On nonobtuse simplicial partitionsBrandts, J.H.; Korotov, S.; Kížek, M.; Šolc, J. Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Download date: 10 May 2018Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. Dedicated to Ivan Hlaváček on his 75th birthdayAbstract. This paper surveys some results on acute and nonobtuse simplices and associated spatial partitions. These partitions are relevant in numerical mathematics, including piecewise polynomial approximation theory and the finite element method. Special attention is paid to a basic type of nonobtuse simplices called path-simplices, the generalization of right triangles to higher dimensions. In addition to applications in numerical mathematics, we give examples of the appearance of acute and nonobtuse simplices in other areas of mathematics.

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This series is aimed at publishing work dealing with the defInition, development and application of fundamental theory and methodology, computational and algorithmic implementations and comprehensive empirical studies in mathematical modelling. Work on new mathematics inspired by the construction of mathematical models, combining theory and experiment and furthering the understanding of the systems being modelled are particularly welcomed.Manuscripts to be considered for publication lie within the following, non-exhaustive list of areas: mathematical modelling in engineering, industrial

We show that the famous maximum angle condition in the finite element analysis is not necessary to achieve the optimal convergence rate when simplicial finite elements are used to solve elliptic problems. This condition is only sufficient. In fact, finite element approximations may converge even though some dihedral angles of simplicial elements tend to π .

The structure of digraphs associated with the congruence x k ≡ y (mod n) Czechoslovak Mathematical Journal, Vol. 61 (2011) Abstract. We assign to each pair of positive integers n and k 2 a digraph G(n, k) whose set of vertices is H = {0, 1, . . . , n − 1} and for which there is a directed edge from a ∈ H to b ∈ H if a k ≡ b (mod n). We investigate the structure of G(n, k). In particular, upper bounds are given for the longest cycle in G(n, k). We find subdigraphs of G(n, k), called fundamental constituents of G(n, k), for which all trees attached to cycle vertices are isomorphic.

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