@unpublished{16293, abstract = {{Kernel transfer operators, which can be regarded as approximations of transfer operators such as the Perron-Frobenius or Koopman operator in reproducing kernel Hilbert spaces, are defined in terms of covariance and cross-covariance operators and have been shown to be closely related to the conditional mean embedding framework developed by the machine learning community. The goal of this paper is to show how the dominant eigenfunctions of these operators in combination with gradient-based optimization techniques can be used to detect long-lived coherent patterns in high-dimensional time-series data. The results will be illustrated using video data and a fluid flow example.}}, author = {{Klus, Stefan and Peitz, Sebastian and Schuster, Ingmar}}, booktitle = {{arXiv:1805.10118}}, title = {{{Analyzing high-dimensional time-series data using kernel transfer operator eigenfunctions}}}, year = {{2018}}, } @article{10129, abstract = {{There are many hard conjectures in graph theory, like Tutte's 5-flow conjecture, and the 5-cycle double cover conjecture, which would be true in general if they would be true for cubic graphs. Since most of them are trivially true for 3-edge-colorable cubic graphs, cubic graphs which are not 3-edge-colorable, often called snarks, play a key role in this context. Here, we survey parameters measuring how far apart a non 3-edge-colorable graph is from being 3-edge-colorable. We study their interrelation and prove some new results. Besides getting new insight into the structure of snarks, we show that such measures give partial results with respect to these important conjectures. The paper closes with a list of open problems and conjectures.}}, author = {{Fiol, M. A. and Mazzuoccolo, Guiseppe and Steffen, Eckhard}}, journal = {{The Electronic Journal of Combinatorics}}, keywords = {{Cubic graph, Tait coloring, Snark, Boole coloring, Berge's conjecture, Tutte's 5-flow conjecture}}, number = {{4}}, title = {{{Measures of Edge-Uncolorability of Cubic Graphs}}}, volume = {{25}}, year = {{2018}}, } @article{10132, author = {{Jin, Ligang and Mazzuoccolo, Giuseppe and Steffen, Eckhard}}, issn = {{1234-3099}}, journal = {{Discussiones Mathematicae Graph Theory}}, pages = {{165--175}}, title = {{{Cores, joins and the Fano-flow conjectures}}}, doi = {{10.7151/dmgt.1999}}, volume = {{38}}, year = {{2018}}, } @article{10142, author = {{Steffen, Eckhard}}, journal = {{Australasian Journal of Combinatorics}}, number = {{1}}, pages = {{153--160}}, title = {{{Approximating Vizing’s independence number conjecture}}}, volume = {{71}}, year = {{2018}}, } @inproceedings{31946, author = {{Nührenbörger, M. and Bönig, D. and Häsel-Weide, Uta and Korff, N. and Scherer, P.}}, booktitle = {{Beiträge zum Mathematikunterricht 2018. Vorträge zur Mathematikdidaktik und zur Schnittstelle Mathematik/Mathematikdidaktik auf der gemeinsamen Jahrestagung der GDM und DMV}}, editor = {{In:, Fachgruppe Didaktik der Mathematik der Universität Paderborn}}, pages = {{103--104}}, title = {{{Inklusiver Mathematikunterricht - vernetzt zwischen Mathematikdidaktik und Sonderpädagogik}}}, year = {{2018}}, } @article{31953, author = {{Moser-Opitz, E. and Grob, U. and Wittich, C. and Häsel-Weide, Uta and Nührenbörger, M.}}, journal = {{Learning Disabilities: A Contemporary Journal}}, number = {{16}}, pages = {{19--35}}, title = {{{Fostering the Computation Competence of Low Achievers through Cooperative Learning in Inclusive Classrooms: A Longitudinal Study}}}, year = {{2018}}, } @misc{31952, author = {{Häsel-Weide, Uta and Nührenbörger, M. and Reinold, M.}}, isbn = {{978-3122009977}}, pages = {{144}}, publisher = {{Klett}}, title = {{{Förderkommentar Lernen zum Zahlenbuch 3}}}, year = {{2018}}, } @misc{31951, author = {{Häsel-Weide, Uta and Nührenbörger, M. and Reinold, M.}}, isbn = {{978-3122009939}}, pages = {{80}}, publisher = {{Klett}}, title = {{{Das Zahlenbuch 3. Förderheft.}}}, year = {{2018}}, } @article{34664, author = {{Black, Tobias}}, issn = {{0036-1410}}, journal = {{SIAM Journal on Mathematical Analysis}}, keywords = {{Applied Mathematics, Computational Mathematics, Analysis}}, number = {{4}}, pages = {{4087--4116}}, publisher = {{Society for Industrial & Applied Mathematics (SIAM)}}, title = {{{Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion}}}, doi = {{10.1137/17m1159488}}, volume = {{50}}, year = {{2018}}, } @article{34666, author = {{Black, Tobias}}, issn = {{0022-0396}}, journal = {{Journal of Differential Equations}}, keywords = {{Analysis, Applied Mathematics}}, number = {{5}}, pages = {{2296--2339}}, publisher = {{Elsevier BV}}, title = {{{Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D}}}, doi = {{10.1016/j.jde.2018.04.035}}, volume = {{265}}, year = {{2018}}, } @article{34667, author = {{Black, Tobias}}, issn = {{0362-546X}}, journal = {{Nonlinear Analysis}}, keywords = {{Applied Mathematics, Analysis}}, pages = {{129--153}}, publisher = {{Elsevier BV}}, title = {{{Global solvability of chemotaxis–fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions}}}, doi = {{10.1016/j.na.2018.10.003}}, volume = {{180}}, year = {{2018}}, } @article{8753, abstract = {{In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a single optimal solution, the set of optimal compromises, the so-called Pareto set, has to be approximated. When the problem under consideration is described by a partial differential equation (PDE), as is the case for fluid flow, the computational cost rapidly increases and makes its direct treatment infeasible. Reduced order modeling is a very popular method to reduce the computational cost, in particular in a multi query context such as uncertainty quantification, parameter estimation or optimization. In this article, we show how to combine reduced order modeling and multiobjective optimal control techniques in order to efficiently solve multiobjective optimal control problems constrained by PDEs. We consider a global, derivative free optimization method as well as a local, gradient-based approach for which the optimality system is derived in two different ways. The methods are compared with regard to the solution quality as well as the computational effort and they are illustrated using the example of the flow around a cylinder and a backward-facing-step channel flow.}}, author = {{Peitz, Sebastian and Ober-Blöbaum, Sina and Dellnitz, Michael}}, issn = {{0167-8019}}, journal = {{Acta Applicandae Mathematicae}}, number = {{1}}, pages = {{171–199}}, title = {{{Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling}}}, doi = {{10.1007/s10440-018-0209-7}}, volume = {{161}}, year = {{2018}}, } @inproceedings{29425, author = {{Jiménez, F. and Ober-Blöbaum, Sina}}, booktitle = {{6th European Conference on Computational Mechanics}}, title = {{{Necessary optimality conditions for optimally controlled dissipative mechanical systems modelled through fractional derivatives}}}, year = {{2018}}, } @inproceedings{29427, author = {{Jiménez, F. and Ober-Blöbaum, Sina}}, booktitle = {{6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018}}, pages = {{50--55}}, title = {{{A fractional variational approach for modelling dissipative mechanical systems continuous and discrete settings}}}, volume = {{51(3)}}, year = {{2018}}, } @inproceedings{31371, author = {{Hoffmann, Max}}, booktitle = {{Beiträge zum Mathematikunterricht 2018}}, pages = {{815--818}}, publisher = {{WTM-Verlag}}, title = {{{Schnittstellenaufgaben im Praxiseinsatz: Aufgabenbeispiel zur „Bleistiftstetigkeit“ und allgemeine Überlegungen zu möglichen Problemen beim Einsatz solcher Aufgaben}}}, doi = {{10.17877/DE290R-19412}}, year = {{2018}}, } @article{31375, author = {{Grieser, Daniel and Hoffmann, Max and Koepf, Wolfram and Kramer, Jürg}}, journal = {{Der Mathematikunterricht}}, pages = {{48–54}}, title = {{{Anfängervorlesungen}}}, volume = {{64 (5)}}, year = {{2018}}, } @misc{31382, author = {{Hoffmann, Max}}, booktitle = {{Mathematische Semesterberichte}}, pages = {{299–301}}, title = {{{Rezension: Dörte Haftendorn: Kurven erkunden und verstehen – Mit GeoGebra und anderen Werkzeugen}}}, doi = {{10.1007/s00591-018-0222-y}}, volume = {{65}}, year = {{2018}}, } @book{31380, editor = {{Greefrath, Gilbert and Hoffmann, Max and Koepf, Wolfram}}, title = {{{Der Mathematikunterricht 64 (5): Mathematik in Schule und Hochschule – wie groß ist die Lücke und wie gehen wir mit ihr um?}}}, year = {{2018}}, } @article{33335, abstract = {{For a class of one-dimensional autoregressive sequences (Xn), we consider the tail behaviour of the stopping time T0=min{n≥1:Xn≤0}. We discuss existing general analytical approaches to this and related problems and propose a new one, which is based on a renewal-type decomposition for the moment generating function of T0 and on the analytical Fredholm alternative. Using this method, we show that Px(T0=n)∼V(x)Rn0 for some 0