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 -