@article{Moenius2021,
  author    = {M{\"o}nius, Katja},
  title     = {Eigenvalues of zero-divisor graphs of finite commutative rings},
  series = {Journal of Algebraic Combinatorics},
  volume    = {54},
  journal   = {Journal of Algebraic Combinatorics},
  issn      = {0925-9899},
  doi       = {10.1007/s10801-020-00989-6},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-232792},
  pages     = {787-802},
  year      = {2021},
  abstract  = {We investigate eigenvalues of the zero-divisor graph Γ(R) of finite commutative rings R and study the interplay between these eigenvalues, the ring-theoretic properties of R and the graph-theoretic properties of Γ(R). The graph Γ(R) is defined as the graph with vertex set consisting of all nonzero zero-divisors of R and adjacent vertices x, y whenever xy=0. We provide formulas for the nullity of Γ(R), i.e., the multiplicity of the eigenvalue 0 of Γ(R). Moreover, we precisely determine the spectra of \(\Gamma ({\mathbb {Z}}_p \times {\mathbb {Z}}_p \times {\mathbb {Z}}_p)\) and \(\Gamma ({\mathbb {Z}}_p \times {\mathbb {Z}}_p \times {\mathbb {Z}}_p \times {\mathbb {Z}}_p)\) for a prime number p. We introduce a graph product ×Γ with the property that Γ(R)≅Γ(R\(_1\))×Γ⋯×ΓΓ(R\(_r\)) whenever R≅R\(_1\)×⋯×R\(_r\). With this product, we find relations between the number of vertices of the zero-divisor graph Γ(R), the compressed zero-divisor graph, the structure of the ring R and the eigenvalues of Γ(R).},
  language  = {en}
}
@article{KalousekMitraSchloemerkemper2021,
  author    = {Kalousek, Martin and Mitra, Sourav and Schl{\"o}merkemper, Anja},
  title     = {Existence of weak solutions of diffuse interface models for magnetic fluids},
  series = {Proceedings in Applied Mathematics and Mechanics},
  volume    = {21},
  journal   = {Proceedings in Applied Mathematics and Mechanics},
  number    = {1},
  doi       = {10.1002/pamm.202100205},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-257642},
  year      = {2021},
  abstract  = {In this article we collect some recent results on the global existence of weak solutions for diffuse interface models involving incompressible magnetic fluids. We consider both the cases of matched and unmatched specific densities. For the model involving fluids with identical densities we consider the free energy density to be a double well potential whereas for the unmatched density case it is crucial to work with a singular free energy density.},
  language  = {en}
}
@article{Schoenlein2020,
  author    = {Sch{\"o}nlein, Michael},
  title     = {Ensemble reachability of homogenous parameter-depedent systems},
  series = {Proceedings in Applied Mathematics and Mechanics},
  volume    = {20},
  journal   = {Proceedings in Applied Mathematics and Mechanics},
  number    = {1},
  doi       = {10.1002/pamm.202000342},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-257637},
  year      = {2020},
  abstract  = {In this paper we consider the class (θA, B) of parameter-dependent linear systems given by matrices A ∈ ℂ\(^{nxn}\) and B ∈ ℂ\(^{nxm}\). This class is of interest for several applications and the frequently met task for such systems is to steer the origin toward a given target family f(θ) by using an input that is independent from the parameter. This paper provides a collection of necessary and sufficient conditions for ensemble reachability for these systems.},
  language  = {en}
}
@misc{Breitenbach2018,
  author    = {Breitenbach, Tim},
  title     = {Codes of examples for SQH method},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-165669},
  year      = {2018},
  abstract  = {Code examples for the paper "On the SQH Scheme to Solve Nonsmooth PDE Optimal Control Problems" by Tim Breitenbach and Alfio Borz{\`i} published in the journal "Numerical Functional Analysis and Optimization", in 2019, DOI: 10.1080/01630563.2019.1599911},
  language  = {en}
}
@article{BreitenbachHelfrichFoersterDandekar2021,
  author    = {Breitenbach, Tim and Helfrich-F{\"o}rster, Charlotte and Dandekar, Thomas},
  title     = {An effective model of endogenous clocks and external stimuli determining circadian rhythms},
  series = {Scientific Reports},
  volume    = {11},
  journal   = {Scientific Reports},
  number    = {1},
  doi       = {10.1038/s41598-021-95391-y},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-261655},
  pages     = {16165},
  year      = {2021},
  abstract  = {Circadian endogenous clocks of eukaryotic organisms are an established and rapidly developing research field. To investigate and simulate in an effective model the effect of external stimuli on such clocks and their components we developed a software framework for download and simulation. The application is useful to understand the different involved effects in a mathematical simple and effective model. This concerns the effects of Zeitgebers, feedback loops and further modifying components. We start from a known mathematical oscillator model, which is based on experimental molecular findings. This is extended with an effective framework that includes the impact of external stimuli on the circadian oscillations including high dose pharmacological treatment. In particular, the external stimuli framework defines a systematic procedure by input-output-interfaces to couple different oscillators. The framework is validated by providing phase response curves and ranges of entrainment. Furthermore, Aschoffs rule is computationally investigated. It is shown how the external stimuli framework can be used to study biological effects like points of singularity or oscillators integrating different signals at once. The mathematical framework and formalism is generic and allows to study in general the effect of external stimuli on oscillators and other biological processes. For an easy replication of each numerical experiment presented in this work and an easy implementation of the framework the corresponding Mathematica files are fully made available. They can be downloaded at the following link: https://www.biozentrum.uni-wuerzburg.de/bioinfo/computing/circadian/.},
  language  = {en}
}
@phdthesis{Jia2023,
  author    = {Jia, Xiaoxi},
  title     = {Augmented Lagrangian Methods invoking (Proximal) Gradient-type Methods for (Composite) Structured Optimization Problems},
  doi       = {10.25972/OPUS-32374},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-323745},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2023},
  abstract  = {This thesis, first, is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints, subsequently, as well as constrained structured optimization problems featuring a composite objective function and set-membership constraints. It is then concerned to convergence and rate-of-convergence analysis of proximal gradient methods for the composite optimization problems in the presence of the Kurdyka--{\L}ojasiewicz property without global Lipschitz assumption.},
  language  = {en}
}
@article{JustSiller2022,
  author    = {Just, Janina and Siller, Hans-Stefan},
  title     = {The role of mathematics in STEM secondary classrooms: a systematic literature review},
  series = {Education Sciences},
  volume    = {12},
  journal   = {Education Sciences},
  number    = {9},
  issn      = {2227-7102},
  doi       = {10.3390/educsci12090629},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-288075},
  year      = {2022},
  abstract  = {Nowadays, science, technology, engineering, and mathematics (STEM) play a critical role in a nation's global competitiveness and prosperity. Thus, there is a need to educate students in these subjects to meet the current and future demands of personal life and society. While applications, especially in science, engineering, and technology, are directly obvious, mathematics underpins the other STEM disciplines. It is recognized that mathematics is the foundation for all other STEM disciplines; the role of mathematics in classrooms is not clear yet. Therefore, the question arises: What is the current role of mathematics in secondary STEM classrooms? To answer this question, we conducted a systematic literature review based on three publication databases (Web of Science, ERIC, and EBSCO Teacher Referral Center). This literature review paper is intended to contribute to the current state of the role of mathematics in STEM education in secondary classrooms. Through the search, starting with 1910 documents, only 14 eligible documents were found. In these, mathematics is often seen as a minor matter and a means to an end in the eyes of science educators. From this, we conclude that the role of mathematics in the STEM classroom should be further strengthened. Overall, the paper highlights a major research gap, and proposes possible initial solutions to close it.},
  language  = {en}
}
@article{Weishaeupl2023,
  author    = {Weish{\"a}upl, Sebastian},
  title     = {The weak Gram law for Hecke \(L\)-functions},
  series = {The Ramanujan Journal},
  volume    = {60},
  journal   = {The Ramanujan Journal},
  number    = {4},
  issn      = {1382-4090},
  doi       = {10.1007/s11139-022-00638-5},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324404},
  pages     = {981-997},
  year      = {2023},
  abstract  = {We generalize a theorem by Titchmarsh about the mean value of Hardy's \(Z\)-function at the Gram points to the Hecke \(L\)-functions, which in turn implies the weak Gram law for them. Instead of proceeding analogously to Titchmarsh with an approximate functional equation we employ a different method using contour integration.},
  language  = {en}
}
@article{AppellBritoReinwand2022,
  author    = {Appell, J{\"u}rgen and Brito, Bel{\´e}n L{\´o}pez and Reinwand, Simon},
  title     = {Counterexamples on compositions},
  series = {Mathematische Semesterberichte},
  volume    = {70},
  journal   = {Mathematische Semesterberichte},
  number    = {1},
  issn      = {0720-728X},
  doi       = {10.1007/s00591-022-00318-x},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324306},
  pages     = {43-56},
  year      = {2022},
  abstract  = {We give a collection of 16 examples which show that compositions \(g\) \(\circ\) \(f\) of well-behaved functions \(f\) and \(g\) can be badly behaved. Remarkably, in 10 of the 16 examples it suffices to take as outer function \(g\) simply a power-type or characteristic function. Such a collection of examples may serve as a source of exercises for a calculus course.},
  language  = {en}
}
@article{LuMoenius2023,
  author    = {Lu, Lu and M{\"o}nius, Katja},
  title     = {Algebraic degree of Cayley graphs over abelian groups and dihedral groups},
  series = {Journal of Algebraic Combinatorics},
  volume    = {57},
  journal   = {Journal of Algebraic Combinatorics},
  number    = {3},
  issn      = {0925-9899},
  doi       = {10.1007/s10801-022-01190-7},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324380},
  pages     = {753-761},
  year      = {2023},
  abstract  = {For a graph \(\Gamma\) , let K be the smallest field containing all eigenvalues of the adjacency matrix of \(\Gamma\) . The algebraic degree \(\deg (\Gamma )\) is the extension degree \([K:\mathbb {Q}]\). In this paper, we completely determine the algebraic degrees of Cayley graphs over abelian groups and dihedral groups.},
  language  = {en}
}