Approximate solution (with error bounds) to a nonlinear,nonautonomous second-order differential equation

Two approximations are developed to the solution of an important nonlinear, nonautonomous second-order differential equation that arises in various fields of science and technology such as operations research, mathematical ecology and epidemiology. The origin of the second-order differential equation from a system of two nonlinear first-order differential equations modelling, for example, Lanchester-type combat between two homogeneous military forces is discussed. Extension of our results to a more general system of nonlinear first-order differential equations is indicated. Error bounds that do not require that the exact solution be known are developed. Some connections between our results and those for the Liouville-Green (or WKB) approximation to the solution of the linear second-order equation are indicated.     

A short form of the McCarthy scales of children's abilities: Methodological and clinical applications

The McCarthy Scales of Children's Abilities (MSCA) was administered to 50 kindergarten-aged children to obtain General Cognitive Indices (GCI). A short form of the MSCA was developed by using a step-wise regression analysis to select the six subtests that best predicted the GCI. The potential use of such a short form for kindergarten screening was discussed.     

Running performance in the heat is improved by similar magnitude with pre-exercise cold-water immersion and mid-exercise facial water spray

This investigation compared the effects of external pre-cooling and mid-exercise cooling methods on running time trial performance and associated physiological responses. Nine trained male runners completed familiarisation and three randomised 5 km running time trials on a non-motorised treadmill in the heat (33°C). The trials included pre-cooling by cold-water immersion (CWI), mid-exercise cooling by intermittent facial water spray (SPRAY), and a control of no cooling (CON). Temperature, cardiorespiratory, muscular activation, and perceptual responses were measured as well as blood concentrations of lactate and prolactin. Performance time was significantly faster with CWI (24.5 ± 2.8 min; P = 0.01) and SPRAY (24.6 ± 3.3 min; P = 0.01) compared to CON (25.2 ± 3.2 min). Both cooling strategies significantly (P < 0.05) reduced forehead temperatures and thermal sensation, and increased muscle activation. Only pre-cooling significantly lowered rectal temperature both pre-exercise (by 0.5 ± 0.3°C; P < 0.01) and throughout exercise, and reduced sweat rate (P < 0.05). Both cooling strategies improved performance by a similar magnitude, and are ergogenic for athletes. The observed physiological changes suggest some involvement of central and psychophysiological mechanisms of performance improvement.     

The impact phase of drop punt kicking for maximal distance and accuracy

Impact is an important aspect of the kicking skill. This study examined foot and ball motion during impact and compared distance and accuracy punt kicks. Two-dimensional high-speed video (4000 Hz) captured data of the shank, foot and ball through impact of 11 elite performers kicking for maximal distance and towards a target 20 m in distance. Four phases were identified during impact, with an overall reduction in foot velocity of 5.0 m · s^?1 (± 1.1 m · s^?1) and increase in ball velocity of 22.7 m · s^?1 (± 2.3 m · s^?1) from the start to end of contact. Higher foot velocity was found in distance compared to accuracy kicks (22.1 ± 1.6 m · s^?1 vs. 17.7 ± 0.9 m · s^?1, P < 0.05), and was considered to produce the significant differences in all impact characteristics excluding foot-to-ball speed ratio. Ankle motion differed between the kicking tasks; distance kicks were characterised by greater rigidity compared to accuracy kicks evident by larger force (834 ± 107 N vs. 588 ± 64 N) and smaller change in ankle angle (2.2 ± 3.3° vs. 7.2 ± 6.4°). Greater rigidity was obtained by altering the position of the ankle at impact start; distance kicks were characterised by greater plantarflexion (130.1 ± 5.8° vs. 123.0 ± 7.9°, P < 0.05), indicating rigidity maybe actively controlled for specific tasks.     

Preschool attendance and kindergarten readiness

Scores on the Georgia Kindergarten Assessment Program (GKAP) of 171 students (81 students who had attended preschool and 90 students who had not attended preschool) were analyzed to determine whether school readiness test performance was influenced by participation in preschool programs. Students who had attended preschool demonstrated statistically higher overall school readiness, higher Physical scores, and higher Personal scores than students who did not attend preschool. No difference, however, was found in GKAP scores as a function of type of preschool attended. Only one gender difference was revealed, that in the Social measure on the GKAP in which girls outperformed boys. Implications of our findings and suggestions for further research are discussed.     

An integrated microfluidic bubble pocket for long-term perfused three-dimensional intestine-on-a-chip model

Perfused three-dimensional (3D) cultures enable long-term in situ growth and monitoring of 3D organoids making them well-suited for investigating organoid development, growth, and function. One of the limitations of this long-term on-chip perfused 3D culture is unintended and disruptive air bubbles. To overcome this obstacle, we invented an imaging platform that integrates an innovative microfluidic bubble pocket for long-term perfused 3D culture of gastrointestinal (GI) organoids. We successfully applied 3D printing technology to create polymer molds that cast polydimethylsiloxane (PDMS) culture chambers in addition to bubble pockets. Our developed platform traps unintended, or induced, air bubbles in an integrated PDMS pocket chamber, where the bubbles diffuse out across the gas permeable PDMS or an outlet tube. We demonstrated that our robust platform integrated with the novel bubble pocket effectively circumvents the development of bubbles into human and mouse GI organoid cultures during long-term perfused time-course imaging. Our platform with the innovative integrated bubble pocket is ideally suited for studies requiring long-term perfusion monitoring of organ growth and morphogenesis as well as function.     

Teacher pedagogical content knowledge,practice, and student achievement†

ABSTRACT

In this exploratory study, we attempted to measure potential changes in teacher knowledge and practice as a result of an intervention, as well as trace such changes through a theoretical path of influence that could inform a model of teacher professional knowledge. We created an instrument to measure pedagogical content knowledge (PCK), studied the impact of a two-year professional development intervention, explored the relationships among teacher variables to attempt to validate a model of teacher professional knowledge, and examined the relationship of teacher professional knowledge and classroom practice on student achievement. Teacher professional knowledge and skill was measured in terms of academic content knowledge (ACK), general pedagogical knowledge (GenPK), PCK and teacher practice. Our PCK instrument identified two factors within PCK: PCK-content knowledge and PCK-pedagogical knowledge. Teacher gains existed for all variables. Only GenPK had a significant relationship to teacher practice. ACK was the only variable that explained a substantial portion of student achievement. Our findings provide empirical evidence that we interpret through the lens of the model of teacher professional knowledge and skill, including PCK [Gess-Newsome, J. (2015). A model of teacher professional knowledge and skill including PCK: Results of the thinking from the PCK summit. In A. Berry, P. Friedrichsen, & J. Loughran (Eds.), Re-examining pedagogical content knowledge in science education (pp. 28–42). London: Routledge Press], highlighting the complexity of measuring teacher professional knowledge and skill.     

Managing Sudden Loss

Managers often face tough, emotional situations at work. One of the biggest is guiding employees and departments successfully through the loss of a coworker. Not only are there emotional components but there are also more technical and procedural responsibilities that may be overlooked. These facilities, technological, and human resources tasks need to be handled sensitively and in a timely manner. Remembering whom to contact, what property needs to be considered, and how to produce final paychecks are just a few of the concerns managers will face in a trying time. This guide aims to serve as a checklist of the basic components and tasks managers will face after the sudden loss of an employee.