Generalized coupled photon transport equations for handling correlated photon streams with distinct frequencies

A generalized form of coupled photon transport equations that can handle correlated light beams with distinct frequencies is introduced. The derivation is based on the principle of energy conservation. For a single frequency, the current formulation reduces to a standard photon transport equation, and for fluorescence and phosphorescence, the diffusion models derived from the proposed photon transport model match for homogenous media. The generalized photon transport model is extended to handle wideband inputs in the frequency domain. © 2012 Optical Society of America.

A review of mathematical equations to assign individual marks from a team mark

BACKGROUND : Team-based learning is an integral part of engineering education today. Development of team skills is now a part of the curriculum at universities as employers demand these skills on graduates. Higher education institutions enforce academic staff to teach, practise and assess team skills, and at the same time, they ask academic staff to supply individual marks and/or grades. Allocating individual marks from a team mark is a very complex and sensitive task that may adversely affect both individual and team performance. A number of both qualitative and quantitative methods are available to address this issue. Quantitative mathematical methods are favoured over qualitative subjective methods as they are more straightforward to explain to the students and they may help minimise conflicts between assessors and students. PURPOSE : This study presents a review of commonly used mathematical equations to allocate individual marks from a team mark. Quantitative analytical equations are favoured over qualitative subjective methods because they are more straightforward to explain to the students and if explained to the students in advance, they may help minimise conflicts between assessors and students. Some of these analytical equations focus primarily on the assessment of the quality of teamwork product (product assessment) while the others put greater emphasis on the assessment of teamwork performance (process assessment). The remaining equations try to strike a balance between product assessment and process assessment. The primary purpose of this study is to discuss the qualitative aspects of quantitative equations. DESIGN/METHOD : This study simulates a set of scenarios of team marks and individual contributions that collectively cover all possible teamwork assessment environments. The available analytical equations are then applied to each case to examine their relative merits with respect to a set of evaluation criteria with exhaustive graphical plots. RESULTS : Although each analytical equations discussed and analysed in this study has its own merits for a particular application scenario, the recent methods such as knee formula in SPARKPLUS and cap formula, are relatively better in terms of a number of evaluation criteria such as fairness, teamwork attitude, balance between process and product assessments etc. In addition to having all favourable properties of knee formula, cap formula explicitly considers the quality of teamwork (i.e., team mark) while allocating individual marks. Cap formula may, however, be difficult to explain to the students due to relatively complex mathematical equations involved. CONCLUSIONS : Not all existing analytical equations that allocate individual marks from a team mark have similar characteristics. Recent methods, knee formula and cap formula, are advantageous in terms of a number of evaluation criteria and are recommended to apply in practice. However, it is important to examine these equations with respect to enhancing students’ learning achievements rather than the students and academic staff’s preferences.

Predictive validity and classification accuracy of ActiGraph energy expenditure equations and cut-points in young children

Objectives
Evaluate the predictive validity of ActiGraph energy expenditure equations and the classification accuracy of physical activity intensity cut-points in preschoolers.

Methods
Forty children aged 4–6 years (5.3±1.0 years) completed a ~150-min room calorimeter protocol involving age-appropriate sedentary, light and moderate-to vigorous-intensity physical activities. Children wore an ActiGraph GT3X on the right mid-axillary line of the hip. Energy expenditure measured by room calorimetry and physical activity intensity classified using direct observation were the criterion methods. Energy expenditure was predicted using Pate and Puyau equations. Physical activity intensity was classified using Evenson, Sirard, Van Cauwenberghe, Pate, Puyau, and Reilly, ActiGraph cut-points.

Results
The Pate equation significantly overestimated VO2 during sedentary behaviors, light physical activities and total VO2 (P<0.001). No difference was found between measured and predicted VO2 during moderate-to vigorous-intensity physical activities (P = 0.072). The Puyau equation significantly underestimated activity energy expenditure during moderate-to vigorous-intensity physical activities, light-intensity physical activities and total activity energy expenditure (P<0.0125). However, no overestimation of activity energy expenditure during sedentary behavior was found. The Evenson cut-point demonstrated significantly higher accuracy for classifying sedentary behaviors and light-intensity physical activities than others. Classification accuracy for moderate-to vigorous-intensity physical activities was significantly higher for Pate than others.

Conclusion
Available ActiGraph equations do not provide accurate estimates of energy expenditure across physical activity intensities in preschoolers. Cut-points of ≤25counts⋅15 s−1 and ≥420 counts⋅15 s−1 for classifying sedentary behaviors and moderate-to vigorous-intensity physical activities, respectively, are recommended.

Applications of symbolic computing for symmetry analysis of differential equations

 This thesis presents a number of applications of symbolic computing to the study of differential equations. In particular, three packages have been produced for the computer algebra system MAPLE and used to find a variety of symmetries (and corresponding invariant solutions) for a range of differential systems.

Assessing the performance of two lung age equations on the Australian population: using data from the cross-sectional BOLD-Australia study

Lung age, a simple concept for patients to grasp, is frequently used as an aid in smoking cessation programs. Lung age equations should be continuously updated and made relevant for target populations. We observed how new lung age equations developed for Australian populations performed when utilizing the Burden of Obstructive Lung Disease (BOLD)-Australia dataset compared to more commonly used equations.

Evaluation of Actical equations and thresholds to predict physical activity intensity in young children

This study examined the validity of current Actical activity energy expenditure (AEE) equations and intensity cut-points in preschoolers using AEE and direct observation as criterion measures. Forty 4–6-year-olds (5.3 ± 1.0 years) completed a ~150-min room calorimeter protocol involving age-appropriate sedentary behaviours (SBs), light intensity physical activities (LPAs) and moderate-to-vigorous intensity physical activities (MVPAs). AEE and/or physical activity intensity were calculated using Actical equations and cut-points by Adolph, Evenson, Pfeiffer and Puyau. Predictive validity was examined using paired sample t-tests. Classification accuracy was evaluated using weighted kappas, sensitivity, specificity and area under the receiver operating characteristic curve. The Pfeiffer equation significantly overestimated AEE during SB and underestimated AEE during LPA (P < 0.0125 for both). There was no significant difference between measured and predicted AEEs during MVPA. The Adolph cut-point showed significantly higher accuracy for classifying SB, LPA and MVPA than all others. The available Actical equation does not provide accurate estimates of AEE across all intensities in preschoolers. However, the Pfeiffer equation performed reasonably well for MVPA. Using cut-points of ≤6 counts · 15 s−1, 7–286 counts · 15 s−1 and ≥ 287 counts · 15 s−1 when classifying SB, LPA and MVPA, respectively, is recommended.

FracSym: automated symbolic computation of Lie symmetries of fractional differential equations

In this paper, we present an algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs) using the method as described by Buckwar & Luchko (1998) and Gazizov, Kasatkin & Lukashchuk (2007, 2009, 2011). The method has been generalised here to allow for the determination of symmetries for FDEs with n independent variables and for systems of partial FDEs. The algorithm has been implemented in the new MAPLE package FracSym (Jefferson and Carminati 2013) which uses routines from the MAPLE symmetry packages DESOLVII (Vu, Jefferson and Carminati, 2012) and ASP (Jefferson and Carminati, 2013). We introduce FracSym by investigating the symmetries of a number of FDEs; specific forms of any arbitrary functions, which may extend the symmetry algebras, are also determined. For each of the FDEs discussed, selected invariant solutions are then presented. © 2013 Elsevier B.V. All rights reserved.

Isotherm, kinetic, and thermodynamic equations for cefalexin removal from liquids using activated carbon synthesized from loofah sponge

Activated carbon (AC) developed from loofah sponge with phosphoric acid activation was applied to absorb cefalexin (CEX) in aqueous solution. AC was characterized by N2 adsorption–desorption isotherms and Fourier transform infrared spectroscopy (FTIR). Factors influencing the adsorption process were investigated. The equilibrium adsorption isotherms and kinetics of CEX were also studied. The results showed that AC prepared from loofah sponge had rough surface and abundant pores. The determination results of specific surface area (810.12 m²/g) and average pore size (5.28 nm) suggested the high adsorption capability. At low concentration, the AC could adsorb about 95% of CEX. The adsorption effect was independent of the temperature and pH. The maximum adsorption amount of CEX was about 55.11 mg/g at 308 K. The equilibrium data agreed well with Freundlich isotherm equation (R² = 0.9957) at 308 K, which indicated multilayer adsorption. FTIR analysis suggested the existence of phosphorus-containing functional groups, C–O bond, and C=C bond on the surface of AC of which the peak intensity of AC after adsorption was slightly lower after adsorption, indicating that the AC surface groups interacted with or were covered by the CEX species.