TY  - JOUR
A1  - Kourou, Maria
A1  - Zarvalis, Konstantinos
T1  - Compact sets in petals and their backward orbits under semigroups of holomorphic functions
JF  - Potential Analysis
N2  - 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.
KW  - semigroup of holomorphic functions
KW  - backward orbit
KW  - petal
KW  - harmonic measure
KW  - condenser capacity
KW  - Koenigs function
KW  - green energy
KW  - hyperbolic area
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-324368
SN  - 0926-2601
VL  - 59
IS  - 4
ER  - 
TY  - JOUR
A1  - Dippell, Marvin
A1  - Esposito, Chiara
A1  - Waldmann, Stefan
T1  - Deformation and Hochschild cohomology of coisotropic algebras
JF  - Annali di Matematica Pura ed Applicata
N2  - 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.
KW  - deformation theory
KW  - differential graded Lie algebra
KW  - coisotropic reduction
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-329069
VL  - 201
IS  - 3
ER  - 
TY  - JOUR
A1  - Greefrath, Gilbert
A1  - Siller, Hans-Stefan
A1  - Klock, Heiner
A1  - Wess, Raphael
T1  - Pre-service secondary teachers’ pedagogical content knowledge for the teaching of mathematical modelling
JF  - Educational Studies in Mathematics
N2  - 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.
KW  - mathematical modelling
KW  - pedagogical content knowledge
KW  - professional competence
KW  - pre-service teacher
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-308259
SN  - 0013-1954
SN  - 1573-0816
VL  - 109
IS  - 2
ER  -