Australian Mathematical Society (AustMS): E-Journals
Not a member yet
3379 research outputs found
Sort by
Finite -groups all of whose nonnormal subgroups have bounded normal cores
No full textDOI:
10.1017/S000497271900075
Generalisation of a result on distinct partitions with bounded part differences
No full textDOI:
10.1017/S000497271900082
Approximation of and by completely monotone functions
No full textWe investigate convergence in the cone of completely monotone fu nctions. Particular attention is paid to the approximation of and by exponentials and stretched exponentials. The need for such an analysis is a consequence of the fact that although stretched exponentials can be approximated by sums of exponentials, exponentials cannot in general be approximated by sums of stretched exponentials.
doi:10.1017/S144618112000001
A semi-analytical pricing formula for European options under the rough Heston-CIR model
No full textWe combine the rough Heston model and the CIR (Cox–Ingersoll–Ross) interest rate together to form a rough Heston-CIR model, so that both the rough behaviour of the volatility and the stochastic nature of the interest rate can be captured. Despite the convoluted structure and non-Markovian property of this model, it still admits a semi-analytical pricing formula for European options, the implementation of which involves solving a fractional Riccati equation. The rough Heston-CIR model is more general, taking both the rough Heston model and the Heston-CIR model as special cases. The influence of rough volatility and stochastic interest rate is shown to be significant through numerical experiments.
doi:10.1017/S144618112000002
'Soft' skills identified by students who peer-led mathematics computing workshops
Get PDFIncreasingly, employers are suggesting that 'soft' skills, such as communication and teamwork, are equally important as 'hard' skills, such as discipline specific knowledge. This makes it imperative for university programs to build in opportunities for students to practise and demonstrate such soft skills. For some years, small groups of students in my second-year numerical methods course have acted as peer-leaders, with each student taking a turn to help run the computer workshops. In 2018, I introduced a PebblePad reflection to give the students the opportunity to identify the skills that they had developed, as well as to reflect on the process. In analysing the students' responses, I found that the students were very positive about the experience and that they were able to articulate a range of soft skills that they had practised and developed during the activity.
References
G. Athony. Factors influencing first-year students' success in mathematics. Int. J. Math. Edu. Sci. Tech., 31(1):3–14, 2000. doi:10.1080/002073900287336
Deakinco. Soft skills for business success. Technical report, Deloitte Access Economics, 2017. https://www2.deloitte.com/au/en/pages/economics/articles/soft-skills-business-success.html
Deakinco. Premium skills. Technical report, Deloitte Access Economics, 2019. https://www2.deloitte.com/au/en/pages/economics/articles/premium-skills.html
M. Demaria, Y. Hodgson, and D. Czech. Perceptions of transferable skills among biomedical science students in the final year of their degree: What are the implications for graduate employability. Int. J. Innov. Sci. Math. Edu., 26(7):11–24, 2018. https://openjournals.library.sydney.edu.au/index.php/CAL/article/view/12651
T. L. Durksen, J. Way, J. Bobis, J. A. Anderson, K. Skilling, and A. J. Martin. Motivation and engagement in mathematics: a qualitative framework for teacher–student interaction. Math. Edu. Res. J., 29:163–181, 2017. doi:10.1007/s13394-017-0199-1
R. Gill. Building employability skills for higher education students: An Australian example. J. Teach. Learn. Grad. Employ., 9(1):84–92, 2018. https://ojs.deakin.edu.au/index.php/jtlge/article/view/739
M. V. Gruzdev, I. V. Kuznetsova, I. Y. Tarkhanova, and E. I. Kazakova. University graduates' soft skills: the employer's opinion. Euro. J. Contemp. Edu., 7(4):690–698, 2018. doi:10.13187/ejced.2018.4.690
B. M. Johnston. Implementing a flipped classroom approach in a university numerical methods mathematics course. Int. J. Math. Edu. Sci. Tech., 48(4):485–498, 2017. doi:10.1080/0020739X.2016.1259516
P. Klaus. Communication breakdown. California Job J., 28(1248):1–9, August 2010. http://connection.ebscohost.com/c/articles/52911024/communication-breakdown
A. Pennington and J. Stanford. The future of work for Australian graduates: the changing landscape of University employment transitions in Australia. Technical report, Graduate Careers Australia, 2019. https://d3n8a8pro7vhmx.cloudfront.net/theausinstitute/pages/3083/attachments/original/1571640129/Future_of_Work_for_Australian_Graduates_GCA_Final_Formatted.pdf?1571640129
M. Pozzi and S. Bonson. I surprised myself: Skills awareness, reflection, and employability in final year mathematics students. In STARS: Students, Transitions, Achievement, Retention and Success, Melbourne, Australia, July 2019. https://eprints.qut.edu.au/131357/
H. M. G. Watt and M. Goos. Theoretical foundations of engagment in mathematics. Math. Edu. Res. J., 29:133–142, 2017. doi:10.1007/s13394-017-0206-
Block monotone iterations for solving coupled systems of nonlinear parabolic equations
Get PDFThe article deals with numerical methods for solving a coupled system of nonlinear parabolic problems, where reaction functions are quasi-monotone nondecreasing. We employ block monotone iterative methods based on the Jacobi and Gauss–Seidel methods incorporated with the upper and lower solutions method. A convergence analysis and the theorem on uniqueness of a solution are discussed. Numerical experiments are presented.
References
Al-Sultani, M. and Boglaev, I. ''Numerical solution of nonlinear elliptic systems by block monotone iterations''. ANZIAM J. 60:C79–C94, 2019. doi:10.21914/anziamj.v60i0.13986
Al-Sultani, M. ''Numerical solution of nonlinear parabolic systems by block monotone iterations''. Tech. Report, 2019. https://arxiv.org/abs/1905.03599
Boglaev, I. ''Inexact block monotone methods for solving nonlinear elliptic problems'' J. Comput. Appl. Math. 269:109–117, 2014. doi:10.1016/j.cam.2014.03.029
Lui, S. H. ''On monotone iteration and Schwarz methods for nonlinear parabolic PDEs''. J. Comput. Appl. Math. 161:449–468, 2003. doi:doi.org/10.1016/j.cam.2003.06.001
Pao, C. V. Nonlinear parabolic and elliptic equations. Plenum Press, New York, 1992. doi:10.1007/s002110050168
Pao C. V. ''Numerical analysis of coupled systems of nonlinear parabolic equations''. SIAM J. Numer. Anal. 36:393–416, 1999. doi:10.1137/S0036142996313166
Varga, R. S. Matrix iterative analysis. Springer, Berlin, 2000. 10.1007/978-3-642-05156-2
Zhao, Y. Numerical solutions of nonlinear parabolic problems using combined-block iterative methods. Masters Thesis, University of North Carolina, 2003. http://dl.uncw.edu/Etd/2003/zhaoy/yaxizhao.pd
Quasiconformal harmonic mappings between domains containing infinity
No full texthttp://dx.doi.org/10.1017/S000497271900127
Transformation formulas for the number of representations of by linear combinations of four triangular numbers
No full textLet and be the set of integers
and the set of positive integers, respectively. For
let be the number of
representations of by . In this paper, by using Ramanujan's theta functions and we present some transformation formulas for , and evaluate , and