@article{33261,
  abstract     = {{We prove that steady state bifurcations in finite-dimensional dynamical systems that are symmetric with respect to a monoid representation generically occur along an absolutely indecomposable subrepresentation. This is stated as a conjecture in [B. Rink and J. Sanders, SIAM J. Math. Anal., 46 (2014), pp. 1577--1609]. It is a generalization of the well-known fact that generic steady state bifurcations in equivariant dynamical systems occur along an absolutely irreducible subrepresentation if the symmetries form a group---finite or compact Lie. Our generalization also includes noncompact symmetry groups. The result has applications in bifurcation theory of homogeneous coupled cell networks as they can be embedded (under mild additional assumptions) into monoid equivariant systems.}},
  author       = {{Schwenker, Sören}},
  issn         = {{0036-1410}},
  journal      = {{SIAM Journal on Mathematical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Analysis}},
  number       = {{3}},
  pages        = {{2466--2485}},
  publisher    = {{Society for Industrial & Applied Mathematics (SIAM)}},
  title        = {{{Generic Steady State Bifurcations in Monoid Equivariant Dynamics with Applications in Homogeneous Coupled Cell Systems}}},
  doi          = {{10.1137/17m116118x}},
  volume       = {{50}},
  year         = {{2018}},
}

@article{45950,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>The maximum principle forms an important qualitative property of second-order elliptic equations; therefore, its discrete analogues, the so-called discrete maximum principles (DMPs), have drawn much attention owing to their role in reinforcing the qualitative reliability of the given numerical scheme. In this paper DMPs are established for nonlinear finite element problems on surfaces with boundary, corresponding to the classical pointwise maximum principles on Riemannian manifolds in the spirit of Pucci &amp; Serrin (2007, The Maximum Principle. Springer). Various real-life examples illustrate the scope of the results.</jats:p>}},
  author       = {{Karátson, János and Kovács, Balázs and Korotov, Sergey}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{2}},
  pages        = {{1241--1265}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary}}},
  doi          = {{10.1093/imanum/dry086}},
  volume       = {{40}},
  year         = {{2018}},
}

@article{45949,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>The maximum principle forms an important qualitative property of second-order elliptic equations; therefore, its discrete analogues, the so-called discrete maximum principles (DMPs), have drawn much attention owing to their role in reinforcing the qualitative reliability of the given numerical scheme. In this paper DMPs are established for nonlinear finite element problems on surfaces with boundary, corresponding to the classical pointwise maximum principles on Riemannian manifolds in the spirit of Pucci &amp; Serrin (2007, The Maximum Principle. Springer). Various real-life examples illustrate the scope of the results.</jats:p>}},
  author       = {{Karátson, János and Kovács, Balázs and Korotov, Sergey}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{2}},
  pages        = {{1241--1265}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary}}},
  doi          = {{10.1093/imanum/dry086}},
  volume       = {{40}},
  year         = {{2018}},
}

@article{45947,
  author       = {{Kovács, Balázs and Lubich, Christian}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{1}},
  pages        = {{121--152}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Linearly implicit full discretization of surface evolution}}},
  doi          = {{10.1007/s00211-018-0962-6}},
  volume       = {{140}},
  year         = {{2018}},
}

@article{45951,
  author       = {{Kovács, Balázs}},
  issn         = {{0749-159X}},
  journal      = {{Numerical Methods for Partial Differential Equations}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Numerical Analysis, Analysis}},
  number       = {{3}},
  pages        = {{1093--1112}},
  publisher    = {{Wiley}},
  title        = {{{Computing arbitrary Lagrangian Eulerian maps for evolving surfaces}}},
  doi          = {{10.1002/num.22340}},
  volume       = {{35}},
  year         = {{2018}},
}

@article{53191,
  abstract     = {{<p>This paper is the first in a series of two dedicated to the study of period relations of the type <disp-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L left-parenthesis one half plus k comma normal upper Pi right-parenthesis element-of left-parenthesis 2 pi i right-parenthesis Superscript d dot k Baseline normal upper Omega Subscript left-parenthesis negative 1 right-parenthesis Sub Superscript k Subscript Baseline reverse-solidus bf upper Q left-parenthesis normal upper Pi right-parenthesis comma one half plus k critical comma">
  <mml:semantics>
    <mml:mrow>
      <mml:mi>L</mml:mi>
      <mml:mstyle scriptlevel="0">
        <mml:mrow class="MJX-TeXAtom-ORD">
          <mml:mo maxsize="1.623em" minsize="1.623em">(</mml:mo>
        </mml:mrow>
      </mml:mstyle>
      <mml:mfrac>
        <mml:mn>1</mml:mn>
        <mml:mn>2</mml:mn>
      </mml:mfrac>
      <mml:mo>+</mml:mo>
      <mml:mi>k</mml:mi>
      <mml:mo>,</mml:mo>
      <mml:mi mathvariant="normal">Π<!-- Π --></mml:mi>
      <mml:mstyle scriptlevel="0">
        <mml:mrow class="MJX-TeXAtom-ORD">
          <mml:mo maxsize="1.623em" minsize="1.623em">)</mml:mo>
        </mml:mrow>
      </mml:mstyle>
      <mml:mspace width="thickmathspace" />
      <mml:mo>∈<!-- ∈ --></mml:mo>
      <mml:mspace width="thickmathspace" />
      <mml:mo stretchy="false">(</mml:mo>
      <mml:mn>2</mml:mn>
      <mml:mi>π<!-- π --></mml:mi>
      <mml:mi>i</mml:mi>
      <mml:msup>
        <mml:mo stretchy="false">)</mml:mo>
        <mml:mrow class="MJX-TeXAtom-ORD">
          <mml:mi>d</mml:mi>
          <mml:mo>⋅<!-- ⋅ --></mml:mo>
          <mml:mi>k</mml:mi>
        </mml:mrow>
      </mml:msup>
      <mml:msub>
        <mml:mi mathvariant="normal">Ω<!-- Ω --></mml:mi>
        <mml:mrow class="MJX-TeXAtom-ORD">
          <mml:mo stretchy="false">(</mml:mo>
          <mml:mo>−<!-- − --></mml:mo>
          <mml:mn>1</mml:mn>
          <mml:msup>
            <mml:mo stretchy="false">)</mml:mo>
            <mml:mi>k</mml:mi>
          </mml:msup>
        </mml:mrow>
      </mml:msub>
      <mml:mrow class="MJX-TeXAtom-ORD">
        <mml:mtext>\bf Q</mml:mtext>
      </mml:mrow>
      <mml:mo stretchy="false">(</mml:mo>
      <mml:mi mathvariant="normal">Π<!-- Π --></mml:mi>
      <mml:mo stretchy="false">)</mml:mo>
      <mml:mo>,</mml:mo>
      <mml:mspace width="1em" />
      <mml:mfrac>
        <mml:mn>1</mml:mn>
        <mml:mn>2</mml:mn>
      </mml:mfrac>
      <mml:mo>+</mml:mo>
      <mml:mi>k</mml:mi>
      <mml:mspace width="thickmathspace" />
      <mml:mtext>critical</mml:mtext>
      <mml:mo>,</mml:mo>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">\begin{equation*} L\Big (\frac {1}{2}+k,\Pi \Big )\;\in \;(2\pi i)^{d\cdot k}\Omega _{(-1)^k}\textrm {\bf Q}(\Pi ),\quad \frac {1}{2}+k\;\text {critical}, \end{equation*}</mml:annotation>
  </mml:semantics>
</mml:math>
</disp-formula>
 for certain automorphic representations <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Pi">
  <mml:semantics>
    <mml:mi mathvariant="normal">Π<!-- Π --></mml:mi>
    <mml:annotation encoding="application/x-tex">\Pi</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula> of a reductive group <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G period">
  <mml:semantics>
    <mml:mrow>
      <mml:mi>G</mml:mi>
      <mml:mo>.</mml:mo>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">G.</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula> In this paper we discuss the case <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G equals normal upper G normal upper L left-parenthesis n plus 1 right-parenthesis times normal upper G normal upper L left-parenthesis n right-parenthesis period">
  <mml:semantics>
    <mml:mrow>
      <mml:mi>G</mml:mi>
      <mml:mo>=</mml:mo>
      <mml:mrow class="MJX-TeXAtom-ORD">
        <mml:mi mathvariant="normal">G</mml:mi>
        <mml:mi mathvariant="normal">L</mml:mi>
      </mml:mrow>
      <mml:mo stretchy="false">(</mml:mo>
      <mml:mi>n</mml:mi>
      <mml:mo>+</mml:mo>
      <mml:mn>1</mml:mn>
      <mml:mo stretchy="false">)</mml:mo>
      <mml:mo>×<!-- × --></mml:mo>
      <mml:mrow class="MJX-TeXAtom-ORD">
        <mml:mi mathvariant="normal">G</mml:mi>
        <mml:mi mathvariant="normal">L</mml:mi>
      </mml:mrow>
      <mml:mo stretchy="false">(</mml:mo>
      <mml:mi>n</mml:mi>
      <mml:mo stretchy="false">)</mml:mo>
      <mml:mo>.</mml:mo>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">G=\mathrm {GL}(n+1)\times \mathrm {GL}(n).</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula> The case <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G equals normal upper G normal upper L left-parenthesis 2 n right-parenthesis">
  <mml:semantics>
    <mml:mrow>
      <mml:mi>G</mml:mi>
      <mml:mo>=</mml:mo>
      <mml:mrow class="MJX-TeXAtom-ORD">
        <mml:mi mathvariant="normal">G</mml:mi>
        <mml:mi mathvariant="normal">L</mml:mi>
      </mml:mrow>
      <mml:mo stretchy="false">(</mml:mo>
      <mml:mn>2</mml:mn>
      <mml:mi>n</mml:mi>
      <mml:mo stretchy="false">)</mml:mo>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">G=\mathrm {GL}(2n)</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula> is discussed in part two. Our method is representation theoretic and relies on the author’s recent results on global rational structures on automorphic representations. We show that the above period relations are intimately related to the field of definition of the global representation <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Pi">
  <mml:semantics>
    <mml:mi mathvariant="normal">Π<!-- Π --></mml:mi>
    <mml:annotation encoding="application/x-tex">\Pi</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula> under consideration. The new period relations we prove are in accordance with Deligne’s Conjecture on special values of <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L">
  <mml:semantics>
    <mml:mi>L</mml:mi>
    <mml:annotation encoding="application/x-tex">L</mml:annotation>
  </mml:semantics>
</mml:math>
</inline-formula>-functions, and the author expects this method to apply to other cases as well.</p>}},
  author       = {{Januszewski, Fabian}},
  issn         = {{0002-9947}},
  journal      = {{Transactions of the American Mathematical Society}},
  keywords     = {{Applied Mathematics, General Mathematics}},
  number       = {{9}},
  pages        = {{6547--6580}},
  publisher    = {{American Mathematical Society (AMS)}},
  title        = {{{On period relations for automorphic 𝐿-functions I}}},
  doi          = {{10.1090/tran/7527}},
  volume       = {{371}},
  year         = {{2018}},
}

@article{48321,
  author       = {{Wessel, Lena and Erath, Kirstin}},
  issn         = {{1863-9690}},
  journal      = {{ZDM}},
  keywords     = {{General Mathematics, Education}},
  number       = {{6}},
  pages        = {{1053--1064}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Theoretical frameworks for designing and analyzing language-responsive mathematics teaching–learning arrangements}}},
  doi          = {{10.1007/s11858-018-0980-y}},
  volume       = {{50}},
  year         = {{2018}},
}

@inproceedings{8575,
  abstract     = {{The transition from high school to university mathematics has proven to be difficult for many students but especially for pre-service secondary teachers. To support these students at mastering this transition, various universities have introduced support measures of various kinds. The WiGeMath project developed a taxonomy that makes it possible to describe and compare these measures concerning their goals as well as their frame characteristics. We will exemplify the use of the taxonomy in the description of one specific innovative measure that was part of the WiGeMath evaluations. Moreover, we will present first results concerning the goal-fulfilment of this measure concerning affective characteristics of the student cohort and their predominant beliefs.}},
  author       = {{Kuklinski, Christiane and Leis, Elena and Liebendörfer, Michael and Hochmuth, Reinhard and Biehler, Rolf and Lankeit, Elisa and Neuhaus, Silke and Schaper, Niclas and Schürmann, Mirko}},
  booktitle    = {{Proceedings of the Second Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2018, 5-7 April 2018)}},
  editor       = {{Durand-Guerrier, V. and Hochmuth, R. and Goodchild, S. and Hogstad, N.M.}},
  keywords     = {{Beliefs., Motivational developments, Novel approaches to teaching, Teacher education, Transition to and across university mathematics}},
  pages        = {{527--536}},
  publisher    = {{INDRUM Network, University of Agder}},
  title        = {{{Evaluating Innovative Measures in University Mathematics – The Case of Affective Outcomes in a Lecture focused on Problem-Solving}}},
  year         = {{2018}},
}

@article{37661,
  author       = {{Rösler, Margit and Voit, Michael}},
  issn         = {{0022-2526}},
  journal      = {{Studies in Applied Mathematics}},
  keywords     = {{Applied Mathematics}},
  number       = {{4}},
  pages        = {{474--500}},
  publisher    = {{Wiley}},
  title        = {{{Beta Distributions and Sonine Integrals for Bessel Functions on Symmetric Cones}}},
  doi          = {{10.1111/sapm.12217}},
  volume       = {{141}},
  year         = {{2018}},
}

@article{40050,
  author       = {{Baeumer, Boris and Luks, Tomasz and Meerschaert, Mark M.}},
  issn         = {{0025-584X}},
  journal      = {{Mathematische Nachrichten}},
  keywords     = {{General Mathematics}},
  number       = {{17-18}},
  pages        = {{2516--2535}},
  publisher    = {{Wiley}},
  title        = {{{Space‐time fractional Dirichlet problems}}},
  doi          = {{10.1002/mana.201700111}},
  volume       = {{291}},
  year         = {{2018}},
}

@article{34843,
  abstract     = {{A polynomial time algorithm to find generators of the lattice of all subfields of a given number field was given in van Hoeij et al. (2013).

This article reports on a massive speedup of this algorithm. This is primary achieved by our new concept of Galois-generating subfields. In general this is a very small set of subfields that determine all other subfields in a group-theoretic way. We compute them by targeted calls to the method from van Hoeij et al. (2013). For an early termination of these calls, we give a list of criteria that imply that further calls will not result in additional subfields.

Finally, we explain how we use subfields to get a good starting group for the computation of Galois groups.}},
  author       = {{Elsenhans, Andreas-Stephan and Klüners, Jürgen}},
  issn         = {{0747-7171}},
  journal      = {{Journal of Symbolic Computation}},
  keywords     = {{Computational Mathematics, Algebra and Number Theory}},
  pages        = {{1--20}},
  publisher    = {{Elsevier BV}},
  title        = {{{Computing subfields of number fields and applications to Galois group computations}}},
  doi          = {{10.1016/j.jsc.2018.04.013}},
  volume       = {{93}},
  year         = {{2018}},
}

@article{34663,
  author       = {{Black, Tobias}},
  issn         = {{1553-524X}},
  journal      = {{Discrete &amp; Continuous Dynamical Systems - B}},
  keywords     = {{Applied Mathematics, Discrete Mathematics and Combinatorics}},
  number       = {{4}},
  pages        = {{1253--1272}},
  publisher    = {{American Institute of Mathematical Sciences (AIMS)}},
  title        = {{{Global existence and asymptotic stability in a competitive two-species chemotaxis system with two signals}}},
  doi          = {{10.3934/dcdsb.2017061}},
  volume       = {{22}},
  year         = {{2017}},
}

@article{34665,
  author       = {{Black, Tobias and Lankeit, Johannes and Mizukami, Masaaki}},
  issn         = {{1424-3199}},
  journal      = {{Journal of Evolution Equations}},
  keywords     = {{Mathematics (miscellaneous)}},
  number       = {{2}},
  pages        = {{561--581}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Singular sensitivity in a Keller–Segel-fluid system}}},
  doi          = {{10.1007/s00028-017-0411-5}},
  volume       = {{18}},
  year         = {{2017}},
}

@article{31272,
  author       = {{Harris, Benjamin and Weich, Tobias}},
  issn         = {{0001-8708}},
  journal      = {{Advances in Mathematics}},
  keywords     = {{General Mathematics}},
  pages        = {{176--236}},
  publisher    = {{Elsevier BV}},
  title        = {{{Wave front sets of reductive Lie group representations III}}},
  doi          = {{10.1016/j.aim.2017.03.025}},
  volume       = {{313}},
  year         = {{2017}},
}

@article{34631,
  author       = {{Hesse, Kerstin and Sloan, Ian H. and Womersley, Robert S.}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{3}},
  pages        = {{579--605}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Radial basis function approximation of noisy scattered data on the sphere}}},
  doi          = {{10.1007/s00211-017-0886-6}},
  volume       = {{137}},
  year         = {{2017}},
}

@article{31267,
  author       = {{Guillarmou, Colin and Hilgert, Joachim and Weich, Tobias}},
  issn         = {{0025-5831}},
  journal      = {{Mathematische Annalen}},
  keywords     = {{General Mathematics}},
  number       = {{3-4}},
  pages        = {{1231--1275}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Classical and quantum resonances for hyperbolic surfaces}}},
  doi          = {{10.1007/s00208-017-1576-5}},
  volume       = {{370}},
  year         = {{2017}},
}

@article{45941,
  author       = {{Kovács, Balázs and Li, Buyang and Lubich, Christian and Power Guerra, Christian A.}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{3}},
  pages        = {{643--689}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Convergence of finite elements on an evolving surface driven by diffusion on the surface}}},
  doi          = {{10.1007/s00211-017-0888-4}},
  volume       = {{137}},
  year         = {{2017}},
}

@article{45942,
  author       = {{Kovács, Balázs and Lubich, Christian}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{2}},
  pages        = {{365--388}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type}}},
  doi          = {{10.1007/s00211-017-0909-3}},
  volume       = {{138}},
  year         = {{2017}},
}

@article{45940,
  author       = {{Kovács, Balázs and Lubich, Christian}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{1}},
  pages        = {{91--117}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations}}},
  doi          = {{10.1007/s00211-017-0868-8}},
  volume       = {{137}},
  year         = {{2017}},
}

@article{45946,
  author       = {{Kovács, Balázs and Power Guerra, Christian Andreas}},
  issn         = {{0749-159X}},
  journal      = {{Numerical Methods for Partial Differential Equations}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Numerical Analysis, Analysis}},
  number       = {{2}},
  pages        = {{518--554}},
  publisher    = {{Wiley}},
  title        = {{{Maximum norm stability and error estimates for the evolving surface finite element method}}},
  doi          = {{10.1002/num.22212}},
  volume       = {{34}},
  year         = {{2017}},
}