Steep resonance of parametrically excited active MEMS cantilevers for dynamic mode in Atomic Force Microscopy. - In: Proceedings in applied mathematics and mechanics, ISSN 1617-7061, Bd. 22 (2023), 1, e202200230, S. 1-6
Ongoing developments in nanotechnology demand higher spatial resolution and thus, higher amplitude sensitivity in Atomic Force Microscopy (AFM). In this work, active cantilevers with integrated sensor and actuator systems are parametrically excited using a novel, analog feedback circuit. With that it is possible to adapt the strength and sign of a cubic nonlinearity which provides a bound to the amplitudes in resonance operation. The system response shows steeper resonance curves and therefore higher amplitude sensitivities compared to forced excited cantilevers. Theoretical findings are validated experimentally.
https://doi.org/10.1002/pamm.202200230
Hamiltonicity of graphs perturbed by a random regular graph. - In: Random structures & algorithms, ISSN 1098-2418, Bd. 62 (2023), 4, S. 857-886
https://doi.org/10.1002/rsa.21122
Hamiltonicity of graphs perturbed by a random geometric graph. - In: Journal of graph theory, ISSN 1097-0118, Bd. 103 (2023), 1, S. 12-22
We study Hamiltonicity in graphs obtained as the union of a deterministic n-vertex graph H with linear degrees and a d-dimensional random geometric graph G d (n, r) for any d ≥ 1. We obtain an asymptotically optimal bound on the minimum r for which a.a.s. H ∪ G d (n, r) is Hamiltonian. Our proof provides a linear time algorithm to find a Hamilton cycle in such graphs.
https://doi.org/10.1002/jgt.22901
Relatively bounded perturbations of J-non-negative operators. - In: Complex analysis and operator theory, ISSN 1661-8262, Bd. 17 (2023), 1, 14, insges. 30 S.
We improve known perturbation results for self-adjoint operators in Hilbert spaces and prove spectral enclosures for diagonally dominant J-self-adjoint operator matrices. These are used in the proof of the central result, a perturbation theorem for J-non-negative operators. The results are applied to singular indefinite Sturm-Liouville operators with Lp-potentials. Known bounds on the non-real eigenvalues of such operators are improved.
https://doi.org/10.1007/s11785-022-01263-2
On the complexity of finding well-balanced orientations with upper bounds on the out-degrees. - In: Journal of combinatorial optimization, ISSN 1573-2886, Bd. 45 (2023), 1, 30, S. 1-14
https://doi.org/10.1007/s10878-022-00962-y
Communication science in Türkiye: how communication research and education developed over the years. - In: Publizistik, ISSN 1862-2569, Bd. 68 (2023), 1, S. 89-108
In Türkiye, communication science falls under the category of social sciences and is regarded as an interdisciplinary scientific field focused on empirical research. The field is influenced by communication science developments of the West in terms of developing theories and methodology, and it faces challenges when it comes to the systematisation of theories and research methods created by different research traditions; their critical evaluation, development, and the failure to put theories to practical use. In order to ascertain the present condition of the field, this article explores the institutionalisation of communication science at universities and its potential tendencies as an academic field of study, its research trends, and the characteristics of communication science studies.
https://doi.org/10.1007/s11616-022-00766-4
Sensitivity analysis of combinatorial optimization problems using evolutionary bilevel optimization and data mining. - In: Annals of mathematics and artificial intelligence, ISSN 1573-7470, Bd. 91 (2023), 2/3, S. 309-328
Sensitivity analysis in general deals with the question of how changes in input data of a model affect its output data. In the context of optimization problems, such an analysis could, for instance, address how changes in capacity constraints affect the optimal solution value. Although well established in the domain of linear programming, sensitivity analysis approaches for combinatorial optimization problems are model-specific, limited in scope and not applicable to practical optimization problems. To overcome these limitations, Schulte et al. developed the concept of bilevel innovization. By using evolutionary bilevel optimization in combination with data mining and visualization techniques, bilevel innovization provides decision-makers with deeper insights into the behavior of the optimization model and supports decision-making related to model building and configuration. Originally introduced in the field of evolutionary computation, most recently bilevel innovization has been proposed as an approach to sensitivity analysis for combinatorial problems in general. Based on previous work on bilevel innovization, our paper illustrates this concept as a tool for sensitivity analysis by providing a comprehensive analysis of the generalized assignment problem. Furthermore, it is investigated how different algorithms for solving the combinatorial problem affect the insights gained by the sensitivity analysis, thus evaluating the robustness and reliability of the sensitivity analysis results.
https://doi.org/10.1007/s10472-022-09827-w
A note on the invertibility of the Gabor frame operator on certain modulation spaces. - In: The journal of Fourier analysis and applications, ISSN 1531-5851, Bd. 29 (2023), 1, 3, S. 1-20
We consider Gabor frames generated by a general lattice and a window function that belongs to one of the following spaces: the Sobolev space $$V_1 = H^1(\mathbb {R}^d)$$, the weighted $$L^2$$-space $$V_2 = L_{1 + |x|}^2(\mathbb {R}^d)$$, and the space $$V_3 = \mathbb {H}^1(\mathbb {R}^d) = V_1 \cap V_2$$consisting of all functions with finite uncertainty product; all these spaces can be described as modulation spaces with respect to suitable weighted $$L^2$$spaces. In all cases, we prove that the space of Bessel vectors in $$V_j$$is mapped bijectively onto itself by the Gabor frame operator. As a consequence, if the window function belongs to one of the three spaces, then the canonical dual window also belongs to the same space. In fact, the result not only applies to frames, but also to frame sequences.
https://doi.org/10.1007/s00041-022-09980-0
A systematic analysis of maximum tolerable tool wear in friction stir welding. - In: Welding in the world, ISSN 1878-6669, Bd. 67 (2023), 2, S. 325-339
Friction stir welding (FSW) is a solid-state joining process with a wide range of applications in the E-mobility, automotive, aerospace and energy industries. However, FSW is subjected to specific challenges including comparatively high process forces and high requirements on the clamping technique as well as tool wear resulting from the tool-workpiece interaction and thermo-mechanical stresses. Geometric-related tool wear can cause premature tool failure, process instabilities or weld seam irregularities. Therefore, tool wear in general, wear limits and tool life are essential factors for the efficient and sustainable implementation of friction stir welding. Against this background, this study analysed areas of significant tool wear on the shoulder and probe as a function of process temperature, weld seam length and weld seam quality. This provided functional correlations for determining limiting conditions on maximum tolerable tool wear. Geometrical deviations of the tool, induced by wear, were detected experimentally at different measuring points on the probe and shoulder and varying weld seam length. The investigations were carried out using a force-controlled robotized welding setup in which AA-6060-T66 sheets with a thickness of 5 mm were joined by weld seams up to 500 m in length. To identify the maximum tolerable tool wear, the weld seam properties were determined by visual and metallographic inspections and by tensile tests at 50-m intervals on the weld seam. It was shown that a 50% reduction in rotational speed (lower temperatures) resulted in less wear and thus in an increase of tool life of up to 150%. In addition, it was shown that the shoulder, like the probe, was also subject to significant wear. These results can be incorporated into FSW maintenance schedules to maximize tool life and minimize scrap rates.
https://doi.org/10.1007/s40194-022-01407-0
Relative genericity of controllablity and stabilizability for differential-algebraic systems. - In: Mathematics of control, signals, and systems, ISSN 1435-568X, Bd. 35 (2023), 1, S. 45-76
https://doi.org/10.1007/s00498-022-00332-3