@article{51208,
abstract = {{AbstractApproximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions.}},
author = {{Gebken, Bennet}},
issn = {{0926-6003}},
journal = {{Computational Optimization and Applications}},
keywords = {{Applied Mathematics, Computational Mathematics, Control and Optimization}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{A note on the convergence of deterministic gradient sampling in nonsmooth optimization}}},
doi = {{10.1007/s10589-024-00552-0}},
year = {{2024}},
}
@article{52218,
author = {{Lenz, Peter and Mahnken, Rolf}},
issn = {{0020-7683}},
journal = {{International Journal of Solids and Structures}},
keywords = {{Applied Mathematics, Mechanical Engineering, Mechanics of Materials, Condensed Matter Physics, General Materials Science, Modeling and Simulation}},
publisher = {{Elsevier BV}},
title = {{{Multiscale simulation of polymer curing of composites combined mean-field homogenisation methods at large strains}}},
doi = {{10.1016/j.ijsolstr.2023.112642}},
volume = {{290}},
year = {{2024}},
}
@article{52233,
abstract = {{ELDIRK methods are defined to have an Explicit Last stage in the general Butcher array of Diagonal Implicit Runge-Kutta methods, with the consequence, that no additional system of equations must be solved, compared to the embedded RK method. Two general formulations for second- and third-order ELDIRK methods have been obtained recently in Mahnken [21] with specific schemes, e.g. for the embedded implicit Euler method, the embedded trapezoidal-rule and the embedded Ellsiepen method. In the first part of this paper, we investigate some general stability characteristics of ELDIRK methods, and it will be shown that the above specific RK schemes are not A-stable. Therefore, in the second part, the above-mentioned general formulations are used for further stability investigations, with the aim to construct new second- and third-order ELDIRK methods which simultaneously are A-stable. Two numerical examples are concerned with the curing for a thermosetting material and phase-field RVE modeling for crystallinity and orientation. The numerical results confirm the theoretical results on convergence order and stability.}},
author = {{Mahnken, Rolf and Westermann, Hendrik}},
issn = {{0178-7675}},
journal = {{Computational Mechanics}},
keywords = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods}}},
doi = {{10.1007/s00466-024-02442-y}},
year = {{2024}},
}
@article{52726,
abstract = {{Heteroclinic structures organize global features of dynamical systems. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analysed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures.}},
author = {{Bick, Christian and von der Gracht, Sören}},
issn = {{2051-1329}},
journal = {{Journal of Complex Networks}},
keywords = {{Applied Mathematics, Computational Mathematics, Control and Optimization, Management Science and Operations Research, Computer Networks and Communications}},
number = {{2}},
publisher = {{Oxford University Press (OUP)}},
title = {{{Heteroclinic dynamics in network dynamical systems with higher-order interactions}}},
doi = {{10.1093/comnet/cnae009}},
volume = {{12}},
year = {{2024}},
}
@article{49905,
abstract = {{For 0 ≤ t ≤ r let m(t, r) be the maximum number s such that every t-edge-connected r-graph has s pairwise disjoint perfect matchings. There are only a few values of m(t, r) known, for instance m(3, 3) = m(4, r) = 1, and m(t, r) ≤ r − 2 for all t = 5,
and m(t, r) ≤ r − 3 if r is even. We prove that m(2l, r) ≤ 3l − 6 for every l ≥ 3 and r ≥ 2l.}},
author = {{Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}},
issn = {{0209-9683}},
journal = {{Combinatorica}},
keywords = {{Computational Mathematics, Discrete Mathematics and Combinatorics}},
pages = {{429--440}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs}}},
doi = {{10.1007/s00493-023-00078-9}},
volume = {{44}},
year = {{2024}},
}
@article{53316,
abstract = {{AbstractThe quasilinear Keller–Segel system $$\begin{aligned} \left\{ \begin{array}{l} u_t=\nabla \cdot (D(u)\nabla u) - \nabla \cdot (S(u)\nabla v), \\ v_t=\Delta v-v+u, \end{array}\right. \end{aligned}$$
u
t
=
∇
·
(
D
(
u
)
∇
u
)
-
∇
·
(
S
(
u
)
∇
v
)
,
v
t
=
Δ
v
-
v
+
u
,
endowed with homogeneous Neumann boundary conditions is considered in a bounded domain $$\Omega \subset {\mathbb {R}}^n$$
Ω
⊂
R
n
, $$n \ge 3$$
n
≥
3
, with smooth boundary for sufficiently regular functions D and S satisfying $$D>0$$
D
>
0
on $$[0,\infty )$$
[
0
,
∞
)
, $$S>0$$
S
>
0
on $$(0,\infty )$$
(
0
,
∞
)
and $$S(0)=0$$
S
(
0
)
=
0
. On the one hand, it is shown that if $$\frac{S}{D}$$
S
D
satisfies the subcritical growth condition $$\begin{aligned} \frac{S(s)}{D(s)} \le C s^\alpha \qquad \text{ for } \text{ all } s\ge 1 \qquad \text{ with } \text{ some } \alpha < \frac{2}{n} \end{aligned}$$
S
(
s
)
D
(
s
)
≤
C
s
α
for
all
s
≥
1
with
some
α
<
2
n
and $$C>0$$
C
>
0
, then for any sufficiently regular initial data there exists a global weak energy solution such that $${ \mathrm{{ess}}} \sup _{t>0} \Vert u(t) \Vert _{L^p(\Omega )}<\infty $$
ess
sup
t
>
0
‖
u
(
t
)
‖
L
p
(
Ω
)
<
∞
for some $$p > \frac{2n}{n+2}$$
p
>
2
n
n
+
2
. On the other hand, if $$\frac{S}{D}$$
S
D
satisfies the supercritical growth condition $$\begin{aligned} \frac{S(s)}{D(s)} \ge c s^\alpha \qquad \text{ for } \text{ all } s\ge 1 \qquad \text{ with } \text{ some } \alpha > \frac{2}{n} \end{aligned}$$
S
(
s
)
D
(
s
)
≥
c
s
α
for
all
s
≥
1
with
some
α
>
2
n
and $$c>0$$
c
>
0
, then the nonexistence of a global weak energy solution having the boundedness property stated above is shown for some initial data in the radial setting. This establishes some criticality of the value $$\alpha = \frac{2}{n}$$
α
=
2
n
for $$n \ge 3$$
n
≥
3
, without any additional assumption on the behavior of D(s) as $$s \rightarrow \infty $$
s
→
∞
, in particular without requiring any algebraic lower bound for D. When applied to the Keller–Segel system with volume-filling effect for probability distribution functions of the type $$Q(s) = \exp (-s^\beta )$$
Q
(
s
)
=
exp
(
-
s
β
)
, $$s \ge 0$$
s
≥
0
, for global solvability the exponent $$\beta = \frac{n-2}{n}$$
β
=
n
-
2
n
is seen to be critical.
}},
author = {{Stinner, Christian and Winkler, Michael}},
issn = {{1424-3199}},
journal = {{Journal of Evolution Equations}},
keywords = {{Mathematics (miscellaneous)}},
number = {{2}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects}}},
doi = {{10.1007/s00028-024-00954-x}},
volume = {{24}},
year = {{2024}},
}
@article{53315,
abstract = {{AbstractIn a smoothly bounded two‐dimensional domain and for a given nondecreasing positive unbounded , for each and the inequality
is shown to hold for any positive fulfilling
This is thereafter applied to nonglobal solutions of the Keller–Segel system coupled to the incompressible Navier–Stokes equations through transport and buoyancy, and it is seen that in any such blow‐up event the corresponding population density cannot remain uniformly integrable over near its explosion time.}},
author = {{Wang, Yulan and Winkler, Michael}},
issn = {{0024-6107}},
journal = {{Journal of the London Mathematical Society}},
keywords = {{General Mathematics}},
number = {{3}},
publisher = {{Wiley}},
title = {{{An interpolation inequality involving $L\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system}}},
doi = {{10.1112/jlms.12885}},
volume = {{109}},
year = {{2024}},
}
@article{53542,
abstract = {{AbstractThis work deals with the extension problem for the fractional Laplacian on Riemannian symmetric spaces G/K of noncompact type and of general rank, which gives rise to a family of convolution operators, including the Poisson operator. More precisely, motivated by Euclidean results for the Poisson semigroup, we study the long-time asymptotic behavior of solutions to the extension problem for $$L^1$$
L
1
initial data. In the case of the Laplace–Beltrami operator, we show that if the initial data are bi-K-invariant, then the solution to the extension problem behaves asymptotically as the mass times the fundamental solution, but this convergence may break down in the non-bi-K-invariant case. In the second part, we investigate the long-time asymptotic behavior of the extension problem associated with the so-called distinguished Laplacian on G/K. In this case, we observe phenomena which are similar to the Euclidean setting for the Poisson semigroup, such as $$L^1$$
L
1
asymptotic convergence without the assumption of bi-K-invariance.}},
author = {{Papageorgiou, Efthymia}},
issn = {{1424-3199}},
journal = {{Journal of Evolution Equations}},
keywords = {{Mathematics (miscellaneous)}},
number = {{2}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces}}},
doi = {{10.1007/s00028-024-00959-6}},
volume = {{24}},
year = {{2024}},
}
@inproceedings{55191,
author = {{Rezat, Sebastian and Visnovska, Jana and Yan, Guorui and Leshota, Moneoang and Sabra, Hussein}},
booktitle = {{Proceedings of the 14th International Congress on Mathematical Education}},
keywords = {{Mathematics, Mathematik, Textbook, Curriculum Resources, Schulbuch}},
pages = {{537–545}},
publisher = {{World Scientific}},
title = {{{Topic Study Group 41: Research and development on textbooks and resources for learning and teaching mathematics}}},
doi = {{10.1142/9789811287152_0065}},
volume = {{1}},
year = {{2024}},
}
@article{53300,
author = {{Brennecken, Dominik}},
issn = {{0022-247X}},
journal = {{Journal of Mathematical Analysis and Applications}},
keywords = {{Applied Mathematics, Analysis}},
number = {{2}},
publisher = {{Elsevier BV}},
title = {{{Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting}}},
doi = {{10.1016/j.jmaa.2024.128125}},
volume = {{535}},
year = {{2024}},
}
@article{52089,
abstract = {{AbstractImage restoration via alternating direction method of multipliers (ADMM) has gained large interest within the last decade. Solving standard problems of Gaussian and Poisson noise, the set of “Total Variation” (TV)-based regularizers proved to be efficient and versatile. In the last few years, the “Total Generalized Variation” (TGV) approach combined TV regularizers of different orders adaptively to better suit local regions in the image. This improved the technique significantly. The approach solved the staircase problem inherent of the first-order TV while keeping the beneficial edge preservation. The iterative minimization for the augmented Lagrangian of TGV problems requires four important parameters: two penalty parameters $${\rho }$$
ρ
and $${\eta }$$
η
and two regularization parameters $${\lambda _{0}}$$
λ
0
and $${\lambda _{1}}$$
λ
1
. The choice of penalty parameters decides on the convergence speed, and the regularization parameters decide on the impact of the respective regularizer and are determined by the noise level in the image. For scientific applications of such algorithms, an automated and thus objective method to determine these parameters is essential to receive unbiased results independent of the user. Obviously, both sets of parameters are to be well chosen to achieve optimal results, too. In this paper, a method is proposed to adaptively choose optimal $${\rho }$$
ρ
and $${\eta }$$
η
values for the iteration to converge faster, based on the primal and dual residuals arising from the optimality conditions of the augmented Lagrangian. Further, we show how to choose $${\lambda _{0}}$$
λ
0
and $${\lambda _{1}}$$
λ
1
based on the inherent noise in the image.}},
author = {{Zietlow, Christian and Lindner, Jörg K. N.}},
issn = {{1017-1398}},
journal = {{Numerical Algorithms}},
keywords = {{Applied Mathematics}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{ADMM-TGV image restoration for scientific applications with unbiased parameter choice}}},
doi = {{10.1007/s11075-024-01759-2}},
year = {{2024}},
}
@article{52958,
author = {{Boeddeker, Christoph and Subramanian, Aswin Shanmugam and Wichern, Gordon and Haeb-Umbach, Reinhold and Le Roux, Jonathan}},
issn = {{2329-9290}},
journal = {{IEEE/ACM Transactions on Audio, Speech, and Language Processing}},
keywords = {{Electrical and Electronic Engineering, Acoustics and Ultrasonics, Computer Science (miscellaneous), Computational Mathematics}},
pages = {{1185--1197}},
publisher = {{Institute of Electrical and Electronics Engineers (IEEE)}},
title = {{{TS-SEP: Joint Diarization and Separation Conditioned on Estimated Speaker Embeddings}}},
doi = {{10.1109/taslp.2024.3350887}},
volume = {{32}},
year = {{2024}},
}
@inproceedings{57895,
abstract = {{In our paper, we present a study in which we investigate which strategies pre-service teachers (PSTs) use to find and, if necessary, reject possible candidates for congruence theorems for quadrilaterals. This study was conducted before the PTSs attended a university geometry course. In this way, statements about learning prerequisites can be made. For the study, we analyzed group discussions of PSTs to identify typical approaches and evaluate them from a mathematical perspective. The results can be considered for the further development of courses for PSTs and generate hypotheses
for further research.}},
author = {{Hoffmann, Max and Schlüter, Sarah}},
booktitle = {{Proceedings of the Fifth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2024, 10-14 June 2024)}},
editor = {{González-Martín, Alejandro S. and Gueudet, Ghislaine and Florensa, Ignasi and Lombard, Nathan}},
keywords = {{Teachers’ and students’ practices at university level, Transition to, across and from university mathematics, Teaching and learning of specific topics in university mathematics, Congruence, Quadrilaterals}},
publisher = {{Escola Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM}},
title = {{{How Do Advanced Pre-Service Teachers Develop Congruence Theorems for Quadrilaterals?}}},
year = {{2024}},
}
@article{49326,
abstract = {{Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by defining a class of admissible maps for every such hypernetwork. We explain how to classify robust cluster synchronization patterns on hypernetworks by finding balanced partitions, and we generalize the concept of a graph fibration to the hypernetwork context. We also show that robust synchronization patterns are only fully determined by polynomial admissible maps of high order. This means that, unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order, i.e., nonlinear, effect. We give a formula, in terms of the order of the hypernetwork, for the degree of the polynomial admissible maps that determine robust synchronization patterns. We also demonstrate that this degree is optimal by investigating a class of examples. We conclude by demonstrating how this effect may cause remarkable synchrony breaking bifurcations that occur at high polynomial degree.}},
author = {{von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}},
issn = {{0036-1399}},
journal = {{SIAM Journal on Applied Mathematics}},
keywords = {{Applied Mathematics}},
number = {{6}},
pages = {{2329--2353}},
publisher = {{Society for Industrial & Applied Mathematics (SIAM)}},
title = {{{Hypernetworks: Cluster Synchronization Is a Higher-Order Effect}}},
doi = {{10.1137/23m1561075}},
volume = {{83}},
year = {{2023}},
}
@article{50271,
author = {{Gharibian, Sevag and Le Gall, François}},
issn = {{0097-5397}},
journal = {{SIAM Journal on Computing}},
keywords = {{General Mathematics, General Computer Science}},
number = {{4}},
pages = {{1009--1038}},
publisher = {{Society for Industrial & Applied Mathematics (SIAM)}},
title = {{{Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture}}},
doi = {{10.1137/22m1513721}},
volume = {{52}},
year = {{2023}},
}
@article{50458,
abstract = {{AbstractConsider a set of jobs connected to a directed acyclic task graph with a fixed source and sink. The edges of this graph model precedence constraints and the jobs have to be scheduled with respect to those. We introduce the server cloud scheduling problem, in which the jobs have to be processed either on a single local machine or on one of infinitely many cloud machines. For each job, processing times both on the server and in the cloud are given. Furthermore, for each edge in the task graph, a communication delay is included in the input and has to be taken into account if one of the two jobs is scheduled on the server and the other in the cloud. The server processes jobs sequentially, whereas the cloud can serve as many as needed in parallel, but induces costs. We consider both makespan and cost minimization. The main results are an FPTAS for the makespan objective for graphs with a constant source and sink dividing cut and strong hardness for the case with unit processing times and delays.}},
author = {{Maack, Marten and Meyer auf der Heide, Friedhelm and Pukrop, Simon}},
issn = {{0178-4617}},
journal = {{Algorithmica}},
keywords = {{Applied Mathematics, Computer Science Applications, General Computer Science}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Server Cloud Scheduling}}},
doi = {{10.1007/s00453-023-01189-x}},
year = {{2023}},
}
@article{51351,
author = {{Steffen, Eckhard and Wolf, Isaak Hieronymus}},
issn = {{0166-218X}},
journal = {{Discrete Applied Mathematics}},
keywords = {{Applied Mathematics, Discrete Mathematics and Combinatorics}},
pages = {{185--189}},
publisher = {{Elsevier BV}},
title = {{{Bounds for the chromatic index of signed multigraphs}}},
doi = {{10.1016/j.dam.2023.05.008}},
volume = {{337}},
year = {{2023}},
}
@article{51357,
author = {{Steffen, Eckhard and Wolf, Isaak Hieronymus}},
issn = {{0012-365X}},
journal = {{Discrete Mathematics}},
keywords = {{Discrete Mathematics and Combinatorics, Theoretical Computer Science}},
publisher = {{Elsevier BV}},
title = {{{Rotation r-graphs}}},
doi = {{10.1016/j.disc.2023.113457}},
year = {{2023}},
}
@article{52806,
author = {{Gilbert, H. and Schürmann, M. and Liebendörfer, M. and Lawson, D. and Hodds, M.}},
issn = {{0020-739X}},
journal = {{International Journal of Mathematical Education in Science and Technology}},
keywords = {{Applied Mathematics, Education, Mathematics (miscellaneous)}},
pages = {{1--26}},
publisher = {{Informa UK Limited}},
title = {{{Post-pandemic online mathematics and statistics support: Practitioners’ opinions in Germany and Great Britain & Ireland}}},
doi = {{10.1080/0020739x.2023.2184282}},
year = {{2023}},
}
@article{45971,
abstract = {{Abstract
An error estimate for a canonical discretization of the harmonic map heat flow into spheres is derived. The numerical scheme uses standard finite elements with a nodal treatment of linearized unit-length constraints. The analysis is based on elementary approximation results and only uses the discrete weak formulation.}},
author = {{Bartels, Sören and Kovács, Balázs and Wang, Zhangxian}},
issn = {{0272-4979}},
journal = {{IMA Journal of Numerical Analysis}},
keywords = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
publisher = {{Oxford University Press (OUP)}},
title = {{{Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints}}},
doi = {{10.1093/imanum/drad037}},
year = {{2023}},
}