30 resultados para Degenerate elliptic equations

em Deakin Research Online - Australia


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The study seeks to determine which of five computer algebra packages is best at finding the Lie point symmetries of systems of partial differential equations with minimal user intervention. The chosen packages are LIEPDE and DIMSYM for REDUCE, LIE and BIGLIE for MUMATH, DESOLV for MAPLE, and MATHLIE for MATHEMATICA. A series of systems of partial differential equations are used in the study. The paper concludes that while all of the computer packages are useful, DESOLV appears to be the most successful system at determining the complete set of Lie point symmetries of systems of partial differential equations.

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We present and describe new reduction routines included in DESOLV which, in many cases, may allow the complete automation of the determination of similarity solutions of partial differential equations.

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In epidemiologic studies, researchers often need to establish a nonlinear exposure-response relation between a continuous risk factor and a health outcome. Furthermore, periodic interviews are often conducted to take repeated measurements from an individual. The authors proposed to use fractional polynomial models to jointly analyze the effects of 2 continuous risk factors on a health outcome. This method was applied to an analysis of the effects of age and cumulative fluoride exposure on forced vital capacity in a longitudinal study of lung function carried out among aluminum workers in Australia (1995-2003). Generalized estimating equations and the quasi-likelihood under the independence model criterion were used. The authors found that the second-degree fractional polynomial models for age and fluoride fitted the data best. The best model for age was robust across different models for fluoride, and the best model for fluoride was also robust. No evidence was found to suggest that the effects of smoking and cumulative fluoride exposure on change in forced vital capacity over time were significant. The trend 1 model, which included the unexposed persons in the analysis of trend in forced vital capacity over tertiles of fluoride exposure, did not fit the data well, and caution should be exercised when this method is used.

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The idea of combining photovoltaic and solar thermal collectors (PVT collectors) to provide electrical and heat energy is not new, however it is an area that has received only limited attention. With concern growing over energy sources and their usage, PVTs have become an area receiving more attention. Although PVTs are not as prevalent as solar thermal systems, the integration of photovoltaic and solar thermal collectors into the walls or roofing structure of a building could provide greater opportunity for the use of renewable solar energy technologies in domestic, commercial and industrial applications. As such, the design of a novel building integrated photovoltaic/thermal (BIPVT) solar collector is theoretically analysed through the use of a modified Hottel-Whillier model. The thermal and electrical efficiency under a range of conditions are subsequently determined and results showing how key design parameters influence the performance of the BIPVT system are presented.

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This study presents a theoretical basis for and outlines the method of finding the Lie point symmetries of systems of partial differential equations. It seeks to determine which of five computer algebra packages is best at finding these symmetries. The chosen packages are LIEPDE and DIMSYM for REDUCE, LIE and BIGLIE for MUMATH, DESOLV for MAPLE, and MATHLIE for MATHEMATICA. This work concludes that while all of the computer packages are useful, DESOLV appears to be the most successful system at determining the complete set of Lie symmetries. Also, the study describes REDUCEVAR, a new package for MAPLE, that reduces the number of independent variables in systems of partial differential equations, using particular Lie point symmetries. It outlines the results of some testing carried out on this package. It concludes that REDUCEVAR is a very useful tool in performing the reduction of independent variables according to Lie's theory and is highly accurate in identifying cases where the symmetries are not suitable for finding S/G equations.

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Chemical equations are representations that use symbols to summarise the net changes occurring in a reaction whereas depictions such as drawings of the submicroscopic level provide representations of the chemical transformations. While the ability to balance and interpret chemical equations is key to understanding many concepts in chemistry, many undergraduate chemistry students struggle to master these skills. The equations contain a great deal of implicit information and novices may not be able to make the connection between the equation and the actual chemical transformations that are occurring. This paper reports on a study which used submicroscopic diagrams to probe students' understanding of chemical equations. Assessment tasks required students to interpret diagrams, construct diagrams and to relate diagrams to symbolic representations. The analysis showed that some students have misconceptions about the molecular nature and chemical formulae and could not distinguish between coefficients and subscripts when representing chemical formulae. While students were generally able to balance a chemical equation presented as a set of diagrams, a significant number could not generate the balanced equation based on a diagram of the progress of a reaction, The study has demonstrated the use of student-generated diagrams to provide insight into students' understandings of chemical equations.

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This paper explores the question or whether Call Center Operators (CCO) share information or knowledge with their clients and if their knowledge sharing behavior has any impact on the sustainability of their relationships with their clients.

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This paper reports on a pedagogical approach to the teaching of chemical equations introduced to first year university students with little previous chemical knowledge. During the instruction period students had to interpret and construct diagrams of reactions at the submicro level, and relate them to chemical equations at the symbolic level with the aim of improving their conceptual understanding of chemical equations and stoichiometry. Students received instruction in symbol conventions, practice through graded tutorial tasks, and feedback on their efforts over the semester. Analysis of the student responses to formative test and summative exam items over consecutive years indicates that there was a consistent improvement in the abilities of the various cohorts to answer stoichiometry questions correctly. The responses provide evidence for diagrams of the submicro level being used as tools for reasoning in solving chemical problems, to recognise misconceptions of chemical formulae and to recognise the value of using various multiple representations of chemical reactions connecting the submicro and symbolic levels of representation. The student-generated submicro diagrams serve as a visualisation tool for teaching and learning abstract concepts in solving stoichiometric problems. We argue that the use of diagrams of the submicro level provides a more complete picture of the reaction, rather than a net summary of a chemical equation, leading to a deeper conceptual understanding.

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This paper presents an overview of modeling light propagation through biological media by solving the photon transport equation. Different variants of the photon transport equation (PTE) are discussed. Several methods for modeling static distributions and the transient response are presented. A discussion on how to mix and match electromagnetic problems with the PTE is also provided.

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Current prediction models for risk of cardiovascular disease (CVD) incidence incorporate smoking as a dichotomous yes/no measure. However, the risk of CVD associated with smoking also varies with the intensity and duration of smoking and there is a strong association between time since quitting and the risk of disease onset. This study aims to develop improved risk prediction equations for CVD incidence incorporating intensity and duration of smoking and time since quitting. The risk of developing a first CVD event was evaluated using a Cox’s model for participants in the Framingham offspring cohort who attended the fourth examination (1988–92) between the ages of 30 and 74 years and were free of CVD (n=3751). The full models based on the smoking variables and other risk factors, and reduced models based on the smoking variables and non-laboratory risk factors demonstrated good discrimination, calibration and global fit. The incorporation of both time since quitting among past smokers and pack-years among current smokers resulted in better predictive performance as compared to a dichotomous current/non-smoker measure and a current/quitter/never smoker measure. Compared to never smokers, the risk of CVD incidence increased with pack-years. Risk among those quitting more than five years prior to the baseline exam and within five years prior to the baseline exam were similar and twice as high as that of never smokers. A CVD risk equation incorporating the effects of pack-years and time since quitting provides an improved tool to quantify risk and guide preventive care.

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We present and describe, with illustrative examples, the MAPLE computer algebra package DESOLVII, which is a major upgrade of DESOLV. DESOLVII now includes new routines allowing the determination of higher symmetries (contact and Lie-Backlund) for systems of both ordinary and partial differential equations.