Australian Mathematical Society (AustMS): E-Journals
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A counterexample to a result of Jaberi and Mahmoodi
No full texthttp://dx.doi.org/10.1017/S000497271200033
On the N-point correlation of van der Corput sequences
No full texthttp://dx.doi.org/10.1017/S000497271200033
Bayesian methods and polynomial chaos: application to finding cardiac bidomain parameters
No full texthttp://dx.doi.org/10.1017/S000497271200033
Any dual operator space is weakly locally reflexive
No full texthttp://dx.doi.org/10.1017/S000497271200033
Computing expected moments of the Rényi parking problem on the circle
Full text linkA highly accurate and efficient method to compute the expected values of the count, sum, and squared norm of the sum of the centre vectors of a random maximal sized collection of non-overlapping unit diameter disks touching a fixed unit-diameter disk is presented. This extends earlier work on Renyi's parking problem [Magyar Tud. Akad. Mat. Kutato Int. Kozl. 3 (1–2), 1958, pp. 109–127]. Underlying the method is a splitting of the the problem conditional on the value of the first disk. This splitting is proven and then used to derive integral equations for the expectations. These equations take a lower block triangular form. They are solved using substitution and approximation of the integrals to very high accuracy using a polynomial approximation within the blocks.
References
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M. P. Clay and N. J. Simányi. Rényi’s parking problem revisited. Stoch. Dyn. 16.2, 1660006 (2016). doi: 10.1142/S0219493716600066
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S. Olver. ApproxFun.jl v0.13.14. 2023. url: https://github.com/JuliaApproximation/ApproxFun.jl
S. Olver and A Townsend. A practical framework for infinite-dimensional linear algebra. Proceedings of the First Workshop for High Performance Technical Computing in Dynamic Languages. 2014, pp. 57–62. doi: 10.1109/HPTCDL.2014.10
A. Rényi. On a one-dimensional problem concerning random space filling. Publ. Math. Inst. Hung. Acad. Sci 3.1–2 (1958), pp. 109–127
H. Weiner. Elementary Treatment of the Parking Problem. Sankhya: Indian J. Stat., A (1961–2002) 31.4 (1969), pp. 483–486. url: http://www.jstor.org/stable/2504961
Galois groups of reciprocal sextic polynomials
No full texthttp://dx.doi.org/10.1017/S000497271200033
Geometric and topological shape analysis: Investigating and summarising the shape of data
No full texthttp://dx.doi.org/10.1017/S000497271200033
On some congruences involving central binomial coefficients
No full texthttp://dx.doi.org/10.1017/S000497271200033
Vertex-primitive s-arc-transitive digraphs of almost simple groups
No full texthttp://dx.doi.org/10.1017/S000497271200033