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    Convergence rate for statistics of point processes

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    http://dx.doi.org/10.1017/S000497271200033

    Stochastic processes with applications in physics and insurance

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    http://dx.doi.org/10.1017/S000497271200033

    Local projection stabilisation for convection-diffusion-reaction equations using a biorthogonal system and adaptive refinement

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    We consider a local projection stabilisation based on biorthogonal systems and adaptive refinement for convection-diffusion-reaction differential equations. The local projection stabilisation and adaptive finite element method are both based on a biorthogonal system. We investigate the numerical efficiency of the approach when compared to the standard finite element method. Numerical examples are presented to demonstrate the performance of the approach. References R. Becker and M. Braack. A finite element pressure gradient stabilization for the Stokes equations based on local projections. In:Calcolo 38.4 (2001), pp. 173–199. doi: 10.1007/s10092-001-8180-4 M. Braack and E. Burman. Local projection stabilization for the Oseen problem and its interpretation as a variational multiscale method. SIAM J. Numer. Anal. 43.6 (2006), pp. 2544–2566. doi: 10.1137/050631227 D. Braess. Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics. Cambridge University Press, 2001. url: https://www.cambridge.org/au/academic/subjects/mathematics/numerical-analysis/finite-elements-theory-fast-solvers-and-applications-solid-mechanics-3rd-edition?format=PB S. C. Brenner and L. R. Scott. The Mathematical Theory of Finite Element Methods. Springer–Verlag, 1994. doi: 10.1007/978-0-387-75934-0 C. Carstensen, M. Feischl, M. Page, and D. Praetorius. Axioms of adaptivity. Comput. Math. Appl. 67.6 (2014), pp. 1195–1253. doi: 10.1016/j.camwa.2013.12.003 L. Chen, P. Sun, and J. Xu. Multilevel homotopic adaptive finite element methods for convection dominated problems. Domain Decomposition Methods in Science and Engineering. Ed. by T. J. Barth, M. Griebel, D. E. Keyes, R. M. Nieminen, D. Roose, T. Schlick, R. Kornhuber, R. Hoppe, J. Périaux, O. Pironneau, O. Widlund, and J. Xu. Springer, 2005, pp. 459–468. doi: 10.1007/3-540-26825-1_47 S. A. Funken and A. Schmidt. Adaptive mesh refinement in 2D—An efficient implementation in Matlab. Comput. Meth. Appl. Math. 20.3 (2020), pp. 459–479. doi: 10.1515/cmam-2018-0220 p. C131). D. Gilbarg and N. S. Trudinger. Elliptic partial differential equations of second order, Springer-Verlag, 2001. doi: 10.1007/978-3-642-61798-0 V. John, P. Knobloch, and J. Novo. Finite elements for scalar convection-dominated equations and incompressible flow problems: A never ending story? Comput. Visual. Sci. 19.5 (2018), pp. 47–63. doi: 10.1007/s00791-018-0290-5 C. Johnson. Numerical Solution of Partial Differential Equations by the Finite Element Method. Dover Books on Mathematics. Dover Publications, 2012. url: https://store.doverpublications.com/048646900x.html B. P. Lamichhane. Higher order mortar finite elements with dual Lagrange multiplier spaces and applications. PhD thesis. University of Stuttgart, 2006. doi: 10.18419/opus-4770 B. P. Lamichhane and J. A. Shaw-Carmody. A local projection stabilisation for convection-diffusion-reaction equations using biorthogonal systems. J. Comput. Appl. Math. 393, 113542 (2020). doi: 10.1016/j.cam.2021.113542 G. Matthies, P. Skrzypacz, and L. Tobiska. Stabilization of local projection type applied to convection-diffusion problems with mixed boundary conditions. Elec. Trans. Numer. Anal. 32 (2008), pp. 90–105. url: https://etna.math.kent.edu/volumes/2001-2010/vol32/abstract.php?vol=32&pages=90-105 H.-G. Roos, M. Stynes, and L. Tobiska. Robust Numerical Methods for Singularly Perturbed Differential Equations: Convection-Diffusion and Flow Problems. Springer, 2008. doi: 10.1007/978-3-540-34467-4 P. Sun, L. Chen, and J. Xu. Numerical Studies of Adaptive Finite Element Methods for Two Dimensional Convection-Dominated Problems. J. Sci. Comput. 43 (2010), pp. 24–43. doi: 10.1007/s10915-009-9337-

    The probability of zero multiplication in finite rings

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    http://dx.doi.org/10.1017/S000497271200033

    Planar immersions with prescribed curl and Jacobian determinant are unique

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    http://dx.doi.org/10.1017/S000497271200033

    An eigenvalue characterisation of the dual EDM cone

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    http://dx.doi.org/10.1017/S000497271200033

    On integer sets with the same representation functions

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    http://dx.doi.org/10.1017/S000497271200033

    On a problem of Richard Guy

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    http://dx.doi.org/10.1017/S000497271200033

    On higher Frobenius-Schur indicators

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    http://dx.doi.org/10.1017/S0004972712000330Similarly to the Frobenius-Schur indicators of irreducible characters we consider higher Frobenius-Schur indicators νpn(χ)=1GgGχ(gpn)\nu_{p^n}(\chi) = \frac{1}{|G|} \sum_{g \in G} \chi(g^{p^n}) for primes pp and nNn \in \N, where GG is a finite group and χ\chi is a generalized character of GG. It turns out that these invariants give answers to interesting questions in representation theory. In particular, we give several characterizations of groups via higher Frobenius-Schur indicators

    On the boundary behaviour of Fridman invariants

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    http://dx.doi.org/10.1017/S000497271200033

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