@article{35613, author = {{Winkler, Michael}}, journal = {{Transactions of the American Mathematical Society}}, pages = {{219--268}}, title = {{{Does spatial homogeneity ultimately prevail in nutrient taxis systems? A paradigm for structure support by rapid diffusion decay in an autonomous parabolic flow.}}}, volume = {{374}}, year = {{2021}}, } @article{37659, author = {{Rösler, Margit and Voit, Michael}}, issn = {{0002-9939}}, journal = {{Proceedings of the American Mathematical Society}}, keywords = {{Applied Mathematics, General Mathematics}}, number = {{3}}, pages = {{1151--1163}}, publisher = {{American Mathematical Society (AMS)}}, title = {{{Positive intertwiners for Bessel functions of type B}}}, doi = {{10.1090/proc/15312}}, volume = {{149}}, year = {{2021}}, } @article{35603, author = {{Tao, Youshan and Winkler, Michael}}, journal = {{Journal of Functional Analysis}}, title = {{{A fully cross-diffusive two-component evolution system: Existence and qualitative analysis via entropy-consistent thin-film-type approximation.}}}, volume = {{281}}, year = {{2021}}, } @article{35606, author = {{Tao, Youshan and Winkler, Michael}}, journal = {{Nonlinear Analysis, Theory, Methods and Applications}}, title = {{{The dampening role of large repulsive convection in a chemotaxis system modeling tumor angiogenesis.}}}, volume = {{208}}, year = {{2021}}, } @article{35612, author = {{Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}}, journal = {{Science China Mathematics}}, pages = {{725--746}}, title = {{{Immediate regularization of measure-type population densities in a two-dimensional chemotaxis system with signal consumption.}}}, volume = {{64}}, year = {{2021}}, } @article{35601, author = {{Ding, Mengyao and Winkler, Michael}}, journal = {{Nonlinear Differential Equatiions and Applicatiions}}, title = {{{Small-density solutiions in Keller-Segel systems involving rapidly decaying diffusivities.}}}, volume = {{28}}, year = {{2021}}, } @article{35605, author = {{Tao, Youshan and Winkler, Michael}}, journal = {{Communications in Mathematical Sciences}}, pages = {{829--849}}, title = {{{Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime.}}}, volume = {{19}}, year = {{2021}}, } @article{35604, author = {{Tao, Youshan and Winkler, Michael}}, journal = {{SIAM Journal on Mathematical Analysis}}, pages = {{1411--1433}}, title = {{{Taxis-driven formation of singular hotspots in a May-Nowak type model for virus infection.}}}, volume = {{53}}, year = {{2021}}, } @article{35610, author = {{Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}}, journal = {{Communications in Partial Differential Equations}}, pages = {{1058--1091}}, title = {{{Local energy estimates and global solvability in a threee-dimensional chemotaxis-fluid system with prescribed signal on the boundary.}}}, volume = {{46}}, year = {{2021}}, } @article{35611, author = {{Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}}, journal = {{Advances in Nonlinear Analysis}}, pages = {{707--731}}, title = {{{Global solvability in a threee-dimensional Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation}}}, volume = {{10}}, year = {{2021}}, } @article{35608, author = {{Tao, Youshan and Winkler, Michael}}, journal = {{Discrete and Continuous Dynamical Systems}}, number = {{--A}}, pages = {{439--454}}, title = {{{Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction}}}, volume = {{41}}, year = {{2021}}, } @article{34840, abstract = {{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. }}, author = {{Klüners, Jürgen and Komatsu, Toru}}, issn = {{0025-5718}}, journal = {{Mathematics of Computation}}, keywords = {{Applied Mathematics, Computational Mathematics, Algebra and Number Theory}}, number = {{329}}, pages = {{1483--1497}}, publisher = {{American Mathematical Society (AMS)}}, title = {{{Imaginary multiquadratic number fields with class group of exponent $3$ and $5$}}}, doi = {{10.1090/mcom/3609}}, volume = {{90}}, year = {{2021}}, } @article{34912, abstract = {{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. }}, author = {{Kirschmer, Markus and Narbonne, Fabien and Ritzenthaler, Christophe and Robert, Damien}}, issn = {{0025-5718}}, journal = {{Mathematics of Computation}}, keywords = {{Applied Mathematics, Computational Mathematics, Algebra and Number Theory}}, number = {{333}}, pages = {{401--449}}, publisher = {{American Mathematical Society (AMS)}}, title = {{{Spanning the isogeny class of a power of an elliptic curve}}}, doi = {{10.1090/mcom/3672}}, volume = {{91}}, year = {{2021}}, } @article{44329, abstract = {{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.}}, author = {{Burban, Igor and Abedin, R.}}, journal = {{Communications in Mathematical Physics}}, number = {{2}}, pages = {{1051–1109}}, title = {{{Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation}}}, doi = {{10.1007/s00220-021-04188-7}}, volume = {{387}}, year = {{2021}}, } @article{34822, abstract = {{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.}}, author = {{Bruns, Julia and Gasteiger, Hedwig and Strahl, Carolin}}, issn = {{2049-6613}}, journal = {{Review of Education}}, keywords = {{content knowledge, domain-specific learning, early childhood education, teacher knowledge}}, number = {{2}}, pages = {{500--538}}, publisher = {{Wiley}}, title = {{{Conceptualising and measuring domain-specific content knowledge of early childhood educators: A systematic review}}}, doi = {{10.1002/rev3.3255}}, volume = {{9}}, year = {{2021}}, } @article{45687, author = {{Bruns, Julia and Schopferer, T.}}, journal = {{. TPS – Theorie und Praxis der Sozialpädagogik}}, pages = {{28--32}}, title = {{{Eine mustergültige Wissenschaft}}}, volume = {{11}}, year = {{2021}}, } @inproceedings{36527, author = {{Jensen, Solveig and Gasteiger, Hedwig and Bruns, Julia}}, booktitle = {{Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education}}, editor = {{Inprasitha, Maitree and Changsri, Narumon and Boonsena, Nisakorn}}, location = {{Khon Kaen, Thailand}}, pages = {{101--109}}, title = {{{Place value and regrouping as seperate constructs of place value understanding}}}, volume = {{3}}, year = {{2021}}, } @article{34823, author = {{Bruns, Julia and Gasteiger, Hedwig and Strahl, Carolin}}, issn = {{2049-6613}}, journal = {{Review of Education}}, number = {{2}}, pages = {{539--540}}, publisher = {{Wiley}}, title = {{{Context and Implications Document for: Conceptualising and measuring domain-specific content knowledge of early childhood educators: A systematic review}}}, doi = {{10.1002/rev3.3256}}, volume = {{9}}, year = {{2021}}, } @inproceedings{36536, author = {{Jensen, Solveig and Gasteiger, Hedwig and Bruns, Julia}}, booktitle = {{Beiträge zum Mathematikunterricht 2021}}, location = {{Lüneburg}}, publisher = {{WTM-Verlag}}, title = {{{Stellenwertverständnis: Verständnis von Stellenwertprinzip und Bündelungsprinzip als separate Konstrukte}}}, doi = {{http://dx.doi.org/10.17877/DE290R-22292}}, year = {{2021}}, } @article{45342, author = {{Schönherr, Johanna and Blomberg, J. and Schukajlow, S. and Leopold, C.}}, journal = {{Contemporary Educational Psychology}}, title = {{{Do emotions and prior performance facilitate the use of the learner-generated drawing strategy? Effects of enjoyment, anxiety, and intramathematical performance on the use of the drawing strategy and modelling performance}}}, doi = {{10.1016/j.cedpsych.2021.101967}}, volume = {{65}}, year = {{2021}}, }