guidelines for elevated temperature conditions. Hence extensive research efforts have gone into the many investigations addressing the flexural-torsional buckling behaviour of cold-formed steel columns at elevated temperatures.This research has reviewed the accuracy of the current design rules in AS/NZS 4600 and the North American Specification in determining the member capacities of cold-formed steel columns using the results from detailed finite element analyses and an experimental study of lipped channel columns. It was found that the current ambient temperature Australian and American design rules accurately predicted the member capacities of pin ended lipped channel columns undergoing flexural torsional buckling at elevated temperatures by simply using the appropriate elevated temperature mechanical properties. However, for fixed ended columns with warping fixity undergoing flexural-torsional buckling, it was found that the current design rules significantly underestimated the column capacities as they disregard the beneficial effect of warping fixity. This research has therefore proposed improved design rules and verified their accuracy using finite element analysis and test results of cold-formed lipped channel columns made of three cross-sections and five different steel grades and thicknesses. This paper presents the details of this research study and the results.

Buckling tests of fire exposed cold-formed steel columns

Cold-formed steel sections are commonly used in low-rise commercial and residential buildings. During fire events, cold-formed steel structural elements in these buildings will be exposed to elevated temperatures. Hence after such events there is a need to evaluate the residual strength of these structural elements. However, only limited information is available in relation to the residual strength of fire exposed cold-formed steel sections. This means conservative decisions are often made in relation to fire exposed building structures. This research is aimed at investigating the buckling capacities of fire exposed cold-formed lipped channel steel sections. A series of compression tests of fire exposed, short lipped channel columns made of varying steel grades and thicknesses was undertaken in this research. Test columns were first exposed to different elevated temperatures up to 800 oC. They were then allowed to cool down at ambient temperatures before they were tested to failure. Similarly tensile coupon tests were also undertaken after being exposed to various elevated temperatures, from which the residual mechanical properties (yield stress and Young’s modulus) of the steels used in this study were derived. Using these mechanical properties, the residual compression capacities of tested short columns were predicted using the currently used design rules in AS/NZS 4600 and AISI cold-formed steel standards. This comparison showed that ambient temperature design rules for compression members can be used to predict the residual compression capacities of fire exposed short or laterally restrained cold-formed steel columns provided the maximum temperature experienced by the columns can be estimated after a fire event. Such residual capacity assessments will allow structural and fire engineers to make an accurate prediction of the safety of fire exposed buildings. This paper presents the details of this experimental study and the results.

Distortional buckling behaviour of fire exposed cold-formed steel columns

Cold-formed steel sections are commonly used in low-rise commercial and residential buildings. During fire events, cold-formed steel structural elements in these buildings can be exposed to elevated temperatures. Hence after such events there is a need to evaluate their residual strengths. However, only limited information is available in relation to the residual strength of fire exposed cold-formed steel sections. This research is aimed at investigating the distortional buckling capacities of fire exposed cold-formed lipped channel sections. A series of compression tests of fire exposed, short lipped channel columns made of varying steel grades and thicknesses was undertaken in this research. Test columns were first exposed to different elevated temperatures up to 800 oC, and then tested to failure after cooling down. Suitable finite element models were developed with post-fire mechanical properties to simulate the behaviour of tested columns and were validated using test results. The residual compression capacities of short columns were also predicted using the current cold-formed steel standards and compared with test and finite element analysis results. This comparison showed that ambient temperature design rules for columns can be used to predict the residual compression capacities of fire exposed short or laterally restrained cold-formed steel columns provided the maximum temperature experienced by the column can be estimated after a fire event. Such residual capacity assessments will allow engineers to evaluate the safety of fire exposed buildings. This paper presents the details of this experimental study, finite element analyses and the results.

Longitudinal performance of polycaprolactone-based scaffold plus recombinant human morphogenetic protein-2 (rhBMP-2) in large preclinical animal model : 6- versus 12 months

There is strong current interest in the use of biodegradable scaffolds in combination with bone growth factors as a valuable alternative to the current gold standard autograft in spinal fusion surgery Yong et al. (2013). Here we report on 6- vs 12- month data set evaluating the longitudinal performance of a CaP coated polycaprolactone (PCL) scaffold loaded with recombinant human bone morphogenetic protein-2 (rhBMP-2) as a bone graft substitute within a preclinical ovine thoracic spine. The results of this study demonstrate the efficacy of scaffold-based delivery of rhBMP-2 in promoting higher fusion grades at 6- and 12- months in comparison to the scaffold alone or autograft group within the same time frame. Fusion grades achieved at six months using PCL+rhBMP-2 are not significantly increased at twelve months post surgery.

Development of fourth-grade students’ understanding of experimental and theoretical probability

Students explored variation and expectation in a probability activity at the end of the first year of a 3-year longitudinal study across grades 4-6. The activity involved experiments in tossing coins both manually and with simulation using the graphing software, TinkerPlots. Initial responses indicated that the students were aware of uncertainty, although an understanding of chance concepts appeared limited. Predicting outcomes of 10 tosses reflected an intuitive notion of equiprobability, with little awareness of variation. Understanding the relationship between experimental and theoretical probability did not emerge until multiple outcomes and representations were generated with the software.