Australian Mathematical Society (AustMS): E-Journals
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Proceedings of the 2022 Mathematics in Industry Study Group
Get PDFThis special Section of the ANZIAM Journal (Electronic Supplement) contains the refereed papers from the 2022 Mathematics in Industry Study Group (MISG2022) held at the University of Newcastle from 14--18 February 2022. This report provides the equation-free outcomes
An unbounded operator with spectrum in a strip and matrix differential operators
No full texthttp://dx.doi.org/10.1017/S000497271200033
Structured singular values on some generalised stochastic matrices
No full texthttp://dx.doi.org/10.1017/S000497271200033
Aerodynamics and Control of Next Generation Electric Rotorcraft
Get PDFInnovative design of helicopters promises great benefitsover conventional aircraft but there are a number oftechnical challenges. Hyper Q Aerospace brought a project tothe 2020 Mathematics-in-Industry Study Group to consider ahelicopter design with a counter-rotating, coaxial, doublerotor. Specific considerations were the vibration andharmonic properties of the rotor blades, the noise from theaircraft and the aerodynamic characteristics.Euler--Bernoulli beam theory and classical airfoil theorywere implemented to consider the vibration and aerodynamicfeatures of the aircraft and the rotor system. Thefundamental lengthwise and lateral harmonics of the bladeswere obtained and compared with typical rotational forcingfrequencies. The modification to the lift generated by thecounter-rotating blades and noise mitigation strategies werediscussed. Improved design strategies were presented
A new regularization for sparse optimization
Get PDFSeveral numerical studies have shown that non-convex sparsity-induced regularization can outperform the convex ℓ1-penalty. In this article, we introduce a new non-convex and non-smooth regularization. This new regularization is a continuous and separable function which provides a tighter approximation to the cardinality function than any ℓq-penalty (0 < q < 1). We then apply the Proximal Gradient Method to solve a regularized optimization problem with the new regularization. The convergence analysis shows that the algorithm converges to a critical point and we also provide a pseudo-code for fast implementation. In addition, we conduct a simple numerical experiment with a regularized least square problem to illustrate the performance of the new regularization.
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A note on open book embeddings of manifolds in
No full texthttp://dx.doi.org/10.1017/S000497271200033