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.

Corneal sensitivity and slit scanning in vivo confocal microscopy of the subbasal nerve plexus of the normal central and peripheral human cornea

Purpose: To determine the subbasal nerve density and tortuosity at 5 corneal locations and to investigate whether these microstructural observations correlate with corneal sensitivity. Method: Sixty eyes of 60 normal human subjects were recruited into 1 of 3 age groups, group 1: aged ,35 years, group 2: aged 35–50 years, and group 3: aged .50 years. All eyes were examined using slit-lamp biomicroscopy, noncontact corneal esthesiometry, and slit scanning in vivo confocal microscopy. Results: The mean subbasal nerve density and the mean corneal sensitivity were greatest centrally (14,731 6 6056 mm/mm2 and 0.38 6 0.21 millibars, respectively) and lowest in the nasal mid periphery (7850 6 4947 mm/mm2 and 0.49 6 0.25 millibars, respectively). The mean subbasal nerve tortuosity coefficient was greatest in the temporal mid periphery (27.3 6 6.4) and lowest in the superior mid periphery (19.3 6 14.1). There was no significant difference in mean total subbasal nerve density between age groups. However, corneal sensation (P = 0.001) and subbasal nerve tortuosity (P = 0.004) demonstrated significant differences between age groups. Subbasal nerve density only showed significant correlations with corneal sensitivity threshold in the temporal cornea and with subbasal nerve tortuosity in the inferior and nasal cornea. However, these correlations were weak. Conclusions: This study quantitatively analyzes living human corneal nerve structure and an aspect of nerve function. There is no strong correlation between subbasal nerve density and corneal sensation. This study provides useful baseline data for the normal living human cornea at central and mid-peripheral locations

In search of a hidden long-term isolated sub-chondritic 142Nd/144Nd reservoir in the deep mantle : implications for the Nd isotope systematics of the Earth

Here we search for evidence of the existence of a sub-chondritic 142Nd/144Nd reservoir that balances the Nd isotope chemistry of the Earth relative to chondrites. If present, it may reside in the source region of deeply sourced mantle plume material. We suggest that lavas from Hawai’i with coupled elevations in 186Os/188Os and 187Os/188Os, from Iceland that represent mixing of upper mantle and lower mantle components, and from Gough with sub-chondritic 143Nd/144Nd and high 207Pb/206Pb, are favorable samples that could reflect mantle sources that have interacted with an Early-Enriched Reservoir (EER) with sub-chondritic 142Nd/144Nd. High-precision Nd isotope analyses of basalts from Hawai’i, Iceland and Gough demonstrate no discernable 142Nd/144Nd deviation from terrestrial standards. These data are consistent with previous high-precision Nd isotope analysis of recent mantle-derived samples and demonstrate that no mantle-derived material to date provides evidence for the existence of an EER in the mantle. We then evaluate mass balance in the Earth with respect to both 142Nd/144Nd and 143Nd/144Nd. The Nd isotope systematics of EERs are modeled for different sizes and timing of formation relative to ε143Nd estimates of the reservoirs in the μ142Nd = 0 Earth, where μ142Nd is ((measured 142Nd/144Nd/terrestrial standard 142Nd/144Nd)−1 * 10−6) and the μ142Nd = 0 Earth is the proportion of the silicate Earth with 142Nd/144Nd indistinguishable from the terrestrial standard. The models indicate that it is not possible to balance the Earth with respect to both 142Nd/144Nd and 143Nd/144Nd unless the μ142Nd = 0 Earth has a ε143Nd within error of the present-day Depleted Mid-ocean ridge basalt Mantle source (DMM). The 4567 Myr age 142Nd–143Nd isochron for the Earth intersects μ142Nd = 0 at ε143Nd of +8 ± 2 providing a minimum ε143Nd for the μ142Nd = 0 Earth. The high ε143Nd of the μ142Nd = 0 Earth is confirmed by the Nd isotope systematics of Archean mantle-derived rocks that consistently have positive ε143Nd. If the EER formed early after solar system formation (0–70 Ma) continental crust and DMM can be complementary reservoirs with respect to Nd isotopes, with no requirement for significant additional reservoirs. If the EER formed after 70 Ma then the μ142Nd = 0 Earth must have a bulk ε143Nd more radiogenic than DMM and additional high ε143Nd material is required to balance the Nd isotope systematics of the Earth.

An examination of the knowledge barriers in participatory design and the prospects for embedded research

Participatory design has the moral and pragmatic tenet of including those who will be most affected by a design into the design process. However, good participation is hard to achieve and results linking project success and degree of participation are inconsistent. Through three case studies examining some of the challenges that different properties of knowledge – novelty, difference, dependence – can impose on the participatory endeavour we examine some of the consequences to the participatory process of failing to bridge across knowledge boundaries – syntactic, semantic, and pragmatic. One pragmatic consequence, disrupting the user’s feeling of involvement to the project, has been suggested as a possible explanation for the inconsistent results linking participation and project success. To aid in addressing these issues a new form of participatory research, called embedded research, is proposed and examined within the framework of the case studies and knowledge framework with a call for future research into its possibilities.

Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term

In this paper, we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. A new implicit difference method is constructed. The stability and convergence are discussed using a new energy method. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis

Practice briefing : Is BOT the best financing model to procure infrastructure projects? A case study of the Hong Kong-Shuhai-Macau Bridge

Abstract: Purpose – Several major infrastructure projects in the Hong Kong Special Administrative Region (HKSAR) have been delivered by the build-operate-transfer (BOT) model since the 1960s. Although the benefits of using BOT have been reported abundantly in the contemporary literature, some BOT projects were less successful than the others. This paper aims to find out why this is so and to explore whether BOT is the best financing model to procure major infrastructure projects. Design/methodology/approach – The benefits of BOT will first be reviewed. Some completed BOT projects in Hong Kong will be examined to ascertain how far the perceived benefits of BOT have been materialized in these projects. A highly profiled project, the Hong Kong-Zhuhai-Macau Bridge, which has long been promoted by the governments of the People's Republic of China, Macau Special Administrative Region and the HKSAR that BOT is the preferred financing model, but suddenly reverted back to the traditional financing model to be funded primarily by the three governments with public money instead, will be studied to explore the true value of the BOT financial model. Findings – Six main reasons for this radical change are derived from the analysis: shorter take-off time for the project; difference in legal systems causing difficulties in drafting BOT agreements; more government control on tolls; private sector uninterested due to unattractive economic package; avoid allegation of collusion between business and the governments; and a comfortable financial reserve possessed by the host governments. Originality/value – The findings from this paper are believed to provide a better understanding to the real benefits of BOT and the governments' main decision criteria in delivering major infrastructure projects.

A comparison of the hazard perception ability of matched groups of healthy drivers aged 35 to 55, 65 to 74, and 75 to 84 years

We examined differences in response latencies obtained during a validated video-based hazard perception driving test between three healthy, community-dwelling groups: 22 mid-aged (35-55 years), 34 young-old (65-74 years), and 23 old-old (75-84 years) current drivers, matched for gender, education level, and vocabulary. We found no significant difference in performance between mid-aged and young-old groups, but the old-old group was significantly slower than the other two groups. The differences between the old-old group and the other groups combined were independently mediated by useful field of view (UFOV), contrast sensitivity, and simple reaction time measures. Given that hazard perception latency has been linked with increased crash risk, these results are consistent with the idea that increased crash risk in older adults could be a function of poorer hazard perception, though this decline does not appear to manifest until age 75+ in healthy drivers.

Inequalities in cardiovascular disease mortality : the role of behavioural, physiological and social risk factors

Background: While the relationship between socioeconomic disadvantage and cardiovascular disease (CVD) is well established, the role that traditional cardiovascular risk factors play in this association remains unclear. We examined the association between education attainment and CVD mortality and the extent to which behavioural, social and physiological factors explained this relationship. Methods: Adults (n=38 355) aged 40-69 years living in Melbourne, Australia were recruited in 1990-1994. Subjects with baseline CVD risk factor data ascertained through questionnaire and physical measurement were followed for an average of 9.4 years with CVD deaths verified by review of medical records and autopsy reports. Results: CVD mortality was higher for those with primary education only compared to those who had completed tertiary education, with a hazard ratio (HR) of 1.66 (95% confidence interval [CI] 1.11-2.49) after adjustment for age, country of birth and gender. Those from the lowest educated group had a more adverse cardiovascular risk factor profile compared to the highest educated group, and adjustment for these risk factors reduced the HR to 1.18 (95% CI 0.78-1.77). In analysis of individual risk factors, smoking and waist circumference explained most of the difference in CVD mortality between the highest and lowest education groups. Conclusions: Most of the excess CVD mortality in lower socioeconomic groups can be explained by known risk factors, particularly smoking and overweight. While targeting cardiovascular risk factors should not divert efforts from addressing the underlying determinants of health inequalities, it is essential that known risk factors are addressed effectively among lower socioeconomic groups.

Rivalry within and between strategic networks : an investigation of the United States Automotive Industry

As a consequence of the increased incidence of collaborative arrangements between firms, the competitive environment characterising many industries has undergone profound change. It is suggested that rivalry is not necessarily enacted by individual firms according to the traditional mechanisms of direct confrontation in factor and product markets, but rather as collaborative orchestration between a number of participants or network members. Strategic networks are recognised as sets of firms within an industry that exhibit denser strategic linkages among themselves than other firms within the same industry. Based on this, strategic networks are determined according to evidence of strategic alliances between firms comprising the industry. As a result, a single strategic network represents a group of firms closely linked according to collaborative ties. Arguably, the collective outcome of these strategic relationships engineered between firms suggest that the collaborative benefits attributed to interorganisational relationships require closer examination in respect to their propensity to influence rivalry in intraindustry environments. Derived in large from the social sciences, network theory allows for the micro and macro examination of the opportunities and constraints inherent in the structure of relationships in strategic networks, establishing a relational approach upon which the conduct and performance of firms can be more fully understood. Research to date has yet to empirically investigate the relationship between strategic networks and rivalry. The limited research that has been completed utilising a network rationale to investigate competitive patterns in contemporary industry environments has been characterised by a failure to directly measure rivalry. Further, this prior research has typically embedded investigation in industry settings dominated by technological or regulatory imperatives, such as the microprocessor and airline industries. These industries, due to the presence of such imperatives, are arguably more inclined to support the realisation of network rivalry, through subscription to prescribed technological standards (eg., microprocessor industry) or by being bound by regulatory constraints dictating operation within particular market segments (airline industry). In order to counter these weaknesses, the proposition guiding research - Are patterns of rivalry predicted by strategic network membership? – is embedded in the United States Light Vehicles Industry, an industry not dominated by technological or regulatory imperatives. Further, rivalry is directly measured and utilised in research, thus distinguishing this investigation from prior research efforts. The timeframe of investigation is 1993 – 1999, with all research data derived from secondary sources. Strategic networks were defined within the United States Light Vehicles Industry based on evidence of horizontal strategic relationships between firms comprising the industry. The measure of rivalry used to directly ascertain the competitive patterns of industry participants was derived from the traditional Herfindahl Index, modified to account for patterns of rivalry observed at the market segment level. Statistical analyses of the strategic network and rivalry constructs found little evidence to support the contention of network rivalry; indeed, greater levels of rivalry were observed between firms comprising the same strategic network than between firms participating in opposing network structures. Based on these results, patterns of rivalry evidenced in the United States Light Vehicle Industry over the period 1993 – 1999 were not found to be predicted by strategic network membership. The findings generated by this research are in contrast to current theorising in the strategic network – rivalry realm. In this respect, these findings are surprising. The relevance of industry type, in conjunction with prevailing network methodology, provides the basis upon which these findings are contemplated. Overall, this study raises some important questions in relation to the relevancy of the network rivalry rationale, establishing a fruitful avenue for further research.

Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term

In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and Gr¨unwald-Letnikov(GL) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

How to tell the difference between production and consumption : a case study in Doctor Who fandom

A television series is tagged with the label "cult" by the media, advertisers, and network executives when it is considered edgy or offbeat, when it appeals to nostalgia, or when it is considered emblematic of a particular subculture. By these criteria, almost any series could be described as cult. Yet certain programs exert an uncanny power over their fans, encouraging them to immerse themselves within a fictional world.In Cult Television leading scholars examine such shows as The X-Files; The Avengers; Doctor Who, Babylon Five; Star Trek; Xena, Warrior Princess; and Buffy the Vampire Slayer to determine the defining characteristics of cult television and map the contours of this phenomenon within the larger scope of popular culture.Contributors: Karen Backstein; David A. Black, Seton Hall U; Mary Hammond, Open U; Nathan Hunt, U of Nottingham; Mark Jancovich; Petra Kuppers, Bryant College; Philippe Le Guern, U of Angers, France; Alan McKee; Toby Miller, New York U; Jeffrey Sconce, Northwestern U; Eva ViethSara Gwenllian-Jones is a lecturer in television and digital media at Cardiff University and co-editor of Intensities: The Journal of Cult Media.Roberta E. Pearson is a reader in media and cultural studies at Cardiff University. She is the author of the forthcoming book Small Screen, Big Universe: Star Trek and Television.

Bulk compressive properties of the heel fat pad during walking: a pilot investigation in plantar heel pain

Background: Altered mechanical properties of the heel pad have been implicated in the development of plantar heel pain. However, the in vivo properties of the heel pad during gait remain largely unexplored in this cohort. The aim of the current study was to characterise the bulk compressive properties of the heel pad in individuals with and without plantar heel pain while walking. ---------- Methods: The sagittal thickness and axial compressive strain of the heel pad were estimated in vivo from dynamic lateral foot radiographs acquired from nine subjects with unilateral plantar heel pain and an equivalent number of matched controls, while walking at their preferred speed. Compressive stress was derived from simultaneously acquired plantar pressure data. Principal viscoelastic parameters of the heel pad, including peak strain, secant modulus and energy dissipation (hysteresis), were estimated from subsequent stress–strain curves.---------- Findings: There was no significant difference in loaded and unloaded heel pad thickness, peak stress, peak strain, or secant and tangent modulus in subjects with and without heel pain. However, the fat pad of symptomatic feet had a significantly lower energy dissipation ratio (0.55 ± 0.17 vs. 0.69 ± 0.08) when compared to asymptomatic feet (P < .05).---------- Interpretation: Plantar heel pain is characterised by reduced energy dissipation ratio of the heel pad when measured in vivo and under physiologically relevant strain rates.

Telephone reliability of the Frenchay Activity Index and EQ-5D amongst older adults

Background Older adults may find it problematic to attend hospital appointments due to the difficulty associated with travelling to, within and from a hospital facility for the purpose of a face-to-face assessment. This study aims to investigate equivalence between telephone and face-to-face administration for the Frenchay Activities Index (FAI) and the Euroqol-5D (EQ-5D) generic health-related quality of life instrument amongst an older adult population. Methods Patients aged >65 (n = 53) who had been discharged to the community following an acute hospital admission underwent telephone administration of the FAI and EQ-5D instruments seven days prior to attending a hospital outpatient appointment where they completed a face-to-face administration of these instruments. Results Overall, 40 subjects' datasets were complete for both assessments and included in analysis. The FAI items had high levels of agreement between the two modes of administration (item kappa's ranged 0.73 to 1.00) as did the EQ-5D (item kappa's ranged 0.67–0.83). For the FAI, EQ-5D VAS and EQ-5D utility score, intraclass correlation coefficients were 0.94, 0.58 and 0.82 respectively with paired t-tests indicating no significant systematic difference (p = 0.100, p = 0.690 and p = 0.290 respectively). Conclusion Telephone administration of the FAI and EQ-5D instruments provides comparable results to face-to-face administration amongst older adults deemed to have cognitive functioning intact at a basic level, indicating that this is a suitable alternate approach for collection of this information.

An examination of the knowledge barriers in participatory design and the prospects for embedded research

Participatory design has the moral and pragmatic tenet of including those who will be most affected by a design into the design process. However, good participation is hard to achieve and results linking project success and degree of participation are inconsistent. Through three case studies examining some of the challenges that different properties of knowledge - novelty, difference, dependence - can impose on the participatory endeavour we examine some of the consequences to the participatory process of failing to bridge across knowledge boundaries - syntactic, semantic, and pragmatic. One pragmatic consequence, disrupting the user's feeling of involvement to the project, has been suggested as a possible explanation for the inconsistent results linking participation and project success. To aid in addressing these issues a new form of participatory research, called embedded research, is proposed and examined within the framework of the case studies and knowledge framework with a call for future research into its possibilities.