@inbook{57407,
  author       = {{Süßmann, Johannes}},
  booktitle    = {{Johann Gottfried Herder. Die Formation seines Werkes in Bückeburg 1771–1776}},
  editor       = {{Brüdermann, Stefan and Laak, Lothar van}},
  isbn         = {{978-3-8353-5687-0}},
  pages        = {{171–189}},
  publisher    = {{Wallstein}},
  title        = {{{Aus Reflexion in Unmittelbarkeit. Herders Bückeburger Geschichtsphilosophie}}},
  volume       = {{80}},
  year         = {{2024}},
}

@article{59616,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>The activation of C(<jats:italic>sp</jats:italic><jats:sup>3</jats:sup>)−F bonds by the commercially available catalyst B(C<jats:sub>6</jats:sub>F<jats:sub>5</jats:sub>)<jats:sub>3</jats:sub> is reported and applied in reactions with arenes, allylic, vinylic and acetylenic silanes, and olefins to achieve a variety of C−C bond formations (45 examples).</jats:p>}},
  author       = {{Hoppe, Axel and Stepen, Arne J. and Köring, Laura and Paradies, Jan}},
  issn         = {{1615-4150}},
  journal      = {{Advanced Synthesis &amp; Catalysis}},
  keywords     = {{fluoride, bond activation, borane, Lewis acid, C-C bond formation}},
  number       = {{13}},
  pages        = {{2933--2938}},
  publisher    = {{Wiley}},
  title        = {{{Tris(pentafluorophenyl)borane‐Catalyzed Functionalization of Benzylic C−F Bonds}}},
  doi          = {{10.1002/adsc.202400511}},
  volume       = {{366}},
  year         = {{2024}},
}

@misc{54235,
  author       = {{Süßmann, Johannes}},
  title        = {{{Religion und Freiheit}}},
  year         = {{2024}},
}

@inbook{59936,
  author       = {{Vukadinovic, Vojin Sasa}},
  booktitle    = {{Jahrbuch Sexualitäten 2024}},
  isbn         = {{978-3-8353-5635-6 }},
  pages        = {{199--207}},
  publisher    = {{Wallstein Verlag}},
  title        = {{{Das It-Girl der Vernunft als Echo der Verhältnisse. Heide Heinz (1939–2022)}}},
  year         = {{2024}},
}

@misc{59832,
  booktitle    = {{ZUKUNFT. Die Diskussionszeitschrift für Politik, Gesellschaft und Kultur}},
  editor       = {{Barberi, Alessandro and Serloth, Barbara and Vukadinovic, Vojin Sasa}},
  isbn         = {{978-3-89656-344-6}},
  number       = {{10}},
  title        = {{{Siebter Oktober Dreiundzwanzig}}},
  year         = {{2024}},
}

@article{60047,
  abstract     = {{<jats:title>Abstract</jats:title><jats:sec>
                <jats:title>Purpose</jats:title>
                <jats:p>Cardiopulmonary exercise testing (CPET) is considered the gold standard for assessing cardiorespiratory fitness. To ensure consistent performance of each test, it is necessary to adapt the power increase of the test protocol to the physical characteristics of each individual. This study aimed to use machine learning models to determine individualized ramp protocols based on non-exercise features. We hypothesized that machine learning models will predict peak oxygen uptake (<jats:inline-formula><jats:alternatives><jats:tex-math>$$\dot{V}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                    <mml:mover>
                      <mml:mi>V</mml:mi>
                      <mml:mo>˙</mml:mo>
                    </mml:mover>
                  </mml:math></jats:alternatives></jats:inline-formula>O<jats:sub>2peak</jats:sub>) and peak power output (PPO) more accurately than conventional multiple linear regression (MLR).</jats:p>
              </jats:sec><jats:sec>
                <jats:title>Methods</jats:title>
                <jats:p>The cross-sectional study was conducted with 274 (♀168, ♂106) participants who performed CPET on a cycle ergometer. Machine learning models and multiple linear regression were used to predict <jats:inline-formula><jats:alternatives><jats:tex-math>$$\dot{V}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                    <mml:mover>
                      <mml:mi>V</mml:mi>
                      <mml:mo>˙</mml:mo>
                    </mml:mover>
                  </mml:math></jats:alternatives></jats:inline-formula>O<jats:sub>2peak</jats:sub> and PPO using non-exercise features. The accuracy of the models was compared using criteria such as root mean square error (RMSE). Shapley additive explanation (SHAP) was applied to determine the feature importance.</jats:p>
              </jats:sec><jats:sec>
                <jats:title>Results</jats:title>
                <jats:p>The most accurate machine learning model was the random forest (RMSE: 6.52 ml/kg/min [95% CI 5.21–8.17]) for <jats:inline-formula><jats:alternatives><jats:tex-math>$$\dot{V}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                    <mml:mover>
                      <mml:mi>V</mml:mi>
                      <mml:mo>˙</mml:mo>
                    </mml:mover>
                  </mml:math></jats:alternatives></jats:inline-formula>O<jats:sub>2peak</jats:sub> prediction and the gradient boosting regression (RMSE: 43watts [95% CI 35–52]) for PPO prediction. Compared to the MLR, the machine learning models reduced the RMSE by up to 28% and 22% for prediction of <jats:inline-formula><jats:alternatives><jats:tex-math>$$\dot{V}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                    <mml:mover>
                      <mml:mi>V</mml:mi>
                      <mml:mo>˙</mml:mo>
                    </mml:mover>
                  </mml:math></jats:alternatives></jats:inline-formula>O<jats:sub>2peak</jats:sub> and PPO, respectively. Furthermore, SHAP ranked body composition data such as skeletal muscle mass and extracellular water as the most impactful features.</jats:p>
              </jats:sec><jats:sec>
                <jats:title>Conclusion</jats:title>
                <jats:p>Machine learning models predict <jats:inline-formula><jats:alternatives><jats:tex-math>$$\dot{V}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                    <mml:mover>
                      <mml:mi>V</mml:mi>
                      <mml:mo>˙</mml:mo>
                    </mml:mover>
                  </mml:math></jats:alternatives></jats:inline-formula>O<jats:sub>2peak</jats:sub> and PPO more accurately than MLR and can be used to individualize CPET protocols. Features that provide information about the participant's body composition contribute most to the improvement of these predictions.</jats:p>
              </jats:sec><jats:sec>
                <jats:title>Trial registration number</jats:title>
                <jats:p>DRKS00031401 (6 March 2023, retrospectively registered).</jats:p>
              </jats:sec>}},
  author       = {{Wenzel, Charlotte and Liebig, Thomas and Swoboda, Adrian and Smolareck, Rika and Schlagheck, Marit Lea and Walzik, David and Groll, Andreas and Goulding, Richie P. and Zimmer, Philipp}},
  issn         = {{1439-6319}},
  journal      = {{European Journal of Applied Physiology}},
  number       = {{11}},
  pages        = {{3421--3431}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Machine learning predicts peak oxygen uptake and peak power output for customizing cardiopulmonary exercise testing using non-exercise features}}},
  doi          = {{10.1007/s00421-024-05543-x}},
  volume       = {{124}},
  year         = {{2024}},
}

@article{63980,
  abstract     = {{Density, viscosity, and self-diffusion coefficients are reported for octan-1-ol and the related ether-alcohols 2-pentoxy-ethan-1-ol, 3-butoxypropan-1-ol, 4-propoxybutan-1-ol, 5-ethoxypentan-1-ol, and 6-methoxyhexan-1-ol covering temperature ranges from 298.15 to 359.15 K. These new data reveal structure–property relationships affected by the presence and the position of the ether moiety in the molecular structure of the ether-alcohols. Compared to octan-1-ol, the presence of the ether moiety causes an increase in intermolecular hydrogen bonding interactions, resulting in higher densities. The increase in density is less pronounced for those ether-octanols that engage in intramolecular hydrogen bonding. As for the effects of the ether moiety on the dynamics, these are generally faster for the ether-alcohols compared to octan-1-ol, suggesting that hydrogen bonding between ether oxygen and hydroxy hydrogen is weaker compared to hydrogen bonding between two hydroxy groups. The activation energies obtained from an Arrhenius analysis are higher for translational motion than for momentum transfer for all alcohols. There are additional finer details across the ether alcohols for these activation barriers. These differences cancel out for the mathematical product of self-diffusion coefficient and viscosity (Dη). The effect of water impurities on the studied properties was also investigated and found to lead to small increases in densities for all alcohols. Viscosities decrease for octan-1-ol and 2-pentoxyethan-1-ol but increase for the other ether-alcohols that can engage in intramolecular hydrogen bonding. Density, viscosity, and self-diffusion coefficients are reported for octan-1-ol and the related ether-alcohols 2-pentoxy-ethan-1-ol, 3-butoxypropan-1-ol, 4-propoxybutan-1-ol, 5-ethoxypentan-1-ol, and 6-methoxyhexan-1-ol covering temperature ranges from 298.15 to 359.15 K. These new data reveal structure–property relationships affected by the presence and the position of the ether moiety in the molecular structure of the ether-alcohols. Compared to octan-1-ol, the presence of the ether moiety causes an increase in intermolecular hydrogen bonding interactions, resulting in higher densities. The increase in density is less pronounced for those ether-octanols that engage in intramolecular hydrogen bonding. As for the effects of the ether moiety on the dynamics, these are generally faster for the ether-alcohols compared to octan-1-ol, suggesting that hydrogen bonding between ether oxygen and hydroxy hydrogen is weaker compared to hydrogen bonding between two hydroxy groups. The activation energies obtained from an Arrhenius analysis are higher for translational motion than for momentum transfer for all alcohols. There are additional finer details across the ether alcohols for these activation barriers. These differences cancel out for the mathematical product of self-diffusion coefficient and viscosity (Dη). The effect of water impurities on the studied properties was also investigated and found to lead to small increases in densities for all alcohols. Viscosities decrease for octan-1-ol and 2-pentoxyethan-1-ol but increase for the other ether-alcohols that can engage in intramolecular hydrogen bonding.}},
  author       = {{Hoffmann, Markus M. and Gonzalez, Anthony A. and Huynh, Mandy T. and Miller, Kashane K. and Gutmann, Torsten and Buntkowsky, Gerd}},
  issn         = {{0021-9568}},
  journal      = {{Journal of Chemical & Engineering Data}},
  number       = {{8}},
  pages        = {{2688–2699}},
  publisher    = {{American Chemical Society}},
  title        = {{{Densities, Viscosities, and Self-Diffusion Coefficients of Octan-1-ol and Related Ether-Alcohols}}},
  doi          = {{10.1021/acs.jced.4c00195}},
  volume       = {{69}},
  year         = {{2024}},
}

@article{51116,
  abstract     = {{Self-piercing riveting is an established joining technique for lightweight materials. To increase the sustainability of the rivet manufacturing process, the authors of the present paper have developed an approach for shortening the process chain by omitting the heat treatment and rivet coating. To do this, use is made of high nitrogen steel as the rivet material. Successful joining with these rivets has already been proven, and it has also been shown that a competitive joint strength can be achieved with these rivets. Up until now, no studies have been conducted of the corrosion behaviour of uncoated rivets in high nitrogen steel compared to conventional rivets made of heat-treatable steel with a coating of Almac® or zinc-nickel with topcoat, and the corrosion behaviour of joints manufactured with these rivets has also not been investigated. Furthermore, the suitability of rivets in high nitrogen steel for structures undergoing cathodic dip painting has not been evaluated to date. These are therefore the aims of the research work presented in this paper. Corrosion behaviour is tested by exposing rivets and joints to a salt spray atmosphere. Cross-cut tests are conducted in order to classify the adhesion of cathodic dip paint to the different rivet surfaces and materials. The results of the experimental test show that the cathodic dip paint has sufficient adhesion to the uncoated rivets in high nitrogen steel and that these rivets can therefore be used in the manufacture of car bodies. Due to the stainless properties of the high nitrogen steel, better corrosion resistance is seen by comparison to the commonly used coatings of Almac® and zinc-nickel with topcoat. A study of the corrosion behaviour of the joints shows that the rivet head diameter and rivet head position, in particular, are decisive for preventing crevice corrosion under the rivet head and contact corrosion within the joint. }},
  author       = {{Uhe, Benedikt and Kuball, Clara-Maria and Merklein, Marion and Meschut, Gerson}},
  journal      = {{Production Engineering}},
  title        = {{{Corrosion behaviour of self-piercing riveted joints with uncoated rivets in high nitrogen steel}}},
  doi          = {{10.1007/s11740-024-01262-6}},
  year         = {{2024}},
}

@inproceedings{55638,
  abstract     = {{<jats:p>Abstract. Traditionally, joints are cylindrical and rotationally symmetric. In the present study, non-rotationally symmetric joints are used for joining steel and Glass mat-reinforced thermoplastic sheets (GMT). In addition, the study also analyzes the impact of non-rotational symmetric joint rotation on the load-bearing capacity. Single lap joint specimens were fabricated using the In-Mold assembly technique for joining steel sheets with GMT. Tensile shear tests were performed on different orientations of the joint geometry, and it was observed that changing the joint orientation influences the load-bearing capacity. The joints are constitutively modeled using beam elements and the influence of joint rotation on load distribution is examined through a static simulation study. </jats:p>}},
  author       = {{Devulapally, Deekshith Reddy and Martin, Sven and Tröster, Thomas}},
  booktitle    = {{Materials Research Proceedings}},
  issn         = {{2474-395X}},
  publisher    = {{Materials Research Forum LLC}},
  title        = {{{Non-rotationally symmetric joints – Mechanisms and load bearing capacity}}},
  doi          = {{10.21741/9781644903131-183}},
  year         = {{2024}},
}

@article{61253,
  abstract     = {{<jats:p>In the SUPER scheme (Swing-UP of the quantum EmitteR population), excitation of a quantum emitter is achieved with two off-resonant, red-detuned laser pulses. This allows the generation of high-quality single photons without the need of complex laser stray light suppression or careful spectral filtering. In the present work, we extend this promising method to quantum emitters, specifically semiconductor quantum dots, inside a resonant optical cavity. A significant advantage of the SUPER scheme is identified in that it eliminates re-excitation of the quantum emitter by suppressing photon emission during the excitation cycle. This, in turn, leads to almost ideal single-photon purity, overcoming a major factor typically limiting the quality of photons generated with quantum emitters in high-quality cavities. We further find that for cavity-mediated biexciton emission of degenerate photon pairs, the SUPER scheme leads to near-perfect biexciton initialization with very high values of polarization entanglement of emitted photon pairs.</jats:p>
          <jats:sec>
            <jats:title/>
            <jats:supplementary-material>
              <jats:permissions>
                <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement>
                <jats:copyright-year>2024</jats:copyright-year>
              </jats:permissions>
            </jats:supplementary-material>
          </jats:sec>}},
  author       = {{Heinisch, Nils and Köcher, Nikolas and Bauch, David and Schumacher, Stefan}},
  issn         = {{2643-1564}},
  journal      = {{Physical Review Research}},
  number       = {{1}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Swing-up dynamics in quantum emitter cavity systems: Near ideal single photons and entangled photon pairs}}},
  doi          = {{10.1103/physrevresearch.6.l012017}},
  volume       = {{6}},
  year         = {{2024}},
}

@article{61900,
  abstract     = {{Background Anti-Muslim and anti-Islam attitudes are widespread in contemporary western societies. A grassroots movement of mosques tries to reduce prejudice by organizing guided mosque tours for non-Muslims. While this is an opportunity for intergroup contact in a social psychological sense, contact occurs under sometimes difficult conditions. As yet, its effects have not been investigated empirically. Objective We examine (a) whether visits have an immediate and medium-term effect on prejudice toward Islam and (b) how they change the visitors’ subjective images of Muslims. Methods (a) We survey N = 324 secondary school students in a three-wave panel study in 6 guided mosque tours in different parts of Germany, including a control sample. The tour programme was in line with common practice in the mosques. Standardized measurements were taken immediately before and after the tour and again several months later. (b) We asked about subjective images of Muslims and had subjects report their spontaneous associations with the term Muslim. Results (a) Most, but not all, mosque visits significantly alleviate anti-Islam prejudice in the short term. The effects fall off after several months. (b) After the visit, the image of Muslims possessed more concrete religious content, while negative and menacing associations, such as oppression of women, threat, or so-called Islamic State have decreased. Conclusions Outgroup contact in a mosque works as predicted by the intergroup contact research, even under less than optimal conditions. However, there is potential for improvement of the setup of tours in the interest of a more sustainable impact.}},
  author       = {{Janzen, Olga and Diekmann, Isabell and Tsolak, Dorian and Salentin, Kurt}},
  issn         = {{2510-1226}},
  journal      = {{Zeitschrift für Religion, Gesellschaft und Politik}},
  keywords     = {{Intergroup contact, Anti-Islam attitudes, Anti-Muslim attitudes, Prejudice, Youth}},
  number       = {{1}},
  pages        = {{ 129–159}},
  publisher    = {{Springer VS}},
  title        = {{{Do Guided Mosque Tours Alleviate the Prejudice of Non-Muslims against Islam and Muslims? Evidence from a Quasi-Experimental Panel Study from Germany}}},
  doi          = {{10.1007/s41682-023-00161-4}},
  volume       = {{8}},
  year         = {{2024}},
}

@inproceedings{56840,
  author       = {{Schmitt, Martin}},
  keywords     = {{Digitalisierung, Digitalgeschichte, Umweltgeschichte, Anthropozän, Computer, Rechenzentrum, Digital History}},
  title        = {{{Digitalisierung und Umwelt – eine verflochtene Digitalgeschichte der Gegenwart im Angesicht des Klimawandels}}},
  year         = {{2024}},
}

@inbook{52511,
  abstract     = {{Sind „soziale Medien“ überhaupt ein Thema für die Geschichtswissenschaft? Ja, denn die längere Geschichte der Digitalisierung, in der die „sozialen Medien“ einzuordnen sind, zählt bereits über 80 Jahre. Konrad Zuse und andere Ingenieure entwickelten seit 1941 die ersten Digitalcomputer, Unternehmer*innen, Wissenschaftler*innen und Staatenlenker*innen setzten diese seit den 1950er Jahren für ihre Zwecke ein, die Zivilgesellschaft adaptierte sie in den darauffolgenden Dekaden – all das prägte die sozio-digitale Landschaft der späteren „sozialen Medien“. Als unmittelbar „nach dem Boom“ etwa um 1970 zahlreiche Industriegesellschaften einen strukturellen Wandel in Wirtschaft, Gesellschaft und Politik durchlebten, war eine Antwort darauf die vermehrte Digitalisierung und Vernetzung. Daraus entwickelte sich die 1990er Jahre als markante Dekade von World Wide Web, Google und Chatdiensten. Die Entwicklung der „sozialen Medien“ ist also unter anderem in eine ökonomische und gesellschaftliche Entwicklung der Aufmerksamkeitsökonomie und in die längeren Veränderungen von Wirtschafts- und Gesellschaftsordnungen der Ausdifferenzierung und partiellen Individualisierung seit den 1960er Jahren einzuordnen. Dadurch lässt sich besser verstehen, welche Prämissen ihnen zugrunde lagen, welche Möglichkeitsräume und Probleme sich daraus ergaben und warum sie die heutige Öffentlichkeit in einer bestimmten Art und Weise dominieren – ohne sie jedoch zu determinieren.}},
  author       = {{Schmitt, Martin}},
  booktitle    = {{Soziale Medien – wie sie wurden, was sie sind }},
  keywords     = {{Digitalgeschichte, Soziale Medien, Technikgeschichte, World Wide Web, Digitalisierung}},
  publisher    = {{Bundeszentrale für politische Bildung}},
  title        = {{{Die Vorgeschichte der „sozialen Medien“. Über die Träume digitaler Vergemeinschaftung und freier Kommunikation}}},
  year         = {{2024}},
}

@inbook{55635,
  author       = {{Hartung, Olaf}},
  booktitle    = {{Geschichtskulturen im digitalen Wandel?}},
  editor       = {{Hartung, Olaf and Krebs, Alexandra and Meyer-Hamme, Johannes}},
  isbn         = {{978-3-7344-1629-3}},
  issn         = {{1435-7658}},
  pages        = {{9--32}},
  publisher    = {{Wochenschau Verlag}},
  title        = {{{Geschichtskulturen im digitalen Wandel? – Zu den Gründen und Zielen dieses Bandes}}},
  year         = {{2024}},
}

@inbook{50073,
  author       = {{Hartung, Olaf}},
  booktitle    = {{Geschichtskulturen im digitalen Wandel?}},
  editor       = {{Hartung, Olaf and Krebs, Alexandra and Meyer-Hamme, Johannes}},
  isbn         = {{978-3-7344-1629-3}},
  issn         = {{1435-7658}},
  pages        = {{152--155}},
  publisher    = {{Wochenschau Verlag}},
  title        = {{{Historisches Lernen in einer ‚(Geschichts-)Kultur der Digitalität‘?}}},
  year         = {{2024}},
}

@misc{51624,
  author       = {{Staffel, Florian}},
  booktitle    = {{Sehepunkte}},
  number       = {{2}},
  title        = {{{Christian Marx: Wegbereiter der Globalisierung. Multinationale Unternehmen der westeuropäischen Chemieindustrie in der Zeit nach dem Boom (1960er-2000er Jahre) (= Nach dem Boom), Göttingen 2023.}}},
  volume       = {{24}},
  year         = {{2024}},
}

@inproceedings{56863,
  author       = {{Schiebel, Fabian Benedikt and Sattler, Florian and Schubert, Philipp Dominik and Apel, Sven and Bodden, Eric}},
  booktitle    = {{38th European Conference on Object-Oriented Programming (ECOOP 2024)}},
  editor       = {{Aldrich, Jonathan and Salvaneschi, Guido}},
  isbn         = {{978-3-95977-341-6}},
  issn         = {{1868-8969}},
  pages        = {{36:1–36:28}},
  publisher    = {{Schloss Dagstuhl – Leibniz-Zentrum für Informatik}},
  title        = {{{Scaling Interprocedural Static Data-Flow Analysis to Large C/C++ Applications: An Experience Report}}},
  doi          = {{10.4230/LIPIcs.ECOOP.2024.36}},
  volume       = {{313}},
  year         = {{2024}},
}

@article{52876,
  author       = {{Arends, Christian and Wolf, Lasse Lennart and Meinecke, Jasmin and Barkhofen, Sonja and Weich, Tobias and Bartley, Tim}},
  issn         = {{2643-1564}},
  journal      = {{Physical Review Research}},
  keywords     = {{General Physics and Astronomy}},
  number       = {{1}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Decomposing large unitaries into multimode devices of arbitrary size}}},
  doi          = {{10.1103/physrevresearch.6.l012043}},
  volume       = {{6}},
  year         = {{2024}},
}

@article{54288,
  abstract     = {{<jats:p>The ability to apply user-chosen large-scale unitary operations with high fidelity to a quantum state is key to realizing future photonic quantum technologies. Here, we realize the implementation of programmable unitary operations on up to 64 frequency-bin modes. To benchmark the performance of our system, we probe different quantum walk unitary operations, in particular, Grover walks on four-dimensional hypercubes with similarities exceeding 95% and quantum walks with 400 steps on circles and finite lines with similarities of 98%. Our results open a path toward implementing high-quality unitary operations, which can form the basis for applications in complex tasks, such as Gaussian boson sampling.</jats:p>
          <jats:sec>
            <jats:title/>
            <jats:supplementary-material>
              <jats:permissions>
                <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement>
                <jats:copyright-year>2024</jats:copyright-year>
              </jats:permissions>
            </jats:supplementary-material>
          </jats:sec>}},
  author       = {{De, Syamsundar and Ansari, Vahid and Sperling, Jan and Barkhofen, Sonja and Brecht, Benjamin and Silberhorn, Christine}},
  issn         = {{2643-1564}},
  journal      = {{Physical Review Research}},
  number       = {{2}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Realization of high-fidelity unitary operations on up to 64 frequency bins}}},
  doi          = {{10.1103/physrevresearch.6.l022040}},
  volume       = {{6}},
  year         = {{2024}},
}

@article{63248,
  abstract     = {{<jats:title>Abstract</jats:title>
          <jats:p>The Navier–Stokes system <jats:disp-formula>
              <jats:alternatives>
                <jats:tex-math>$$\begin{aligned} \left\{ \begin{array}{l} u_t + (u\cdot \nabla ) u =\Delta u+\nabla P + f(x,t), \\ \nabla \cdot u=0, \end{array} \right. \end{aligned}$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mtable>
                      <mml:mtr>
                        <mml:mtd>
                          <mml:mfenced>
                            <mml:mrow>
                              <mml:mtable>
                                <mml:mtr>
                                  <mml:mtd>
                                    <mml:mrow>
                                      <mml:msub>
                                        <mml:mi>u</mml:mi>
                                        <mml:mi>t</mml:mi>
                                      </mml:msub>
                                      <mml:mo>+</mml:mo>
                                      <mml:mrow>
                                        <mml:mo>(</mml:mo>
                                        <mml:mi>u</mml:mi>
                                        <mml:mo>·</mml:mo>
                                        <mml:mi>∇</mml:mi>
                                        <mml:mo>)</mml:mo>
                                      </mml:mrow>
                                      <mml:mi>u</mml:mi>
                                      <mml:mo>=</mml:mo>
                                      <mml:mi>Δ</mml:mi>
                                      <mml:mi>u</mml:mi>
                                      <mml:mo>+</mml:mo>
                                      <mml:mi>∇</mml:mi>
                                      <mml:mi>P</mml:mi>
                                      <mml:mo>+</mml:mo>
                                      <mml:mi>f</mml:mi>
                                      <mml:mrow>
                                        <mml:mo>(</mml:mo>
                                        <mml:mi>x</mml:mi>
                                        <mml:mo>,</mml:mo>
                                        <mml:mi>t</mml:mi>
                                        <mml:mo>)</mml:mo>
                                      </mml:mrow>
                                      <mml:mo>,</mml:mo>
                                    </mml:mrow>
                                  </mml:mtd>
                                </mml:mtr>
                                <mml:mtr>
                                  <mml:mtd>
                                    <mml:mrow>
                                      <mml:mrow/>
                                      <mml:mi>∇</mml:mi>
                                      <mml:mo>·</mml:mo>
                                      <mml:mi>u</mml:mi>
                                      <mml:mo>=</mml:mo>
                                      <mml:mn>0</mml:mn>
                                      <mml:mo>,</mml:mo>
                                    </mml:mrow>
                                  </mml:mtd>
                                </mml:mtr>
                              </mml:mtable>
                            </mml:mrow>
                          </mml:mfenced>
                        </mml:mtd>
                      </mml:mtr>
                    </mml:mtable>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:disp-formula>is considered along with homogeneous Dirichlet boundary conditions in a smoothly bounded planar domain <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$\Omega $$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mi>Ω</mml:mi>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>. It is firstly, inter alia, observed that if <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$T&gt;0$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>T</mml:mi>
                    <mml:mo>&gt;</mml:mo>
                    <mml:mn>0</mml:mn>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> and <jats:disp-formula>
              <jats:alternatives>
                <jats:tex-math>$$\begin{aligned} \int _0^T \bigg \{ \int _\Omega |f(x,t)| \cdot \ln ^\frac{1}{2} \big (|f(x,t)|+1\big ) dx \bigg \}^2 dt &lt;\infty , \end{aligned}$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mtable>
                      <mml:mtr>
                        <mml:mtd>
                          <mml:mrow>
                            <mml:msubsup>
                              <mml:mo>∫</mml:mo>
                              <mml:mn>0</mml:mn>
                              <mml:mi>T</mml:mi>
                            </mml:msubsup>
                            <mml:mrow>
                              <mml:mo>{</mml:mo>
                            </mml:mrow>
                            <mml:msub>
                              <mml:mo>∫</mml:mo>
                              <mml:mi>Ω</mml:mi>
                            </mml:msub>
                            <mml:mrow>
                              <mml:mo>|</mml:mo>
                              <mml:mi>f</mml:mi>
                              <mml:mrow>
                                <mml:mo>(</mml:mo>
                                <mml:mi>x</mml:mi>
                                <mml:mo>,</mml:mo>
                                <mml:mi>t</mml:mi>
                                <mml:mo>)</mml:mo>
                              </mml:mrow>
                              <mml:mo>|</mml:mo>
                            </mml:mrow>
                            <mml:mo>·</mml:mo>
                            <mml:msup>
                              <mml:mo>ln</mml:mo>
                              <mml:mfrac>
                                <mml:mn>1</mml:mn>
                                <mml:mn>2</mml:mn>
                              </mml:mfrac>
                            </mml:msup>
                            <mml:mrow>
                              <mml:mo>(</mml:mo>
                            </mml:mrow>
                            <mml:mrow>
                              <mml:mo>|</mml:mo>
                              <mml:mi>f</mml:mi>
                              <mml:mrow>
                                <mml:mo>(</mml:mo>
                                <mml:mi>x</mml:mi>
                                <mml:mo>,</mml:mo>
                                <mml:mi>t</mml:mi>
                                <mml:mo>)</mml:mo>
                              </mml:mrow>
                              <mml:mo>|</mml:mo>
                            </mml:mrow>
                            <mml:mo>+</mml:mo>
                            <mml:mn>1</mml:mn>
                            <mml:mrow>
                              <mml:mo>)</mml:mo>
                            </mml:mrow>
                            <mml:mi>d</mml:mi>
                            <mml:mi>x</mml:mi>
                            <mml:msup>
                              <mml:mrow>
                                <mml:mo>}</mml:mo>
                              </mml:mrow>
                              <mml:mn>2</mml:mn>
                            </mml:msup>
                            <mml:mi>d</mml:mi>
                            <mml:mi>t</mml:mi>
                            <mml:mo>&lt;</mml:mo>
                            <mml:mi>∞</mml:mi>
                            <mml:mo>,</mml:mo>
                          </mml:mrow>
                        </mml:mtd>
                      </mml:mtr>
                    </mml:mtable>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:disp-formula>then for all divergence-free <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$u_0\in L^2(\Omega ;{\mathbb {R}}^2)$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:msub>
                      <mml:mi>u</mml:mi>
                      <mml:mn>0</mml:mn>
                    </mml:msub>
                    <mml:mo>∈</mml:mo>
                    <mml:msup>
                      <mml:mi>L</mml:mi>
                      <mml:mn>2</mml:mn>
                    </mml:msup>
                    <mml:mrow>
                      <mml:mo>(</mml:mo>
                      <mml:mi>Ω</mml:mi>
                      <mml:mo>;</mml:mo>
                      <mml:msup>
                        <mml:mrow>
                          <mml:mi>R</mml:mi>
                        </mml:mrow>
                        <mml:mn>2</mml:mn>
                      </mml:msup>
                      <mml:mo>)</mml:mo>
                    </mml:mrow>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>, a corresponding initial-boundary value problem admits a weak solution <jats:italic>u</jats:italic> with <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$u|_{t=0}=u_0$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:msub>
                      <mml:mrow>
                        <mml:mi>u</mml:mi>
                        <mml:mo>|</mml:mo>
                      </mml:mrow>
                      <mml:mrow>
                        <mml:mi>t</mml:mi>
                        <mml:mo>=</mml:mo>
                        <mml:mn>0</mml:mn>
                      </mml:mrow>
                    </mml:msub>
                    <mml:mo>=</mml:mo>
                    <mml:msub>
                      <mml:mi>u</mml:mi>
                      <mml:mn>0</mml:mn>
                    </mml:msub>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>. For any positive and nondecreasing <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$L\in C^0([0,\infty ))$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>L</mml:mi>
                    <mml:mo>∈</mml:mo>
                    <mml:msup>
                      <mml:mi>C</mml:mi>
                      <mml:mn>0</mml:mn>
                    </mml:msup>
                    <mml:mrow>
                      <mml:mo>(</mml:mo>
                      <mml:mrow>
                        <mml:mo>[</mml:mo>
                        <mml:mn>0</mml:mn>
                        <mml:mo>,</mml:mo>
                        <mml:mi>∞</mml:mi>
                        <mml:mo>)</mml:mo>
                      </mml:mrow>
                      <mml:mo>)</mml:mo>
                    </mml:mrow>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> such that <jats:disp-formula>
              <jats:alternatives>
                <jats:tex-math>$$\begin{aligned} \frac{L(\xi )}{\ln ^\frac{1}{2} \xi } \rightarrow 0 \qquad \text{ as } \xi \rightarrow \infty , \end{aligned}$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mtable>
                      <mml:mtr>
                        <mml:mtd>
                          <mml:mrow>
                            <mml:mfrac>
                              <mml:mrow>
                                <mml:mi>L</mml:mi>
                                <mml:mo>(</mml:mo>
                                <mml:mi>ξ</mml:mi>
                                <mml:mo>)</mml:mo>
                              </mml:mrow>
                              <mml:mrow>
                                <mml:msup>
                                  <mml:mo>ln</mml:mo>
                                  <mml:mfrac>
                                    <mml:mn>1</mml:mn>
                                    <mml:mn>2</mml:mn>
                                  </mml:mfrac>
                                </mml:msup>
                                <mml:mi>ξ</mml:mi>
                              </mml:mrow>
                            </mml:mfrac>
                            <mml:mo>→</mml:mo>
                            <mml:mn>0</mml:mn>
                            <mml:mspace/>
                            <mml:mspace/>
                            <mml:mtext>as</mml:mtext>
                            <mml:mspace/>
                            <mml:mi>ξ</mml:mi>
                            <mml:mo>→</mml:mo>
                            <mml:mi>∞</mml:mi>
                            <mml:mo>,</mml:mo>
                          </mml:mrow>
                        </mml:mtd>
                      </mml:mtr>
                    </mml:mtable>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:disp-formula>this is complemented by a statement on nonexistence of such a solution in the presence of smooth initial data and a suitably constructed <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$f:\Omega \times (0,T)\rightarrow {\mathbb {R}}^2$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>f</mml:mi>
                    <mml:mo>:</mml:mo>
                    <mml:mi>Ω</mml:mi>
                    <mml:mo>×</mml:mo>
                    <mml:mrow>
                      <mml:mo>(</mml:mo>
                      <mml:mn>0</mml:mn>
                      <mml:mo>,</mml:mo>
                      <mml:mi>T</mml:mi>
                      <mml:mo>)</mml:mo>
                    </mml:mrow>
                    <mml:mo>→</mml:mo>
                    <mml:msup>
                      <mml:mrow>
                        <mml:mi>R</mml:mi>
                      </mml:mrow>
                      <mml:mn>2</mml:mn>
                    </mml:msup>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> fulfilling <jats:disp-formula>
              <jats:alternatives>
                <jats:tex-math>$$\begin{aligned} \int _0^T \bigg \{ \int _\Omega |f(x,t)| \cdot L\big (|f(x,t)|\big ) dx \bigg \}^2 dt &lt; \infty . \end{aligned}$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mtable>
                      <mml:mtr>
                        <mml:mtd>
                          <mml:mrow>
                            <mml:msubsup>
                              <mml:mo>∫</mml:mo>
                              <mml:mn>0</mml:mn>
                              <mml:mi>T</mml:mi>
                            </mml:msubsup>
                            <mml:mrow>
                              <mml:mo>{</mml:mo>
                            </mml:mrow>
                            <mml:msub>
                              <mml:mo>∫</mml:mo>
                              <mml:mi>Ω</mml:mi>
                            </mml:msub>
                            <mml:mrow>
                              <mml:mo>|</mml:mo>
                              <mml:mi>f</mml:mi>
                              <mml:mrow>
                                <mml:mo>(</mml:mo>
                                <mml:mi>x</mml:mi>
                                <mml:mo>,</mml:mo>
                                <mml:mi>t</mml:mi>
                                <mml:mo>)</mml:mo>
                              </mml:mrow>
                              <mml:mo>|</mml:mo>
                            </mml:mrow>
                            <mml:mo>·</mml:mo>
                            <mml:mrow>
                              <mml:mi>L</mml:mi>
                              <mml:mrow>
                                <mml:mo>(</mml:mo>
                              </mml:mrow>
                              <mml:mo>|</mml:mo>
                              <mml:mi>f</mml:mi>
                              <mml:mrow>
                                <mml:mo>(</mml:mo>
                                <mml:mi>x</mml:mi>
                                <mml:mo>,</mml:mo>
                                <mml:mi>t</mml:mi>
                                <mml:mo>)</mml:mo>
                              </mml:mrow>
                              <mml:mo>|</mml:mo>
                              <mml:mrow>
                                <mml:mo>)</mml:mo>
                              </mml:mrow>
                              <mml:mi>d</mml:mi>
                              <mml:mi>x</mml:mi>
                            </mml:mrow>
                            <mml:msup>
                              <mml:mrow>
                                <mml:mo>}</mml:mo>
                              </mml:mrow>
                              <mml:mn>2</mml:mn>
                            </mml:msup>
                            <mml:mi>d</mml:mi>
                            <mml:mi>t</mml:mi>
                            <mml:mo>&lt;</mml:mo>
                            <mml:mi>∞</mml:mi>
                            <mml:mo>.</mml:mo>
                          </mml:mrow>
                        </mml:mtd>
                      </mml:mtr>
                    </mml:mtable>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:disp-formula>This resolves a fine structure in the borderline case <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$p=1$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>p</mml:mi>
                    <mml:mo>=</mml:mo>
                    <mml:mn>1</mml:mn>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> and <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$q=2$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>q</mml:mi>
                    <mml:mo>=</mml:mo>
                    <mml:mn>2</mml:mn>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> appearing in results on existence of weak solutions for sources in <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$L^q((0,T);L^p(\Omega ;{\mathbb {R}}^2))$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:msup>
                      <mml:mi>L</mml:mi>
                      <mml:mi>q</mml:mi>
                    </mml:msup>
                    <mml:mrow>
                      <mml:mo>(</mml:mo>
                      <mml:mrow>
                        <mml:mo>(</mml:mo>
                        <mml:mn>0</mml:mn>
                        <mml:mo>,</mml:mo>
                        <mml:mi>T</mml:mi>
                        <mml:mo>)</mml:mo>
                      </mml:mrow>
                      <mml:mo>;</mml:mo>
                      <mml:msup>
                        <mml:mi>L</mml:mi>
                        <mml:mi>p</mml:mi>
                      </mml:msup>
                      <mml:mrow>
                        <mml:mo>(</mml:mo>
                        <mml:mi>Ω</mml:mi>
                        <mml:mo>;</mml:mo>
                        <mml:msup>
                          <mml:mrow>
                            <mml:mi>R</mml:mi>
                          </mml:mrow>
                          <mml:mn>2</mml:mn>
                        </mml:msup>
                        <mml:mo>)</mml:mo>
                      </mml:mrow>
                      <mml:mo>)</mml:mo>
                    </mml:mrow>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> when <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$p\in (1,\infty ]$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>p</mml:mi>
                    <mml:mo>∈</mml:mo>
                    <mml:mo>(</mml:mo>
                    <mml:mn>1</mml:mn>
                    <mml:mo>,</mml:mo>
                    <mml:mi>∞</mml:mi>
                    <mml:mo>]</mml:mo>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> and <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$q\in [1,\infty ]$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>q</mml:mi>
                    <mml:mo>∈</mml:mo>
                    <mml:mo>[</mml:mo>
                    <mml:mn>1</mml:mn>
                    <mml:mo>,</mml:mo>
                    <mml:mi>∞</mml:mi>
                    <mml:mo>]</mml:mo>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> satisfy <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$\frac{1}{p}+\frac{1}{q}\le \frac{3}{2}$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mfrac>
                      <mml:mn>1</mml:mn>
                      <mml:mi>p</mml:mi>
                    </mml:mfrac>
                    <mml:mo>+</mml:mo>
                    <mml:mfrac>
                      <mml:mn>1</mml:mn>
                      <mml:mi>q</mml:mi>
                    </mml:mfrac>
                    <mml:mo>≤</mml:mo>
                    <mml:mfrac>
                      <mml:mn>3</mml:mn>
                      <mml:mn>2</mml:mn>
                    </mml:mfrac>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>, and on nonexistence if here <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$p\in [1,\infty )$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>p</mml:mi>
                    <mml:mo>∈</mml:mo>
                    <mml:mo>[</mml:mo>
                    <mml:mn>1</mml:mn>
                    <mml:mo>,</mml:mo>
                    <mml:mi>∞</mml:mi>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> and <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$q\in [1,\infty )$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mi>q</mml:mi>
                    <mml:mo>∈</mml:mo>
                    <mml:mo>[</mml:mo>
                    <mml:mn>1</mml:mn>
                    <mml:mo>,</mml:mo>
                    <mml:mi>∞</mml:mi>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula> are such that <jats:inline-formula>
              <jats:alternatives>
                <jats:tex-math>$$\frac{1}{p}+\frac{1}{q}&gt;\frac{3}{2}$$</jats:tex-math>
                <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mfrac>
                      <mml:mn>1</mml:mn>
                      <mml:mi>p</mml:mi>
                    </mml:mfrac>
                    <mml:mo>+</mml:mo>
                    <mml:mfrac>
                      <mml:mn>1</mml:mn>
                      <mml:mi>q</mml:mi>
                    </mml:mfrac>
                    <mml:mo>&gt;</mml:mo>
                    <mml:mfrac>
                      <mml:mn>3</mml:mn>
                      <mml:mn>2</mml:mn>
                    </mml:mfrac>
                  </mml:mrow>
                </mml:math>
              </jats:alternatives>
            </jats:inline-formula>.</jats:p>}},
  author       = {{Winkler, Michael}},
  issn         = {{0025-5831}},
  journal      = {{Mathematische Annalen}},
  number       = {{2}},
  pages        = {{3023--3054}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Externally forced blow-up and optimal spaces for source regularity in the two-dimensional Navier–Stokes system}}},
  doi          = {{10.1007/s00208-024-02987-6}},
  volume       = {{391}},
  year         = {{2024}},
}

