TY - JOUR AB - In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby ‘modified’ equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the differential equation has a geometric property then the modified equation may share it. In this way, known properties of differential equations can be applied to the approximation. But for partial differential equations, the known modified equations are of higher order, limiting applicability of the theory. Therefore, we study symmetric solutions of discretized partial differential equations that arise from a discrete variational principle. These symmetric solutions obey infinite-dimensional functional equations. We show that these equations admit second-order modified equations which are Hamiltonian and also possess first-order Lagrangians in modified coordinates. The modified equation and its associated structures are computed explicitly for the case of rotating travelling waves in the nonlinear wave equation. AU - McLachlan, Robert I AU - Offen, Christian ID - 19941 IS - 3 JF - Journal of Geometric Mechanics TI - Backward error analysis for variational discretisations of partial differential equations VL - 14 ER - TY - JOUR AB - Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation laws. To predict Hamiltonian dynamics based on discrete trajectory observations, incorporation of prior knowledge about Hamiltonian structure greatly improves predictions. This is typically done by learning the system's Hamiltonian and then integrating the Hamiltonian vector field with a symplectic integrator. For this, however, Hamiltonian data needs to be approximated based on the trajectory observations. Moreover, the numerical integrator introduces an additional discretisation error. In this paper, we show that an inverse modified Hamiltonian structure adapted to the geometric integrator can be learned directly from observations. A separate approximation step for the Hamiltonian data avoided. The inverse modified data compensates for the discretisation error such that the discretisation error is eliminated. The technique is developed for Gaussian Processes. AU - Offen, Christian AU - Ober-Blöbaum, Sina ID - 23382 JF - Chaos: An Interdisciplinary Journal of Nonlinear Science TI - Symplectic integration of learned Hamiltonian systems VL - 32(1) ER - TY - CONF AU - Dröse, Jennifer ID - 40613 T2 - Beiträge zum Mathematikunterricht TI - Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen ER - TY - CONF AU - Graf, Lara Marie AU - Häsel-Weide, Uta AU - Nührenbörger, Marcus AU - Höveler, Karina ID - 47520 T2 - Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik TI - Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen ER - TY - CONF AU - Schwerin, Imke ID - 47519 T2 - Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik TI - Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis ER - TY - CHAP AU - Dellori, Anna AU - Wessel, Lena ED - Karunakaran, S.S. ED - Higgins, A. ID - 48407 T2 - Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education TI - Pre-service Teachers' Professional Development: Relating Abstract Algebra and School Algebra ER - TY - JOUR AU - Wessel, Lena AU - Dröse, Jennifer ID - 48408 JF - mathematik lehren TI - Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten VL - 233 ER - TY - CHAP AU - Wessel, Lena AU - Leuders, Timo ED - Biehler, Rolf ED - Liebendörfer, Michael ED - Gueudet, G. ED - Rasmussen, C. ED - Winslow, C. ID - 46160 SN - 1869-4918 T2 - Practice-Oriented Research in Tertiary Mathematics Education TI - Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Learning of Group Theory ER - TY - JOUR AU - Dellori, Anna AU - Wessel, Lena ID - 48325 JF - Beiträge zum Mathematikunterricht 2022 TI - Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung in der Algebra ER - TY - CHAP AU - Dröse, Jennifer AU - Neugebauer, P. AU - Delucchi Danhier, R. AU - Mertins, B. ED - Kleine, P. ED - Graulich, N. ED - Kuhn, J. ED - Schindler, M. ID - 45373 T2 - Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis TI - Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen ER - TY - JOUR AU - Prediger, S. AU - Dröse, Jennifer AU - Stahnke, R. AU - Ademmer, C. ID - 45374 JF - Journal of Mathematics Teacher Education TI - Teacher expertise for fostering at-risk students’ understanding of basic concepts: conceptual model and evidence for growth ER - TY - CONF AU - Dröse, Jennifer AU - Griese, B. AU - Wessel, Lena ID - 45379 T2 - Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) TI - Prosepctive teachers‘ diagnostic judgements on students’ under- standing of conditional probabilities ER - TY - CONF AB - Hamilton-Jacobi reachability methods for safety-critical control have been well studied, but the safety guarantees derived rely on the accuracy of the numerical computation. Thus, it is crucial to understand and account for any inaccuracies that occur due to uncertainty in the underlying dynamics and environment as well as the induced numerical errors. To this end, we propose a framework for modeling the error of the value function inherent in Hamilton-Jacobi reachability using a Gaussian process. The derived safety controller can be used in conjuncture with arbitrary controllers to provide a safe hybrid control law. The marginal likelihood of the Gaussian process then provides a confidence metric used to determine switches between a least restrictive controller and a safety controller. We test both the prediction as well as the correction capabilities of the presented method in a classical pursuit-evasion example. AU - Vertovec, Nikolaus AU - Ober-Blöbaum, Sina AU - Margellos, Kostas ID - 30733 TI - Verification of safety critical control policies using kernel methods ER - TY - CHAP AU - Dellori, Anna AU - Wessel, Lena ED - Trigueros, M. ED - Barquero, B. ED - Hochmuth, R. ED - Peters, J. ID - 48385 T2 - Proceedings of INDRUM2022 TI - Design principles for intertwining local and nonlocal mathematics - The case of relating registers and representations in abstract algebra ER - TY - JOUR AB - AbstractTeachers’ in-depth diagnostic thinking has been shown to be crucial for student-centered teaching as they need to perceive and interpret students’ understanding for well-informed decision-making on adaptive teaching practices. The paper presents a content-related approach to analyzing diagnostic thinking processes with respect to the mathematical knowledge elements that prospective teachers identify as students’ resources and obstacles. Prospective teachers’ challenge is that some relevant knowledge elements first have to be unpacked, because compact concepts (such as the place value concept) or procedures (such as for multi-digit multiplication) comprise several smaller knowledge elements (such as the positional property) that have to be made explicit for students to foster their learning processes adequately. Our study examines what knowledge elements prospective teachers perceive and interpret in a transcript vignettes on multi-digit multiplication (of decimal and natural numbers) and its underlying basic arithmetic concepts (place value understanding and meaning of multiplication) in written diagnostic judgments on students’ resources and obstacles (N = 196). A comparative design within the vignette is used to investigate how far the process of perceiving can be supported by thematic cues. The analysis reveals that those knowledge elements cued in the vignette by being already unpacked and explicitly addressed are perceived and interpreted more often (but with lower correctness) than those that are uncued and therefore have to be unpacked by the prospective teachers themselves. This confirms the need to prepare prospective teachers for unpacking mathematical concepts themselves. AU - Dröse, Jennifer AU - Prediger, Susanne ID - 40607 JF - Journal für Mathematik-Didaktik KW - Education KW - General Mathematics SN - 0173-5322 TI - Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements ER - TY - CONF AU - Dröse, Jennifer AU - Griese, Birgit AU - Wessel, Lena ID - 48389 T2 - Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) TI - Prospective teachers’ diagnostic judgments on students’ understanding of conditional probabilities ER - TY - CONF AU - Dröse, Jennifer AU - Wessel, Lena ED - Fernandez, C. ED - Llinares, S. ED - Gutiérrez, A. ED - Planas, N. ID - 45378 T2 - Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME TI - Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task ER - TY - JOUR AB - In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in the mathematical theory of resonances, in particular how invariant Ruelle distributions arise as residues of weighted zeta functions. Then we derive a correspondence between weighted and semiclassical zeta functions in the setting of negatively curved surfaces. Combining this with results of Hilgert, Guillarmou and Weich yields a high frequency interpretation of invariant Ruelle distributions as quantum mechanical matrix coefficients in constant negative curvature. We finish by presenting numerical calculations of phase space distributions in the more physical setting of 3-disk scattering systems. AU - Barkhofen, Sonja AU - Schütte, Philipp AU - Weich, Tobias ID - 31057 IS - 24 JF - Journal of Physics A: Mathematical and Theoretical TI - Semiclassical formulae For Wigner distributions VL - 55 ER - TY - THES AB - Vorgestellt wird ein Entwicklungsforschungsprojekt zur Konzeption und Durchführung einer Veranstaltung "Geometrie für Lehramtsstudierende". Die Schwerpunkte des Projekts sind zum einen die inhaltliche Gestaltung der Veranstaltung und zum anderen die Umsetzung von Professionsorientierung. Bezogen auf den inhaltlichen Aufbau wird das auf metrischen Räumen aufbauende Axiomensystem der "Saccheri-Ebene" vorgestellt und mit alternativen axiomatischen Zugängen zur ebenen Geometrie verglichen. Die Frage nach der Umsetzung von Professionsorientierung in Fachveranstaltungen ist eng mit der Problematik der zweiten Diskontinuität verbunden. In der Arbeit wird dieses Problem auf Grundlage der Synthese von theoretischen Hintergründen zur Bedeutung von mathematischem Wissen und Können für professionelle Handlungskompetenz von Mathematiklehrkräften diskutiert und darauf aufbauend werden theoriebasierte Entwurfsprinzipien für professionsorientierte Fachveranstaltungen entworfen. Zentrale Elemente der methodischen Gestaltung sind die sogenannten "Schnittstellenwochen" zu den Themen Kongruenz und Symmetrie sowie das begleitende Schnittstellen-ePortfolio. Das zentrale Ergebnis der Arbeit ist ein theoretisch fundiertes und empirisch evaluiertes ganzheitliches Veranstaltungskonzept für eine professionsorientierte Geometrie-Veranstaltung für Lehramtsstudierende, dessen Konzeption auf andere Fachveranstaltungen übertragbar ist. Darüber hinaus ergeben sich im Rahmen der durchgeführten Entwicklungsforschung verschiedene neue Beiträge zur Geometriedidaktik in Schule- und Hochschule. AU - Hoffmann, Max ID - 31363 TI - Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie für Lehramtsstudierende ER - TY - JOUR AU - Bux, Kai-Uwe AU - Hilgert, Joachim AU - Weich, Tobias ID - 35322 IS - 2 JF - Journal of Spectral Theory KW - Geometry and Topology KW - Mathematical Physics KW - Statistical and Nonlinear Physics SN - 1664-039X TI - Poisson transforms for trees of bounded degree VL - 12 ER - TY - JOUR AU - Hilgert, Joachim AU - Weich, Tobias AU - Bux, K.-U. ID - 51385 JF - J. of Spectral Theory TI - Poisson transforms for trees of bounded degree VL - 12 ER - TY - GEN AU - Hilgert, Joachim ID - 51554 T2 - Mathematische Semesterberichte TI - Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021 VL - 69 ER - TY - CONF AU - Werth, Gerda ID - 52574 T2 - Beiträge zum Mathematikunterricht TI - Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings ER - TY - JOUR AU - Nüske, Feliks AU - Gelß, Patrick AU - Klus, Stefan AU - Clementi, Cecilia ID - 24169 JF - Physica D: Nonlinear Phenomena SN - 0167-2789 TI - Tensor-based computation of metastable and coherent sets ER - TY - JOUR AU - Klus, Stefan AU - Gelß, Patrick AU - Nüske, Feliks AU - Noé, Frank ID - 24170 JF - Machine Learning: Science and Technology SN - 2632-2153 TI - Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry ER - TY - JOUR AU - Goelz, Christian AU - Mora, Karin AU - Stroehlein, Julia Kristin AU - Haase, Franziska Katharina AU - Dellnitz, Michael AU - Reinsberger, Claus AU - Vieluf, Solveig ID - 21195 JF - Cognitive Neurodynamics TI - Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults ER - TY - JOUR AB - We present a flexible trust region descend algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive problems, i.e., problems that have at least one objective function that is computationally expensive. The method is derivative-free in the sense that neither need derivative information be available for the expensive objectives nor are gradients approximated using repeated function evaluations as is the case in finite-difference methods. Instead, a multiobjective trust region approach is used that works similarly to its well-known scalar pendants. Local surrogate models constructed from evaluation data of the true objective functions are employed to compute possible descent directions. In contrast to existing multiobjective trust region algorithms, these surrogates are not polynomial but carefully constructed radial basis function networks. This has the important advantage that the number of data points scales linearly with the parameter space dimension. The local models qualify as fully linear and the corresponding general scalar framework is adapted for problems with multiple objectives. Convergence to Pareto critical points is proven and numerical examples illustrate our findings. AU - Berkemeier, Manuel Bastian AU - Peitz, Sebastian ID - 21337 IS - 2 JF - Mathematical and Computational Applications TI - Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models VL - 26 ER - TY - JOUR AB - The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the conditioning approach. In this paper, we are interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to the spectrum of the full generator. We prove a new relative error bound in terms of the eigenfunction approximation error for reversible systems. We also present numerical examples indicating that, if Kramers–Moyal (KM) type approximations are used to compute the spectrum of the reduced generator, it seems largely insensitive to the time window used for the KM estimators. We analyze the implications of these observations for systems driven by underdamped Langevin dynamics, and show how meaningful effective dynamics can be defined in this setting. AU - Nüske, Feliks AU - Koltai, Péter AU - Boninsegna, Lorenzo AU - Clementi, Cecilia ID - 21820 JF - Entropy SN - 1099-4300 TI - Spectral Properties of Effective Dynamics from Conditional Expectations ER - TY - JOUR AB - In this article, we present an efficient descent method for locally Lipschitz continuous multiobjective optimization problems (MOPs). The method is realized by combining a theoretical result regarding the computation of descent directions for nonsmooth MOPs with a practical method to approximate the subdifferentials of the objective functions. We show convergence to points which satisfy a necessary condition for Pareto optimality. Using a set of test problems, we compare our method to the multiobjective proximal bundle method by M\"akel\"a. The results indicate that our method is competitive while being easier to implement. While the number of objective function evaluations is larger, the overall number of subgradient evaluations is lower. Finally, we show that our method can be combined with a subdivision algorithm to compute entire Pareto sets of nonsmooth MOPs. AU - Gebken, Bennet AU - Peitz, Sebastian ID - 16867 JF - Journal of Optimization Theory and Applications TI - An efficient descent method for locally Lipschitz multiobjective optimization problems VL - 188 ER - TY - JOUR AB - It is a challenging task to identify the objectives on which a certain decision was based, in particular if several, potentially conflicting criteria are equally important and a continuous set of optimal compromise decisions exists. This task can be understood as the inverse problem of multiobjective optimization, where the goal is to find the objective function vector of a given Pareto set. To this end, we present a method to construct the objective function vector of an unconstrained multiobjective optimization problem (MOP) such that the Pareto critical set contains a given set of data points with prescribed KKT multipliers. If such an MOP can not be found, then the method instead produces an MOP whose Pareto critical set is at least close to the data points. The key idea is to consider the objective function vector in the multiobjective KKT conditions as variable and then search for the objectives that minimize the Euclidean norm of the resulting system of equations. By expressing the objectives in a finite-dimensional basis, we transform this problem into a homogeneous, linear system of equations that can be solved efficiently. Potential applications of this approach include the identification of objectives (both from clean and noisy data) and the construction of surrogate models for expensive MOPs. AU - Gebken, Bennet AU - Peitz, Sebastian ID - 16295 JF - Journal of Global Optimization TI - Inverse multiobjective optimization: Inferring decision criteria from data VL - 80 ER - TY - THES AB - Ein zentraler Aspekt bei der Untersuchung dynamischer Systeme ist die Analyse ihrer invarianten Mengen wie des globalen Attraktors und (in)stabiler Mannigfaltigkeiten. Insbesondere wenn das zugrunde liegende System von einem Parameter abhängt, ist es entscheidend, sie im Bezug auf diesen Parameter effizient zu verfolgen. Für die Berechnung invarianter Mengen stützen wir uns für ihre Approximation auf numerische Algorithmen. Typischerweise können diese Methoden jedoch nur auf endlich-dimensionale dynamische Systeme angewendet werden. In dieser Arbeit präsentieren wir daher einen numerischen Rahmen für die globale dynamische Analyse unendlich-dimensionaler Systeme. Wir werden Einbettungstechniken verwenden, um das core dynamical system (CDS) zu definieren, welches ein dynamisch äquivalentes endlich-dimensionales System ist.Das CDS wird dann verwendet, um eingebettete invariante Mengen, also eins-zu-eins Bilder, mittels Mengen-orientierten numerischen Methoden zu approximieren. Bei der Konstruktion des CDS ist es entscheidend, eine geeignete Beobachtungsabbildung auszuwählen und die geeignete inverse Abbildung zu entwerfen. Dazu werden wir geeignete numerische Implementierungen des CDS für DDEs und PDEs vorstellen. Für eine nachfolgende geometrische Analyse der eingebetteten invarianten Menge betrachten wir eine Lerntechnik namens diffusion maps, die ihre intrinsische Geometrie enthüllt sowie ihre Dimension schätzt. Schließlich wenden wir unsere entwickelten numerischen Methoden an einigen bekannten unendlich-dimensionale dynamischen Systeme an, wie die Mackey-Glass-Gleichung, die Kuramoto-Sivashinsky-Gleichung und die Navier-Stokes-Gleichung. AU - Gerlach, Raphael ID - 32057 TI - The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems ER - TY - JOUR AU - Delarue, Benjamin AU - Ramacher, Pablo ID - 32016 IS - 6 JF - Journal of Symplectic Geometry TI - Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions VL - 19 ER - TY - JOUR AU - Li, Jiaao AU - Ma, Yulai AU - Miao, Zhengke AU - Shi, Yongtang AU - Wang, Weifan AU - Zhang, Cun-Quan ID - 34042 JF - Journal of Combinatorial Theory, Series B KW - Computational Theory and Mathematics KW - Discrete Mathematics and Combinatorics KW - Theoretical Computer Science SN - 0095-8956 TI - Nowhere-zero 3-flows in toroidal graphs VL - 153 ER - TY - JOUR AB - A locally compact contraction group is a pair (G,α), where G is a locally compact group and α:G→G an automorphism such that αn(x)→e pointwise as n→∞. We show that every surjective, continuous, equivariant homomorphism between locally compact contraction groups admits an equivariant continuous global section. As a consequence, extensions of locally compact contraction groups with abelian kernel can be described by continuous equivariant cohomology. For each prime number p, we use 2-cocycles to construct uncountably many pairwise non-isomorphic totally disconnected, locally compact contraction groups (G,α) which are central extensions0→Fp((t))→G→Fp((t))→0 of the additive group of the field of formal Laurent series over Fp=Z/pZ by itself. By contrast, there are only countably many locally compact contraction groups (up to isomorphism) which are torsion groups and abelian, as follows from a classification of the abelian locally compact contraction groups. AU - Glöckner, Helge AU - Willis, George A. ID - 34786 JF - Journal of Algebra KW - Contraction group KW - Torsion group KW - Extension KW - Cocycle KW - Section KW - Equivariant cohomology KW - Abelian group KW - Nilpotent group KW - Isomorphism types SN - 0021-8693 TI - Decompositions of locally compact contraction groups, series and extensions VL - 570 ER - TY - JOUR AU - Glöckner, Helge AU - Willis, George A. ID - 34790 JF - J. Reine Angew. Math. KW - 22D05 KW - 22A05 KW - 20E18 SN - 0075-4102 TI - Locally pro-p contraction groups are nilpotent VL - 781 ER - TY - JOUR AU - Glöckner, Helge ID - 34795 IS - 1 JF - Mathematische Nachrichten SN - 0025-584X TI - Direct limits of regular Lie groups VL - 294 ER - TY - GEN AB - Let $G$ be a Lie group over a totally disconnected local field and $\alpha$ be an analytic endomorphism of $G$. The contraction group of $\alpha$ ist the set of all $x\in G$ such that $\alpha^n(x)\to e$ as $n\to\infty$. Call sequence $(x_{-n})_{n\geq 0}$ in $G$ an $\alpha$-regressive trajectory for $x\in G$ if $\alpha(x_{-n})=x_{-n+1}$ for all $n\geq 1$ and $x_0=x$. The anti-contraction group of $\alpha$ is the set of all $x\in G$ admitting an $\alpha$-regressive trajectory $(x_{-n})_{n\geq 0}$ such that $x_{-n}\to e$ as $n\to\infty$. The Levi subgroup is the set of all $x\in G$ whose $\alpha$-orbit is relatively compact, and such that $x$ admits an $\alpha$-regressive trajectory $(x_{-n})_{n\geq 0}$ such that $\{x_{-n}\colon n\geq 0\}$ is relatively compact. The big cell associated to $\alpha$ is the set $\Omega$ of all all products $xyz$ with $x$ in the contraction group, $y$ in the Levi subgroup and $z$ in the anti-contraction group. Let $\pi$ be the mapping from the cartesian product of the contraction group, Levi subgroup and anti-contraction group to $\Omega$ which maps $(x,y,z)$ to $xyz$. We show: $\Omega$ is open in $G$ and $\pi$ is \'{e}tale for suitable immersed Lie subgroup structures on the three subgroups just mentioned. Moreover, we study group-theoretic properties of contraction groups and anti-contraction groups. AU - Glöckner, Helge ID - 34806 T2 - arXiv:2101.02981 TI - Contraction groups and the big cell for endomorphisms of Lie groups over local fields ER - TY - CONF AU - Ober-Blöbaum, Sina AU - Vermeeren, M. ID - 29421 T2 - 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC TI - Superconvergence of galerkin variational integrators VL - 54(19) ER - TY - JOUR AB - Model predictive control is a prominent approach to construct a feedback control loop for dynamical systems. Due to real-time constraints, the major challenge in MPC is to solve model-based optimal control problems in a very short amount of time. For linear-quadratic problems, Bemporad et al. have proposed an explicit formulation where the underlying optimization problems are solved a priori in an offline phase. In this article, we present an extension of this concept in two significant ways. We consider nonlinear problems and - more importantly - problems with multiple conflicting objective functions. In the offline phase, we build a library of Pareto optimal solutions from which we then obtain a valid compromise solution in the online phase according to a decision maker's preference. Since the standard multi-parametric programming approach is no longer valid in this situation, we instead use interpolation between different entries of the library. To reduce the number of problems that have to be solved in the offline phase, we exploit symmetries in the dynamical system and the corresponding multiobjective optimal control problem. The results are verified using two different examples from autonomous driving. AU - Ober-Blöbaum, Sina AU - Peitz, Sebastian ID - 16294 JF - International Journal of Robust and Nonlinear Control TI - Explicit multiobjective model predictive control for nonlinear systems with symmetries VL - 31(2) ER - TY - JOUR AU - Djema, Walid AU - Giraldi, Laetitia AU - Maslovskaya, Sofya AU - Bernard, Olivier ID - 29543 JF - Automatica KW - Electrical and Electronic Engineering KW - Control and Systems Engineering SN - 0005-1098 TI - Turnpike features in optimal selection of species represented by quota models VL - 132 ER - TY - GEN AB - We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane. AU - Schütte, Philipp AU - Weich, Tobias AU - Delarue, Benjamin ID - 31058 TI - Resonances and weighted zeta functions for obstacle scattering via smooth models ER - TY - GEN AU - Hoffmann, Max ID - 31385 T2 - Mathematische Semesterberichte TI - Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie VL - 68 ER - TY - CHAP AU - Hoffmann, Max ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 31364 SN - 2197-8751 T2 - Lehrinnovationen in der Hochschulmathematik. praxisrelevant – didaktisch fundiert – forschungsbasiert TI - Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn ER - TY - JOUR AB - Abstract For a compact Riemannian locally symmetric space $\mathcal M$ of rank 1 and an associated vector bundle $\mathbf V_{\tau }$ over the unit cosphere bundle $S^{\ast }\mathcal M$, we give a precise description of those classical (Pollicott–Ruelle) resonant states on $\mathbf V_{\tau }$ that vanish under covariant derivatives in the Anosov-unstable directions of the chaotic geodesic flow on $S^{\ast }\mathcal M$. In particular, we show that they are isomorphically mapped by natural pushforwards into generalized common eigenspaces of the algebra of invariant differential operators $D(G,\sigma )$ on compatible associated vector bundles $\mathbf W_{\sigma }$ over $\mathcal M$. As a consequence of this description, we obtain an exact band structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions on the representations $\tau$ and $\sigma$ defining the bundles $\mathbf V_{\tau }$ and $\mathbf W_{\sigma }$, we obtain a very explicit description of the generalized common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections of $\mathbf W_{\sigma }$. Our methods of proof are based on representation theory and Lie theory. AU - Küster, Benjamin AU - Weich, Tobias ID - 31261 IS - 11 JF - International Mathematics Research Notices KW - General Mathematics SN - 1073-7928 TI - Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces VL - 2021 ER - TY - JOUR AU - Häsel-Weide, Uta AU - Nührenbürger, Marcus ID - 31576 IS - 14 JF - Zeitschrift für Grundschulforschung (ZfG) TI - Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen. ER - TY - JOUR AU - Häsel-Weide, Uta AU - Schöttler, Christian ID - 31577 IS - 2 JF - Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP) SN - 2701-9012 TI - Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen ER - TY - JOUR AU - Li, Jiaao AU - Ma, Yulai AU - Shi, Yongtang AU - Wang, Weifan AU - Wu, Yezhou ID - 32810 JF - European Journal of Combinatorics KW - Discrete Mathematics and Combinatorics SN - 0195-6698 TI - On 3-flow-critical graphs VL - 100 ER - TY - JOUR AB - The kinetic Brownian motion on the sphere bundle of a Riemannian manifold M is a stochastic process that models a random perturbation of the geodesic flow. If M is an orientable compact constantly curved surface, we show that in the limit of infinitely large perturbation the L2-spectrum of the infinitesimal generator of a time-rescaled version of the process converges to the Laplace spectrum of the base manifold. AU - Kolb, Martin AU - Weich, Tobias AU - Wolf, Lasse ID - 33278 IS - 4 JF - Annales Henri Poincaré TI - Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature VL - 23 ER - TY - GEN AU - Weich, Tobias AU - Budde, Julia ID - 32099 T2 - arXiv:2103.02968v1 TI - Wave Front Sets of Nilpotent Lie Group Representations ER - TY - JOUR AB - While 2D Gibbsian particle systems might exhibit orientational order resulting in a lattice-like structure, these particle systems do not exhibit positional order if the interaction between particles satisfies some weak assumptions. Here we investigate to which extent particles within a box of size may fluctuate from their ideal lattice position. We show that particles near the center of the box typically show a displacement at least of order . Thus we extend recent results on the hard disk model to particle systems with fairly arbitrary particle spins and interaction. Our result applies to models such as rather general continuum Potts type models, e.g. with Widom–Rowlinson or Lenard-Jones-type interaction. AU - Richthammer, Thomas AU - Fiedler, Michael ID - 33481 JF - Stochastic Processes and their Applications TI - A lower bound on the displacement of particles in 2D Gibbsian particle systems VL - 132 ER - TY - JOUR AU - Hanusch, Maximilian ID - 34818 JF - Differential Geometry and its Applications KW - Geometry and Topology KW - Analysis SN - 0926-2245 TI - Symmetries of analytic curves VL - 74 ER - TY - CHAP AU - Biehler, Rolf ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35720 T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik TI - Mathematikvorkurse als Brücke in das Studium–Einführung ER - TY - CHAP AU - Biehler, Rolf AU - Eichler, Andreas AU - Hochmuth, Reinhard AU - Rach, Stefanie AU - Schaper, Niclas ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35730 SN - 2197-8751 T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik TI - Einführung: Lehrinnovationen in der Hochschulmathematik – praxisrelevant – didaktisch fundiert – forschungsbasiert ER - TY - JOUR AU - Biehler, Rolf AU - Fleischer, Yannik ID - 35737 JF - Teaching Statistics KW - Education KW - Statistics and Probability SN - 0141-982X TI - Introducing students to machine learning with decision trees using CODAP and Jupyter Notebooks VL - 43 ER - TY - BOOK ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35734 SN - 2197-8751 TI - Lehrinnovationen in der Hochschulmathematik ER - TY - CHAP AU - Frischemeier, Daniel AU - Podworny, Susanne AU - Biehler, Rolf ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35752 SN - 2197-8751 T2 - Konzepte und Studien Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematikzur Hochschuldidaktik und Lehrerbildung Mathematik TI - Integration fachwissenschaftlicher und fachdidaktischer Komponenten in der Lehramtsausbildung Mathematik Grundschule am Beispiel einer Veranstaltung zur Leitidee „Daten, Häufigkeit und Wahrscheinlichkeit“ ER - TY - CHAP AU - Fleischmann, Yael AU - Biehler, Rolf AU - Gold, Alexander AU - Mai, Tobias ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35746 SN - 2197-8751 T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik TI - Integration digitaler Lernmaterialien in die Präsenzlehre am Beispiel des Mathematikvorkurses für Ingenieure an der Universität Paderborn ER - TY - JOUR AU - Frischemeier, Daniel AU - Biehler, Rolf AU - Podworny, Susanne AU - Budde, Lea ID - 35751 IS - S1 JF - Teaching Statistics KW - Education KW - Statistics and Probability SN - 0141-982X TI - A first introduction to data science education in secondary schools: Teaching and learning about data exploration withCODAPusing survey data VL - 43 ER - TY - JOUR AU - Biehler, Rolf AU - Weigand, Hans-Georg ID - 35744 IS - 228 JF - mathematik lehren TI - 3D-Geometrie–virtuell und real VL - 2021 ER - TY - CHAP AU - Hochmuth, Reinhard AU - Biehler, Rolf AU - Blum, Werner AU - Achmetli, Kay AU - Rode, Jana AU - Krawitz, Janina AU - Schukajlow, Stanislaw AU - Bender, Peter AU - Haase, Jürgen ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35757 SN - 2197-8751 T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik TI - Fachwissen zur Arithmetik bei Grundschullehramtsstudierenden – Entwicklung im ersten Semester und Veränderungen durch eine Lehrinnovation ER - TY - CHAP AU - Gold, Alexander AU - Fleischmann, Yael AU - Mai, Tobias AU - Biehler, Rolf AU - Kempen, Leander ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35755 SN - 2197-8751 T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik TI - Die Online-Lernmaterialien im Online-Mathematikvorkurs studiVEMINT: Konzeption und Ergebnisse von Nutzer- und Evaluationsstudien ER - TY - CHAP AU - Kempen, Leander AU - Biehler, Rolf ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35776 SN - 2197-8751 T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik TI - Design-Based Research in der Hochschullehre am Beispiel der Lehrveranstaltung „Einführung in die Kultur der Mathematik“ ER - TY - JOUR AU - Höper, Lukas AU - Malin, Leah AU - Biehler, Rolf ID - 35761 IS - 228 JF - mathematik lehren TI - Schatten von 3D-Objekten: Modellierung mit GeoGebra 3D und Anwendungen in der Computergrafik VL - 2021 ER - TY - JOUR AU - Hüsing, Sven AU - Weiser, Niklas AU - Biehler, Rolf ID - 35763 IS - 228 JF - mathematik lehren TI - Faszination 3D-Film: Entwicklung einer 3D-Konstruktion VL - 2021 ER - TY - JOUR AB - AbstractThe aim of the special issue is to bring together important current international research on innovative teaching and learning practices in mathematics in engineering education, and to develop deeper understandings of the characteristics of current teaching and learning practices that can inform the design and implementation of future innovative practice. The focus of this review paper is to provide a state-of-the-art overview of this emerging field at the cross-roads between mathematics and engineering education, in addition to introducing the papers of this special issue. To guide this paper, we posed three review questions: (1) How can current (teaching/learning/study) practices of mathematics in engineering education be characterized with a view towards innovation?; (2) What are the ‘resources’ (cognitive, material, digital, social) used, and what are those that appear also well suited for innovative courses?; (3) What are promising innovative practices in mathematics in engineering education, and what are the implications for curriculum reform? Looking back across the studies we summarized in the review, we conclude that they are lagging behind the more fundamental changes that are happening in engineering education, whilst addressing selected aspects of innovative changes within the current system of engineering education. At the same time, the nine papers of this special issue contribute new perspectives for innovative practices in mathematics in engineering education, for a better understanding of current practices and for future research. AU - Pepin, Birgit AU - Biehler, Rolf AU - Gueudet, Ghislaine ID - 35778 IS - 2 JF - International Journal of Research in Undergraduate Mathematics Education KW - Education KW - Mathematics (miscellaneous) SN - 2198-9745 TI - Mathematics in Engineering Education: a Review of the Recent Literature with a View towards Innovative Practices VL - 7 ER - TY - JOUR AU - Podworny, Susanne AU - Biehler, Rolf ID - 35781 IS - 4 JF - Mathematical Thinking and Learning KW - Developmental and Educational Psychology KW - Education KW - General Mathematics SN - 1098-6065 TI - The process of actively building a model for a randomization test – insights into learners’ modeling activities based on a case study VL - 24 ER - TY - CHAP AU - Winsløw, Carl AU - Biehler, Rolf AU - Jaworski, Barbara AU - Rønning, Frode AU - Wawro, Megan ED - Durand-Guerrier, V. ED - Hochmuth, R. ED - Nardi, E. ED - Winsløw, C. ID - 35704 SN - 9780429346859 T2 - Research and Development in University Mathematics Education TI - Education and professional development of university mathematics teachers ER - TY - JOUR AU - Schürmann, Mirko AU - Liebendörfer, Michael AU - Gildehaus, Lara AU - Schaper, Niclas AU - Hochmuth, Reinhard AU - Biehler, Rolf AU - Lankeit, Elisa AU - Kuklinski, Christiane AU - Ruge, Johanna ID - 24786 JF - Sigma newsletter TI - Opportunities and Possibilities of a Network of Mathematical Learning and Support Centres in Germany VL - 22 ER - TY - CHAP AU - Rach, Stefanie AU - Liebendörfer, Michael ED - Hein, Kerstin ED - Heil, Cathleen ED - Ruwisch, Silke ED - Prediger, Susanne ID - 37485 SN - 978-3-95987-184-6 T2 - Beiträge zum Mathematikunterricht 2021 vom GDM-Monat 2021 der Gesellschaft für Didaktik der Mathematik (GDM) (1.-25. März 2021) TI - Die Bedeutung affektiver Merkmale beim Mathematiklernen ER - TY - JOUR AB - Abstract 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. AU - Büchele, Stefan AU - Liebendörfer, Michael AU - Lankeit, Elisa ID - 37474 IS - 4 JF - Teaching Mathematics and its Applications: An International Journal of the IMA KW - Education KW - General Mathematics SN - 0268-3679 TI - Increasing the effect of a remedial mathematics course by switching to an online format during the COVID-19 crisis: evidence from a German university VL - 40 ER - TY - JOUR AB - Das gymnasiale Lehramtsstudium der Mathematik ist an deutschen Universitäten unterschiedlich organisiert. Traditionell wurden am Studienbeginn die Fachvorlesungen zur Analysis und Linearen Algebra gemeinsam mit Fachstudierenden gehört. In jüngerer Zeit verbreiten sich alternative Modelle z. B. mit Brückenvorlesungen, die oft spezifisch für das Gymnasiallehramt angeboten werden. Sie können gemeinsame Veranstaltungen mit Fachstudierenden ergänzen oder ersetzen. Dieser Beitrag zeigt auf, welche Modelle wie häufig verbreitet sind, und spricht an, welche hochschuldidaktischen Fragen an der Studiengestaltung hängen. AU - Gildehaus, Lara AU - Göller, Robin AU - Liebendörfer, Michael ID - 37483 IS - 111 JF - Mitteilungen der Gesellschaft für Didaktik der Mathematik SN - 2512-9155 TI - Gymnasiales Lehramt Mathematik studieren – eine Übersicht zur Studienorganisation in Deutschland VL - 47 ER - TY - CONF AU - Vajen, Bastian AU - Gildehaus, Lara AU - Liebendörfer, Michael AU - Wolf, Christoph ED - Kenner, Steve ED - Oeftering, T. ID - 37481 T2 - Schriftenreihe der DVPB. Standortbestimmung Politische Bildung: Gesellschaftspolitische Herausforderungen, Zivilgesellschaft und das vermeintliche Neutralitätsgebot TI - Mathematisierung als Herausforderung für die politische Bildung ER - TY - CHAP AU - Göller, Robin AU - Gildehaus, Lara AU - Liebendörfer, Michael AU - Steuding, Jörn ED - Blunck, Andrea ED - Motzer, Renate ID - 37480 T2 - Mathematik und Gender: Berichte und Beiträge des Arbeitskreise Frauen und Mathematik TI - Prüfungsformate als Ansatzpunkt gendersensibler universitärer Lehre im Fach Mathematik VL - 5 ER - TY - CONF AU - Haak, Inka AU - Gildehaus, Lara AU - Liebendörfer, Michael ID - 37478 T2 - Naturwissenschaftlicher Unterricht und Lehrerbildung im Umbruch? TI - Genese und Funktionen von Lerngruppen in der Studieneingangsphase ER - TY - JOUR AB - Abstract 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. AU - Kempen, Leander AU - Liebendörfer, Michael ID - 37473 IS - 4 JF - Teaching Mathematics and its Applications: An International Journal of the IMA KW - Education KW - General Mathematics SN - 0268-3679 TI - University students’ fully digital study of mathematics: an identification of student-groups via their resources usage and a characterization by personal and affective characteristics VL - 40 ER - TY - CONF AU - Liebendörfer, Michael AU - Hochmuth, Reinhard AU - Rode, Jana AU - Schukajlow, Stanislaw ED - Inprasitha, M. ED - Changsri, N. ED - Boonsena, N. ID - 37487 T2 - Interim Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education TI - The Mathematical Beliefs and Interest Development of Pre-Service Primary Teachers VL - 3 ER - TY - JOUR AU - Krapf, Regula AU - Liebendörfer, Michael ID - 37494 IS - 44 JF - mathematica didactica KW - Extrinsische Motivation TI - Was bewirkt die Pflichtabgabe von Übungsaufgaben in der Hochschulmathematik? – Ein empirischer Vergleich VL - 2 ER - TY - JOUR AU - Winkler, Michael ID - 35616 JF - Nonlinear Analysis: Real World Applications TI - Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system with gradient-dependent flux limitation. VL - 59 ER - TY - JOUR AU - Winkler, Michael ID - 35615 JF - Zeitschrift für Angewandte Mathematik und Physik TI - Suppressing blow-up by gradient-dependent flux limitation in a planar Keller-Segel-Navier-Stokes system. VL - 72 ER - TY - JOUR AU - Winkler, Michael ID - 35614 JF - International Mathematics Research Notices TI - Can rotational fluxes impede the tendency toward spatial homogeneity in nutrient taxis (-Stokes) systems? VL - 2021 ER - TY - JOUR AU - Winkler, Michael ID - 35617 JF - Applied Mathematics Letters TI - Boundedness in a three-dimensional Keller-Segel-Stokes system with subcritical sensitivity. VL - 112 ER - TY - JOUR AU - Winkler, Michael ID - 35613 JF - Transactions of the American Mathematical Society TI - Does spatial homogeneity ultimately prevail in nutrient taxis systems? A paradigm for structure support by rapid diffusion decay in an autonomous parabolic flow. VL - 374 ER - TY - JOUR AU - Rösler, Margit AU - Voit, Michael ID - 37659 IS - 3 JF - Proceedings of the American Mathematical Society KW - Applied Mathematics KW - General Mathematics SN - 0002-9939 TI - Positive intertwiners for Bessel functions of type B VL - 149 ER - TY - JOUR AU - Tao, Youshan AU - Winkler, Michael ID - 35603 JF - Journal of Functional Analysis TI - A fully cross-diffusive two-component evolution system: Existence and qualitative analysis via entropy-consistent thin-film-type approximation. VL - 281 ER - TY - JOUR AU - Tao, Youshan AU - Winkler, Michael ID - 35606 JF - Nonlinear Analysis, Theory, Methods and Applications TI - The dampening role of large repulsive convection in a chemotaxis system modeling tumor angiogenesis. VL - 208 ER - TY - JOUR AU - Wang, Yulan AU - Winkler, Michael AU - Xiang, Zhaoyin ID - 35612 JF - Science China Mathematics TI - Immediate regularization of measure-type population densities in a two-dimensional chemotaxis system with signal consumption. VL - 64 ER - TY - JOUR AU - Ding, Mengyao AU - Winkler, Michael ID - 35601 JF - Nonlinear Differential Equatiions and Applicatiions TI - Small-density solutiions in Keller-Segel systems involving rapidly decaying diffusivities. VL - 28 ER - TY - JOUR AU - Tao, Youshan AU - Winkler, Michael ID - 35605 JF - Communications in Mathematical Sciences TI - Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime. VL - 19 ER - TY - JOUR AU - Tao, Youshan AU - Winkler, Michael ID - 35604 JF - SIAM Journal on Mathematical Analysis TI - Taxis-driven formation of singular hotspots in a May-Nowak type model for virus infection. VL - 53 ER - TY - JOUR AU - Wang, Yulan AU - Winkler, Michael AU - Xiang, Zhaoyin ID - 35610 JF - Communications in Partial Differential Equations TI - Local energy estimates and global solvability in a threee-dimensional chemotaxis-fluid system with prescribed signal on the boundary. VL - 46 ER - TY - JOUR AU - Wang, Yulan AU - Winkler, Michael AU - Xiang, Zhaoyin ID - 35611 JF - Advances in Nonlinear Analysis TI - Global solvability in a threee-dimensional Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation VL - 10 ER - TY - JOUR AU - Tao, Youshan AU - Winkler, Michael ID - 35608 IS - --A JF - Discrete and Continuous Dynamical Systems TI - Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction VL - 41 ER - TY - JOUR AB - 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. AU - Klüners, Jürgen AU - Komatsu, Toru ID - 34840 IS - 329 JF - Mathematics of Computation KW - Applied Mathematics KW - Computational Mathematics KW - Algebra and Number Theory SN - 0025-5718 TI - Imaginary multiquadratic number fields with class group of exponent $3$ and $5$ VL - 90 ER - TY - JOUR AB - 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. AU - Kirschmer, Markus AU - Narbonne, Fabien AU - Ritzenthaler, Christophe AU - Robert, Damien ID - 34912 IS - 333 JF - Mathematics of Computation KW - Applied Mathematics KW - Computational Mathematics KW - Algebra and Number Theory SN - 0025-5718 TI - Spanning the isogeny class of a power of an elliptic curve VL - 91 ER - TY - JOUR AB - This paper is devoted to algebro-geometric study of infinite dimensional Lie bialgebras, which arise from solutions of the classical Yang–Baxter equation. We regard trigonometric solutions of this equation as twists of the standard Lie bialgebra cobracket on an appropriate affine Lie algebra and work out the corresponding theory of Manin triples, putting it into an algebro-geometric context. As a consequence of this approach, we prove that any trigonometric solution of the classical Yang–Baxter equation arises from an appropriate algebro-geometric datum. The developed theory is illustrated by some concrete examples. AU - Burban, Igor AU - Abedin, R. ID - 44329 IS - 2 JF - Communications in Mathematical Physics TI - Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation VL - 387 ER - TY - JOUR AB - The role of domain-specific content knowledge is discussed controversially for the early childhood context. Therefore, this review aims at untangling the research on domain-specific content knowledge for early childhood educators by systematically reviewing the conceptual and operational definition of and results on early childhood educators' content knowledge in different domains. Using the scientific databases ERIC, PsycInfo and Web of Sciences, we identified 36 studies on early childhood educators' domain-specific content knowledge. By comparing these studies, we found that conceptualizations of early childhood educators' content knowledge move on a continuum between a scientific related perspective and a practice related perspective. The scientific related perspective defines content knowledge as the knowledge of key concepts, facts and rules of the domain integrating knowledge taught in primary, secondary or upper secondary school. The practice related perspective includes knowledge of key concepts, facts and rules of the domain limited to the knowledge explicitly relevant for teaching in early childhood education as well as selected domain-specific knowledge of children and teaching. Our review shows that the results and implications drawn by the study authors depend on how these authors conceptualize early childhood educators' content knowledge on this continuum. Further research, therefore, needs to consider carefully how early childhood educators' content knowledge is conceptualized. The paper further discusses gaps in this research field, such as validating methods for measuring early childhood educators' content knowledge or implementing more rigorous experimental designs to examine effects of early childhood educators' content knowledge. AU - Bruns, Julia AU - Gasteiger, Hedwig AU - Strahl, Carolin ID - 34822 IS - 2 JF - Review of Education KW - content knowledge KW - domain-specific learning KW - early childhood education KW - teacher knowledge SN - 2049-6613 TI - Conceptualising and measuring domain-specific content knowledge of early childhood educators: A systematic review VL - 9 ER - TY - JOUR AU - Bruns, Julia AU - Schopferer, T. ID - 45687 JF - . TPS – Theorie und Praxis der Sozialpädagogik TI - Eine mustergültige Wissenschaft VL - 11 ER - TY - CONF AU - Jensen, Solveig AU - Gasteiger, Hedwig AU - Bruns, Julia ED - Inprasitha, Maitree ED - Changsri, Narumon ED - Boonsena, Nisakorn ID - 36527 T2 - Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education TI - Place value and regrouping as seperate constructs of place value understanding VL - 3 ER - TY - JOUR AU - Bruns, Julia AU - Gasteiger, Hedwig AU - Strahl, Carolin ID - 34823 IS - 2 JF - Review of Education SN - 2049-6613 TI - Context and Implications Document for: Conceptualising and measuring domain-specific content knowledge of early childhood educators: A systematic review VL - 9 ER - TY - CONF AU - Jensen, Solveig AU - Gasteiger, Hedwig AU - Bruns, Julia ID - 36536 T2 - Beiträge zum Mathematikunterricht 2021 TI - Stellenwertverständnis: Verständnis von Stellenwertprinzip und Bündelungsprinzip als separate Konstrukte ER -