[{"date_updated":"2023-06-06T09:17:10Z","author":[{"first_name":"Mohamed Ahmed","full_name":"Sherif, Mohamed Ahmed","last_name":"Sherif"},{"last_name":"da Silva","full_name":"da Silva, Ana Alexandra Morim","first_name":"Ana Alexandra Morim"},{"full_name":"Pestryakova, Svetlana","last_name":"Pestryakova","first_name":"Svetlana"},{"full_name":"Ahmed, Abdullah Fathi","last_name":"Ahmed","first_name":"Abdullah Fathi"},{"first_name":"Sven","full_name":"Niemann, Sven","last_name":"Niemann"},{"first_name":"Axel-Cyrille Ngonga","last_name":"Ngomo","full_name":"Ngomo, Axel-Cyrille Ngonga"}],"volume":10,"doi":"10.1038/s41597-023-02199-8","publication_status":"published","publication_identifier":{"issn":["2052-4463"]},"citation":{"ama":"Sherif MA, da Silva AAM, Pestryakova S, Ahmed AF, Niemann S, Ngomo A-CN. IngridKG: A FAIR Knowledge Graph of Graffiti. <i>Scientific Data</i>. 2023;10(1). doi:<a href=\"https://doi.org/10.1038/s41597-023-02199-8\">10.1038/s41597-023-02199-8</a>","ieee":"M. A. Sherif, A. A. M. da Silva, S. Pestryakova, A. F. Ahmed, S. Niemann, and A.-C. N. Ngomo, “IngridKG: A FAIR Knowledge Graph of Graffiti,” <i>Scientific Data</i>, vol. 10, no. 1, Art. no. 318, 2023, doi: <a href=\"https://doi.org/10.1038/s41597-023-02199-8\">10.1038/s41597-023-02199-8</a>.","chicago":"Sherif, Mohamed Ahmed, Ana Alexandra Morim da Silva, Svetlana Pestryakova, Abdullah Fathi Ahmed, Sven Niemann, and Axel-Cyrille Ngonga Ngomo. “IngridKG: A FAIR Knowledge Graph of Graffiti.” <i>Scientific Data</i> 10, no. 1 (2023). <a href=\"https://doi.org/10.1038/s41597-023-02199-8\">https://doi.org/10.1038/s41597-023-02199-8</a>.","mla":"Sherif, Mohamed Ahmed, et al. “IngridKG: A FAIR Knowledge Graph of Graffiti.” <i>Scientific Data</i>, vol. 10, no. 1, 318, Springer Science and Business Media LLC, 2023, doi:<a href=\"https://doi.org/10.1038/s41597-023-02199-8\">10.1038/s41597-023-02199-8</a>.","bibtex":"@article{Sherif_da Silva_Pestryakova_Ahmed_Niemann_Ngomo_2023, title={IngridKG: A FAIR Knowledge Graph of Graffiti}, volume={10}, DOI={<a href=\"https://doi.org/10.1038/s41597-023-02199-8\">10.1038/s41597-023-02199-8</a>}, number={1318}, journal={Scientific Data}, publisher={Springer Science and Business Media LLC}, author={Sherif, Mohamed Ahmed and da Silva, Ana Alexandra Morim and Pestryakova, Svetlana and Ahmed, Abdullah Fathi and Niemann, Sven and Ngomo, Axel-Cyrille Ngonga}, year={2023} }","short":"M.A. Sherif, A.A.M. da Silva, S. Pestryakova, A.F. Ahmed, S. Niemann, A.-C.N. Ngomo, Scientific Data 10 (2023).","apa":"Sherif, M. A., da Silva, A. A. M., Pestryakova, S., Ahmed, A. F., Niemann, S., &#38; Ngomo, A.-C. N. (2023). IngridKG: A FAIR Knowledge Graph of Graffiti. <i>Scientific Data</i>, <i>10</i>(1), Article 318. <a href=\"https://doi.org/10.1038/s41597-023-02199-8\">https://doi.org/10.1038/s41597-023-02199-8</a>"},"intvolume":"        10","project":[{"_id":"104","name":"INGRID: INGRID: Informationssystem Graffiti in Deutschland","grant_number":"289287267"}],"_id":"45484","user_id":"6593","department":[{"_id":"574"},{"_id":"115"}],"article_number":"318","type":"journal_article","status":"public","publisher":"Springer Science and Business Media LLC","date_created":"2023-06-06T09:12:39Z","title":"IngridKG: A FAIR Knowledge Graph of Graffiti","issue":"1","year":"2023","keyword":["Library and Information Sciences","Statistics","Probability and Uncertainty","Computer Science Applications","Education","Information Systems","Statistics and Probability"],"language":[{"iso":"eng"}],"publication":"Scientific Data","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Graffiti is an urban phenomenon that is increasingly attracting the interest of the sciences. To the best of our knowledge, no suitable data corpora are available for systematic research until now. The Information System Graffiti in Germany project (<jats:sc>Ingrid</jats:sc>) closes this gap by dealing with graffiti image collections that have been made available to the project for public use. Within <jats:sc>Ingrid</jats:sc>, the graffiti images are collected, digitized and annotated. With this work, we aim to support the rapid access to a comprehensive data source on <jats:sc>Ingrid</jats:sc> targeted especially by researchers. In particular, we present <jats:sc>Ingrid</jats:sc>KG, an RDF knowledge graph of annotated graffiti, abides by the Linked Data and FAIR principles. We weekly update <jats:sc>Ingrid</jats:sc>KG by augmenting the new annotated graffiti to our knowledge graph. Our generation pipeline applies RDF data conversion, link discovery and data fusion approaches to the original data. The current version of <jats:sc>Ingrid</jats:sc>KG contains 460,640,154 triples and is linked to 3 other knowledge graphs by over 200,000 links. In our use case studies, we demonstrate the usefulness of our knowledge graph for different applications.</jats:p>","lang":"eng"}]},{"article_number":"101189","keyword":["Management Science and Operations Research","Statistics","Probability and Uncertainty","Strategy and Management","Economics and Econometrics","Geography","Planning and Development"],"language":[{"iso":"eng"}],"_id":"53238","user_id":"51811","department":[{"_id":"277"}],"status":"public","type":"journal_article","publication":"Socio-Economic Planning Sciences","title":"A private sustainable partner selection model for green public-private partnerships and regional economic development","doi":"10.1016/j.seps.2021.101189","date_updated":"2024-04-15T13:16:33Z","publisher":"Elsevier BV","date_created":"2024-04-04T15:50:16Z","author":[{"last_name":"Tavana","id":"31858","full_name":"Tavana, Madjid","first_name":"Madjid"},{"first_name":"Arash","full_name":"Khalili Nasr, Arash","last_name":"Khalili Nasr"},{"last_name":"Mina","full_name":"Mina, Hassan","first_name":"Hassan"},{"first_name":"Jerzy","last_name":"Michnik","full_name":"Michnik, Jerzy"}],"volume":83,"year":"2022","citation":{"ama":"Tavana M, Khalili Nasr A, Mina H, Michnik J. A private sustainable partner selection model for green public-private partnerships and regional economic development. <i>Socio-Economic Planning Sciences</i>. 2022;83. doi:<a href=\"https://doi.org/10.1016/j.seps.2021.101189\">10.1016/j.seps.2021.101189</a>","ieee":"M. Tavana, A. Khalili Nasr, H. Mina, and J. Michnik, “A private sustainable partner selection model for green public-private partnerships and regional economic development,” <i>Socio-Economic Planning Sciences</i>, vol. 83, Art. no. 101189, 2022, doi: <a href=\"https://doi.org/10.1016/j.seps.2021.101189\">10.1016/j.seps.2021.101189</a>.","chicago":"Tavana, Madjid, Arash Khalili Nasr, Hassan Mina, and Jerzy Michnik. “A Private Sustainable Partner Selection Model for Green Public-Private Partnerships and Regional Economic Development.” <i>Socio-Economic Planning Sciences</i> 83 (2022). <a href=\"https://doi.org/10.1016/j.seps.2021.101189\">https://doi.org/10.1016/j.seps.2021.101189</a>.","mla":"Tavana, Madjid, et al. “A Private Sustainable Partner Selection Model for Green Public-Private Partnerships and Regional Economic Development.” <i>Socio-Economic Planning Sciences</i>, vol. 83, 101189, Elsevier BV, 2022, doi:<a href=\"https://doi.org/10.1016/j.seps.2021.101189\">10.1016/j.seps.2021.101189</a>.","bibtex":"@article{Tavana_Khalili Nasr_Mina_Michnik_2022, title={A private sustainable partner selection model for green public-private partnerships and regional economic development}, volume={83}, DOI={<a href=\"https://doi.org/10.1016/j.seps.2021.101189\">10.1016/j.seps.2021.101189</a>}, number={101189}, journal={Socio-Economic Planning Sciences}, publisher={Elsevier BV}, author={Tavana, Madjid and Khalili Nasr, Arash and Mina, Hassan and Michnik, Jerzy}, year={2022} }","short":"M. Tavana, A. Khalili Nasr, H. Mina, J. Michnik, Socio-Economic Planning Sciences 83 (2022).","apa":"Tavana, M., Khalili Nasr, A., Mina, H., &#38; Michnik, J. (2022). A private sustainable partner selection model for green public-private partnerships and regional economic development. <i>Socio-Economic Planning Sciences</i>, <i>83</i>, Article 101189. <a href=\"https://doi.org/10.1016/j.seps.2021.101189\">https://doi.org/10.1016/j.seps.2021.101189</a>"},"intvolume":"        83","publication_status":"published","publication_identifier":{"issn":["0038-0121"]}},{"language":[{"iso":"eng"}],"keyword":["Statistics","Probability and Uncertainty","Numerical Analysis","Statistics and Probability"],"user_id":"186","department":[{"_id":"475"},{"_id":"19"},{"_id":"200"}],"_id":"50024","status":"public","type":"journal_article","publication":"The R Journal","doi":"10.32614/rj-2022-017","title":"The smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series","author":[{"first_name":"Yuanhua","last_name":"Feng","full_name":"Feng, Yuanhua"},{"full_name":"Gries, Thomas","last_name":"Gries","first_name":"Thomas"},{"last_name":"Letmathe","full_name":"Letmathe, Sebastian","first_name":"Sebastian"},{"first_name":"Dominik","full_name":"Schulz, Dominik","last_name":"Schulz"}],"date_created":"2023-12-21T12:09:31Z","volume":14,"publisher":"The R Foundation","date_updated":"2024-06-12T12:57:13Z","citation":{"apa":"Feng, Y., Gries, T., Letmathe, S., &#38; Schulz, D. (2022). The smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series. <i>The R Journal</i>, <i>14</i>(1), 182–195. <a href=\"https://doi.org/10.32614/rj-2022-017\">https://doi.org/10.32614/rj-2022-017</a>","short":"Y. Feng, T. Gries, S. Letmathe, D. Schulz, The R Journal 14 (2022) 182–195.","bibtex":"@article{Feng_Gries_Letmathe_Schulz_2022, title={The smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series}, volume={14}, DOI={<a href=\"https://doi.org/10.32614/rj-2022-017\">10.32614/rj-2022-017</a>}, number={1}, journal={The R Journal}, publisher={The R Foundation}, author={Feng, Yuanhua and Gries, Thomas and Letmathe, Sebastian and Schulz, Dominik}, year={2022}, pages={182–195} }","mla":"Feng, Yuanhua, et al. “The Smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series.” <i>The R Journal</i>, vol. 14, no. 1, The R Foundation, 2022, pp. 182–95, doi:<a href=\"https://doi.org/10.32614/rj-2022-017\">10.32614/rj-2022-017</a>.","ama":"Feng Y, Gries T, Letmathe S, Schulz D. The smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series. <i>The R Journal</i>. 2022;14(1):182-195. doi:<a href=\"https://doi.org/10.32614/rj-2022-017\">10.32614/rj-2022-017</a>","chicago":"Feng, Yuanhua, Thomas Gries, Sebastian Letmathe, and Dominik Schulz. “The Smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series.” <i>The R Journal</i> 14, no. 1 (2022): 182–95. <a href=\"https://doi.org/10.32614/rj-2022-017\">https://doi.org/10.32614/rj-2022-017</a>.","ieee":"Y. Feng, T. Gries, S. Letmathe, and D. Schulz, “The smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series,” <i>The R Journal</i>, vol. 14, no. 1, pp. 182–195, 2022, doi: <a href=\"https://doi.org/10.32614/rj-2022-017\">10.32614/rj-2022-017</a>."},"intvolume":"        14","page":"182-195","year":"2022","issue":"1","publication_status":"published","publication_identifier":{"issn":["2073-4859"]}},{"language":[{"iso":"eng"}],"keyword":["Statistics","Probability and Uncertainty","Numerical Analysis","Statistics and Probability"],"user_id":"186","_id":"50025","status":"public","type":"journal_article","publication":"The R Journal","doi":"10.32614/rj-2022-017","title":"The smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series","date_created":"2023-12-21T12:09:53Z","author":[{"full_name":"Feng, Yuanhua","id":"20760","last_name":"Feng","first_name":"Yuanhua"},{"id":"186","full_name":"Gries, Thomas","last_name":"Gries","first_name":"Thomas"},{"first_name":"Sebastian","last_name":"Letmathe","full_name":"Letmathe, Sebastian"},{"first_name":"Dominik","full_name":"Schulz, Dominik","last_name":"Schulz"}],"volume":14,"date_updated":"2025-11-10T09:32:36Z","publisher":"The R Foundation","citation":{"ama":"Feng Y, Gries T, Letmathe S, Schulz D. The smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series. <i>The R Journal</i>. 2022;14(1):182-195. doi:<a href=\"https://doi.org/10.32614/rj-2022-017\">10.32614/rj-2022-017</a>","chicago":"Feng, Yuanhua, Thomas Gries, Sebastian Letmathe, and Dominik Schulz. “The Smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series.” <i>The R Journal</i> 14, no. 1 (2022): 182–95. <a href=\"https://doi.org/10.32614/rj-2022-017\">https://doi.org/10.32614/rj-2022-017</a>.","ieee":"Y. Feng, T. Gries, S. Letmathe, and D. Schulz, “The smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series,” <i>The R Journal</i>, vol. 14, no. 1, pp. 182–195, 2022, doi: <a href=\"https://doi.org/10.32614/rj-2022-017\">10.32614/rj-2022-017</a>.","apa":"Feng, Y., Gries, T., Letmathe, S., &#38; Schulz, D. (2022). The smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series. <i>The R Journal</i>, <i>14</i>(1), 182–195. <a href=\"https://doi.org/10.32614/rj-2022-017\">https://doi.org/10.32614/rj-2022-017</a>","mla":"Feng, Yuanhua, et al. “The Smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series.” <i>The R Journal</i>, vol. 14, no. 1, The R Foundation, 2022, pp. 182–95, doi:<a href=\"https://doi.org/10.32614/rj-2022-017\">10.32614/rj-2022-017</a>.","bibtex":"@article{Feng_Gries_Letmathe_Schulz_2022, title={The smoots Package in R for Semiparametric Modeling of Trend Stationary Time Series}, volume={14}, DOI={<a href=\"https://doi.org/10.32614/rj-2022-017\">10.32614/rj-2022-017</a>}, number={1}, journal={The R Journal}, publisher={The R Foundation}, author={Feng, Yuanhua and Gries, Thomas and Letmathe, Sebastian and Schulz, Dominik}, year={2022}, pages={182–195} }","short":"Y. Feng, T. Gries, S. Letmathe, D. Schulz, The R Journal 14 (2022) 182–195."},"page":"182-195","intvolume":"        14","year":"2022","issue":"1","publication_status":"published","publication_identifier":{"issn":["2073-4859"]}},{"language":[{"iso":"eng"}],"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability","Statistical and Nonlinear Physics"],"publication":"Journal of Statistical Mechanics: Theory and Experiment","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>The defining feature of active particles is that they constantly propel themselves by locally converting chemical energy into directed motion. This active self-propulsion prevents them from equilibrating with their thermal environment (e.g. an aqueous solution), thus keeping them permanently out of equilibrium. Nevertheless, the spatial dynamics of active particles might share certain equilibrium features, in particular in the steady state. We here focus on the time-reversal symmetry of individual spatial trajectories as a distinct equilibrium characteristic. We investigate to what extent the steady-state trajectories of a trapped active particle obey or break this time-reversal symmetry. Within the framework of active Ornstein–Uhlenbeck particles we find that the steady-state trajectories in a harmonic potential fulfill path-wise time-reversal symmetry exactly, while this symmetry is typically broken in anharmonic potentials.</jats:p>"}],"date_created":"2022-06-28T07:27:41Z","publisher":"IOP Publishing","title":"How irreversible are steady-state trajectories of a trapped active particle?","issue":"3","year":"2021","department":[{"_id":"27"}],"user_id":"15278","_id":"32243","project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"article_number":"033216","type":"journal_article","status":"public","volume":2021,"author":[{"last_name":"Dabelow","full_name":"Dabelow, Lennart","first_name":"Lennart"},{"first_name":"Stefano","full_name":"Bo, Stefano","last_name":"Bo"},{"last_name":"Eichhorn","full_name":"Eichhorn, Ralf","first_name":"Ralf"}],"date_updated":"2022-06-28T07:28:14Z","doi":"10.1088/1742-5468/abe6fd","publication_identifier":{"issn":["1742-5468"]},"publication_status":"published","intvolume":"      2021","citation":{"ieee":"L. Dabelow, S. Bo, and R. Eichhorn, “How irreversible are steady-state trajectories of a trapped active particle?,” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2021, no. 3, Art. no. 033216, 2021, doi: <a href=\"https://doi.org/10.1088/1742-5468/abe6fd\">10.1088/1742-5468/abe6fd</a>.","chicago":"Dabelow, Lennart, Stefano Bo, and Ralf Eichhorn. “How Irreversible Are Steady-State Trajectories of a Trapped Active Particle?” <i>Journal of Statistical Mechanics: Theory and Experiment</i> 2021, no. 3 (2021). <a href=\"https://doi.org/10.1088/1742-5468/abe6fd\">https://doi.org/10.1088/1742-5468/abe6fd</a>.","ama":"Dabelow L, Bo S, Eichhorn R. How irreversible are steady-state trajectories of a trapped active particle? <i>Journal of Statistical Mechanics: Theory and Experiment</i>. 2021;2021(3). doi:<a href=\"https://doi.org/10.1088/1742-5468/abe6fd\">10.1088/1742-5468/abe6fd</a>","apa":"Dabelow, L., Bo, S., &#38; Eichhorn, R. (2021). How irreversible are steady-state trajectories of a trapped active particle? <i>Journal of Statistical Mechanics: Theory and Experiment</i>, <i>2021</i>(3), Article 033216. <a href=\"https://doi.org/10.1088/1742-5468/abe6fd\">https://doi.org/10.1088/1742-5468/abe6fd</a>","short":"L. Dabelow, S. Bo, R. Eichhorn, Journal of Statistical Mechanics: Theory and Experiment 2021 (2021).","bibtex":"@article{Dabelow_Bo_Eichhorn_2021, title={How irreversible are steady-state trajectories of a trapped active particle?}, volume={2021}, DOI={<a href=\"https://doi.org/10.1088/1742-5468/abe6fd\">10.1088/1742-5468/abe6fd</a>}, number={3033216}, journal={Journal of Statistical Mechanics: Theory and Experiment}, publisher={IOP Publishing}, author={Dabelow, Lennart and Bo, Stefano and Eichhorn, Ralf}, year={2021} }","mla":"Dabelow, Lennart, et al. “How Irreversible Are Steady-State Trajectories of a Trapped Active Particle?” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2021, no. 3, 033216, IOP Publishing, 2021, doi:<a href=\"https://doi.org/10.1088/1742-5468/abe6fd\">10.1088/1742-5468/abe6fd</a>."}},{"volume":11,"date_created":"2023-06-09T15:31:17Z","author":[{"last_name":"Duman","full_name":"Duman, Papatya","id":"72752","first_name":"Papatya"}],"date_updated":"2023-06-09T15:33:34Z","publisher":"MDPI AG","doi":"10.3390/g11010009","title":"Does Informational Equivalence Preserve Strategic Behavior? Experimental Results on Trockel’s Model of Selten’s Chain Store Story","issue":"1","publication_identifier":{"issn":["2073-4336"]},"publication_status":"published","intvolume":"        11","citation":{"ieee":"P. Duman, “Does Informational Equivalence Preserve Strategic Behavior? Experimental Results on Trockel’s Model of Selten’s Chain Store Story,” <i>Games</i>, vol. 11, no. 1, Art. no. 9, 2020, doi: <a href=\"https://doi.org/10.3390/g11010009\">10.3390/g11010009</a>.","chicago":"Duman, Papatya. “Does Informational Equivalence Preserve Strategic Behavior? Experimental Results on Trockel’s Model of Selten’s Chain Store Story.” <i>Games</i> 11, no. 1 (2020). <a href=\"https://doi.org/10.3390/g11010009\">https://doi.org/10.3390/g11010009</a>.","ama":"Duman P. Does Informational Equivalence Preserve Strategic Behavior? Experimental Results on Trockel’s Model of Selten’s Chain Store Story. <i>Games</i>. 2020;11(1). doi:<a href=\"https://doi.org/10.3390/g11010009\">10.3390/g11010009</a>","mla":"Duman, Papatya. “Does Informational Equivalence Preserve Strategic Behavior? Experimental Results on Trockel’s Model of Selten’s Chain Store Story.” <i>Games</i>, vol. 11, no. 1, 9, MDPI AG, 2020, doi:<a href=\"https://doi.org/10.3390/g11010009\">10.3390/g11010009</a>.","short":"P. Duman, Games 11 (2020).","bibtex":"@article{Duman_2020, title={Does Informational Equivalence Preserve Strategic Behavior? Experimental Results on Trockel’s Model of Selten’s Chain Store Story}, volume={11}, DOI={<a href=\"https://doi.org/10.3390/g11010009\">10.3390/g11010009</a>}, number={19}, journal={Games}, publisher={MDPI AG}, author={Duman, Papatya}, year={2020} }","apa":"Duman, P. (2020). Does Informational Equivalence Preserve Strategic Behavior? Experimental Results on Trockel’s Model of Selten’s Chain Store Story. <i>Games</i>, <i>11</i>(1), Article 9. <a href=\"https://doi.org/10.3390/g11010009\">https://doi.org/10.3390/g11010009</a>"},"year":"2020","user_id":"72752","_id":"45561","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Statistics","Probability and Uncertainty","Statistics and Probability"],"article_number":"9","publication":"Games","type":"journal_article","status":"public","abstract":[{"lang":"eng","text":"<jats:p>The purpose of this study is to experimentally test Trockel’s game, which is a modelling of the classical Chain Store Game (CSG), and determine whether one of the two theories of Equality and Deterrence may better account for the observed behavior. The CSG is an example of a simple game in extensive form where the actual behavior of well-informed players cannot be expected to agree with the clear results of game theoretical reasoning. To explain the disagreement between the theory and the expected behavior, Trockel’s game is proposed as an alternative modelling of the scenario. The existence of more than one equilibrium in Trockel’s game opens a door for reputation building. This study is the first attempt to experimentally test this alternative game with the same purpose. According to my data, there is some evidence in favor of both Equality and Deterrence Hypotheses. However, since the strategies compatible with the Equality Hypothesis are played more frequently, I observe some patterns which share the same intuition with the Deterrence Hypothesis.</jats:p>"}]},{"publication":"Annals of Mathematics","abstract":[{"text":"We give asymptotic upper and lower bounds for the number of squarefree d (0 < d ≤ X) such that the equation x² − dy²= −1 is solvable. These estimates, as usual, can equivalently be interpreted in terms of real quadratic fields with a fundamental unit with norm −1 and give strong evidence in the direction of a conjecture due to P. Stevenhagen.","lang":"eng"}],"language":[{"iso":"eng"}],"keyword":["Statistics","Probability and Uncertainty","Mathematics (miscellaneous)"],"issue":"3","year":"2010","date_created":"2022-12-23T09:09:02Z","publisher":"Annals of Mathematics","title":"On the negative Pell equation","type":"journal_article","status":"public","department":[{"_id":"102"}],"user_id":"93826","_id":"34886","publication_identifier":{"issn":["0003-486X"]},"publication_status":"published","intvolume":"       172","page":"2035-2104","citation":{"apa":"Fouvry, É., &#38; Klüners, J. (2010). On the negative Pell equation. <i>Annals of Mathematics</i>, <i>172</i>(3), 2035–2104. <a href=\"https://doi.org/10.4007/annals.2010.172.2035\">https://doi.org/10.4007/annals.2010.172.2035</a>","mla":"Fouvry, Étienne, and Jürgen Klüners. “On the Negative Pell Equation.” <i>Annals of Mathematics</i>, vol. 172, no. 3, Annals of Mathematics, 2010, pp. 2035–104, doi:<a href=\"https://doi.org/10.4007/annals.2010.172.2035\">10.4007/annals.2010.172.2035</a>.","short":"É. Fouvry, J. Klüners, Annals of Mathematics 172 (2010) 2035–2104.","bibtex":"@article{Fouvry_Klüners_2010, title={On the negative Pell equation}, volume={172}, DOI={<a href=\"https://doi.org/10.4007/annals.2010.172.2035\">10.4007/annals.2010.172.2035</a>}, number={3}, journal={Annals of Mathematics}, publisher={Annals of Mathematics}, author={Fouvry, Étienne and Klüners, Jürgen}, year={2010}, pages={2035–2104} }","chicago":"Fouvry, Étienne, and Jürgen Klüners. “On the Negative Pell Equation.” <i>Annals of Mathematics</i> 172, no. 3 (2010): 2035–2104. <a href=\"https://doi.org/10.4007/annals.2010.172.2035\">https://doi.org/10.4007/annals.2010.172.2035</a>.","ieee":"É. Fouvry and J. Klüners, “On the negative Pell equation,” <i>Annals of Mathematics</i>, vol. 172, no. 3, pp. 2035–2104, 2010, doi: <a href=\"https://doi.org/10.4007/annals.2010.172.2035\">10.4007/annals.2010.172.2035</a>.","ama":"Fouvry É, Klüners J. On the negative Pell equation. <i>Annals of Mathematics</i>. 2010;172(3):2035-2104. doi:<a href=\"https://doi.org/10.4007/annals.2010.172.2035\">10.4007/annals.2010.172.2035</a>"},"volume":172,"author":[{"full_name":"Fouvry, Étienne","last_name":"Fouvry","first_name":"Étienne"},{"first_name":"Jürgen","last_name":"Klüners","full_name":"Klüners, Jürgen","id":"21202"}],"date_updated":"2023-03-06T09:50:37Z","doi":"10.4007/annals.2010.172.2035"}]