@article{61042,
  abstract     = {{We introduce the concept of a k-token signed graph and study some of its combinatorial and algebraic properties. We prove that two switching isomorphic signed graphs have switching isomorphic token graphs. Moreover, we show that the Laplacian spectrum of a balanced signed graph is contained in the Laplacian spectra of its k-token signed graph. Besides, we introduce and study the unbalance level of a signed graph, which is a new parameter that measures how far a signed graph is from being balanced. Moreover, we study the relation between the frustration index and the unbalance level of signed graphs and their token signed graphs.}},
  author       = {{Dalfó, C. and Fiol, M. A. and Steffen, Eckhard}},
  issn         = {{0925-9899}},
  journal      = {{Journal of Algebraic Combinatorics}},
  number       = {{1}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{On token signed graphs}}},
  doi          = {{10.1007/s10801-025-01416-4}},
  volume       = {{62}},
  year         = {{2025}},
}

@article{61125,
  author       = {{Biehler, Rolf and Liebendörfer, Michael and Schmitz, Angela and Reich, Birte}},
  journal      = {{Mitteilungen der Deutschen Mathematiker-Vereinigung}},
  number       = {{3}},
  pages        = {{170–171}},
  publisher    = {{De Gruyter}},
  title        = {{{studiVEMINT Mathematik-Online-Vorkurs jetzt mit 300 integrierten Lernvideos frei verfügbar}}},
  volume       = {{33}},
  year         = {{2025}},
}

@article{54970,
  author       = {{Quack, Carolin and Bruns, Julia}},
  journal      = {{Frühe Bildung}},
  number       = {{2}},
  pages        = {{72--78}},
  title        = {{{Mathematikbezogenes Wissen, Einstellungen und Lerngelegenheiten als Einflussfaktoren der situativen Beobachtung und Wahrnehmung angehender frühpädagogischer Fachkräfte}}},
  doi          = {{https://doi.org/10.1026/2191-9186/a000712}},
  volume       = {{14}},
  year         = {{2025}},
}

@article{62291,
  abstract     = {{In [Jalowy, Kabluchko, Marynych, arXiv:2504.11593v1, 2025], the authors discuss a user-friendly approach to determine the limiting empirical zero distribution of a sequence of real-rooted polynomials, as the degree goes to $\infty$. In this note, we aim to apply it to a vast range of examples of polynomials providing a unifying source for limiting empirical zero distributions.
 We cover Touchard, Fubini, Eulerian, Narayana and little $q$-Laguerre polynomials as well as hypergeometric polynomials including the classical Hermite, Laguerre and Jacobi polynomials. We construct polynomials whose empirical zero distributions converge to the free multiplicative normal and Poisson distributions. Furthermore, we study polynomials generated by some differential operators. As one inverse result, we derive coefficient asymptotics of the characteristic polynomial of random covariance matrices.}},
  title        = {{{Zeros and exponential profiles of polynomials II: Examples}}},
  doi          = {{10.48550/ARXIV.2509.11248}},
  year         = {{2025}},
}

@article{56131,
  abstract     = {{This article provides a comprehensive mathematical-didactic analysis of how the highly relevant topic symmetry can be prepared for the university education of PSTs. Methodologically, the analysis is embedded in a design research cycle and serves as preparation for the actual design of learning activities. The procedure of "specifying and structuring" learning objects is used and adapted in such a way that, in addition to mathematical aspects, profession-oriented references to school mathematics are also considered. An essential result of the analysis is the formulation of so-called interface aspects to symmetry, which prove to be helpful in establishing such references. }},
  author       = {{Hoffmann, Max}},
  journal      = {{Recherches en Didactique des Mathématiques}},
  number       = {{2}},
  pages        = {{85--120}},
  title        = {{{Symmetry as a Topic for the University Education of Pre-Service Teachers}}},
  doi          = {{10.46298/rdm.14256}},
  volume       = {{45}},
  year         = {{2025}},
}

@inproceedings{65246,
  author       = {{Hoffmann, Max}},
  booktitle    = {{Proceedings of the Fourteenth Congress of the European Society for Research in Mathematics Education (CERME14)}},
  editor       = {{Bosch, Marianna and Bolondi, Giorgio and Carreira, Susana and Gaidoschik, Michael and Spagnolo, Camilla}},
  pages        = {{2245--2252}},
  publisher    = {{Free University of Bozen-Bolzano and ERME}},
  title        = {{{Using scriptwriting as a response format for interface tasks: Exemplary analyses in the context of symmetry}}},
  year         = {{2025}},
}

@article{53413,
  abstract     = {{For negatively curved symmetric spaces it is known that the poles of the
scattering matrices defined via the standard intertwining operators for the
spherical principal representations of the isometry group are either given as
poles of the intertwining operators or as quantum resonances, i.e. poles of the
meromorphically continued resolvents of the Laplace-Beltrami operator. We
extend this result to classical locally symmetric spaces of negative curvature
with convex-cocompact fundamental group using results of Bunke and Olbrich. The
method of proof forces us to exclude the spectral parameters corresponding to
singular Poisson transforms.}},
  author       = {{Delarue, Benjamin and Hilgert, Joachim}},
  issn         = {{0949-5932}},
  journal      = {{Journal of Lie Theory}},
  number       = {{(4)}},
  pages        = {{787----804}},
  title        = {{{Quantum resonances and scattering poles of classical rank one locally  symmetric spaces}}},
  volume       = {{35}},
  year         = {{2025}},
}

@article{65657,
  author       = {{Hoffmann, Jan Sören and Stoppel, Hans-Jürgen}},
  journal      = {{mathematik lehren}},
  number       = {{253}},
  pages        = {{8--12}},
  title        = {{{Das Sieb des Eratosthenes}}},
  year         = {{2025}},
}

@article{65713,
  author       = {{Stoppel, Hans-Jürgen and Plangg, Simon and Büscher, Carina}},
  journal      = {{mathemathik lehren}},
  number       = {{253}},
  pages        = {{2--7}},
  publisher    = {{Friedrich Verlag}},
  title        = {{{Mathematik weiterdenken - Wie informatisches Denken die Mathematik stärkt}}},
  year         = {{2025}},
}

@inbook{64806,
  author       = {{Biehler, Rolf and Kawakami, T. and Lampen, E. and Weiland, T. and Zapata-Cardona, L.}},
  booktitle    = {{Proceedings of the 15th International Congress on Mathematical Education}},
  editor       = {{Beswick, K. and Kaur, B. and Makar, K. and Ochoviet, C. and Venkat, H.}},
  pages        = {{198--203}},
  publisher    = {{MERGA}},
  title        = {{{Statistics and data science education as a vehicle for empowering citizens – short summary of a survey}}},
  volume       = {{1}},
  year         = {{2025}},
}

@unpublished{62262,
  abstract     = {{We construct the first examples of chamber-regular lattices on C̃₂-buildings. Assuming a conjecture of Kantor our list of examples becomes a classification for chamber-regular C̃₂-lattices on locally-finite C̃₂-buildings. The links of special vertices in the buildings we construct, are all isomorphic to (the incidence graph of) the unique generalized quadrangle Q of order (3,5). In particular our constructions involve chamber-regular actions on Q. These actions on Q are the first (and if Kantor's conjecture holds the only) chamber-regular actions on a finite generalized quadrangle and therefore interesting in their own right. Moreover Q is not Moufang and therefore none of our examples is a Bruhat-Tits building and all our lattices are exotic building lattices.}},
  author       = {{Stamer, Franziska and Titz Mite, Thomas }},
  pages        = {{29}},
  title        = {{{On Chamber-regular C̃₂-Lattices}}},
  year         = {{2025}},
}

@article{66278,
  author       = {{Biehler, Rolf and Kawakami, Takashi and Lampen, Erna and Weiland, Travis and Zapata-Cardona, Lucía}},
  journal      = {{European Mathematical Society Magazine}},
  number       = {{136}},
  pages        = {{49–52}},
  title        = {{{Statistics and data science education as a vehicle for empowering citizens–short summary of a survey}}},
  doi          = {{10.17619/UNIPB/1-2633}},
  year         = {{2025}},
}

@article{51208,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>Approximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions.</jats:p>}},
  author       = {{Gebken, Bennet}},
  issn         = {{0926-6003}},
  journal      = {{Computational Optimization and Applications}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Control and Optimization}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{A note on the convergence of deterministic gradient sampling in nonsmooth optimization}}},
  doi          = {{10.1007/s10589-024-00552-0}},
  year         = {{2024}},
}

@article{46019,
  abstract     = {{We derive efficient algorithms to compute weakly Pareto optimal solutions for smooth, convex and unconstrained multiobjective optimization problems in general Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical system in the multiobjective setting, which trajectories converge weakly to Pareto optimal solutions. Discretization of this system yields an inertial multiobjective algorithm which generates sequences that converge weakly to Pareto optimal solutions. We employ Nesterov acceleration to define an algorithm with an improved convergence rate compared to the plain multiobjective steepest descent method (Algorithm 1). A further improvement in terms of efficiency is achieved by avoiding the solution of a quadratic subproblem to compute a common step direction for all objective functions, which is usually required in first-order methods. Using a different discretization of our inertial gradient-like dynamical system, we obtain an accelerated multiobjective gradient method that does not require the solution of a subproblem in each step (Algorithm 2). While this algorithm does not converge in general, it yields good results on test problems while being faster than standard steepest descent.}},
  author       = {{Sonntag, Konstantin and Peitz, Sebastian}},
  journal      = {{Journal of Optimization Theory and Applications}},
  publisher    = {{Springer}},
  title        = {{{Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems}}},
  doi          = {{10.1007/s10957-024-02389-3}},
  year         = {{2024}},
}

@unpublished{51334,
  abstract     = {{The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points, where in each iteration, an approximation of the subdifferential is computed in an efficient manner and then used to compute a common descent direction for all objective functions. To prove convergence, we present some new optimality results for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these, we can show that every accumulation point of the sequence generated by our algorithm is Pareto critical under common assumptions. Computational efficiency for finding Pareto critical points is numerically demonstrated for multiobjective optimal control of an obstacle problem.}},
  author       = {{Sonntag, Konstantin and Gebken, Bennet and Müller, Georg and Peitz, Sebastian and Volkwein, Stefan}},
  booktitle    = {{arXiv:2402.06376}},
  title        = {{{A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces}}},
  year         = {{2024}},
}

@unpublished{52691,
  abstract     = {{We prove Feynman-Kac formulas for the semigroups generated by selfadjoint
operators in a class containing Fr\"ohlich Hamiltonians known from solid state
physics. The latter model multi-polarons, i.e., a fixed number of quantum
mechanical electrons moving in a polarizable crystal and interacting with the
quantized phonon field generated by the crystal's vibrational modes. Both the
electrons and phonons can be confined to suitable open subsets of Euclidean
space. We also include possibly very singular magnetic vector potentials and
electrostatic potentials. Our Feynman-Kac formulas comprise Fock space
operator-valued multiplicative functionals and can be applied to every vector
in the underlying Hilbert space. In comparison to the renormalized Nelson
model, for which analogous Feynman-Kac formulas are known, the analysis of the
creation and annihilation terms in the multiplicative functionals requires
novel ideas to overcome difficulties caused by the phonon dispersion relation
being constant. Getting these terms under control and generalizing other
construction steps so as to cover confined systems are the main achievements of
this article.}},
  author       = {{Hinrichs, Benjamin and Matte, Oliver}},
  booktitle    = {{arXiv:2403.12147}},
  title        = {{{Feynman-Kac formulas for semigroups generated by multi-polaron  Hamiltonians in magnetic fields and on general domains}}},
  year         = {{2024}},
}

@article{52726,
  abstract     = {{Heteroclinic structures organize global features of dynamical systems. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analysed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures.}},
  author       = {{Bick, Christian and von der Gracht, Sören}},
  issn         = {{2051-1329}},
  journal      = {{Journal of Complex Networks}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Control and Optimization, Management Science and Operations Research, Computer Networks and Communications}},
  number       = {{2}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Heteroclinic dynamics in network dynamical systems with higher-order interactions}}},
  doi          = {{10.1093/comnet/cnae009}},
  volume       = {{12}},
  year         = {{2024}},
}

@article{49905,
  abstract     = {{For 0 ≤ t ≤ r let m(t, r) be the maximum number s such that every t-edge-connected r-graph has s pairwise disjoint perfect matchings. There are only a few values of m(t, r) known, for instance m(3, 3) = m(4, r) = 1, and m(t, r) ≤ r − 2 for all t  = 5,
and m(t, r) ≤ r − 3 if r is even. We prove that m(2l, r) ≤ 3l − 6 for every l ≥ 3 and r ≥ 2l.}},
  author       = {{Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}},
  issn         = {{0209-9683}},
  journal      = {{Combinatorica}},
  keywords     = {{Computational Mathematics, Discrete Mathematics and Combinatorics}},
  pages        = {{429--440}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs}}},
  doi          = {{10.1007/s00493-023-00078-9}},
  volume       = {{44}},
  year         = {{2024}},
}

@article{53101,
  abstract     = {{In this work, we consider optimal control problems for mechanical systems with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an affine control term. Classically, Pontryagin's maximum principle gives necessary optimality conditions for the optimal control problem. For smooth problems, alternatively, a variational approach based on an augmented objective can be followed. Here, we propose a new Lagrangian approach leading to equivalent necessary optimality conditions in the form of Euler-Lagrange equations. Thus, the differential geometric structure (similar to classical Lagrangian dynamics) can be exploited in the framework of optimal control problems. In particular, the formulation enables the symplectic discretisation of the optimal control problem via variational integrators in a straightforward way.}},
  author       = {{Leyendecker, Sigrid and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Almagro, Rodrigo T. Sato Martín de and Szemenyei, Flóra Orsolya}},
  issn         = {{2158-2491}},
  journal      = {{Journal of Computational Dynamics}},
  keywords     = {{Optimal control problem, Lagrangian system, Hamiltonian system, Variations, Pontryagin's maximum principle.}},
  pages        = {{0--0}},
  publisher    = {{American Institute of Mathematical Sciences (AIMS)}},
  title        = {{{A new Lagrangian approach to control affine systems with a quadratic Lagrange term}}},
  doi          = {{10.3934/jcd.2024017}},
  year         = {{2024}},
}

@article{52584,
  author       = {{Rezat, Sebastian}},
  journal      = {{ZDM – Mathematics Education}},
  publisher    = {{Springer}},
  title        = {{{Research on curriculum resources in mathematics education: a survey of the field}}},
  doi          = {{10.1007/s11858-024-01559-x}},
  year         = {{2024}},
}