Department of Mathematics and Statistics

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    On the (dis)continuity of the Fourier transform of measures
    (2021) Spindeler, Timo; Strungaru, Nicolae
    In this paper, we will study the continuity of the Fourier transform of measures with respect to the vague topology. We show that the Fourier transform is vaguely discontinuous on R, but becomes continuous when restricting to a class of Fourier transformable measures such that either the measures, or their Fourier transforms are equi-translation bounded. We discuss continuity of the Fourier transform in the product and norm topology. We show that vague convergence of positive definite measures implies the equi translation boundedness of the Fourier transforms, which explains the continuity of the Fourier transform on the cone of positive definite measures. In the appendix, we characterize vague precompactness of a set of measures in arbitrary LCAG, and the necessity of second countability property of a group for defining the autocorrelation measure.
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    Development of large scale STEM problem databases for student learning and assessment tools
    (2021) Lorimer, Shelley; Davis, Jeffrey A.
    Problem databases in STEM courses are used in tools for the development of student learning and final assessment. In addition, large problem databases are used to develop models for automatic assessment and feedback of students’ work. However, the availability of large, open source, problem databases for specific courses is limited, and in-house development of a wide variety of problems can take years. In this paper, the framework for a problem database in STEM courses was created using semantic analysis of sentence structure and composition. Problem statements were analyzed to determine the key grammatical constructs that are used in commonly posed problems. Based on this analysis, software was developed to create large problem databases which allow for simple extension to other courses. Using a first-year mechanics course this software was populated with a few generalized questions and sentence structures to create a large problem database.
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    Teaching first-year engineering in an online learning environment
    (2021) Lorimer, Shelley; Davis, Jeffrey A.
    Teaching models in face-to-face classes have evolved over time with goals to maximize student learning through the use of learning models such as problem based, experiential, cooperative, active and discovery learning to name a few. Mastery of these teaching models requires an instructor to be knowledgeable and proficient with different media (e.g. whiteboard, projector, demonstration equipment, feedback tools, communication tools, learning management systems) while teaching and assessing students. When switching to different types of delivery methods (face-to-face, online, and hybrid) it is important to ensure that alternative teaching and learning methods and media are possible to accommodate and enhance learning. The recent Pandemic has caused a rapid transition to online teaching without time to adjust teaching and learning methodologies. This has caused changes in both the teaching environment and the learning community which are factors in both social and constructivism learning theories. In terms of the environment, students are now isolated physically and move around in a virtual environment; their experience and motivation varied by technology and societal factor. Similarly, changes in the learning community were found as students are no longer physically in groups but exist in virtual communities which affect student motivation and support. The research in this paper focuses on the effects of the shift to an online teaching modality. It first looks at the influencing factors in constructivism learning theory (such as the environment and community) and develops an inventory of concepts and techniques used to teach first year engineering both within a face-to-face and online learning environment. The paper then reflects on challenges found in recent online teaching experiences within an online environment in different first-year engineering courses, and finally discusses opportunities for improvements.
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    Assessment activities in teaching first-year engineering mechanics
    (2021) Lorimer, Shelley; Davis, Jeffrey A.
    Assessment activities play a significant role in teaching first-year engineering mechanics courses to ensure that accreditation standards are met. Traditionally, for in-person lecture-based course delivery, assessments involved a mix of problem-solving assignments, lab reports, and examinations. In terms of exams, they were often delivered in a time restricted in-person invigilated setting to uphold academic integrity and ensure that assessments demonstrate course learning outcomes. With the accelerated move to online delivery of lecture material during the Covid pandemic many instructors were required to rapidly transform to an online or blended mode of assessment. This paper speaks to that rapid transformation of first-year assessments and how prior teaching experiences in engineering education were used to ease the difficulty of this transition.
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    Measuring the analgesic effect of adding pre-operative single-shot rectus sheath blocks to postoperative rectus sheath continuous blocks for major urological surgery: a double-blind randomised study
    (2021) Green, James; Niu, Shuang; Verrier, Michelle; Buro, Karen; Lupul, Nicholas; Douglas, Chris; Fairey, Adrian; Dillane, Derek
    Continuous rectus sheath block offers an alternative to epidural analgesia for postoperative analgesia after midline abdominal surgery.1–4 Catheters can be placed under ultrasound guidance3 or under direct vision during closure of the surgical incision.2 A disadvantage of surgically placed rectus sheath catheters is that they are inserted at the end of surgery. Therefore, unlike epidural catheters inserted pre-operatively, the patient does not benefit intra-operatively and the block may not be fully established in the early recovery phase of care. We hypothesised that the addition of ultrasound-guided pre-operative bilateral single-shot rectus sheath blocks to surgically inserted postoperative continuous rectus sheath blocks would improve postoperative analgesia in the first 24 h after surgery. To this end, we designed a prospective, randomised, double-blind, placebo-controlled trial where the primary outcome was opioid consumption in the first 24 h postoperatively. Secondary outcomes included intra-operative opioid requirement, and Numerical Rating Scale (NRS)-11 pain scores in the postanaesthesia care unit (PACU) and at 24 and 48 h postoperatively. This study was approved by the Health Research Ethics Board of the University of Alberta (protocol number 00078459, date of registration 7 February 2018, ClinicalTrials.gov identifier: NCT03458598).