Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

8-Ammonionaphthalene-2-sulfonate monohydrate : the zwitterionic hydrate of 1,7-Cleve's acid

The structure of 8-amino-2-naphthalenesulfonic acid monohydrate (1,7-Cleve's acid hydrate), C10H9NO3S.H2O, shows the presence of a sulfonate-aminium group zwitterion, both groups and the water molecule of solvation giving cyclic R3/3(8) intermolecular hydrogen-bonding interactions forming chains which extend down a axis of the unit cell. Additional peripheral associations, including weak aromatic ring pi-pi interactions [centroid-centroid distance 3.6299(15)A], result in a two-dimensional sheet structure.

Zero- one- and two-dimensional hydrogen-bonded structures in the 1:1 proton-transfer compounds of 4,5-dichlorophthalic acid with the monocyclic heteroaromatic Lewis bases 2-aminopyrimidine, nicotinamide and isonicotinamide

The structures of the anhydrous 1:1 proton-transfer compounds of 4,5-dichlorophthalic acid (DCPA) with the monocyclic heteroaromatic Lewis bases 2-aminopyrimidine, 3-(aminocarboxy) pyridine (nicotinamide) and 4-(aminocarbonyl) pyridine (isonicotinamide), namely 2-aminopyrimidinium 2-carboxy-4,5-dichlorobenzoate C4H6N3+ C8H3Cl2O4- (I), 3-(aminocarbonyl) pyridinium 2-carboxy-4,5-dichlorobenzoate C6H7N2O+ C8H3Cl2O4- (II) and the unusual salt adduct 4-(aminocarbonyl) pyridinium 2-carboxy-4,5-dichlorobenzoate 2-carboxymethyl-4,5-dichlorobenzoic acid (1/1/1) C6H7N2O+ C8H3Cl2O4-.C9H6Cl2O4 (III) have been determined at 130 K. Compound (I) forms discrete centrosymmetric hydrogen-bonded cyclic bis(cation--anion) units having both R2/2(8) and R2/1(4) N-H...O interactions. In compound (II) the primary N-H...O linked cation--anion units are extended into a two-dimensional sheet structure via amide-carboxyl and amide-carbonyl N-H...O interactions. The structure of (III) reveals the presence of an unusual and unexpected self-synthesized methyl monoester of the acid as an adduct molecule giving one-dimensional hydrogen-bonded chains. In all three structures the hydrogen phthalate anions are

Information for regulating action in sport : metastability and emergence of tactical solutions under ecological constraints

The aims of this chapter are twofold. First, we show how experiments related to nonlinear dynamical systems theory can bring about insights on the interconnectedness of different information sources for action. These include the amount of information as emphasised in conventional models of cognition and action in sport and the nature of perceptual information typically emphasised in the ecological approach. The second aim was to show how, through examining the interconnectedness of these information sources, one can study the emergence of novel tactical solutions in sport; and design experiments where tactical/decisional creativity can be observed. Within this approach it is proposed that perceptual and affective information can be manipulated during practice so that the athlete's cognitive and action systems can be transposed to a meta-stable dynamical performance region where the creation of novel action information may reside.

Ethyl-eicosapentaenoic acid in first-episode psychosis : a 1H-MRS study

Ethyl-eicosapentaenoic acid (E-EPA) is an omega-3 fatty acid that has been used in a range of neuropsychiatric conditions with some benefits. However, its mechanism of action is unknown. Here, we investigate its effects on in vivo brain metabolism in first-episode psychosis (FEP). Proton magnetic resonance spectroscopy at 3 T was performed in the temporal lobes of 24 FEP patients before and after 12 weeks of treatment in the context of a larger double-blind, placebo-controlled E-EPA augmentation study. Treatment group effects for glutathione (F1,12=6.1, p=0.03), and a hemisphere-by-group interaction for glutamine/glutamate (F1,20=4.4, p=0.049) were found. Glutathione increased bilaterally and glutamate/glutamine increased in the left hemisphere following E-EPA administration. Improvement in negative symptoms correlated with metabolic brain changes, particularly glutathione (r=-0.57). These results suggest that E-EPA augmentation alters glutathione availability and modulates the glutamine/glutamate cycle in early psychosis, with some of the metabolic brain changes being correlated with negative symptom improvement. Larger confirmatory studies of these postulated metabolic brain effects of E-EPA are warranted.

Inhibition of myeloperoxidase-mediated hypochlorous acid production by nitroxides

Tissue damage resulting from the extracellular production of HOCl (hypochlorous acid) by the MPO (myeloperoxidase)-hydrogen peroxide-chloride system of activated phagocytes is implicated as a key event in the progression of a number of human inflammatory diseases. Consequently, there is considerable interest in the development of therapeutically useful MPO inhibitors. Nitroxides are well established antioxidant compounds of low toxicity that can attenuate oxidative damage in animal models of inflammatory disease. They are believed to exert protective effects principally by acting as superoxide dismutase mimetics or radical scavengers. However, we show here that nitroxides can also potently inhibit MPO-mediated HOCl production, with the nitroxide 4-aminoTEMPO inhibiting HOCl production by MPO and by neutrophils with IC50 values of approx. 1 and 6 μM respectively. Structure–activity relationships were determined for a range of aliphatic and aromatic nitroxides, and inhibition of oxidative damage to two biologically-important protein targets (albumin and perlecan) are demonstrated. Inhibition was shown to involve one-electron oxidation of the nitroxides by the compound I form of MPO and accumulation of compound II. Haem destruction was also observed with some nitroxides. Inhibition of neutrophil HOCl production by nitroxides was antagonized by neutrophil-derived superoxide, with this attributed to superoxide-mediated reduction of compound II. This effect was marginal with 4-aminoTEMPO, probably due to the efficient superoxide dismutase-mimetic activity of this nitroxide. Overall, these data indicate that nitroxides have considerable promise as therapeutic agents for the inhibition of MPO-mediated damage in inflammatory diseases.

Clinical efficacy and safety of zoledronic acid in osteoporosis and Paget's disease

Osteoporosis and Paget’s bone disease are the most common diseases of the bone. In addition to glucocorticoid treatment, there are many other secondary causes of osteoporosis. Bisphosphonates are used to treat these bone conditions. Zoledronic acid is the most potent bisphosphonate at inhibiting bone resorption. In osteoporosis, zoledronic acid increases bone mineral density for at least 1 year following a single intravenous administration. The efficacy and safety of zoledronic acid in the treatment of osteoporosis and Paget’s bone disease are reviewed. This article also covers the studies of the effects of zoledronic acid in the bone loss associated with the secondary osteoporosis.

Anti-cancer activity of zoledronic acid in breast cancer

Background: Zoledronic acid is used to prevent the bone loss associated with antioestrogen treatments in subjects with breast cancer. Preclinical studies suggest that zoledronic acid may have anticancer activity in its own right. This anticancer possibility with zoledronic acid has not been investigated extensively in clinical trials. Objectives/methods: This evaluation is of a large clinical trial that investigated the effect of zoledronic acid on cancer outcomes in premenopausal women with breast cancer. Results: The trial showed that after 4 years, 94.0% of subjects who were treated with zoledronic acid were disease-free compared with 90.8% of those not treated with zoledronic acid. Recurrence survival was a secondary end point; this occurred in 94.0% with, and 90.9% without, zoledronic acid treatment. Conclusions: Zoledronic acid does have anticancer activity in premenopausal women with cancer.

Clinical efficacy and safety of zoledronic acid in prostate and breast cancer

The anti-estrogen treatment for hormone-sensitive breast cancer and the androgen deprivation therapy for prostate cancer can lead to the development of osteoporosis and bone fractures. Metastases associated with prostate and breast cancer can also occur in bone. Bisphosphonates are used in these types of bone dysfunction. Zoledronic acid is the most potent bisphosphonate. In osteoporosis, zoledronic acid inhibits bone reabsorption and increases bone mineral density for at least a year after intravenous administration. The efficacy and safety of zoledronic acid in osteoporosis secondary to hormone-sensitive cancers (prostate and breast), and in the bone metastases associated with these cancers are reviewed.

Social innovation to solve homelessness : wicked solutions for wicked problems

Homelessness is a complex problem that manifests in all societies. This intractable and ‘wicked’ issue resists single-agency solutions and its resolution and requires a large, on-going investment of financial and professional resources that few organisations can sustain. This paper adopts a social innovation framework to examine government and community sector responses to homelessness. While recent evaluations and policy prescriptions have suggested better integrated and more co-ordinated service delivery models for addressing homelessness, there is little understanding of the innovation framework in which alternative service system paradigms emerge. A framework that identifies/distils and explains different innovation levels is put forward. The framework highlights that while government may lead strategic level innovations, community organisations are active in developing innovation at the service and client level. Moreover, community organisations may be unaware of the innovative capacity that resides in their creative responses to resolving social crisis and marginalisation through being without shelter.