@article{37474,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>Due to the COVID-19 crisis, many courses have been offered digitally. Using data from n = 1,173 business students participating in a preparatory mathematics course at a German university that covered the same content as in 2018, 2019 and 2020, we examine how students’ participation and the effect of the preparatory course changed. The data show that the participation rate has fallen slightly, but students’ participation is rather similar to preceding years. Interestingly, students have participated more intensively. There are clear signs of dishonesty in the self-test (use of a calculator) and significant changes in predictors of performance. In particular, the effect of students’ engagement in the course on their performance substantially increased. Further, we found a gender gap in performance affecting women. Finally, the data show that digital courses can be as effective as on-campus courses.</jats:p>}},
  author       = {{Büchele, Stefan and Liebendörfer, Michael and Lankeit, Elisa}},
  issn         = {{0268-3679}},
  journal      = {{Teaching Mathematics and its Applications: An International Journal of the IMA}},
  keywords     = {{Education, General Mathematics}},
  number       = {{4}},
  pages        = {{478--496}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Increasing the effect of a remedial mathematics course by switching to an online format during the COVID-19 crisis: evidence from a German university}}},
  doi          = {{10.1093/teamat/hrab013}},
  volume       = {{40}},
  year         = {{2021}},
}

@article{37473,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>We investigated university students’ study of mathematics in the digital setting context of the COVID-19 pandemic. We gathered data from a survey of 89 students enrolled in a ‘Linear Algebra 1’ course including affective variables, learning strategies, social relatedness and resources considered useful. The results indicate students’ high effort and self-regulation and a high variation in affective characteristics and social relatedness. All the traditional aspects of mathematics teaching (lecture, tutorials and lecture notes) were rated as particularly useful. In addition, the videos from external resources were rated as equally useful as the teaching team’s videos. In contrast, traditional literature such as textbooks was rarely considered useful. The most useful resource rated was communication with peers, underlining the important role of social learning despite fully digital learning environments. Finally, a cluster analysis based on students’ rated usefulness of the resources led to three different user-types. Whereas the ‘digitals’ find the external digital resources very useful (videos, webpages, etc.), the ‘traditionalists’ rate the digitalized traditional resources best (lecture, tutorials, etc.). All resources receive uniformly good ratings from a third group (‘all resource users’). We reflect on our findings in light of the pandemic and describe directions for future research.</jats:p>}},
  author       = {{Kempen, Leander and Liebendörfer, Michael}},
  issn         = {{0268-3679}},
  journal      = {{Teaching Mathematics and its Applications: An International Journal of the IMA}},
  keywords     = {{Education, General Mathematics}},
  number       = {{4}},
  pages        = {{436--454}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{University students’ fully digital study of mathematics: an identification of student-groups via their resources usage and a characterization by personal and affective characteristics}}},
  doi          = {{10.1093/teamat/hrab020}},
  volume       = {{40}},
  year         = {{2021}},
}

@article{37649,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>Let $V_k$ denote Dunkl’s intertwining operator associated with some root system $R$ and multiplicity $k$. For two multiplicities $k, k^{\prime }$ on $R$, we study the intertwiner $V_{k^{\prime },k} = V_{k^{\prime }}\circ V_k^{-1}$ between Dunkl operators with multiplicities $k$ and $k^{\prime }.$ It has been a long-standing conjecture that $V_{k^{\prime },k}$ is positive if $k^{\prime } \geq k \geq 0.$ We disprove this conjecture by constructing counterexamples for root system $B_n$. This matter is closely related to the existence of Sonine-type integral representations between Dunkl kernels and Bessel functions with different multiplicities. In our examples, such Sonine formulas do not exist. As a consequence, we obtain necessary conditions on Sonine formulas for Heckman–Opdam hypergeometric functions of type $BC_n$ and conditions for positive branching coefficients between multivariable Jacobi polynomials.</jats:p>}},
  author       = {{Rösler, Margit and Voit, Michael}},
  issn         = {{1073-7928}},
  journal      = {{International Mathematics Research Notices}},
  keywords     = {{General Mathematics}},
  number       = {{17}},
  pages        = {{13202--13230}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Sonine Formulas and Intertwining Operators in Dunkl Theory}}},
  doi          = {{10.1093/imrn/rnz313}},
  volume       = {{2021}},
  year         = {{2021}},
}

@article{37659,
  author       = {{Rösler, Margit and Voit, Michael}},
  issn         = {{0002-9939}},
  journal      = {{Proceedings of the American Mathematical Society}},
  keywords     = {{Applied Mathematics, General Mathematics}},
  number       = {{3}},
  pages        = {{1151--1163}},
  publisher    = {{American Mathematical Society (AMS)}},
  title        = {{{Positive intertwiners for Bessel functions of type B}}},
  doi          = {{10.1090/proc/15312}},
  volume       = {{149}},
  year         = {{2021}},
}

@article{34840,
  abstract     = {{In this paper we obtain a complete list of imaginary n-quadratic fields with class groups of exponent 3 and 5 under ERH for every positive integer n where an n-quadratic field is a number field of degree 2ⁿ represented as the composite of n quadratic fields. }},
  author       = {{Klüners, Jürgen and Komatsu, Toru}},
  issn         = {{0025-5718}},
  journal      = {{Mathematics of Computation}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Algebra and Number Theory}},
  number       = {{329}},
  pages        = {{1483--1497}},
  publisher    = {{American Mathematical Society (AMS)}},
  title        = {{{Imaginary multiquadratic number fields with class group of exponent $3$ and $5$}}},
  doi          = {{10.1090/mcom/3609}},
  volume       = {{90}},
  year         = {{2021}},
}

@article{34912,
  abstract     = {{Let E be an ordinary elliptic curve over a finite field and g be a positive integer. Under some technical assumptions, we give an algorithm to span the isomorphism classes of principally polarized abelian varieties in the isogeny class of E⁹ . The varieties are first described as hermitian lattices over (not necessarily maximal) quadratic orders and then geometrically in terms of their algebraic theta null point. We also show how to algebraically compute Siegel modular forms of even weight given as polynomials in the theta constants by a careful choice of an affine lift of the theta null point. We then use these results to give an algebraic computation of Serre’s obstruction for principally polarized abelian threefolds isogenous to E³ and of the Igusa modular form in dimension 4. We illustrate our algorithms with examples of curves with many rational points over finite fields. }},
  author       = {{Kirschmer, Markus and Narbonne, Fabien and Ritzenthaler, Christophe and Robert, Damien}},
  issn         = {{0025-5718}},
  journal      = {{Mathematics of Computation}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Algebra and Number Theory}},
  number       = {{333}},
  pages        = {{401--449}},
  publisher    = {{American Mathematical Society (AMS)}},
  title        = {{{Spanning the isogeny class of a power of an elliptic curve}}},
  doi          = {{10.1090/mcom/3672}},
  volume       = {{91}},
  year         = {{2021}},
}

@article{34673,
  author       = {{Black, Tobias and Fuest, Mario and Lankeit, Johannes}},
  issn         = {{0044-2275}},
  journal      = {{Zeitschrift für angewandte Mathematik und Physik}},
  keywords     = {{Applied Mathematics, General Physics and Astronomy, General Mathematics}},
  number       = {{3}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems}}},
  doi          = {{10.1007/s00033-021-01524-8}},
  volume       = {{72}},
  year         = {{2021}},
}

@article{34675,
  author       = {{Black, Tobias and Wu, Chunyan}},
  issn         = {{0044-2275}},
  journal      = {{Zeitschrift für angewandte Mathematik und Physik}},
  keywords     = {{Applied Mathematics, General Physics and Astronomy, General Mathematics}},
  number       = {{4}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation}}},
  doi          = {{10.1007/s00033-021-01565-z}},
  volume       = {{72}},
  year         = {{2021}},
}

@article{35952,
  author       = {{Daniel-Söltenfuß, Desiree and Schwabl, Franziska}},
  issn         = {{0172-2875}},
  journal      = {{Zeitschrift für Berufs- und Wirtschaftspädagogik}},
  keywords     = {{Applied Mathematics, General Mathematics}},
  number       = {{3}},
  pages        = {{431--460}},
  publisher    = {{Wissenschaftliche Verlagsgesellschaft mbH}},
  title        = {{{Selbstreguliertes Lernen im berufsschulischen Übergangssystem}}},
  doi          = {{10.25162/zbw-2021-0019}},
  volume       = {{117}},
  year         = {{2021}},
}

@article{46135,
  author       = {{Schall, Johannes and Deconinck, Marielle and Bart, Nikolai and Florian, Matthias and Helversen, Martin and Dangel, Christian and Schmidt, Ronny and Bremer, Lucas and Bopp, Frederik and Hüllen, Isabell and Gies, Christopher and Reuter, Dirk and Wieck, Andreas D. and Rodt, Sven and Finley, Jonathan J. and Jahnke, Frank and Ludwig, Arne and Reitzenstein, Stephan}},
  issn         = {{2511-9044}},
  journal      = {{Advanced Quantum Technologies}},
  keywords     = {{Electrical and Electronic Engineering, Computational Theory and Mathematics, Condensed Matter Physics, Mathematical Physics, Nuclear and High Energy Physics, Electronic, Optical and Magnetic Materials, Statistical and Nonlinear Physics}},
  number       = {{6}},
  publisher    = {{Wiley}},
  title        = {{{Bright Electrically Controllable Quantum‐Dot‐Molecule Devices Fabricated by In Situ Electron‐Beam Lithography}}},
  doi          = {{10.1002/qute.202100002}},
  volume       = {{4}},
  year         = {{2021}},
}

@article{40250,
  author       = {{Jain, Mitisha and Gerstmann, Uwe and Schmidt, Wolf Gero and Aldahhak, Hazem}},
  issn         = {{0192-8651}},
  journal      = {{Journal of Computational Chemistry}},
  keywords     = {{Computational Mathematics, General Chemistry}},
  number       = {{6}},
  pages        = {{413--420}},
  publisher    = {{Wiley}},
  title        = {{{Adatom mediated adsorption of            <scp>N‐heterocyclic</scp>            carbenes on Cu(111) and Au(111)}}},
  doi          = {{10.1002/jcc.26801}},
  volume       = {{43}},
  year         = {{2021}},
}

@article{53333,
  author       = {{Winkler, Michael}},
  issn         = {{2036-2145}},
  journal      = {{ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE}},
  keywords     = {{Mathematics (miscellaneous), Theoretical Computer Science}},
  pages        = {{141--172}},
  publisher    = {{Scuola Normale Superiore - Edizioni della Normale}},
  title        = {{{$L^1$ solutions to parabolic Keller-Segel systems involving arbitrary superlinear degradation}}},
  doi          = {{10.2422/2036-2145.202005_016}},
  year         = {{2021}},
}

@article{33262,
  abstract     = {{The authors of Berg et al. [J. Algebra 348 (2011) 446–461] provide an algorithm for finding a complete system of primitive orthogonal idempotents for CM, where M is any finite R-trivial monoid. Their method relies on a technical result stating that R-trivial monoid are equivalent to so-called weakly ordered monoids. We provide an alternative algorithm, based only on the simple observation that an R-trivial monoid may be realized by upper triangular matrices. This approach is inspired by results in the field of coupled cell network dynamical systems, where L-trivial monoids (the opposite notion) correspond to so-called feed-forward networks. We first show that our algorithm works for ZM, after which we prove that it also works for RM where R is an arbitrary ring with a known complete system of primitive orthogonal idempotents. In particular, our algorithm works if R is any field. In this respect our result constitutes a considerable generalization of the results in Berg et al. [J. Algebra 348 (2011) 446–461]. Moreover, the system of idempotents for RM is obtained from the one our algorithm yields for ZM in a straightforward manner. In other words, for any finite R-trivial monoid M our algorithm only has to be performed for ZM, after which a system of idempotents follows for any ring with a given system of idempotents.}},
  author       = {{Nijholt, Eddie and Rink, Bob and Schwenker, Sören}},
  issn         = {{0219-4988}},
  journal      = {{Journal of Algebra and Its Applications}},
  keywords     = {{Applied Mathematics, Algebra and Number Theory}},
  number       = {{12}},
  publisher    = {{World Scientific Pub Co Pte Ltd}},
  title        = {{{A new algorithm for computing idempotents of ℛ-trivial monoids}}},
  doi          = {{10.1142/s0219498821502273}},
  volume       = {{20}},
  year         = {{2020}},
}

@article{45954,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>$L^2$ norm error estimates of semi- and full discretizations of wave equations with dynamic boundary conditions, using bulk–surface finite elements and Runge–Kutta methods, are studied. The analysis rests on an abstract formulation and error estimates, via energy techniques, within this abstract setting. Four prototypical linear wave equations with dynamic boundary conditions are analysed, which fit into the abstract framework. For problems with velocity terms or with acoustic boundary conditions we prove surprising results: for such problems the spatial convergence order is shown to be less than 2. These can also be observed in the presented numerical experiments.</jats:p>}},
  author       = {{Hipp, David and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{1}},
  pages        = {{638--728}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates}}},
  doi          = {{10.1093/imanum/drz073}},
  volume       = {{41}},
  year         = {{2020}},
}

@article{45953,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>$L^2$ norm error estimates of semi- and full discretizations of wave equations with dynamic boundary conditions, using bulk–surface finite elements and Runge–Kutta methods, are studied. The analysis rests on an abstract formulation and error estimates, via energy techniques, within this abstract setting. Four prototypical linear wave equations with dynamic boundary conditions are analysed, which fit into the abstract framework. For problems with velocity terms or with acoustic boundary conditions we prove surprising results: for such problems the spatial convergence order is shown to be less than 2. These can also be observed in the presented numerical experiments.</jats:p>}},
  author       = {{Hipp, David and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{1}},
  pages        = {{638--728}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates}}},
  doi          = {{10.1093/imanum/drz073}},
  volume       = {{41}},
  year         = {{2020}},
}

@article{45955,
  author       = {{Akrivis, Georgios and Feischl, Michael and Kovács, Balázs and Lubich, Christian}},
  issn         = {{0025-5718}},
  journal      = {{Mathematics of Computation}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Algebra and Number Theory}},
  number       = {{329}},
  pages        = {{995--1038}},
  publisher    = {{American Mathematical Society (AMS)}},
  title        = {{{Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation}}},
  doi          = {{10.1090/mcom/3597}},
  volume       = {{90}},
  year         = {{2020}},
}

@article{45952,
  author       = {{Kovács, Balázs and Li, Buyang and Lubich, Christian}},
  issn         = {{1463-9963}},
  journal      = {{Interfaces and Free Boundaries}},
  keywords     = {{Applied Mathematics}},
  number       = {{4}},
  pages        = {{443--464}},
  publisher    = {{European Mathematical Society - EMS - Publishing House GmbH}},
  title        = {{{A convergent algorithm for forced mean curvature flow driven by diffusion on the surface}}},
  doi          = {{10.4171/ifb/446}},
  volume       = {{22}},
  year         = {{2020}},
}

@article{35822,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>The derivative concept plays a major role in economics. However, its use in economics is very heterogeneous, sometimes inconsistent, and contradicts students’ prior knowledge from school. This applies in particular to the common economic interpretation of the derivative as the amount of change while increasing the production by one unit. Hence, in calculus courses for economics students, learners should acquire an understanding of the derivative that is mathematically acceptable and connected to their prior knowledge, but which also takes into account its practical use in economics. In this paper we first develop a theoretical model describing such an understanding of the derivative for economics students. We then present an exploratory study investigating the extent to which economics students have such an understanding after their calculus course. The results indicate that many of them might not have acquired this kind of understanding, in particular concerning the common economic interpretation of the derivative. The study furthermore yields possible gaps in students’ understanding and possible misconceptions.</jats:p>}},
  author       = {{Feudel, Frank and Biehler, Rolf}},
  issn         = {{0173-5322}},
  journal      = {{Journal für Mathematik-Didaktik}},
  keywords     = {{Education, General Mathematics}},
  number       = {{1}},
  pages        = {{273--305}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Students’ Understanding of the Derivative Concept in the Context of Mathematics for Economics}}},
  doi          = {{10.1007/s13138-020-00174-z}},
  volume       = {{42}},
  year         = {{2020}},
}

@article{35712,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>Mathematics learning support centres (MLSC) are widely established and evaluated in English-speaking countries (such as the UK, Ireland and Australia). In most of these countries, several national surveys on MLSCs exist. They give an overview of the number of MLSCs as well as their characteristics in these countries. In Germany, there is a lack of studies on MLSCs and the landscape of MLSCs has not been described yet. This article presents basic information concerning counts of MLSCs and their characteristics at universities. Based on a three-step approach of analysing university homepages and additional personal contact via email or phone calls, we gathered typical MLSC features (e.g. staff quantities and qualification, opening and support hours, supported study programmes). We analysed 190 universities from a web-based register on study programmes. In total, we found 61 MLSCs located at 51 German universities. Another 16 support centres were specialized on mathematics didactics, which means they focussed on didactical and methodological support for preservice teacher students and often provided different teaching materials. Thirty-eight centres were located at universities (62.3%) and 23 MLSCs at universities of applied sciences and comparable universities (37.7%). The MLSCs were different in their sizes of staff and opening hours, and both the numbers of staff and the service hours differed greatly. The student groups MLSCs at German universities focus on differ concerning characteristics like study programme or semester. We will provide the main categories describing these groups. We seek to answer research questions concerning the characteristics of MLSCs in Germany and discuss the results compared to international findings. This information is useful for further international collaborative research, for example a standardized international survey. From a national perspective, these findings support networking and collaborations between the MLSCs as well. As some German MLSCs are facing financial cuts, these results might help in gaining additional funding.</jats:p>}},
  author       = {{Schürmann, Mirko and Gildehaus, Lara and Liebendörfer, Michael and Schaper, Niclas and Biehler, Rolf and Hochmuth, Reinhard and Kuklinski, Christiane and Lankeit, Elisa}},
  issn         = {{0268-3679}},
  journal      = {{Teaching Mathematics and its Applications: An International Journal of the IMA}},
  keywords     = {{Education, General Mathematics}},
  number       = {{2}},
  pages        = {{99--113}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Mathematics learning support centres in Germany—an overview}}},
  doi          = {{10.1093/teamat/hraa007}},
  volume       = {{40}},
  year         = {{2020}},
}

@article{33866,
  abstract     = {{<jats:p>Helhmoltz–Kirchhoff equations of motions of vortices of an incompressible fluid in the plane define a dynamics with singularities and this leads to a Zermelo navigation problem describing the ship travel in such a field where the control is the heading angle. Considering one vortex, we define a time minimization problem which can be analyzed with the technics of geometric optimal control combined with numerical simulations, the geometric frame being the extension of Randers metrics in the punctured plane, with rotational symmetry. Candidates as minimizers are parameterized thanks to the Pontryagin Maximum Principle as extremal solutions of a Hamiltonian vector field. We analyze the time minimal solution to transfer the ship between two points where during the transfer the ship can be either in a strong current region in the vicinity of the vortex or in a weak current region. The analysis is based on a micro-local classification of the extremals using mainly the integrability properties of the dynamics due to the rotational symmetry. The discussion is complex and related to the existence of an isolated extremal (Reeb) circle due to the vortex singularity. The explicit computation of cut points where the extremal curves cease to be optimal is given and the spheres are described in the case where at the initial point the current is weak.</jats:p>}},
  author       = {{Bonnard, Bernard and Cots, Olivier and Wembe Moafo, Boris Edgar}},
  issn         = {{1292-8119}},
  journal      = {{ESAIM: Control, Optimisation and Calculus of Variations}},
  keywords     = {{Computational Mathematics, Control and Optimization, Control and Systems Engineering}},
  publisher    = {{EDP Sciences}},
  title        = {{{A Zermelo navigation problem with a vortex singularity}}},
  doi          = {{10.1051/cocv/2020058}},
  volume       = {{27}},
  year         = {{2020}},
}