@phdthesis{Barth2022,
  author    = {Barth, Dominik},
  title     = {Computation of multi-branch-point covers and applications in Galois theory},
  doi       = {10.25972/OPUS-27702},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-277025},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {We present a technique for computing multi-branch-point covers with prescribed ramification and demonstrate the applicability of our method in relatively large degrees by computing several families of polynomials with symplectic and linear Galois groups. As a first application, we present polynomials over \(\mathbb{Q}(\alpha,t)\) for the primitive rank-3 groups \(PSp_4(3)\) and \(PSp_4(3).C_2\) of degree 27 and for the 2-transitive group \(PSp_6(2)\) in its actions on 28 and 36 points, respectively. Moreover, the degree-28 polynomial for \(PSp_6(2)\) admits infinitely many totally real specializations. Next, we present the first (to the best of our knowledge) explicit polynomials for the 2-transitive linear groups \(PSL_4(3)\) and \(PGL_4(3)\) of degree 40, and the imprimitive group \(Aut(PGL_4(3))\) of degree 80. Additionally, we negatively answer a question by K{\"o}nig whether there exists a degree-63 rational function with rational coefficients and monodromy group \(PSL_6(2)\) ramified over at least four points. This is achieved due to the explicit computation of the corresponding hyperelliptic genus-3 Hurwitz curve parameterizing this family, followed by a search for rational points on it. As a byproduct of our calculations we obtain the first explicit \(Aut(PSL_6(2))\)-realizations over \(\mathbb{Q}(t)\). At last, we present a technique by Elkies for bounding the transitivity degree of Galois groups. This provides an alternative way to verify the Galois groups from the previous chapters and also yields a proof that the monodromy group of a degree-276 cover computed by Monien is isomorphic to the sporadic 2-transitive Conway group \(Co_3\).},
  subject      = {Galois-Theorie},
  language  = {en}
}
@article{KakaroumpasSoleriGibert2022,
  author    = {Kakaroumpas, Spyridon and Soler i Gibert, Od{\´i}},
  title     = {Dyadic product BMO in the Bloom setting},
  series = {Journal of the London Mathematical Society},
  volume    = {106},
  journal   = {Journal of the London Mathematical Society},
  number    = {2},
  issn      = {0024-6107},
  doi       = {10.1112/jlms.12588},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-318602},
  pages     = {899 -- 935},
  year      = {2022},
  abstract  = {{\´O}. Blasco and S. Pott showed that the supremum of operator norms over L\(^{2}\) of all bicommutators (with the same symbol) of one-parameter Haar multipliers dominates the biparameter dyadic product BMO norm of the symbol itself. In the present work we extend this result to the Bloom setting, and to any exponent 1 < p < ∞. The main tool is a new characterization in terms of paraproducts and two-weight John-Nirenberg inequalities for dyadic product BMO in the Bloom setting. We also extend our results to the whole scale of indexed spaces between little bmo and product BMO in the general multiparameter setting, with the appropriate iterated commutator in each case.},
  language  = {en}
}
@phdthesis{Lechner2022,
  author    = {Lechner, Theresa},
  title     = {Proximal Methods for Nonconvex Composite Optimization Problems},
  doi       = {10.25972/OPUS-28907},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-289073},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {Optimization problems with composite functions deal with the minimization of the sum of a smooth function and a convex nonsmooth function. In this thesis several numerical methods for solving such problems in finite-dimensional spaces are discussed, which are based on proximity operators. After some basic results from convex and nonsmooth analysis are summarized, a first-order method, the proximal gradient method, is presented and its convergence properties are discussed in detail. Known results from the literature are summarized and supplemented by additional ones. Subsequently, the main part of the thesis is the derivation of two methods which, in addition, make use of second-order information and are based on proximal Newton and proximal quasi-Newton methods, respectively. The difference between the two methods is that the first one uses a classical line search, while the second one uses a regularization parameter instead. Both techniques lead to the advantage that, in contrast to many similar methods, in the respective detailed convergence analysis global convergence to stationary points can be proved without any restricting precondition. Furthermore, comprehensive results show the local convergence properties as well as convergence rates of these algorithms, which are based on rather weak assumptions. Also a method for the solution of the arising proximal subproblems is investigated. In addition, the thesis contains an extensive collection of application examples and a detailed discussion of the related numerical results.},
  subject      = {Optimierung},
  language  = {en}
}
@article{DashkovskiySlynko2022,
  author    = {Dashkovskiy, Sergey and Slynko, Vitalii},
  title     = {Stability conditions for impulsive dynamical systems},
  series = {Mathematics of Control, Signals, and Systems},
  volume    = {34},
  journal   = {Mathematics of Control, Signals, and Systems},
  number    = {1},
  issn      = {1435-568X},
  doi       = {10.1007/s00498-021-00305-y},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-268390},
  pages     = {95-128},
  year      = {2022},
  abstract  = {In this work, we consider impulsive dynamical systems evolving on an infinite-dimensional space and subjected to external perturbations. We look for stability conditions that guarantee the input-to-state stability for such systems. Our new dwell-time conditions allow the situation, where both continuous and discrete dynamics can be unstable simultaneously. Lyapunov like methods are developed for this purpose. Illustrative finite and infinite dimensional examples are provided to demonstrate the application of the main results. These examples cannot be treated by any other published approach and demonstrate the effectiveness of our results.},
  language  = {en}
}
@phdthesis{Stumpf2022,
  author    = {Stumpf, Pascal},
  title     = {On coverings and reduced residues in combinatorial number theory},
  doi       = {10.25972/OPUS-29350},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-293504},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {Our starting point is the Jacobsthal function \(j(m)\), defined for each positive integer \(m\) as the smallest number such that every \(j(m)\) consecutive integers contain at least one integer relatively prime to \(m\). It has turned out that improving on upper bounds for \(j(m)\) would also lead to advances in understanding the distribution of prime numbers among arithmetic progressions. If \(P_r\) denotes the product of the first \(r\) prime numbers, then a conjecture of Montgomery states that \(j(P_r)\) can be bounded from above by \(r (\log r)^2\) up to some constant factor. However, the until now very promising sieve methods seem to have reached a limit here, and the main goal of this work is to develop other combinatorial methods in hope of coming a bit closer to prove the conjecture of Montgomery. Alongside, we solve a problem of Recam{\´a}n about the maximum possible length among arithmetic progressions in the least (positive) reduced residue system modulo \(m\). Lastly, we turn towards three additive representation functions as introduced by Erdős, S{\´a}rk{\"o}zy and S{\´o}s who studied their surprising different monotonicity behavior. By an alternative approach, we answer a question of S{\´a}rk{\"o}zy and demostrate that another conjecture does not hold.},
  subject      = {Kombinatorische Zahlentheorie},
  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}
}
@misc{Kanzow2022,
  author    = {Kanzow, Christian},
  title     = {Y. Cui, J.-S. Pang: "Modern Nonconvex Nondifferentiable Optimization"},
  series = {Jahresbericht der Deutschen Mathematiker-Vereinigung},
  volume    = {124},
  journal   = {Jahresbericht der Deutschen Mathematiker-Vereinigung},
  number    = {2},
  issn      = {0012-0456},
  doi       = {10.1365/s13291-022-00250-y},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324346},
  pages     = {137-143},
  year      = {2022},
  abstract  = {No abstract available.},
  language  = {en}
}
@article{KanzowMehlitz2022,
  author    = {Kanzow, Christian and Mehlitz, Patrick},
  title     = {Convergence properties of monotone and nonmonotone proximal gradient methods revisited},
  series = {Journal of Optimization Theory and Applications},
  volume    = {195},
  journal   = {Journal of Optimization Theory and Applications},
  number    = {2},
  issn      = {0022-3239},
  doi       = {10.1007/s10957-022-02101-3},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324351},
  pages     = {624-646},
  year      = {2022},
  abstract  = {Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the objective function is of simple enough structure. The available convergence theory associated with these methods (mostly) requires the derivative of the smooth part of the objective function to be (globally) Lipschitz continuous, and this might be a restrictive assumption in some practically relevant scenarios. In this paper, we readdress this classical topic and provide convergence results for the classical (monotone) proximal gradient method and one of its nonmonotone extensions which are applicable in the absence of (strong) Lipschitz assumptions. This is possible since, for the price of forgoing convergence rates, we omit the use of descent-type lemmas in our analysis.},
  language  = {en}
}
@article{KourouZarvalis2022,
  author    = {Kourou, Maria and Zarvalis, Konstantinos},
  title     = {Compact sets in petals and their backward orbits under semigroups of holomorphic functions},
  series = {Potential Analysis},
  volume    = {59},
  journal   = {Potential Analysis},
  number    = {4},
  issn      = {0926-2601},
  doi       = {10.1007/s11118-022-10036-7},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324368},
  pages     = {1913-1939},
  year      = {2022},
  abstract  = {Let (ϕ\(_t\))\(_{t≥0}\) be a semigroup of holomorphic functions in the unit disk \(\mathbb {D}\) and K a compact subset of \(\mathbb {D}\). We investigate the conditions under which the backward orbit of K under the semigroup exists. Subsequently, the geometric characteristics, as well as, potential theoretic quantities for the backward orbit of K are examined. More specifically, results are obtained concerning the asymptotic behavior of its hyperbolic area and diameter, the harmonic measure and the capacity of the condenser that K forms with the unit disk.},
  language  = {en}
}
@article{FallMinlendRatzkin2022,
  author    = {Fall, Mouhammed Moustapha and Minlend, Ignace Aristide and Ratzkin, Jesse},
  title     = {Foliation of an Asymptotically Flat End by Critical Capacitors},
  series = {The Journal of Geometric Analysis},
  volume    = {32},
  journal   = {The Journal of Geometric Analysis},
  number    = {2},
  issn      = {1559-002X},
  doi       = {10.1007/s12220-021-00746-6},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-269997},
  year      = {2022},
  abstract  = {We construct a foliation of an asymptotically flat end of a Riemannian manifold by hypersurfaces which are critical points of a natural functional arising in potential theory. These hypersurfaces are perturbations of large coordinate spheres, and they admit solutions of a certain over-determined boundary value problem involving the Laplace-Beltrami operator. In a key step we must invert the Dirichlet-to-Neumann operator, highlighting the nonlocal nature of our problem.},
  language  = {en}
}
@article{EastonvanDalenGoebetal.2022,
  author    = {Easton, Andrew and van Dalen, Okki and Goeb, Rainer and Di Bucchianico, Alessandro},
  title     = {Bivariate copula monitoring},
  series = {Quality and Reliability Engineering International},
  volume    = {38},
  journal   = {Quality and Reliability Engineering International},
  number    = {3},
  doi       = {10.1002/qre.3034},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-276501},
  pages     = {1272 -- 1288},
  year      = {2022},
  abstract  = {The assumption of multivariate normality underlying the Hotelling T\(^{2}\) chart is often violated for process data. The multivariate dependency structure can be separated from marginals with the help of copula theory, which permits to model association structures beyond the covariance matrix. Copula-based estimation and testing routines have reached maturity regarding a variety of practical applications. We have constructed a rich design matrix for the comparison of the Hotelling T\(^{2}\) chart with the copula test by Verdier and the copula test by Vuong, which allows for weighting the observations adaptively. Based on the design matrix, we have conducted a large and computationally intensive simulation study. The results show that the copula test by Verdier performs better than Hotelling T\(^{2}\) in a large variety of out-of-control cases, whereas the weighted Vuong scheme often fails to provide an improvement.},
  language  = {en}
}
@article{CampanaBorzi2022,
  author    = {Campana, Francesca Cal{\`a} and Borz{\`i}, Alfio},
  title     = {On the SQH Method for Solving Differential Nash Games},
  series = {Journal of Dynamical and Control Systems},
  volume    = {28},
  journal   = {Journal of Dynamical and Control Systems},
  issn      = {1573-8698},
  doi       = {10.1007/s10883-021-09546-1},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-269111},
  pages     = {739-755},
  year      = {2022},
  abstract  = {A sequentialquadratic Hamiltonian schemefor solving open-loop differential Nash games is proposed and investigated. This method is formulated in the framework of the Pontryagin maximum principle and represents an efficient and robust extension of the successive approximations strategy for solving optimal control problems. Theoretical results are presented that prove the well-posedness of the proposed scheme, and results of numerical experiments are reported that successfully validate its computational performance.},
  language  = {en}
}
@article{KrausMouchaRoth2022,
  author    = {Kraus, Daniela and Moucha, Annika and Roth, Oliver},
  title     = {A sharp Bernstein-type inequality and application to the Carleson embedding theorem with matrix weights},
  series = {Analysis and Mathematical Physics},
  volume    = {12},
  journal   = {Analysis and Mathematical Physics},
  number    = {1},
  issn      = {1664-235X},
  doi       = {10.1007/s13324-021-00639-5},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-270485},
  year      = {2022},
  abstract  = {We prove a sharp Bernstein-type inequality for complex polynomials which are positive and satisfy a polynomial growth condition on the positive real axis. This leads to an improved upper estimate in the recent work of Culiuc and Treil (Int. Math. Res. Not. 2019: 3301-3312, 2019) on the weighted martingale Carleson embedding theorem with matrix weights. In the scalar case this new upper bound is optimal.},
  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{DippellEspositoWaldmann2022,
  author    = {Dippell, Marvin and Esposito, Chiara and Waldmann, Stefan},
  title     = {Deformation and Hochschild cohomology of coisotropic algebras},
  series = {Annali di Matematica Pura ed Applicata},
  volume    = {201},
  journal   = {Annali di Matematica Pura ed Applicata},
  number    = {3},
  doi       = {10.1007/s10231-021-01158-7},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-329069},
  pages     = {1295-1323},
  year      = {2022},
  abstract  = {Coisotropic algebras consist of triples of algebras for which a reduction can be defined and unify in a very algebraic fashion coisotropic reduction in several settings. In this paper, we study the theory of (formal) deformation of coisotropic algebras showing that deformations are governed by suitable coisotropic DGLAs. We define a deformation functor and prove that it commutes with reduction. Finally, we study the obstructions to existence and uniqueness of coisotropic algebras and present some geometric examples.},
  language  = {en}
}
@article{GreefrathSillerKlocketal.2022,
  author    = {Greefrath, Gilbert and Siller, Hans-Stefan and Klock, Heiner and Wess, Raphael},
  title     = {Pre-service secondary teachers' pedagogical content knowledge for the teaching of mathematical modelling},
  series = {Educational Studies in Mathematics},
  volume    = {109},
  journal   = {Educational Studies in Mathematics},
  number    = {2},
  issn      = {0013-1954},
  doi       = {10.1007/s10649-021-10038-z},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-308259},
  pages     = {383-407},
  year      = {2022},
  abstract  = {The article deals with the pedagogical content knowledge of mathematical modelling as part of the professional competence of pre-service teachers. With the help of a test developed for this purpose from a conceptual model, we examine whether this pedagogical content knowledge can be promoted in its different facets—especially knowledge about modelling tasks and about interventions—by suitable university seminars. For this purpose, the test was administered to three groups in a seminar for the teaching of mathematical modelling: (1) to those respondents who created their own modelling tasks for use with students, (2) to those trained to intervene in mathematical modelling processes, and (3) participating students who are not required to address mathematical modelling. The findings of the study—based on variance analysis—indicate that certain facets (knowledge of modelling tasks, modelling processes, and interventions) have increased significantly in both experimental groups but to varying degrees. By contrast, pre-service teachers in the control group demonstrated no significant change to their level of pedagogical content knowledge.},
  language  = {en}
}
@phdthesis{Kortum2022,
  author    = {Kortum, Joshua},
  title     = {Global Existence and Uniqueness Results for Nematic Liquid Crystal and Magnetoviscoelastic Flows},
  doi       = {10.25972/OPUS-27827},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-278271},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {Liquid crystals and polymeric fluids are found in many technical applications with liquid crystal displays probably being the most prominent one. Ferromagnetic materials are well established in industrial and everyday use, e.g. as magnets in generators, transformers and hard drive disks. Among ferromagnetic materials, we find a subclass which undergoes deformations if an external magnetic field is applied. This effect is exploited in actuators, magnetoelastic sensors, and new fluid materials have been produced which retain their induced magnetization during the flow. A central issue consists of a proper modelling for those materials. Several models exist regarding liquid crystals and liquid crystal flows, but up to now, none of them has provided a full insight into all observed effects. On materials encompassing magnetic, elastic and perhaps even fluid dynamic effects, the mathematical literature seems sparse in terms of models. To some extent, one can unify the modeling of nematic liquid crystals and magnetoviscoelastic materials employing a so-called energetic variational approach. Using the least action principle from theoretical physics, the actual task reduces to finding appropriate energies describing the observed behavior. The procedure leads to systems of evolutionary partial differential equations, which are analyzed in this work. From the mathematical point of view, fundamental questions on existence, uniqueness and stability of solutions remain unsolved. Concerning the Ericksen-Leslie system modelling nematic liquid crystal flows, an approximation to this model is given by the so-called Ginzburg-Landau approximation. Solutions to the latter are intended to approximately represent solutions to the Ericksen-Leslie system. Indeed, we verify this presumption in two spatial dimensions. More precisely, it is shown that weak solutions of the Ginzburg-Landau approximation converge to solutions of the Ericksen-Leslie system in the energy space for all positive times of evolution. In order to do so, theory for the Euler equations invented by DiPerna and Majda on weak compactness and concentration measures is used. The second part of the work deals with a system of partial differential equations modelling magnetoviscoelastic fluids. We provide a well-posedness result in two spatial dimensions for large energies and large times. Along the verification of that conclusion, existing theory on the Ericksen-Leslie system and the harmonic map flow is deployed and suitably extended.},
  subject      = {Magnetoelastizit{\"a}t},
  language  = {en}
}
@article{HelinKretschmann2022,
  author    = {Helin, Tapio and Kretschmann, Remo},
  title     = {Non-asymptotic error estimates for the Laplace approximation in Bayesian inverse problems},
  series = {Numerische Mathematik},
  volume    = {150},
  journal   = {Numerische Mathematik},
  number    = {2},
  doi       = {10.1007/s00211-021-01266-9},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-265399},
  pages     = {521-549},
  year      = {2022},
  abstract  = {In this paper we study properties of the Laplace approximation of the posterior distribution arising in nonlinear Bayesian inverse problems. Our work is motivated by Schillings et al. (Numer Math 145:915-971, 2020. https://doi.org/10.1007/s00211-020-01131-1), where it is shown that in such a setting the Laplace approximation error in Hellinger distance converges to zero in the order of the noise level. Here, we prove novel error estimates for a given noise level that also quantify the effect due to the nonlinearity of the forward mapping and the dimension of the problem. In particular, we are interested in settings in which a linear forward mapping is perturbed by a small nonlinear mapping. Our results indicate that in this case, the Laplace approximation error is of the size of the perturbation. The paper provides insight into Bayesian inference in nonlinear inverse problems, where linearization of the forward mapping has suitable approximation properties.},
  language  = {en}
}
@techreport{GerberQuarder2022,
  author    = {Gerber, Sebastian and Quarder, Jascha},
  title     = {Erfassung von Aspekten professioneller Kompetenz zum Lehren des Simulierens und mathematischen Modellierens mit digitalen Werkzeugen. Ein Testinstrument},
  doi       = {10.25972/OPUS-27359},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-273597},
  pages     = {42},
  year      = {2022},
  abstract  = {Die Auseinandersetzung mit Simulations- und Modellierungsaufgaben, die mit digitalen Werkzeugen zu bearbeiten sind, stellt ver{\"a}nderte Anforderungen an Mathematiklehrkr{\"a}fte in der Unterrichtsplanung und -durchf{\"u}hrung. Werden digitale Werkzeuge sinnvoll eingesetzt, so unterst{\"u}tzen sie Simulations- und Modellierungsprozesse und erm{\"o}glichen realit{\"a}tsn{\"a}here Sachkontexte im Mathematikunterricht. F{\"u}r die empirische Untersuchung professioneller Kompetenzen zum Lehren des Simulierens und mathematischen Modellierens mit digitalen Werkzeugen ist es notwendig, Aspekte globaler Lehrkompetenzen von (angehenden) Mathematiklehrkr{\"a}ften bereichsspezifisch auszudeuten. Daher haben wir ein Testinstrument entwickelt, das die {\"U}berzeugungen, die Selbstwirksamkeitserwartungen und das fachdidaktische Wissen zum Lehren des Simulierens und mathematischen Modellierens mit digitalen Werkzeugen erfasst. Erg{\"a}nzt wird das Testinstrument durch selbstberichtete Vorerfahrungen zum eigenen Gebrauch digitaler Werkzeuge sowie zur Verwendung digitaler Werkzeuge in Unterrichtsplanung und -durchf{\"u}hrung. Das Testinstrument ist geeignet, um mittels Analysen von Veranstaltungsgruppen im Pr{\"a}-Post-Design den Zuwachs der oben beschriebenen Kompetenz von (angehenden) Mathematiklehrkr{\"a}ften zu messen. Somit k{\"o}nnen in Zukunft anhand der Ergebnisse die Wirksamkeit von Lehrveranstaltungen, die diese Kompetenz f{\"o}rdern (sollen), untersucht und evaluiert werden. Der Beitrag gliedert sich in zwei Teile: Zun{\"a}chst werden in der Testbeschreibung das zugrundeliegende Konstrukt und der Anwendungsbereich des Testinstruments sowie dessen Aufbau und Hinweise zur Durchf{\"u}hrung beschrieben. Zudem wird die Testg{\"u}te anhand der Pilotierungsergebnisse {\"u}berpr{\"u}ft. Im zweiten Teil befindet sich das vollst{\"a}ndige Testinstrument.},
  subject      = {GeoGebra},
  language  = {de}
}
@phdthesis{Schmeller2022,
  author    = {Schmeller, Christof},
  title     = {Uniform distribution of zero ordinates of Epstein zeta-functions},
  doi       = {10.25972/OPUS-25199},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-251999},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {The dissertation investigates the wide class of Epstein zeta-functions in terms of uniform distribution modulo one of the ordinates of their nontrivial zeros. Main results are a proof of a Landau type theorem for all Epstein zeta-functions as well as uniform distribution modulo one for the zero ordinates of all Epstein zeta-functions asscoiated with binary quadratic forms.},
  subject      = {Zetafunktion},
  language  = {en}
}