Positive intertwiners for Bessel functions of type B - Rösler, Margit; Voit, Michael (Proceedings of the American Mathematical Society)
Keywords: Applied Mathematics; General Mathematics

A fully cross-diffusive two-component evolution system: Existence and qualitative analysis via entropy-consistent thin-film-type approximation. - Tao, Youshan; Winkler, Michael (Journal of Functional Analysis)

The dampening role of large repulsive convection in a chemotaxis system modeling tumor angiogenesis. - Tao, Youshan; Winkler, Michael (Nonlinear Analysis, Theory, Methods and Applications)

Immediate regularization of measure-type population densities in a two-dimensional chemotaxis system with signal consumption. - Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin (Science China Mathematics)

Small-density solutiions in Keller-Segel systems involving rapidly decaying diffusivities. - Ding, Mengyao; Winkler, Michael (Nonlinear Differential Equatiions and Applicatiions)

Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime. - Tao, Youshan; Winkler, Michael (Communications in Mathematical Sciences)

Taxis-driven formation of singular hotspots in a May-Nowak type model for virus infection. - Tao, Youshan; Winkler, Michael (SIAM Journal on Mathematical Analysis)

Local energy estimates and global solvability in a threee-dimensional chemotaxis-fluid system with prescribed signal on the boundary. - Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin (Communications in Partial Differential Equations)

Global solvability in a threee-dimensional Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation - Wang, Yulan; Winkler, Michael; Xiang, Zhaoyin (Advances in Nonlinear Analysis)

Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction - Tao, Youshan; Winkler, Michael (Discrete and Continuous Dynamical Systems)

Imaginary multiquadratic number fields with class group of exponent $3$ and $5$ - Klüners, Jürgen; Komatsu, Toru (Mathematics of Computation)
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.
Keywords: Applied Mathematics; Computational Mathematics; Algebra and Number Theory

Spanning the isogeny class of a power of an elliptic curve - Kirschmer, Markus; Narbonne, Fabien; Ritzenthaler, Christophe; Robert, Damien (Mathematics of Computation)
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.
Keywords: Applied Mathematics; Computational Mathematics; Algebra and Number Theory

Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation - Burban, Igor; Abedin, R. (Communications in Mathematical Physics)
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.

Conceptualising and measuring domain-specific content knowledge of early childhood educators: A systematic review - Bruns, Julia; Gasteiger, Hedwig; Strahl, Carolin (Review of Education)
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.
Keywords: content knowledge; domain-specific learning; early childhood education; teacher knowledge

Eine mustergültige Wissenschaft - Bruns, Julia; Schopferer, T. (. TPS – Theorie und Praxis der Sozialpädagogik)

Place value and regrouping as seperate constructs of place value understanding - Jensen, Solveig; Gasteiger, Hedwig; Bruns, Julia (Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education)

Context and Implications Document for: Conceptualising and measuring domain-specific content knowledge of early childhood educators: A systematic review - Bruns, Julia; Gasteiger, Hedwig; Strahl, Carolin (Review of Education)

Stellenwertverständnis: Verständnis von Stellenwertprinzip und Bündelungsprinzip als separate Konstrukte - Jensen, Solveig; Gasteiger, Hedwig; Bruns, Julia (Beiträge zum Mathematikunterricht 2021)

The role of strategy-based motivation in mathematical problem solving: The case of learner-generated drawings - Schönherr, Johanna; Schukajlow, S.; Blomberg, J.; Leopold, C. (Learning and Instruction)

Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems - Black, Tobias; Fuest, Mario; Lankeit, Johannes (Zeitschrift für angewandte Mathematik und Physik)
Keywords: Applied Mathematics; General Physics and Astronomy; General Mathematics