@article{46569, abstract = {{AbstractExternal visualization (i.e., physically embodied visualization) is central to the teaching and learning of mathematics. As external visualization is an important part of mathematics at all levels of education, it is diverse, and research on external visualization has become a wide and complex field. The aim of this scoping review is to characterize external visualizations in recent mathematics education research in order to develop a common ground and guide future research. A qualitative content analysis of the full texts of 130 studies published between 2018 and 2022 applied a deductive-inductive coding procedure to assess four dimensions: visualization product or process, type of visualization, media, and purpose. The analysis revealed different types of external visualizations including visualizations with physical resemblance ranging from pictorial to abstract visualizations as well as three types of visualizations with structural resemblance: length, area, and relational visualizations. Future research should include measures of visualization products or processes to help explain the demands and affordances that different types of visualizations present to learners and teachers.}}, author = {{Schoenherr, Johanna and Schukajlow, Stanislaw}}, issn = {{1863-9690}}, journal = {{ZDM – Mathematics Education}}, keywords = {{General Mathematics, Education}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Characterizing external visualization in mathematics education research: a scoping review}}}, doi = {{10.1007/s11858-023-01494-3}}, year = {{2023}}, } @article{53533, author = {{Ernst, Alena and Schmidt, Kai-Uwe}}, issn = {{0305-0041}}, journal = {{Mathematical Proceedings of the Cambridge Philosophical Society}}, keywords = {{General Mathematics}}, number = {{1}}, pages = {{129--160}}, publisher = {{Cambridge University Press (CUP)}}, title = {{{Intersection theorems for finite general linear groups}}}, doi = {{10.1017/s0305004123000075}}, volume = {{175}}, year = {{2023}}, } @inproceedings{31849, author = {{Hoffmann, Max and Biehler, Rolf}}, booktitle = {{Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)}}, editor = {{Trigueros, Marı́a and Barquero, Berta and Hochmuth, Reinhard and Peters, Jana}}, keywords = {{Teaching and learning of specific topics in university mathematics, Transition to, across and from university mathematics, Student Teachers, Geometry, Congruence, Double Discontinuity.}}, publisher = {{University of Hannover and INDRUM.}}, title = {{{Student Teachers ’ Knowledge of Congruence before a University Course on Geometry}}}, year = {{2023}}, } @article{43105, author = {{Black, Tobias and Fuest, Mario and Lankeit, Johannes and Mizukami, Masaaki}}, issn = {{1468-1218}}, journal = {{Nonlinear Analysis: Real World Applications}}, keywords = {{Applied Mathematics, Computational Mathematics, General Economics, Econometrics and Finance, General Engineering, General Medicine, Analysis}}, publisher = {{Elsevier BV}}, title = {{{Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source}}}, doi = {{10.1016/j.nonrwa.2023.103868}}, volume = {{73}}, year = {{2023}}, } @article{44077, author = {{Maack, Marten}}, issn = {{0167-6377}}, journal = {{Operations Research Letters}}, keywords = {{Applied Mathematics, Industrial and Manufacturing Engineering, Management Science and Operations Research, Software}}, number = {{3}}, pages = {{220--225}}, publisher = {{Elsevier BV}}, title = {{{Online load balancing on uniform machines with limited migration}}}, doi = {{10.1016/j.orl.2023.02.013}}, volume = {{51}}, year = {{2023}}, } @article{45757, abstract = {{AbstractThree prominent low order implicit time integration schemes are the first order implicit Euler-method, the second order trapezoidal rule and the second order Ellsiepen method. Its advantages are stability and comparatively low computational cost, however, they require the solution of a nonlinear system of equations. This paper presents a general approach for the construction of third order Runge–Kutta methods by embedding the above mentioned implicit schemes into the class of ELDIRK-methods. These will be defined to have an Explicit Last stage in the general Butcher array of Diagonal Implicit Runge–Kutta (DIRK) methods, with the consequence, that no additional system of equations must be solved. The main results—valid also for non-linear ordinary differential equations—are as follows: Two extra function calculations are required in order to embed the implicit Euler-method and one extra function calculation is required for the trapezoidal-rule and the Ellsiepen method, in order to obtain the third order properties, respectively. Two numerical examples are concerned with a parachute with viscous damping and a two-dimensional laser beam simulation. Here, we verify the higher order convergence behaviours of the proposed new ELDIRK-methods, and its successful performances for asymptotically exact global error estimation of so-called reversed embedded RK-method are shown. }}, author = {{Mahnken, Rolf}}, issn = {{0178-7675}}, journal = {{Computational Mechanics}}, keywords = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation}}}, doi = {{10.1007/s00466-023-02347-2}}, year = {{2023}}, } @article{46256, author = {{Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}}, issn = {{0895-4801}}, journal = {{SIAM Journal on Discrete Mathematics}}, keywords = {{General Mathematics}}, number = {{3}}, pages = {{1548--1565}}, publisher = {{Society for Industrial & Applied Mathematics (SIAM)}}, title = {{{Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs}}}, doi = {{10.1137/22m1500654}}, volume = {{37}}, year = {{2023}}, } @article{40607, abstract = {{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.}}, author = {{Dröse, Jennifer and Prediger, Susanne}}, issn = {{0173-5322}}, journal = {{Journal für Mathematik-Didaktik}}, keywords = {{Education, General Mathematics}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements}}}, doi = {{10.1007/s13138-022-00214-w}}, year = {{2023}}, } @article{46100, author = {{Hinrichs, Benjamin and Janssen, Daan W. and Ziebell, Jobst}}, issn = {{0022-247X}}, journal = {{Journal of Mathematical Analysis and Applications}}, keywords = {{Applied Mathematics, Analysis}}, number = {{1}}, publisher = {{Elsevier BV}}, title = {{{Super-Gaussian decay of exponentials: A sufficient condition}}}, doi = {{10.1016/j.jmaa.2023.127558}}, volume = {{528}}, year = {{2023}}, } @article{44081, author = {{Serino, Laura and Gil López, Jano and Stefszky, Michael and Ricken, Raimund and Eigner, Christof and Brecht, Benjamin and Silberhorn, Christine}}, issn = {{2691-3399}}, journal = {{PRX Quantum}}, keywords = {{General Physics and Astronomy, Mathematical Physics, Applied Mathematics, Electronic, Optical and Magnetic Materials, Electrical and Electronic Engineering, General Computer Science}}, number = {{2}}, publisher = {{American Physical Society (APS)}}, title = {{{Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States}}}, doi = {{10.1103/prxquantum.4.020306}}, volume = {{4}}, year = {{2023}}, } @article{53338, abstract = {{AbstractWe give an overview of analytical results concerned with chemotaxis systems where the signal is absorbed. We recall results on existence and properties of solutions for the prototypical chemotaxis‐consumption model and various variants and review more recent findings on its ability to support the emergence of spatial structures.}}, author = {{Lankeit, Johannes and Winkler, Michael}}, issn = {{0022-2526}}, journal = {{Studies in Applied Mathematics}}, keywords = {{Applied Mathematics}}, number = {{4}}, pages = {{1197--1229}}, publisher = {{Wiley}}, title = {{{Depleting the signal: Analysis of chemotaxis‐consumption models—A survey}}}, doi = {{10.1111/sapm.12625}}, volume = {{151}}, year = {{2023}}, } @article{29843, author = {{Castenow, Jannik and Kling, Peter and Knollmann, Till and Meyer auf der Heide, Friedhelm}}, issn = {{0890-5401}}, journal = {{Information and Computation}}, keywords = {{Computational Theory and Mathematics, Computer Science Applications, Information Systems, Theoretical Computer Science}}, publisher = {{Elsevier BV}}, title = {{{A Discrete and Continuous Study of the Max-Chain-Formation Problem}}}, doi = {{10.1016/j.ic.2022.104877}}, year = {{2022}}, } @article{30861, abstract = {{AbstractWe consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP). According to Pontryagin’s maximum principle, optimal solutions are concatenations of singular and bang arcs and exhibit the chattering or Fuller phenomenon, which is problematic for applications. To avoid chattering, we introduce a reduced model which is still biologically relevant and retains the important structural features of the original problem. Using a combination of analytical and numerical methods, we show that the singular arc is dominant in the studied DOCPs and exhibits the turnpike property. This property is further used in order to design simple and realistic suboptimal control strategies.}}, author = {{Caillau, Jean-Baptiste and Djema, Walid and Gouzé, Jean-Luc and Maslovskaya, Sofya and Pomet, Jean-Baptiste}}, issn = {{0022-3239}}, journal = {{Journal of Optimization Theory and Applications}}, keywords = {{Applied Mathematics, Management Science and Operations Research, Control and Optimization}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Turnpike Property in Optimal Microbial Metabolite Production}}}, doi = {{10.1007/s10957-022-02023-0}}, year = {{2022}}, } @article{31982, abstract = {{AbstractWe show that for a generic conformal metric perturbation of a compact hyperbolic 3-manifold $$\Sigma $$ Σ with Betti number $$b_1$$ b 1 , the order of vanishing of the Ruelle zeta function at zero equals $$4-b_1$$ 4 - b 1 , while in the hyperbolic case it is equal to $$4-2b_1$$ 4 - 2 b 1 . This is in contrast to the 2-dimensional case where the order of vanishing is a topological invariant. The proof uses the microlocal approach to dynamical zeta functions, giving a geometric description of generalized Pollicott–Ruelle resonant differential forms at 0 in the hyperbolic case and using first variation for the perturbation. To show that the first variation is generically nonzero we introduce a new identity relating pushforwards of products of resonant and coresonant 2-forms on the sphere bundle $$S\Sigma $$ S Σ with harmonic 1-forms on $$\Sigma $$ Σ .}}, author = {{Cekić, Mihajlo and Delarue, Benjamin and Dyatlov, Semyon and Paternain, Gabriel P.}}, issn = {{0020-9910}}, journal = {{Inventiones mathematicae}}, keywords = {{General Mathematics}}, number = {{1}}, pages = {{303--394}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds}}}, doi = {{10.1007/s00222-022-01108-x}}, volume = {{229}}, year = {{2022}}, } @article{31479, author = {{Baswana, Surender and Gupta, Shiv and Knollmann, Till}}, issn = {{0178-4617}}, journal = {{Algorithmica}}, keywords = {{Applied Mathematics, Computer Science Applications, General Computer Science}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Mincut Sensitivity Data Structures for the Insertion of an Edge}}}, doi = {{10.1007/s00453-022-00978-0}}, year = {{2022}}, } @article{33264, abstract = {{We investigate bifurcations in feedforward coupled cell networks. Feedforward structure (the absence of feedback) can be defined by a partial order on the cells. We use this property to study generic one-parameter steady state bifurcations for such networks. Branching solutions and their asymptotics are described in terms of Taylor coefficients of the internal dynamics. They can be determined via an algorithm that only exploits the network structure. Similar to previous results on feedforward chains, we observe amplifications of the growth rates of steady state branches induced by the feedforward structure. However, contrary to these earlier results, as the interaction scenarios can be more complicated in general feedforward networks, different branching patterns and different amplifications can occur for different regions in the space of Taylor coefficients.}}, author = {{von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}}, issn = {{0951-7715}}, journal = {{Nonlinearity}}, keywords = {{Applied Mathematics, General Physics and Astronomy, Mathematical Physics, Statistical and Nonlinear Physics}}, number = {{4}}, pages = {{2073--2120}}, publisher = {{IOP Publishing}}, title = {{{Amplified steady state bifurcations in feedforward networks}}}, doi = {{10.1088/1361-6544/ac5463}}, volume = {{35}}, year = {{2022}}, } @article{33332, author = {{Bopp, Frederik and Rojas, Jonathan and Revenga, Natalia and Riedl, Hubert and Sbresny, Friedrich and Boos, Katarina and Simmet, Tobias and Ahmadi, Arash and Gershoni, David and Kasprzak, Jacek and Ludwig, Arne and Reitzenstein, Stephan and Wieck, Andreas and Reuter, Dirk and Müller, Kai and Finley, Jonathan J.}}, issn = {{2511-9044}}, journal = {{Advanced Quantum Technologies}}, keywords = {{Electrical and Electronic Engineering, Computational Theory and Mathematics, Condensed Matter Physics, Mathematical Physics, Nuclear and High Energy Physics, Electronic, Optical and Magnetic Materials, Statistical and Nonlinear Physics}}, publisher = {{Wiley}}, title = {{{Quantum Dot Molecule Devices with Optical Control of Charge Status and Electronic Control of Coupling}}}, doi = {{10.1002/qute.202200049}}, year = {{2022}}, } @article{34261, abstract = {{Mechanical clinching is used to create lightweight hybrid structures. In order to estimate the service life of clinched components, its fatigue properties need to be known under different mechanical loading conditions. In addition to fatigue, corrosion is another factor that affects the fatigue life of clinched joints. In the literature, many corrosion and high-cycle fatigue damage models exist. However, little is known about how both phenomena interact in clinched joints. In this article, the influence of galvanic corrosion on clinched EN AW-6014/HCT590X + Z sheets on the fatigue life is investigated by means of numerical simulations and experimental results. An accurate prediction of the Wöhler lines of non-corroded and pre-corroded clinched specimens is shown.}}, author = {{Harzheim, Sven and Hofmann, Martin and Wallmersperger, Thomas}}, issn = {{1537-6494}}, journal = {{Mechanics of Advanced Materials and Structures}}, keywords = {{Mechanical Engineering, Mechanics of Materials, General Materials Science, General Mathematics, Civil and Structural Engineering}}, pages = {{1--6}}, publisher = {{Informa UK Limited}}, title = {{{Numerical fatigue life prediction of corroded and non-corroded clinched joints}}}, doi = {{10.1080/15376494.2022.2140233}}, year = {{2022}}, } @article{35306, author = {{Guedes Bonthonneau, Yannick and Weich, Tobias}}, issn = {{1435-9855}}, journal = {{Journal of the European Mathematical Society}}, keywords = {{Applied Mathematics, General Mathematics}}, number = {{3}}, pages = {{851--923}}, publisher = {{European Mathematical Society - EMS - Publishing House GmbH}}, title = {{{Ruelle–Pollicott resonances for manifolds with hyperbolic cusps}}}, doi = {{10.4171/jems/1103}}, volume = {{24}}, year = {{2022}}, } @article{34633, author = {{Hesse, Kerstin and Le Gia, Quoc Thong}}, issn = {{0377-0427}}, journal = {{Journal of Computational and Applied Mathematics}}, keywords = {{Applied Mathematics, Computational Mathematics}}, publisher = {{Elsevier BV}}, title = {{{L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data}}}, doi = {{10.1016/j.cam.2022.114118}}, volume = {{408}}, year = {{2022}}, }