@article{GreefrathSillerKlocketal.2022, author = {Greefrath, Gilbert and Siller, Hans-Stefan and Klock, Heiner and Wess, Raphael}, title = {Pre-service secondary teachers' pedagogical content knowledge for the teaching of mathematical modelling}, series = {Educational Studies in Mathematics}, volume = {109}, journal = {Educational Studies in Mathematics}, number = {2}, issn = {0013-1954}, doi = {10.1007/s10649-021-10038-z}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-308259}, pages = {383-407}, year = {2022}, abstract = {The article deals with the pedagogical content knowledge of mathematical modelling as part of the professional competence of pre-service teachers. With the help of a test developed for this purpose from a conceptual model, we examine whether this pedagogical content knowledge can be promoted in its different facets—especially knowledge about modelling tasks and about interventions—by suitable university seminars. For this purpose, the test was administered to three groups in a seminar for the teaching of mathematical modelling: (1) to those respondents who created their own modelling tasks for use with students, (2) to those trained to intervene in mathematical modelling processes, and (3) participating students who are not required to address mathematical modelling. The findings of the study—based on variance analysis—indicate that certain facets (knowledge of modelling tasks, modelling processes, and interventions) have increased significantly in both experimental groups but to varying degrees. By contrast, pre-service teachers in the control group demonstrated no significant change to their level of pedagogical content knowledge.}, language = {en} } @article{KanzowLechner2021, author = {Kanzow, Christian and Lechner, Theresa}, title = {Globalized inexact proximal Newton-type methods for nonconvex composite functions}, series = {Computational Optimization and Applications}, volume = {78}, journal = {Computational Optimization and Applications}, number = {2}, doi = {10.1007/s10589-020-00243-6}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-283715}, pages = {377-410}, year = {2021}, abstract = {Optimization problems with composite functions consist of an objective function which is the sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited by the class of proximal gradient methods and some of their generalizations like proximal Newton and quasi-Newton methods. The current literature on these classes of methods almost exclusively considers the case where also the smooth term is convex. Here we present a globalized proximal Newton-type method which allows the smooth term to be nonconvex. The method is shown to have nice global and local convergence properties, and some numerical results indicate that this method is very promising also from a practical point of view.}, language = {en} } @article{DippellEspositoWaldmann2022, author = {Dippell, Marvin and Esposito, Chiara and Waldmann, Stefan}, title = {Deformation and Hochschild cohomology of coisotropic algebras}, series = {Annali di Matematica Pura ed Applicata}, volume = {201}, journal = {Annali di Matematica Pura ed Applicata}, number = {3}, doi = {10.1007/s10231-021-01158-7}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-329069}, pages = {1295-1323}, year = {2022}, abstract = {Coisotropic algebras consist of triples of algebras for which a reduction can be defined and unify in a very algebraic fashion coisotropic reduction in several settings. In this paper, we study the theory of (formal) deformation of coisotropic algebras showing that deformations are governed by suitable coisotropic DGLAs. We define a deformation functor and prove that it commutes with reduction. Finally, we study the obstructions to existence and uniqueness of coisotropic algebras and present some geometric examples.}, language = {en} } @article{CampanaCiaramellaBorzi2021, author = {Campana, Francesca Cal{\`a} and Ciaramella, Gabriele and Borz{\`i}, Alfio}, title = {Nash Equilibria and Bargaining Solutions of Differential Bilinear Games}, series = {Dynamic Games and Applications}, volume = {11}, journal = {Dynamic Games and Applications}, number = {1}, doi = {10.1007/s13235-020-00351-2}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-283897}, pages = {1-28}, year = {2021}, abstract = {This paper is devoted to a theoretical and numerical investigation of Nash equilibria and Nash bargaining problems governed by bilinear (input-affine) differential models. These systems with a bilinear state-control structure arise in many applications in, e.g., biology, economics, physics, where competition between different species, agents, and forces needs to be modelled. For this purpose, the concept of Nash equilibria (NE) appears appropriate, and the building blocks of the resulting differential Nash games are different control functions associated with different players that pursue different non-cooperative objectives. In this framework, existence of Nash equilibria is proved and computed with a semi-smooth Newton scheme combined with a relaxation method. Further, a related Nash bargaining (NB) problem is discussed. This aims at determining an improvement of all players' objectives with respect to the Nash equilibria. Results of numerical experiments successfully demonstrate the effectiveness of the proposed NE and NB computational framework.}, language = {en} } @article{GerberQuarderGreefrathetal.2023, author = {Gerber, Sebastian and Quarder, Jascha and Greefrath, Gilbert and Siller, Hans-Stefan}, title = {Promoting adaptive intervention competence for teaching simulations and mathematical modelling with digital tools}, series = {Frontiers in Education}, volume = {8}, journal = {Frontiers in Education}, issn = {2504-284X}, doi = {10.3389/feduc.2023.1141063}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-323701}, year = {2023}, abstract = {Providing adaptive, independence-preserving and theory-guided support to students in dealing with real-world problems in mathematics lessons is a major challenge for teachers in their professional practice. This paper examines this challenge in the context of simulations and mathematical modelling with digital tools: in addition to mathematical difficulties when autonomously working out individual solutions, students may also experience challenges when using digital tools. These challenges need to be closely examined and diagnosed, and might - if necessary - have to be overcome by intervention in such a way that the students can subsequently continue working independently. Thus, if a difficulty arises in the working process, two knowledge dimensions are necessary in order to provide adapted support to students. For teaching simulations and mathematical modelling with digital tools, more specifically, these knowledge dimensions are: pedagogical content knowledge about simulation and modelling processes supported by digital tools (this includes knowledge about phases and difficulties in the working process) and pedagogical content knowledge about interventions during the mentioned processes (focussing on characteristics of suitable interventions as well as their implementation and effects on the students' working process). The two knowledge dimensions represent cognitive dispositions as the basis for the conceptualisation and operationalisation of a so-called adaptive intervention competence for teaching simulations and mathematical modelling with digital tools. In our article, we present a domain-specific process model and distinguish different types of teacher interventions. Then we describe the design and content of a university course at two German universities aiming to promote this domain-specific professional adaptive intervention competence, among others. In a study using a quasi-experimental pre-post design (N = 146), we confirm that the structure of cognitive dispositions of adaptive intervention competence for teaching simulations and mathematical modelling with digital tools can be described empirically by a two-dimensional model. In addition, the effectiveness of the course is examined and confirmed quantitatively. Finally, the results are discussed, especially against the background of the sample and the research design, and conclusions are derived for possibilities of promoting professional adaptive intervention competence in university courses.}, language = {en} } @article{DashkovskiyKapustyanSchmid2020, author = {Dashkovskiy, Sergey and Kapustyan, Oleksiy and Schmid, Jochen}, title = {A local input-to-state stability result w.r.t. attractors of nonlinear reaction-diffusion equations}, series = {Mathematics of Control, Signals, and Systems}, volume = {32}, journal = {Mathematics of Control, Signals, and Systems}, number = {3}, doi = {10.1007/s00498-020-00256-w}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-281099}, pages = {309-326}, year = {2020}, abstract = {We establish the local input-to-state stability of a large class of disturbed nonlinear reaction-diffusion equations w.r.t. the global attractor of the respective undisturbed system.}, language = {en} } @article{HeinsRothWaldmann2023, author = {Heins, Michael and Roth, Oliver and Waldmann, Stefan}, title = {Convergent star products on cotangent bundles of Lie groups}, series = {Mathematische Annalen}, volume = {386}, journal = {Mathematische Annalen}, number = {1-2}, issn = {0025-5831}, doi = {10.1007/s00208-022-02384-x}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324324}, pages = {151-206}, year = {2023}, abstract = {For a connected real Lie group G we consider the canonical standard-ordered star product arising from the canonical global symbol calculus based on the half-commutator connection of G. This star product trivially converges on polynomial functions on T\(^*\)G thanks to its homogeneity. We define a nuclear Fr{\´e}chet algebra of certain analytic functions on T\(^*\)G, for which the standard-ordered star product is shown to be a well-defined continuous multiplication, depending holomorphically on the deformation parameter \(\hbar\). This nuclear Fr{\´e}chet algebra is realized as the completed (projective) tensor product of a nuclear Fr{\´e}chet algebra of entire functions on G with an appropriate nuclear Fr{\´e}chet algebra of functions on \({\mathfrak {g}}^*\). The passage to the Weyl-ordered star product, i.e. the Gutt star product on T\(^*\)G, is shown to preserve this function space, yielding the continuity of the Gutt star product with holomorphic dependence on \(\hbar\).}, language = {en} } @article{KourouZarvalis2022, author = {Kourou, Maria and Zarvalis, Konstantinos}, title = {Compact sets in petals and their backward orbits under semigroups of holomorphic functions}, series = {Potential Analysis}, volume = {59}, journal = {Potential Analysis}, number = {4}, issn = {0926-2601}, doi = {10.1007/s11118-022-10036-7}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324368}, pages = {1913-1939}, year = {2022}, abstract = {Let (ϕ\(_t\))\(_{t≥0}\) be a semigroup of holomorphic functions in the unit disk \(\mathbb {D}\) and K a compact subset of \(\mathbb {D}\). We investigate the conditions under which the backward orbit of K under the semigroup exists. Subsequently, the geometric characteristics, as well as, potential theoretic quantities for the backward orbit of K are examined. More specifically, results are obtained concerning the asymptotic behavior of its hyperbolic area and diameter, the harmonic measure and the capacity of the condenser that K forms with the unit disk.}, language = {en} } @article{JotzMehtaPapantonis2023, author = {Jotz, M. and Mehta, R. A. and Papantonis, T.}, title = {Modules and representations up to homotopy of Lie n-algebroids}, series = {Journal of Homotopy and Related Structures}, volume = {18}, journal = {Journal of Homotopy and Related Structures}, number = {1}, issn = {2193-8407}, doi = {10.1007/s40062-022-00322-x}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324333}, pages = {23-70}, year = {2023}, abstract = {This paper studies differential graded modules and representations up to homotopy of Lie n-algebroids, for general \(n\in {\mathbb {N}}\). The adjoint and coadjoint modules are described, and the corresponding split versions of the adjoint and coadjoint representations up to homotopy are explained. In particular, the case of Lie 2-algebroids is analysed in detail. The compatibility of a Poisson bracket with the homological vector field of a Lie n-algebroid is shown to be equivalent to a morphism from the coadjoint module to the adjoint module, leading to an alternative characterisation of non-degeneracy of higher Poisson structures. Moreover, the Weil algebra of a Lie n-algebroid is computed explicitly in terms of splittings, and representations up to homotopy of Lie n-algebroids are used to encode decomposed VB-Lie n-algebroid structures on double vector bundles.}, language = {en} } @article{SteudingTongsomporn2023, author = {Steuding, J{\"o}rn and Tongsomporn, Janyarak}, title = {On the order of growth of Lerch zeta functions}, series = {Mathematics}, volume = {11}, journal = {Mathematics}, number = {3}, issn = {2227-7390}, doi = {10.3390/math11030723}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-303981}, year = {2023}, abstract = {We extend Bourgain's bound for the order of growth of the Riemann zeta function on the critical line to Lerch zeta functions. More precisely, we prove L(λ, α, 1/2 + it) ≪ t\(^{13/84+ϵ}\) as t → ∞. For both, the Riemann zeta function as well as for the more general Lerch zeta function, it is conjectured that the right-hand side can be replaced by t\(^ϵ\) (which is the so-called Lindel{\"o}f hypothesis). The growth of an analytic function is closely related to the distribution of its zeros.}, language = {en} }