Dynamics of a single species in a fluctuating environment under periodic yield harvesting

We discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem was studied by Brauer and Sanchez (2003) who attempted the proof of the existence of two positive periodic solutions; the flaw in their argument is corrected. We obtain estimates for positive attracting and repelling periodic solutions and describe behavior of other solutions. Extinction and blow-up times are evaluated for solutions with small and large initial data; dependence of the number of periodic solutions on the parameter sigma associated with the intensity of harvesting is explored. As sigma grows, the number of periodic solutions drops from two to zero. We provide bounds for the bifurcation parameter whose value in practice can be efficiently approximated numerically

Development of students' mathematical discourse through individual and group work with nonstandard problems on existence and uniqueness theorem.

Research shows that students’ learning is affected by the types of tasks. We explore how the use of nonstandard problems influences understanding of the Existence and Uniqueness Theorems (EUTs) by a group of engineering students. The focus is on the development of students’ mathematical discourse during the individual and group work with nonstandard problems. We present the evidence indicating that students developed new mathematical routines gaining a deeper understanding of EUTs and appreciated the experience

Individual and group work with nonstandard problems in an ordinary differential equations course for engineering students

We explore understanding of the Existence and Uniqueness Theorems (EUTs) by a group of engineering students working on nonstandard problems. Students presented three sets of solutions: individual solutions produced in the first tutorial, individual solutions submitted as a homework, and solutions submitted after the discussion with peers in small groups during the second tutorial. The focus of the study is on the role of individual and group work with nonstandard problems. The results show that students gained a deeper understanding of EUTs and appreciated the experience

Non-standard Problems in an Ordinary Differential Equations Course

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A New Tool for the Assessment of the Development of Students’ Mathematical Competencies

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A new tool for the assessment of the development of students' mathematical competencies

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Mathematical models for assessment of vehicle crashworthiness: a review

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Crash Response of a Repaired Vehicle-Influence of Welding UHSS Members

Author's accepted manuscriptAutomakers generally recommend not to weld structural parts after a vehicle crash, and these should be replaced as a whole part in case of a crash event. Sectioning of these members is also not recommended and use of the repair manual is mandatory in case of fracture of such parts. However, repair shops may not adhere to these instructions and use incorrect repair procedures on these members which would modify their strength properties. This study analyses the impact of welding structural members in a vehicle like the A-pillar which use Ultra-High Strength Steels (UHSS) for reducing the weight of the vehicle and improving the crashworthiness of the structure. The research conducted in this paper highlights the differences in the crash performance of a repaired vehicle as opposed to baseline injury values for the vehicle. The performance of the modified vehicle when tested for different loadcases shows reduced crash performance as compared to the baseline performance and it can be concluded that welding or sectioning the UHSS parts would influence the crashworthiness of a vehicle. This paper only focuses on structural integrity of the repaired vehicle in a crash event. The performance of the vehicle in occupant injury is kept out of scope for this study.acceptedVersio