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.

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.

Utilizing robustness of positive buck-boost converter against input voltage and load current disturbances

A Positive Buck- Boost (PBB) converter is a known DC-DC converter that can operate in step up and step down modes. Unlike Buck, Boost, and Inverting Buck Boost converters, the inductor current of a PBB can be controlled independently of its voltage conversion ratio. In other words, the inductor of PBB can be utilised as an energy storage unit in addition to its main function of energy transfer. In this paper, the capability of PBB to store energy has been utilised to achieve robustness against input voltage fluctuations and output current changes. The control strategy has been developed to keep accuracy, affordability, and simplicity acceptable. To improve the efficiency of the system a Smart Load Controller (SLC) has been suggested. Applying SLC extra current storage occurs when there is sudden loads change otherwise little extra current is stored.

Integrity determination of RTK solutions in precision farming applications

Integrity of Real Time Kinematic (RTK) positioning solutions relates to the confidential level that can be placed in the information provided by the RTK system. It includes the ability of the RTK system to provide timely valid warnings to users when the system must not be used for the intended operation. For instance, in the controlled traffic farming (CTF) system that controls traffic separates wheel beds and root beds, RTK positioning error causes overlap and increases the amount of soil compaction. The RTK system’s integrity capacity can inform users when the actual positional errors of the RTK solutions have exceeded Horizontal Protection Levels (HPL) within a certain Time-To-Alert (TTA) at a given Integrity Risk (IR). The later is defined as the probability that the system claims its normal operational status while actually being in an abnormal status, e.g., the ambiguities being incorrectly fixed and positional errors having exceeded the HPL. The paper studies the required positioning performance (RPP) of GPS positioning system for PA applications such as a CTF system, according to literature review and survey conducted among a number of farming companies. The HPL and IR are derived from these RPP parameters. A RTK-specific rover autonomous integrity monitoring (RAIM) algorithm is developed to determine the system integrity according to real time outputs, such as residual square sum (RSS), HDOP values. A two-station baseline data set is analyzed to demonstrate the concept of RTK integrity and assess the RTK solution continuity, missed detection probability and false alarm probability.

Feedback information and consumer motivation : the moderation role of positive and negative reference values in self-regulation

Marketers spend considerable resources to motivate people to consume their products and services as a means of goal attainment (Bagozzi and Dholakia, 1999). Why people increase, decrease, or stop consuming some products is based largely on how well they perceive they are doing in pursuit of their goals (Carver and Scheier, 1992). Yet despite the importance for marketers in understanding how current performance influences a consumer’s future efforts, this topic has received little attention in marketing research. Goal researchers generally agree that feedback about how well or how poorly people are doing in achieving their goals affects their motivation (Bandura and Cervone, 1986; Locke and Latham, 1990). Yet there is less agreement about whether positive and negative performance feedback increases or decreases future effort (Locke and Latham, 1990). For instance, while a customer of a gym might cancel his membership after receiving negative feedback about his fitness, the same negative feedback might cause another customer to visit the gym more often to achieve better results. A similar logic can apply to many products and services from the use of cosmetics to investing in mutual funds. The present research offers managers key insights into how to engage customers and keep them motivated. Given that connecting customers with the company is a top research priority for managers (Marketing Science Institute, 2006), this article provides suggestions for performance metrics including four questions that managers can use to apply the findings.

The implicit structure of positive characteristics

The implicit structure of positive character traits was examined in two studies of 190 and 100 undergraduates. Participants judged the pairwise covariation or semantic similarity of 42 positive characteristics using a sorting or a rating task. Characteristics were drawn from a new classification of strengths and virtues, the Five-Factor Model, and a taxonomy of values. Participants showed consistent patterns of perceived association among the characteristics across the study conditions. Multidimensional scaling yielded three consistent dimensions underlying these judgments (“warmth vs. self-control,” “vivacity vs. decency,” and “wisdom vs. power”). Cluster analyses yielded six consistent groupings—“self-control,” “love,” “wisdom,” “drive,” “vivacity,” and “collaboration”—that corresponded only moderately to the virtue classification. All three taxonomies were systematically related to this implicit structure, but none captured it satisfactorily on its own. Revisions to positive psychology’s classification of strengths are proposed.

Ion exchange treatment of saline solutions using lanxess S108H strong acid cation resin

Common to many types of water and wastewater is the presence of sodium ions which can be removed by desalination technologies, such as reverse osmosis and ion exchange. The focus of this investigation was ion exchange as it potentially offered several advantages compared to competing methods. The equilibrium and column behaviour of a strong acid cation (SAC) resin was examined for the removal of sodium ions from aqueous sodium chloride solutions of varying normality as well as a coal seam gas water sample. The influence of the bottle-point method to generate the sorption isotherms was evaluated and data interpreted with the Langmuir Vageler, Competitive Langmuir, Freundlich, and Dubinin-Astakhov models. With the constant concentration bottle point method, the predicted maximum exchange levels of sodium ions on the resin ranged from 61.7 to 67.5 g Na/kg resin. The general trend was that the lower the initial concentration of sodium ions in the solution, the lower the maximum capacity of the resin for sodium ions. In contrast, the constant mass bottle point method was found to be problematic in that the isotherm profiles may not be complete, if experimental parameters were not chosen carefully. Column studies supported the observations of the equilibrium studies, with maximum sodium loading of ca. 62.9 g Na/kg resin measured, which was in excellent agreement with the predictions of the data from the constant concentration bottle point method. Equilibria involving coal seam gas water were more complex due to the presence of sodium bicarbonate in solution, albeit the maximum loading capacity for sodium ions was in agreement with the results from the more simple sodium chloride solutions.

Workplace stress: What is the role of positive mental health?

Objective: To examine whether positive mental health (PMH)—a positively focused well-being construct—moderates the job stress–distress relationship. Methods: Longitudinal regression was used to test two waves of matched, population-level data from a sample of older, working Australian adults (n = 3291) to see whether PMH modified the relationship between work stress and later psychological distress. Results: Time 1 work stress was positively associated with distress at both time points. Positive mental health was negatively associated with work stress at both time points. Positive mental health modified the impact of work stress on psychological distress. This effect only occurred for those with the highest levels of PMH. Conclusions: Positive mental health may help protect workers from the effect of workplace stress but only in a small proportion of the population. Therefore, to improve workplace mental health, workplaces need to both prevent stress and promote PMH.

The significance of controlled conditions in lentiviral vector titration and in the use of multiplicity of infection (MOI) for predicting gene transfer events

Background: Although lentiviral vectors have been widely used for in vitro and in vivo gene therapy researches, there have been few studies systematically examining various conditions that may affect the determination of the number of viable vector particles in a vector preparation and the use of Multiplicity of Infection (MOI) as a parameter for the prediction of gene transfer events. Methods: Lentiviral vectors encoding a marker gene were packaged and supernatants concentrated. The number of viable vector particles was determined by in vitro transduction and fluorescent microscopy and FACs analyses. Various factors that may affect the transduction process, such as vector inoculum volume, target cell number and type, vector decay, variable vector - target cell contact and adsorption periods were studied. MOI between 0-32 was assessed on commonly used cell lines as well as a new cell line. Results: We demonstrated that the resulting values of lentiviral vector titre varied with changes of conditions in the transduction process, including inoculum volume of the vector, the type and number of target cells, vector stability and the length of period of the vector adsorption to target cells. Vector inoculum and the number of target cells determine the frequencies of gene transfer event, although not proportionally. Vector exposure time to target cells also influenced transduction results. Varying these parameters resulted in a greater than 50-fold differences in the vector titre from the same vector stock. Commonly used cell lines in vector titration were less sensitive to lentiviral vector-mediated gene transfer than a new cell line, FRL 19. Within 0-32 of MOI used transducing four different cell lines, the higher the MOI applied, the higher the efficiency of gene transfer obtained. Conclusion: Several variables in the transduction process affected in in vitro vector titration and resulted in vastly different values from the same vector stock, thus complicating the use of MOI for predicting gene transfer events. Commonly used target cell lines underestimated vector titre. However, within a certain range of MOI, it is possible that, if strictly controlled conditions are observed in the vector titration process, including the use of a sensitive cell line, such as FRL 19 for vector titration, lentivector-mediated gene transfer events could be predicted. © 2004 Zhang et al; licensee BioMed Central Ltd.

Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brown-ian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et al., J. Magnetic Resonance, 190 (2008) 255-270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.

Rover autonomous integrity monitoring of GNSS RTK positioning solutions with multi-constellations

This paper studies receiver autonomous integrity monitoring (RAIM) algorithms and performance benefits of RTK solutions with multiple-constellations. The proposed method is generally known as Multi-constellation RAIM -McRAIM. The McRAIM algorithms take advantage of the ambiguity invariant character to assist fast identification of multiple satellite faults in the context of multiple constellations, and then detect faulty satellites in the follow-up ambiguity search and position estimation processes. The concept of Virtual Galileo Constellation (VGC) is used to generate useful data sets of dual-constellations for performance analysis. Experimental results from a 24-h data set demonstrate that with GPS&VGC constellations, McRAIM can significantly enhance the detection and exclusion probabilities of two simultaneous faulty satellites in RTK solutions.

Use of hydrotalcites for the removal of toxic anions from aqueous solutions

The removal of toxic anions has been achieved using hydrotalcite via two methods: (1) coprecipitation and (2) thermal activation. Hydrotalcite formed via the coprecipitation method, using solutions containing arsenate and vanadate up to pH 10, are able to remove more than 95% of the toxic anions (0.2 M) from solution. The removal of toxic anions in solutions with a pH of >10 reduces the removal uptake percentage to 75%. Raman spectroscopy observed multiple A1 stretching modes of V−O and As−O at 930 and 810 cm−1, assigned to vanadate and arsenate, respectively. Analysis of the intensity and position of the A1 stretching modes helped to identify the vanadate and arsenate specie intercalated into the hydrotalcite structure. It has been determined that 3:1 hydrotalcite structure predominantly intercalate anions into the interlayer region, while the 2:1 and 4:1 hydrotalcite structures shows a large portion of anions being removed from solution by adsorption processes. Treatment of carbonate solutions (0.2 M) containing arsenate and vanadate (0.2 M) three times with thermally activated hydrotalcite has been shown to remove 76% and 81% of the toxic anions, respectively. Thermally activated hydrotalcite with a Mg:Al ratio of 2:1, 3:1, and 4:1 have all been shown to remove 95% of arsenate and vanadate (25 ppm). At increased concentrations of arsenate and vanadate, the removal uptake percentage decreased significantly, except for the 4:1 thermally activated hydrotalcite. Thermally activated Bayer hydrotalcite has also been shown to be highly effective in the removal of arsenate and vanadate. The thermal activation of the solid residue component (red mud) removes 30% of anions from solution (100 ppm of both anions), while seawater-neutralized red mud removes 70%. The formation of hydrotalcite during the seawater neutralization process removes anions via two mechanisms, rather than one observed for thermally activated red mud.