Publikationen an der Fakultät für Mathematik und Naturwissenschaften ab 2019

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Baidiuk, Dmytro; Derkach, Volodymyr; Hassi, Seppo
Unitary boundary pairs for isometric operators in Pontryagin spaces and generalized coresolvents. - In: Complex analysis and operator theory, ISSN 1661-8262, Bd. 15 (2021), 2, 32, insges. 52 S.

https://doi.org/10.1007/s11785-020-01073-4
Hasselmann, Sebastian; Kopittke, Caroline; Götz, Maria; Witzel, Patrick; Riffel, Jacqueline; Heinrich, Doris
Tailored nanotopography of photocurable composites for control of cell migration. - In: RSC Advances, ISSN 2046-2069, Bd. 11 (2021), 8, S. 4286-4296

External mechanical stimuli represent elementary signals for living cells to adapt to their adjacent environment. These signals range from bulk material properties down to nanoscopic surface topography and trigger cell behaviour. Here, we present a novel approach to generate tailored surface roughnesses in the nanometer range to tune surface properties by particle size and volume ratio. Time-resolved local mean-squared displacement (LMSD) analysis of amoeboid cell migration reveals that nanorough surfaces alter effectively cell migration velocities and the active cell migration phases. Since the UV curable composite material is easy to fabricate and can be structured via different light based processes, it is possible to generate hierarchical 3D cell scaffolds for tissue engineering or lab-on-a-chip applications with adjustable surface roughness in the nanometre range.



https://doi.org/10.1039/D0RA06530G
Köhler, Michael; Kluitmann, Jonas
In situ assembly of gold nanoparticles in the presence of poly-DADMAC resulting in hierarchical and highly fractal nanostructures. - In: Applied Sciences, ISSN 2076-3417, Bd. 11 (2021), 3, 1191, S. 1-13

The presence of the polycationic macromolecule poly(diallyldimethylammonium chloride) (poly-DADMAC) has a strong effect on the shape and size of colloidal gold nanoparticles formed by the reduction of tetrachloroauric acid with ascorbic acid in aqueous solution. It slows down nanoparticle growth and supports the formation of nonspherical, partially highly fractal and hierarchical nanoparticle shapes. Four structural levels have been recognized from the near-spherical gold nanoparticles in the lower nanometer range over compact aggregates in the midnanometer range and flower and star-like particles in the submicron range up to larger filamentous aggregates. High-contrast scanning electron microscope (SEM) images show that single gold nanoparticles and clusters of them are connected by bundles of macromolecules in large aggregates. The investigation showed that a large spectrum of different nanoparticle shapes and sizes can be accessed by tuning the poly-DADMAC concentrations and their ratio to other reactants. The nanoassemblies with a very high specific surface area might be of interest for SERS and heterogeneous catalysis.



https://doi.org/10.3390/app11031191
Eichfelder, Gabriele; Jahn, Johannes
Optimality conditions in discrete-continuous nonlinear optimization. - In: Minimax theory and its applications, ISSN 2199-1413, Bd. 6 (2021), 1, S. 127-144

Schweser, Thomas;
Generalized hypergraph coloring. - In: Discussiones mathematicae, ISSN 2083-5892, Bd. 41 (2021), 1, S. 103-121

https://doi.org/10.7151/dmgt.2168
Berger, Thomas; Snoo, Hendrik S. V. de; Trunk, Carsten; Winkler, Henrik
Linear relations and their singular chains. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2021. - 1 Online-Ressource (17 Seiten). - (Preprint ; M21,01)
https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2021200018
Ryzhkov, Nikolay V.; Ledovich, Olesya; Eggert, Lara; Bund, Andreas; Paszuk, Agnieszka; Hannappel, Thomas; Klyukin, Konstantin; Alexandrov, Vitaly; Skorb, Ekaterina V.
Layer-by-layer polyelectrolyte assembly for the protection of GaP surfaces from photocorrosion. - In: ACS applied nano materials, ISSN 2574-0970, Bd. 4 (2021), 1, S. 425-431

Polyelectrolyte layer-by-layer assemblies are known as protective coatings for corrosion inhibition. Here, we demonstrate that polyelectrolyte multilayers of poly(ethyleneimine) (PEI) and poly(styrene sulfonate) (PSS)-(PEI/PSS)x-adsorbed at the GaP(100) photocathode surface remarkably mitigate the photocorrosion of GaP without decreasing its photoconversion efficiency. The activity of the polybase-polyacid complex is based on buffering pH changes at the solid-liquid interface. We carried out ab initio molecular dynamics-based simulations of the GaP(100) surface in contact with liquid water and demonstrated that an increase in the proton concentration enhances GaP dissolution. We used the scanning vibrating electrode technique (SVET) to characterize the distribution of photocorrosion activity areas over bare and polyelectrolyte-coated GaP surfaces and we showed that a polyelectrolyte coating impedes the dissolution kinetics. Data obtained using the SVET were compared to photoetched pores on the semiconductor surface. Voltammetric and chronoamperometric measurements were also performed to evaluate photoconversion efficiencies before and after the application of the protective coatings.



https://doi.org/10.1021/acsanm.0c02768
Eichfelder, Gabriele; Warnow, Leo
Proximity measures based on KKT points for constrained multi-objective optimization. - In: Journal of global optimization, ISSN 1573-2916, Bd. 80 (2021), 1, S. 63-86

An important aspect of optimization algorithms, for instance evolutionary algorithms, are termination criteria that measure the proximity of the found solution to the optimal solution set. A frequently used approach is the numerical verification of necessary optimality conditions such as the Karush-Kuhn-Tucker (KKT) conditions. In this paper, we present a proximity measure which characterizes the violation of the KKT conditions. It can be computed easily and is continuous in every efficient solution. Hence, it can be used as an indicator for the proximity of a certain point to the set of efficient (Edgeworth-Pareto-minimal) solutions and is well suited for algorithmic use due to its continuity properties. This is especially useful within evolutionary algorithms for candidate selection and termination, which we also illustrate numerically for some test problems.



https://doi.org/10.1007/s10898-020-00971-3
Han, Jie; Kohayakawa, Yoshiharu; Morris, Patrick; Person, Yury
Finding any given 2-factor in sparse pseudorandom graphs efficiently. - In: Journal of graph theory, ISSN 1097-0118, Bd. 96 (2021), 1, S. 87-108

https://doi.org/10.1002/jgt.22576
Eichfelder, Gabriele; Klamroth, Kathrin; Niebling, Julia
Nonconvex constrained optimization by a filtering branch and bound. - In: Journal of global optimization, ISSN 1573-2916, Bd. 80 (2021), 1, S. 31-61

A major difficulty in optimization with nonconvex constraints is to find feasible solutions. As simple examples show, the [alpha]BB-algorithm for single-objective optimization may fail to compute feasible solutions even though this algorithm is a popular method in global optimization. In this work, we introduce a filtering approach motivated by a multiobjective reformulation of the constrained optimization problem. Moreover, the multiobjective reformulation enables to identify the trade-off between constraint satisfaction and objective value which is also reflected in the quality guarantee. Numerical tests validate that we indeed can find feasible and often optimal solutions where the classical single-objective [alpha]BB method fails, i.e., it terminates without ever finding a feasible solution.



https://doi.org/10.1007/s10898-020-00956-2