Pedagogical challenges in making mathematics relevant for Indigenous Australians

After the invasion and occupation of their land by Europeans, Indigenous Australians were expected to benefit from a Western education system based on that of the dominant Europeans. Gradually educators realized that Aboriginal children learn differently and that Indigenous culture and pedagogy has validity and strength. Of course, educators also need to be acutely aware of the diversity of Indigenous cultures in Australia and that there is not a monolithic sense of Aboriginal identity or Aboriginal pedagogy. Dispossession and alienation, poor health and few employment opportunities must also affect educational interest, attendance, application and performance. In this paper the characteristics of Indigenous learners are examined and pedagogical strategies to assist in both students' learning and teachers' delivery are explored. The message conveyed in this paper has particular relevance for teaching mathematics to Aboriginal learners. It is also of considerable value in teaching mathematics to nonAboriginal students, in Australia and elsewhere.     

Superior antioxidant polymer films created through the incorporation of grape tannins in ethyl cellulose

Agro-wastes represent an abundant and economical source of antioxidant compounds. Extraction and incorporation of antioxidants from these compounds into ethyl cellulose films provides the basis for an active packaging material. Grape tannin extract (GT) incorporation into ethyl cellulose results in hydrogen bonding between polyphenols and ethyl cellulose strands, which allows for the polyphenols to remain active and to be securely incorporated. Incorporation of 0.5 % GT in ethyl cellulose produced a significant increase (p < 0.01) in antioxidant activity while not altering physical or mechanical properties. A higher loading of GT at 3.0 % into ethyl cellulose resulted in further improvement in antioxidant activity (12-fold), while a slight decrease in the tensile properties was noted due to the plasticizing effect of GT as a consequence of disruption of the intermolecular hydrogen bonding.     

Investigation of surface plasmon resonance using cylindrical dielectric-metal-dielectric (C-DMD) plasmonic configuration

In this paper we have proposed a technique based on image analysis of the surface plasmon excitation at the metal-dielectric interface of inside silver coated fused silica capillary glass tube. Chemical deposition technique has been used for the deposition of silver. Angular interrogation in Kretschmann-like configuration is realized by non-radial transverse illumination of this cylindrical dielectric-metal-dielectric (C-DMD) structure with a He–Ne laser source. Here the uniform film deposition of the inside surface of the capillary is not that crucial except within the transversely illuminated working area concerned. Moreover, the proposed technique has been validated experimentally for sensing different aqueous dielectric samples inserted inside the tube.     

A class of finite difference schemes for interface problems with an HOC approach

In this paper, we propose a new methodology for numerically solving elliptic and parabolic equations with discontinuous coefficients and singular source terms. This new scheme is obtained by clubbing a recently developed higher‐order compact methodology with special interface treatment for the points just next to the points of discontinuity. The overall order of accuracy of the scheme is at least second. We first formulate the scheme for one‐dimensional (1D) problems, and then extend it directly to two‐dimensional (2D) problems in polar coordinates. In the process, we also perform convergence and related analysis for both the cases. Finally, we show a new direction of implementing the methodology to 2D problems in cartesian coordinates. We then conduct numerous numerical studies on a number of problems, both for 1D and 2D cases, including the flow past circular cylinder governed by the incompressible Navier–Stokes equations. We compare our results with existing numerical and experimental results. In all the cases, our formulation is found to produce better results on coarser grids. For the circular cylinder problem, the scheme used is seen to capture all the flow characteristics including the famous von Kármán vortex street. Copyright © 2016 John Wiley & Sons, Ltd.     

Dioxane Dibromide–Mediated Solvent‐Free Synthesis of Vicinal Dibromides

Structurally varied vicinal dibromides have been synthesized in high yield and good purity through highly stereoselective anti‐addition of bromine across the olefinic linkages using dioxane dibromide (DD) under solvent‐free conditions.     

Reaction of bis-Lactone in Rigid Polycycles with Alkyl Lithiums. Synthesis of Novel Oxa-Cace Compounds

Reaction of bis-lactone embodied in the rigid tircyclo [5.2.1.0^2,6] decane 5 with MeLi and t-BuLi produced the novel oxa-cage compounds 9 and 11 instead of the expected ketones 6.     

Coexistence and harvesting control policy in a food chain model with mutual defense of prey

A model is proposed to understand the dynamics in a food chain (one predator‐two prey). Unlike many approaches, we consider mutualism (for defense against predators) between the two groups of prey. We investigate the conditions for coexistence and exclusion. Unlike Elettreby's (2009) results, we show that prey can coexist in the absence of predators (as expected since there is no competition between prey). We also show the existence of Hopf bifurcation and limit cycle in the model, and numerically present bifurcation diagrams in terms of mutualism and harvesting. When the harvest is practiced for profit making, we provide the threshold effort value that determines the profitability of the harvest. We show that there is zero profit when the constant effort is applied. Below (resp. above) , there will always be gain (resp. loss). In the case of gain, we provide the optimal effort and optimal steady states that produce maximum profit and ensure coexistence. Recommendations for resource managers As a result of our investigation, we bring the following to the attention of management:

• 1. In the absence of predators, different groups of prey can coexist if they mutually help each other (no competition among them).
• 2. There is a maximal effort to invest in order to gain profit from the harvest. Above , the investment will result in a loss.
• 3. In the case of profit from harvest, policy makers should recommend the optimal effort to be applied and the optimal stock to harvest. This will guarantee maximum profit while ensuring sustainability of all species.