@article{63241,
author = {{Schmitt-Richter, Lena Katharina and Wüllner, Sabrina and Schmidt, Katharina and Ebeling, Muna}},
journal = {{Pädagogikunterricht. Die Fachzeitschrift für die pädagogische Fächergruppe.}},
number = {{4}},
pages = {{65--70}},
title = {{{Von der Idee zur Umsetzung – Der Schulversuch an der Maria-Montessori-Gesamtschule in Düsseldorf}}},
volume = {{45}},
year = {{2025}},
}
@article{63250,
abstract = {{Abstract
An initial-boundary value problem for
$$\begin{aligned} \left\{ \begin{array}{ll}u_{tt} = \big (\gamma (\Theta ) u_{xt}\big )_x + au_{xx} - \big (f(\Theta )\big )_x, \qquad & x\in \Omega , \ t>0, \\[1mm] \Theta _t = \Theta _{xx} + \gamma (\Theta ) u_{xt}^2 - f(\Theta ) u_{xt}, \qquad & x\in \Omega , \ t>0, \end{array} \right. \end{aligned}$$
u
tt
=
(
γ
(
Θ
)
u
xt
)
x
+
a
u
xx
-
(
f
(
Θ
)
)
x
,
x
∈
Ω
,
t
>
0
,
[
1
m
m
]
Θ
t
=
Θ
xx
+
γ
(
Θ
)
u
xt
2
-
f
(
Θ
)
u
xt
,
x
∈
Ω
,
t
>
0
,
is considered in an open bounded real interval
$$\Omega $$
Ω
. Under the assumption that
$$\gamma \in C^0([0,\infty ))$$
γ
∈
C
0
(
[
0
,
∞
)
)
and
$$f\in C^0([0,\infty ))$$
f
∈
C
0
(
[
0
,
∞
)
)
are such that
$$f(0)=0$$
f
(
0
)
=
0
, and
$$k_\gamma \le \gamma \le K_\gamma $$
k
γ
≤
γ
≤
K
γ
as well as
$$\begin{aligned} |f(\xi )| \le K_f \cdot (\xi +1)^\alpha \qquad \hbox {for all } \xi \ge 0 \end{aligned}$$
|
f
(
ξ
)
|
≤
K
f
·
(
ξ
+
1
)
α
for all
ξ
≥
0
with some
$$k_\gamma>0, K_\gamma>0, K_f>0$$
k
γ
>
0
,
K
γ
>
0
,
K
f
>
0
and
$$\alpha <\frac{3}{2}$$
α
<
3
2
, for all suitably regular initial data of arbitrary size a statement on global existence of a global weak solution is derived. By particularly covering the thermodynamically consistent choice
$$f\equiv id$$
f
≡
i
d
of predominant physical relevance, this appears to go beyond previous related literature which seems to either rely on independence of
$$\gamma $$
γ
on
$$\Theta $$
Θ
, or to operate on finite time intervals.
}},
author = {{Winkler, Michael}},
issn = {{0044-2275}},
journal = {{Zeitschrift für angewandte Mathematik und Physik}},
number = {{5}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Large-data solutions in one-dimensional thermoviscoelasticity involving temperature-dependent viscosities}}},
doi = {{10.1007/s00033-025-02582-y}},
volume = {{76}},
year = {{2025}},
}
@article{63249,
abstract = {{Abstract
The model
$$\begin{aligned} \left\{ \begin{array}{l}u_{tt} = \big (\gamma (\Theta ) u_{xt}\big )_x + au_{xx} - \big (f(\Theta )\big )_x, \\[1mm] \Theta _t = \Theta _{xx} + \gamma (\Theta ) u_{xt}^2 - f(\Theta ) u_{xt}, \end{array} \right. \end{aligned}$$
u
tt
=
(
γ
(
Θ
)
u
xt
)
x
+
a
u
xx
-
(
f
(
Θ
)
)
x
,
[
1
m
m
]
Θ
t
=
Θ
xx
+
γ
(
Θ
)
u
xt
2
-
f
(
Θ
)
u
xt
,
for thermoviscoelastic evolution in one-dimensional Kelvin–Voigt materials is considered. By means of an approach based on maximal Sobolev regularity theory of scalar parabolic equations, it is shown that if
$$\gamma _0>0$$
γ
0
>
0
is fixed, then there exists
$$\delta =\delta (\gamma _0)>0$$
δ
=
δ
(
γ
0
)
>
0
with the property that for suitably regular initial data of arbitrary size an associated initial boundary value problem posed in an open bounded interval admits a global classical solution whenever
$$\gamma \in C^2([0,\infty ))$$
γ
∈
C
2
(
[
0
,
∞
)
)
and
$$f\in C^2([0,\infty ))$$
f
∈
C
2
(
[
0
,
∞
)
)
are such that
$$f(0)=0$$
f
(
0
)
=
0
and
$$|f(\xi )| \le K_f \cdot (\xi +1)^\alpha $$
|
f
(
ξ
)
|
≤
K
f
·
(
ξ
+
1
)
α
for all
$$\xi \ge 0$$
ξ
≥
0
and some
$$K_f>0$$
K
f
>
0
and
$$\alpha <\frac{3}{2}$$
α
<
3
2
, and that
$$\begin{aligned} \gamma _0 \le \gamma (\xi ) \le \gamma _0 + \delta \qquad \hbox {for all } \xi \ge 0. \end{aligned}$$
γ
0
≤
γ
(
ξ
)
≤
γ
0
+
δ
for all
ξ
≥
0
.
This is supplemented by a statement on global existence of certain strong solutions, particularly continuous in both components, under weaker conditions on the initial data.
}},
author = {{Winkler, Michael}},
issn = {{1424-3199}},
journal = {{Journal of Evolution Equations}},
number = {{4}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Large-data regular solutions in a one-dimensional thermoviscoelastic evolution problem involving temperature-dependent viscosities}}},
doi = {{10.1007/s00028-025-01144-z}},
volume = {{25}},
year = {{2025}},
}
@article{63246,
abstract = {{Abstract
The hyperbolic-parabolic model
$$\begin{aligned} \left\{ \begin{array}{ll} u_{tt} = u_{xx} - \big (f(\Theta )\big )_x, \qquad & x\in \Omega , \ t>0, \\ \Theta _t = \Theta _{xx} - f(\Theta ) u_{xt}, \qquad & x\in \Omega , \ t>0, \end{array} \right. \end{aligned}$$
u
tt
=
u
xx
-
(
f
(
Θ
)
)
x
,
x
∈
Ω
,
t
>
0
,
Θ
t
=
Θ
xx
-
f
(
Θ
)
u
xt
,
x
∈
Ω
,
t
>
0
,
for the evolution of the displacement variable
u
and the temperature
$$\Theta \ge 0$$
Θ
≥
0
during thermoelastic interaction in a one-dimensional bounded interval
$$\Omega $$
Ω
is considered. Whereas the literature has provided comprehensive results on global solutions for sufficiently regular initial data
$$(u_0,u_{0t},\Theta _0)=(u,u_t,\Theta )|_{t=0}$$
(
u
0
,
u
0
t
,
Θ
0
)
=
(
u
,
u
t
,
Θ
)
|
t
=
0
when
$$f\equiv id$$
f
≡
i
d
, it seems to have remained open so far how far a solution theory can be built solely on the two fundamental physical principles of energy conservation and entropy nondecrease. The present manuscript addresses this by asserting global existence of weak solutions under assumptions which are energy- and entropy-minimal in the sense of allowing for any initial data
$$u_0\in W_0^{1,2}(\Omega )$$
u
0
∈
W
0
1
,
2
(
Ω
)
,
$$u_{0t} \in L^2(\Omega )$$
u
0
t
∈
L
2
(
Ω
)
and
$$0\le \Theta _0\in L^1(\Omega )$$
0
≤
Θ
0
∈
L
1
(
Ω
)
, and which apply to arbitrary
$$f\in C^1([0,\infty ))$$
f
∈
C
1
(
[
0
,
∞
)
)
with
$$f(0)=0$$
f
(
0
)
=
0
and
$$f'>0$$
f
′
>
0
on
$$[0,\infty )$$
[
0
,
∞
)
.
}},
author = {{Winkler, Michael}},
issn = {{0944-2669}},
journal = {{Calculus of Variations and Partial Differential Equations}},
number = {{1}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Rough solutions in one-dimensional nonlinear thermoelasticity}}},
doi = {{10.1007/s00526-025-03170-8}},
volume = {{65}},
year = {{2025}},
}
@article{63244,
abstract = {{
The Cauchy problem in
\mathbb{R}^{n}
for the cross-diffusion system
\begin{cases}u_{t} = \nabla \cdot (D(u)\nabla u) - \nabla\cdot (u\nabla v), \\ 0 = \Delta v +u,\end{cases}
is considered for
n\ge 2
and under assumptions ensuring that
D
suitably generalizes the prototype given by
D(\xi)=(\xi+1)^{-\alpha}, \quad \xi\ge 0.
Under the assumption that
\alpha>1
, it is shown that for any
r_{\star}>0
and
\delta\in (0,1)
one can find radially symmetric initial data from
C_{0}^{\infty}(\mathbb{R}^{n})
such that the corresponding solution blows up within some finite time, and that this explosion occurs throughout certain spheres in an appropriate sense, with any such sphere being located in the annulus
\overline{B}_{r_\star+\delta}(0)\setminus B_{(1-\delta)r_\star}(0)
.This is complemented by a result revealing that when
\alpha<1
, any finite-mass unbounded radial solution must blow up exclusively at the spatial origin.
}},
author = {{Winkler, Michael}},
issn = {{1435-9855}},
journal = {{Journal of the European Mathematical Society}},
publisher = {{European Mathematical Society - EMS - Publishing House GmbH}},
title = {{{Can diffusion degeneracies enhance complexity in chemotactic aggregation? Finite-time blow-up on spheres in a quasilinear Keller–Segel system}}},
doi = {{10.4171/jems/1607}},
year = {{2025}},
}
@article{63247,
author = {{Tao, Youshan and Winkler, Michael}},
issn = {{0022-0396}},
journal = {{Journal of Differential Equations}},
pages = {{197--239}},
publisher = {{Elsevier BV}},
title = {{{A switch in dimension dependence of critical blow-up exponents in a Keller-Segel system involving indirect signal production}}},
doi = {{10.1016/j.jde.2024.12.040}},
volume = {{423}},
year = {{2025}},
}
@article{63252,
author = {{Tao, Youshan and Winkler, Michael}},
issn = {{1674-7283}},
journal = {{Science China Mathematics}},
number = {{12}},
pages = {{2867--2900}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{A unified approach to existence theories for singular chemotaxis systems with nonlinear signal production}}},
doi = {{10.1007/s11425-023-2397-y}},
volume = {{68}},
year = {{2025}},
}
@article{63344,
abstract = {{Abstract
A Neumann-type initial-boundary value problem for
$$\begin{aligned} \left\{ \begin{array}{l} u_{tt} = \nabla \cdot (\gamma (\Theta ) \nabla u_t) + a \nabla \cdot (\gamma (\Theta ) \nabla u) + \nabla \cdot f(\Theta ), \\ \Theta _t = D\Delta \Theta + \Gamma (\Theta ) |\nabla u_t|^2 + F(\Theta )\cdot \nabla u_t, \end{array} \right. \end{aligned}$$
u
tt
=
∇
·
(
γ
(
Θ
)
∇
u
t
)
+
a
∇
·
(
γ
(
Θ
)
∇
u
)
+
∇
·
f
(
Θ
)
,
Θ
t
=
D
Δ
Θ
+
Γ
(
Θ
)
|
∇
u
t
|
2
+
F
(
Θ
)
·
∇
u
t
,
is considered in a smoothly bounded domain
$$\Omega \subset \mathbb {R}^n$$
Ω
⊂
R
n
,
$$n\ge 1$$
n
≥
1
. In the case when
$$n=1$$
n
=
1
,
$$\gamma \equiv \Gamma $$
γ
≡
Γ
and
$$f\equiv F$$
f
≡
F
, this system coincides with the standard model for heat generation in a viscoelastic material of Kelvin-Voigt type, well-understood in situations in which
$$\gamma =const$$
γ
=
c
o
n
s
t
. Covering scenarios in which all key ingredients
$$\gamma ,\Gamma ,f$$
γ
,
Γ
,
f
and F may depend on the temperature
$$\Theta $$
Θ
here, for initial data which merely satisfy
$$u_0\in W^{1,p+2}(\Omega )$$
u
0
∈
W
1
,
p
+
2
(
Ω
)
,
$$u_{0t}\in W^{1,p}(\Omega )$$
u
0
t
∈
W
1
,
p
(
Ω
)
and
$$\Theta _0\in W^{1,p}(\Omega )$$
Θ
0
∈
W
1
,
p
(
Ω
)
with some
$$p\ge 2$$
p
≥
2
such that
$$p>n$$
p
>
n
, a result on local-in-time existence and uniqueness is derived in a natural framework of weak solvability.}},
author = {{Winkler, Michael}},
issn = {{0095-4616}},
journal = {{Applied Mathematics & Optimization}},
number = {{2}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters}}},
doi = {{10.1007/s00245-025-10243-9}},
volume = {{91}},
year = {{2025}},
}
@article{63242,
abstract = {{Abstract
For
$$p>2$$
p
>
2
, the equation
$$\begin{aligned} u_t = u^p u_{xx}, \qquad x\in \mathbb {R}, \ t\in \mathbb {R}, \end{aligned}$$
u
t
=
u
p
u
xx
,
x
∈
R
,
t
∈
R
,
is shown to admit positive and spatially increasing smooth solutions on all of
$$\mathbb {R}\times \mathbb {R}$$
R
×
R
which are precisely of the form of an accelerating wave for
$$t<0$$
t
<
0
, and of a wave slowing down for
$$t>0$$
t
>
0
. These solutions satisfy
$$u(\cdot ,t)\rightarrow 0$$
u
(
·
,
t
)
→
0
in
$$L^\infty _{loc}(\mathbb {R})$$
L
loc
∞
(
R
)
as
$$t\rightarrow + \infty $$
t
→
+
∞
and as
$$t\rightarrow -\infty $$
t
→
-
∞
, and exhibit a yet apparently undiscovered phenomenon of transient rapid spatial growth, in the sense that
$$\begin{aligned} \lim _{x\rightarrow +\infty } x^{-1} u(x,t) \quad \text{ exists } \text{ for } \text{ all } t<0, \end{aligned}$$
lim
x
→
+
∞
x
-
1
u
(
x
,
t
)
exists
for
all
t
<
0
,
that
$$\begin{aligned} \lim _{x\rightarrow +\infty } x^{-\frac{2}{p}} u(x,t) \quad \text{ exists } \text{ for } \text{ all } t>0, \end{aligned}$$
lim
x
→
+
∞
x
-
2
p
u
(
x
,
t
)
exists
for
all
t
>
0
,
but that
$$\begin{aligned} u(x,0)=K e^{\alpha x} \qquad \text{ for } \text{ all } x\in \mathbb {R}\end{aligned}$$
u
(
x
,
0
)
=
K
e
α
x
for
all
x
∈
R
with some
$$K>0$$
K
>
0
and
$$\alpha >0$$
α
>
0
.
}},
author = {{Hanfland, Celina and Winkler, Michael}},
issn = {{2296-9020}},
journal = {{Journal of Elliptic and Parabolic Equations}},
number = {{3}},
pages = {{2041--2063}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Exactly wave-type homoclinic orbits and emergence of transient exponential growth in a super-fast diffusion equation}}},
doi = {{10.1007/s41808-025-00316-9}},
volume = {{11}},
year = {{2025}},
}
@article{63164,
abstract = {{ Refined investigation of chemotaxis processes has revealed a significant role of degeneracies in corresponding motilities in a number of application contexts. A rapidly growing literature concerned with the analysis of resulting mathematical models has been capable of solving fundamental issues, but various problems have remained open, or even newly arisen. The goal of the paper consists in a summary of some developments in this area, and particularly in the discussion of the question how far the introduction of degeneracies may influence the behavior of solutions to chemotaxis systems. }},
author = {{Winkler, Michael}},
issn = {{0218-2025}},
journal = {{Mathematical Models and Methods in Applied Sciences}},
number = {{02}},
pages = {{283--343}},
publisher = {{World Scientific Pub Co Pte Ltd}},
title = {{{Effects of degeneracies in taxis-driven evolution}}},
doi = {{10.1142/s0218202525400020}},
volume = {{35}},
year = {{2025}},
}
@inproceedings{60746,
author = {{Jakobeit, Darius and Peña López, Mario and Schenke, Maximilian and Haucke-Korber, Barnabas and Wallscheid, Oliver}},
booktitle = {{2025 IEEE International Electric Machines & Drives Conference (IEMDC)}},
publisher = {{IEEE}},
title = {{{Structural Optimization of Meta-Reinforcement Learning-based Finite-Control-Set Direct Torque Control of Permanent Magnet Synchronous Motors}}},
doi = {{10.1109/iemdc60492.2025.11061179}},
year = {{2025}},
}
@inproceedings{60745,
author = {{Haucke-Korber, Barnabas and Aung, Nyi Nyi and Schenke, Maximilian and Peña López, Mario and Jakobeit, Darius and Wallscheid, Oliver}},
booktitle = {{2025 IEEE International Electric Machines & Drives Conference (IEMDC)}},
publisher = {{IEEE}},
title = {{{Reinforcement Learning-based Direct Torque Control of Externally Excited Synchronous Motors: a Proof of Concept}}},
doi = {{10.1109/iemdc60492.2025.11061093}},
year = {{2025}},
}
@unpublished{61759,
abstract = {{Intersection distribution and non-hitting index are concepts introduced recently by Li and Pott as a new way to view the behaviour of a collection of finite field polynomials. With both an algebraic interpretation via the intersection of a polynomial with a set of lines, and a geometric interpretation via a (q+1)-set possessing an internal nucleus, the concepts have proved their usefulness as a new way to view various long-standing problems, and have applications in areas such as Kakeya sets. In this paper, by exploiting connections with diverse areas including the theory of algebraic curves, cyclotomy and the enumeration of irreducible polynomials, we establish new results and resolve various Open Problems of Li and Pott. We prove geometric results which shed new light on the relationship between intersection distribution and projective equivalence of polynomials, and algebraic results which describe and characterise the degree of Sf - the index of the largest non-zero entry in the intersection distribution of f. We provide new insights into the non-hitting spectrum, and show the limitations of the non-hitting index as a tool for characterisation. Finally, the benefits provided by the connections to other areas are evidenced in two short new proofs of the cubic case. }},
author = {{Klawuhn, Lukas-André Dominik and Huczynska, Sophie and Paterson, Maura}},
pages = {{36}},
title = {{{The Intersection Distribution: New Results and Perspectives}}},
year = {{2025}},
}
@inproceedings{60744,
author = {{Peña López, Mario and Schenke, Maximilian and Jakobeit, Darius and Haucke-Korber, Barnabas and Wallscheid, Oliver}},
booktitle = {{2025 IEEE International Electric Machines & Drives Conference (IEMDC)}},
publisher = {{IEEE}},
title = {{{Reinforcement Learning Control of Three-Level Converter Permanent Magnet Synchronous Machine Drives}}},
doi = {{10.1109/iemdc60492.2025.11061032}},
year = {{2025}},
}
@unpublished{63384,
abstract = {{Two fundamental ways to represent a group are as permutations and as matrices. In this paper, we study linear representations of groups that intertwine with a permutation representation. Recently, D'Alconzo and Di Scala investigated how small the matrices in such a linear representation can be. The minimal dimension of such a representation is the \emph{linear dimension of the group action} and this has applications in cryptography and cryptosystems.
We develop the idea of linear dimension from an algebraic point of view by using the theory of permutation modules. We give structural results about representations of minimal dimension and investigate the implications of faithfulness, transitivity and primitivity on the linear dimension. Furthermore, we compute the linear dimension of several classes of finite primitive permutation groups. We also study wreath products, allowing us to determine the linear dimension of imprimitive group actions. Finally, we give the linear dimension of almost simple finite $2$-transitive groups, some of which may be used for further applications in cryptography. Our results also open up many new questions about linear representations of group actions.}},
author = {{Devillers, Alice and Giudici, Michael and Hawtin, Daniel R. and Klawuhn, Lukas-André Dominik and Morgan, Luke}},
title = {{{Linear dimension of group actions}}},
year = {{2025}},
}
@article{62906,
abstract = {{Ausgangspunkt des Beitrags sind die wiederkehrenden Zuschauerproteste gegen die Kommerzialisierung des Fußballs und die Frage nach einer Erklärung für deren Entstehung. Gezeigt wird, dass Zuschauerproteste bereits umfassend beforscht sind, bislang allerdings keine theoretische Einordung zu ihrer Entwicklung vorgelegt wurde. Entsprechend liegt das Ziel des Beitrags darin, unter Rückgriff auf systemtheoretische Überlegungen, insbesondere auch zur Funktion des Publikums für den Fußball, und typologische Unterscheidungen, angereichert durch kulturanthropologische Betrachtungen, theoretische Erklärungen für die Ursprünge und Bedeutung von Zuschauerprotesten zu liefern. Im Anschluss hieran wird betrachtet, wie sich Zuschauerproteste in theoretische Konzepte zu Protestbewegungen einordnen lassen, um abschließend deren Nutzen für die Fußballclubs und -verbände zu bestimmen.}},
author = {{Riedl, Lars and Meier, Heiko}},
issn = {{2568-0420}},
journal = {{FuG – Zeitschrift für Fußball und Gesellschaft}},
number = {{2-2023}},
pages = {{97 -- 119}},
publisher = {{Verlag Barbara Budrich GmbH}},
title = {{{Protest gegen Kommerzialisierung im Fußball: Theoretische Überlegungen zu Entstehung, Strukturen und Nutzen}}},
doi = {{10.3224/fug.v5i2.02}},
volume = {{5}},
year = {{2025}},
}
@article{63347,
abstract = {{Friction-spinning is an incremental thermomechanical forming process that has huge potential due to its simple yet effective mechanism of utilising friction between a rotating workpiece and a forming tool to increase the workpiece’s temperature, which reduces the required forces and increases formability during the forming process. Despite the simplicity of the process’s setup, the thermomechanical loads and high relative velocities involved, especially in the contact zone, make the application of classical methods for characterising friction inaccurate. It is therefore essential to find a way to describe the frictional behaviour under real process conditions to be able to gain a holistic understanding of the process and the effect of the adjustable parameters on the outcome, especially the temperature. To achieve this goal, an experimental setup that considers the actual process boundary conditions in forming tubes made of EN AW-6060 was used to measure in situ normal and frictional forces, in addition to process temperatures, under varying rotational speed and feed rate values.}},
author = {{Wiens, Eugen and Hijazi, Dina and Jüttner, Maik and Homberg, Werner and Kensy, Mark Dennis and Tillmann, Wolfgang}},
issn = {{2504-4494}},
journal = {{Journal of Manufacturing and Materials Processing}},
number = {{9}},
publisher = {{MDPI AG}},
title = {{{In Situ Investigation of the Frictional Behaviour in Friction-Spinning}}},
doi = {{10.3390/jmmp9090302}},
volume = {{9}},
year = {{2025}},
}
@unpublished{63394,
abstract = {{We study the statistics of the number of real eigenvalues in the elliptic deformation of the real Ginibre ensemble. As the matrix dimension grows, the law of large numbers and the central limit theorem for the number of real eigenvalues are well understood, but the probabilities of rare events remain largely unexplored. Large deviation type results have been obtained only in extreme cases, when either a vanishingly small proportion of eigenvalues are real or almost all eigenvalues are real. Here, in both the strong and weak asymmetry regimes, we derive the probabilities of rare events in the moderate-to-large deviation regime, thereby providing a natural connection between the previously known regime of Gaussian fluctuations and the large deviation regime. Our results are new even for the classical real Ginibre ensemble.}},
author = {{Byun, Sung-Soo and Jalowy, Jonas and Lee, Yong-Woo and Schehr, Grégory}},
booktitle = {{arXiv:2511.09191}},
title = {{{Moderate-to-large deviation asymptotics for real eigenvalues of the elliptic Ginibre matrices}}},
year = {{2025}},
}
@unpublished{63393,
abstract = {{We study the evolution of zeros of high polynomial powers under the heat flow. For any fixed polynomial $P(z)$, we prove that the empirical zero distribution of its heat-evolved $n$-th power converges to a distribution on the complex plane as $n$ tends to infinity. We describe this limit distribution $μ_t$ as a function of the time parameter $t$ of the heat evolution: For small time, zeros start to spread out in approximately semicircular distributions, then intricate curves start to form and merge, until for large time, the zero distribution approaches a widespread semicircle law through the initial center of mass. The Stieltjes transform of the limit distribution $μ_t$ satisfies a self-consistent equation and a Burgers' equation. The present paper deals with general complex-rooted polynomials for which, in contrast to the real-rooted case, no free-probabilistic representation for $μ_t$ is available.}},
author = {{Höfert, Antonia and Jalowy, Jonas and Kabluchko, Zakhar}},
booktitle = {{arXiv:2512.17808}},
title = {{{Zeros of polynomial powers under the heat flow}}},
year = {{2025}},
}
@inbook{63390,
author = {{Buhl, Heike M. and Hilkenmeier, Johanna}},
booktitle = {{Handbuch Entwicklungs- und Erziehungspsychologie}},
editor = {{Kracke, Bärbel and Noack, Peter}},
publisher = {{Springer}},
title = {{{Bildung und Lesesozialisation im Elternhaus}}},
doi = {{10.1007/978-3-642-54061-5_10-2}},
year = {{2025}},
}