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    Open Access
    A simplified silver phosphate extraction method for oxygen isotope analysis of bioapatite
    (Wiley, 2018-06-21) Shabaga, BM; Gough, H; Fayek, M; Hoppa, RD
    Rationale: Although phosphatic materials are chemically complex and are prone to exchange oxygen isotopes with their environments, the phosphate (PO43-) component of these materials is robust and retains its original oxygen isotopic composition. As a result, there are currently several methods for the isolation of phosphate oxygen through the precipitation of silver phosphate (Ag3PO4). However, some of these techniques produce Ag3PO4 of questionable purity, while nearly all are lengthy and/or require relatively large sample sizes. Methods: Five milligrams of bioapatite from modern cow teeth (enamel and cementum) were pre-treated for removal of organic material prior to digestion in 2M HF. The digested samples were titrated with silver ammine solution at 50°C to precipitate Ag3PO4. Oxygen isotopic data were collected using a Thermal Combustion Elemental Analyzer (TC/EA) paired with a Delta VPlus isotope ratio mass spectrometer via a ConFlo III universal interface. Results: The quality of Ag3PO4 is dependent on effective removal of organic material and the volume of silver ammine solution used during titration. A two-step pre-treatment of 2.5% NaOCl, followed by a 0.125M NaOH solution is the most effective treatment for the removal of organic material from both enamel and cementum. Optimal yields of Ag3PO4 were achieved using 1.8 mL of silver ammine solution. The reproducibility of the phosphate δ18O compositions ranges from 0.3 to 0.4‰ (1σ) for modern cow teeth. Conclusions: We present a simplified method for phosphate extraction from organic-rich phosphatic material. Our method gave reproducible 18O values for enamel and cementum from cows’ teeth.
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    Complex Hadamard diagonalisable graphs
    (Linear Algebra and its Applications, 2020) Chan, A.; Fallat, S.; Kirkland, S.; Lin, J.; Nasserasr, S.; Plosker, S.
    In light of recent interest in Hadamard diagonalisable graphs (graphs whose Laplacian matrix is diagonalisable by a Hadamard matrix), we generalise this notion from real to complex Hadamard matrices.We give some basic properties and methods of constructing such graphs. We show that a large class of complex Hadamard diagonalisable graphs have vertex sets forming an equitable partition, and that the Laplacian eigenvalues must be even integers. We provide a number of examples and constructions of complex Hadamard diagonalisable graphs, including two special classes of graphs: the Cayley graphs over Z^d_r , and the non–complete extended p–sum (NEPS). We discuss necessary and sufficient conditions for (\alpha, \beta)–Laplacian fractional revival and perfect state transfer on continuous–time quantum walks described by complex Hadamard diagonalisable graphs and provide examples of such quantum state transfer.
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    On split graphs with four distinct eigenvalues
    (Discrete Applied Mathematics, 2020) Goldberg, F.; Kirkland, S.; Varghese, A.; Vijayakumar, A.
    It is a well-known fact that a graph of diameter d has at least d + 1 eigenvalues. A graph is d-extremal, if it has diameter d and exactly d+1 eigenvalues. A graph is split if its vertex set can be partitioned into a clique and a stable set. Such graphs have diameter at most 3. We obtain a complete classification of the connected bidegreed 3-extremal split graphs using the association of split graphs with combinatorial designs. We also construct certain families of non-bidegreed 3-extremal split graphs.
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    The Karpelevic region revisited
    (Journal of Mathematical Analysis and Applications, 2020) Kirkland, S.; Laffey, T.; Smigoc, H.
    We consider the Karpelevic region \Theta_n in the complex plane consisting of all eigenvalues of all stochastic matrices of order n. We provide an alternative characterisation of \Theta_n that sharpens the original description given by Karpelevic. In particular, for each \theta in [0; 2\pi); we identify the point on the boundary of \Theta_n with argument \theta. We further prove that if n is a natural number with n at least 2, and t is in \Theta_n, then t is a subdominant eigenvalue of some stochastic matrix of order n.
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    The effectiveness of matching sales influence tactics to consumers’ avoidance versus approach shopping motivations
    (Emerald Group Publishing Limited, 2017) Guo, Wenxia; Main, Kelley J.
    Abstract Purpose - Adaptive selling can help build positive relationships between sales agents and consumers. The literature shows that consumers respond positively to sales agents under approach, but not avoidance motivations. The current research demonstrates a circumstance under which consumers with avoidance goals can also respond positively, something not previously shown in the literature. Design/methodology/approach - This research paper uses three experimental betweensubject designs to test hypotheses. Findings - The current research identifies appropriate sales influence tactics (e.g., a customer-autonomy-oriented or a loss-avoidance oriented influence tactic) where consumers with avoidance motivations can also respond to sales agents positively by the evidence of higher purchase intentions. In addition, this research shows that consumers with approach motivations may not always respond positively to salespeople. Further, goal facilitation appraisals of the salespeople serve as a mechanism between consumers’ shopping motivations and their behavioral responses (e.g., purchase intentions). Originality/value - First, while the prior literature demonstrates that approach motivations generally lead to more positive effects (Elliot and Thrash 2002), our research indicates that avoidance motivations can also have positive effects, which is a finding that has not been demonstrated in the literature thus far. Second, this research identifies goal facilitation appraisals as one underlying process that explains the interactive effect between matching influence tactics and consumers’ approach/avoidance motivations when shopping. Third, we integrate regulatory focus theory by using gain- or loss avoidance-oriented sales influence tactics to match approach and avoidance motivations.