@inbook{31551, author = {{Häsel-Weide, Uta and Nührenbörger, Marcus}}, booktitle = {{Kinder lernen Zukunft – Anforderungen und tragfähige Grundlagen}}, editor = {{Hecker, Ulrich and Lassek, Maresi and Ramseger, Jörg}}, pages = {{108--118}}, publisher = {{Grundschulverband}}, title = {{{Tragfähige Grundlagen}}}, volume = {{Band 150}}, year = {{2020}}, } @inbook{31552, author = {{Heckmann, Lara and Häsel-Weide, Uta}}, booktitle = {{Beiträge zum Mathematikunterricht 2020}}, editor = {{Siller, Hans-Stefan and Weigel, Wolfgang and Wörler, Jan Franz}}, isbn = {{978-3-95987-139-6}}, pages = {{393--396}}, publisher = {{WTM Verlag}}, title = {{{Aufgaben für den inklusiven Mathematikunterricht - aus der Sicht von Lehrkräften.}}}, year = {{2020}}, } @inbook{31549, author = {{Häsel-Weide, Uta}}, booktitle = {{Didaktik des Unterrichts bei Lernschwierigkeiten: Ein Handbuch für Studium und Praxis}}, editor = {{Heimlich, Ulrich and Wember, Franz B.}}, isbn = {{978-3170355699}}, pages = {{308--318}}, publisher = {{W. Kohlhammer GmbH}}, title = {{{Sachrechnen}}}, year = {{2020}}, } @inbook{31550, author = {{Häsel-Weide, Uta}}, booktitle = {{Handbuch Lehrerinnen- und Lehrerbildung}}, editor = {{Cramer, Colin and König, Johannes and Rothland, Martin and Blömeke, Sigrid}}, isbn = {{978-3-8252-5473-5}}, pages = {{462--469}}, publisher = {{Julius Klinkhardt}}, title = {{{Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule.}}}, year = {{2020}}, } @misc{33273, abstract = {{Dieses Lernangebot widmet sich der linearen Algebra als dem Teil der Mathematik, der neben der Optimierung und der Stochastik die Grundlage für praktisch alle Entwicklungen im Bereich Künstliche Intelligenz (KI) darstellt. Das Fach ist jedoch für Anfänger meist ungewohnt abstrakt und wird daher oft als besonders schwierig und unanschaulich empfunden. In diesem Kurs wird das Erlernen mathematischer Kenntnisse in linearer Algebra verknüpft mit dem aktuellen und faszinierenden Anwendungsfeld der künstlichen neuronalen Netze (KNN). Daraus ergeben sich in natürlicher Weise Anwendungsbeispiele, an denen die wesentlichen Konzepte der linearen Algebra erklärt werden können. Behandelte Themen sind: Der Vektorraum der reellen Zahlentupel, reelle Vektorräume allgemein Lineare Abbildungen Matrizen Koordinaten und darstellende Matrizen Lineare Gleichungssysteme, Gaußalgorithmus Determinante Ein Ausblick auf nichtlineare Techniken, die für neuronale Netzwerke relevant sind.}}, author = {{Schramm, Thomas and Gasser, Ingenuin and Schwenker, Sören and Seiler, Ruedi and Lohse, Alexander and Zobel, Kay}}, publisher = {{Hamburg Open Online University}}, title = {{{Linear Algebra driven by Data Science}}}, year = {{2020}}, } @article{33282, abstract = {{We derive a criterium for the almost sure finiteness of perpetual integrals of L ́evy processes for a class of real functions including all continuous functions and for general one- dimensional L ́evy processes that drifts to plus infinity. This generalizes previous work of D ̈oring and Kyprianou, who considered L ́evy processes having a local time, leaving the general case as an open problem. It turns out, that the criterium in the general situation simplifies significantly in the situation, where the process has a local time, but we also demonstrate that in general our cri- terium can not be reduced. This answers an open problem posed in D ̈oring, L. and Kyprianou, A. (2015).}}, author = {{Kolb, Martin and Savov, Mladen}}, journal = {{Bernoulli}}, keywords = {{L ́evy processes, Perpetual integrals, Potential measures}}, number = {{2}}, pages = {{1453--1472}}, publisher = {{Bernoulli Society for Mathematical Statistics and Probability}}, title = {{{A Characterization of the Finiteness of Perpetual Integrals of Levy Processes}}}, doi = {{https://doi.org/10.48550/arXiv.1903.03792}}, volume = {{26}}, year = {{2020}}, } @article{33330, abstract = {{Reciprocal relations are binary relations Q with entries Q(i,j)∈[0,1], and such that Q(i,j)+Q(j,i)=1. Relations of this kind occur quite naturally in various domains, such as preference modeling and preference learning. For example, Q(i,j) could be the fraction of voters in a population who prefer candidate i to candidate j. In the literature, various attempts have been made at generalizing the notion of transitivity to reciprocal relations. In this paper, we compare three important frameworks of generalized transitivity: g-stochastic transitivity, T-transitivity, and cycle-transitivity. To this end, we introduce E-transitivity as an even more general notion. We also use this framework to extend an existing hierarchy of different types of transitivity. As an illustration, we study transitivity properties of probabilities of pairwise preferences, which are induced as marginals of an underlying probability distribution on rankings (strict total orders) of a set of alternatives. In particular, we analyze the interesting case of the so-called Babington Smith model, a parametric family of distributions of that kind.}}, author = {{Haddenhorst, Björn and Hüllermeier, Eyke and Kolb, Martin}}, journal = {{International Journal of Approximate Reasoning}}, number = {{2}}, pages = {{373--407}}, publisher = {{Elsevier}}, title = {{{Generalized transitivity: A systematic comparison of concepts with an application to preferences in the Babington Smith model}}}, doi = {{https://doi.org/10.1016/j.ijar.2020.01.007}}, volume = {{119}}, year = {{2020}}, } @article{34828, author = {{Hanusch, Maximilian}}, issn = {{0019-3577}}, journal = {{Indagationes Mathematicae}}, keywords = {{regularity of Lie groups}}, number = {{1}}, pages = {{152--176}}, publisher = {{Elsevier BV}}, title = {{{The regularity problem for Lie groups with asymptotic estimate Lie algebras}}}, doi = {{10.1016/j.indag.2019.12.001}}, volume = {{31}}, year = {{2020}}, } @article{34830, author = {{Hanusch, Maximilian}}, journal = {{Journal of Lie Theory}}, keywords = {{Lie theory, strong Trotter property}}, number = {{1}}, pages = {{025--032}}, publisher = {{Heldermann Verlag}}, title = {{{The Strong Trotter Property for Locally μ-convex Lie Groups}}}, volume = {{30}}, year = {{2020}}, } @article{45383, author = {{Dröse, Jennifer and Prediger, Susanne}}, journal = {{Journal für Mathematik-Didaktik, 41(2)}}, pages = {{399--422}}, title = {{{Enhancing Fifth Graders’ Awareness of Syntactic Features in Mathematical Word Problems: A Design Research Study on the Variation Principle}}}, doi = {{doi.org/10.1007/s13138-019-00153-z}}, year = {{2020}}, } @inbook{29413, author = {{Flaßkamp, K. and Ober-Blöbaum, Sina and Peitz, S. }}, booktitle = {{Advances in Dynamics, Optimization and Computation}}, editor = {{Junge, Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}}, pages = {{209--237}}, publisher = {{Springer International Publishing}}, title = {{{Symmetry in optimal control: A multiobjective model predictive control approach}}}, year = {{2020}}, } @article{31553, author = {{Seitz, Susanne and Häsel-Weide, Uta and Wilke, Yannik and Wallner, Melina}}, journal = {{K:ON Kölner Online-Journal für Lehrer*innenbildung}}, number = {{2}}, title = {{{Expertise von Lehrpersonen für inklusiven Mathematikunterricht der Sekundarstufe - Ausgangspunkte zur Professionalisierungsforschung.}}}, doi = {{10.18716/ojs/kON/2020.2.03}}, year = {{2020}}, } @inproceedings{45384, author = {{Dröse, Jennifer}}, booktitle = {{Beiträge zum Mathematikunterricht 2020 }}, editor = {{Siller, H.-S. and Weigel, W. and Wöler, J. F.}}, pages = {{233--236}}, publisher = {{WTM}}, title = {{{Verstehensgrundlagen diagnostizieren - Welche Wissenselemente fokussieren Lehrkräfte?}}}, year = {{2020}}, } @inbook{45386, author = {{Dröse, Jennifer and Eisen, V. and Prediger, Susanne and Altieri, M. and Schellenbach, M. and Menning, R.}}, booktitle = {{Mathematik lehren 223}}, pages = {{38--40}}, title = {{{Textaufgaben lesen lernen – eine digital gestützte Einheit mit App }}}, year = {{2020}}, } @inbook{17994, abstract = {{In this work we review the novel framework for the computation of finite dimensional invariant sets of infinite dimensional dynamical systems developed in [6] and [36]. By utilizing results on embedding techniques for infinite dimensional systems we extend a classical subdivision scheme [8] as well as a continuation algorithm [7] for the computation of attractors and invariant manifolds of finite dimensional systems to the infinite dimensional case. We show how to implement this approach for the analysis of delay differential equations and partial differential equations and illustrate the feasibility of our implementation by computing the attractor of the Mackey-Glass equation and the unstable manifold of the one-dimensional Kuramoto-Sivashinsky equation.}}, author = {{Gerlach, Raphael and Ziessler, Adrian}}, booktitle = {{Advances in Dynamics, Optimization and Computation}}, editor = {{Junge, Oliver and Schütze, Oliver and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}}, isbn = {{9783030512637}}, issn = {{2198-4182}}, pages = {{66--85}}, publisher = {{Springer International Publishing}}, title = {{{The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems}}}, doi = {{10.1007/978-3-030-51264-4_3}}, volume = {{304}}, year = {{2020}}, } @article{16712, abstract = {{We investigate self-adjoint matrices A∈Rn,n with respect to their equivariance properties. We show in particular that a matrix is self-adjoint if and only if it is equivariant with respect to the action of a group Γ2(A)⊂O(n) which is isomorphic to ⊗nk=1Z2. If the self-adjoint matrix possesses multiple eigenvalues – this may, for instance, be induced by symmetry properties of an underlying dynamical system – then A is even equivariant with respect to the action of a group Γ(A)≃∏ki=1O(mi) where m1,…,mk are the multiplicities of the eigenvalues λ1,…,λk of A. We discuss implications of this result for equivariant bifurcation problems, and we briefly address further applications for the Procrustes problem, graph symmetries and Taylor expansions.}}, author = {{Dellnitz, Michael and Gebken, Bennet and Gerlach, Raphael and Klus, Stefan}}, issn = {{1468-9367}}, journal = {{Dynamical Systems}}, number = {{2}}, pages = {{197--215}}, title = {{{On the equivariance properties of self-adjoint matrices}}}, doi = {{10.1080/14689367.2019.1661355}}, volume = {{35}}, year = {{2020}}, } @article{51386, author = {{Hilgert, Joachim and Barnum, H.}}, journal = {{J. of Lie Theory}}, pages = {{315--344}}, title = {{{Spectral Properties of Convex Bodies}}}, volume = {{30}}, year = {{2020}}, } @misc{51559, author = {{Hilgert, Joachim}}, booktitle = {{Mathematische Semesterberichte}}, pages = {{301–305}}, title = {{{Titu Andreescu und Vlad Crisan: Mathematical Induction – A powerful and elegant method of proof. XYZ Press 2017 und Florian André Dalwigk: Vollständige Induktion – Beispiele und Aufgaben bis zum Umfallen. Springer Spektrum 2019}}}, doi = {{10.1007/s00591-020-00282-4}}, volume = {{67}}, year = {{2020}}, } @misc{51557, author = {{Hilgert, Joachim}}, booktitle = {{Mathematische Semesterberichte}}, pages = {{307–309}}, title = {{{Fabio Toscano: The Secret Formula – How a Mathematical Duel Inflamed Renaissance Italy and Uncovered the Cubic Equation. Princeton University Press 2020}}}, doi = {{10.1007/s00591-020-00283-3}}, volume = {{67}}, year = {{2020}}, } @misc{51561, author = {{Hilgert, Joachim}}, booktitle = {{Mathematische Semesterberichte}}, pages = {{123–124}}, title = {{{Robert Bosch: OPT ART – From Mathematical Optimization to Visual Design. Princeton University Press 2019}}}, doi = {{10.1007/s00591-020-00272-6}}, volume = {{67}}, year = {{2020}}, }