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Detecting initial guesses for trajectories in the (P)CRTBP. <i>AIAA/AAS Astrodynamics Specialist Conference</i>.","short":"B. Thiere, S. Ober-Blöbaum, P. Pergola, in: AIAA/AAS Astrodynamics Specialist Conference, 2010.","chicago":"Thiere, B., Sina Ober-Blöbaum, and P. Pergola. “Detecting Initial Guesses for Trajectories in the (P)CRTBP.” In <i>AIAA/AAS Astrodynamics Specialist Conference</i>, 2010."},"publication":"AIAA/AAS Astrodynamics Specialist Conference","_id":"29467","language":[{"iso":"eng"}],"user_id":"15694","conference":{"end_date":"2010-08-05","location":"Toronto, Canada, USA","start_date":"2010-08-02"},"author":[{"last_name":"Thiere","first_name":"B.","full_name":"Thiere, B."},{"id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"},{"full_name":"Pergola, P.","first_name":"P.","last_name":"Pergola"}],"year":"2010","title":"Detecting initial guesses for trajectories in the (P)CRTBP","status":"public","date_updated":"2022-01-24T07:22:43Z"},{"citation":{"chicago":"Ober-Blöbaum, Sina, and A. Walther. “Computation of Derivatives for Structure Preserving Optimal Control Using Automatic Differentiation.” In <i>Proceedings of Applied Mathematics and Mechanics</i>, 10(1):585–86, 2010.","short":"S. 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Womersley_2010, title={Numerical integration on the sphere}, booktitle={Handbook of Geomathematics }, publisher={Springer Verlag}, author={Hesse, Kerstin and H. Sloan, Ian and S. Womersley,  Robert }, editor={Freeden, Willi and Nashed , Zuhair  and Sonar, Thomas}, year={2010}, pages={1187-1220.} }","ama":"Hesse K, H. Sloan I, S. Womersley  Robert . Numerical integration on the sphere. In: Freeden W, Nashed  Z, Sonar T, eds. <i>Handbook of Geomathematics </i>. 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Positive convolution structure for a class of Heckman–Opdam hypergeometric functions of type BC. <i>Journal of Functional Analysis</i>. 2010;258(8):2779-2800. doi:<a href=\"https://doi.org/10.1016/j.jfa.2009.12.007\">10.1016/j.jfa.2009.12.007</a>","bibtex":"@article{Rösler_2010, title={Positive convolution structure for a class of Heckman–Opdam hypergeometric functions of type BC}, volume={258}, DOI={<a href=\"https://doi.org/10.1016/j.jfa.2009.12.007\">10.1016/j.jfa.2009.12.007</a>}, number={8}, journal={Journal of Functional Analysis}, publisher={Elsevier BV}, author={Rösler, Margit}, year={2010}, pages={2779–2800} }","apa":"Rösler, M. (2010). Positive convolution structure for a class of Heckman–Opdam hypergeometric functions of type BC. <i>Journal of Functional Analysis</i>, <i>258</i>(8), 2779–2800. <a href=\"https://doi.org/10.1016/j.jfa.2009.12.007\">https://doi.org/10.1016/j.jfa.2009.12.007</a>","ieee":"M. Rösler, “Positive convolution structure for a class of Heckman–Opdam hypergeometric functions of type BC,” <i>Journal of Functional Analysis</i>, vol. 258, no. 8, pp. 2779–2800, 2010, doi: <a href=\"https://doi.org/10.1016/j.jfa.2009.12.007\">10.1016/j.jfa.2009.12.007</a>.","chicago":"Rösler, Margit. “Positive Convolution Structure for a Class of Heckman–Opdam Hypergeometric Functions of Type BC.” <i>Journal of Functional Analysis</i> 258, no. 8 (2010): 2779–2800. <a href=\"https://doi.org/10.1016/j.jfa.2009.12.007\">https://doi.org/10.1016/j.jfa.2009.12.007</a>.","short":"M. Rösler, Journal of Functional Analysis 258 (2010) 2779–2800."},"status":"public","volume":258,"user_id":"93826","_id":"39924","publisher":"Elsevier BV","page":"2779-2800"},{"citation":{"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} }","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>","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.","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>.","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>"},"status":"public","user_id":"93826","volume":172,"page":"2035-2104","_id":"34886","publisher":"Annals of Mathematics","abstract":[{"lang":"eng","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."}],"issue":"3","publication":"Annals of Mathematics","keyword":["Statistics","Probability and Uncertainty","Mathematics (miscellaneous)"],"type":"journal_article","department":[{"_id":"102"}],"date_created":"2022-12-23T09:09:02Z","date_updated":"2023-03-06T09:50:37Z","publication_status":"published","intvolume":"       172","year":"2010","title":"On the negative Pell equation","publication_identifier":{"issn":["0003-486X"]},"author":[{"last_name":"Fouvry","first_name":"Étienne","full_name":"Fouvry, Étienne"},{"last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen","id":"21202"}],"doi":"10.4007/annals.2010.172.2035","language":[{"iso":"eng"}]},{"date_created":"2022-12-23T09:22:49Z","department":[{"_id":"102"}],"keyword":["General Mathematics"],"type":"journal_article","issue":"2","publication":"Proceedings of the London Mathematical Society","related_material":{"link":[{"relation":"confirmation","url":"https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=fc7ab412993fd2bf0069de42fbef1ecc69137755"}]},"abstract":[{"text":"We call a positive square-free integer d special, if d is not divisible by primes congruent to 3 mod 4. We show that the period of the expansion of in continued fractions is asymptotically more often odd than even, when we restrict to special integers. We note that this period is always even for a non-special square-free integer d. It is well known that the above period is odd if and only if the negative Pell equation x²−dy²=−1 is solvable. The latter problem is solvable if and only if the narrow and the ordinary class groups of ℚ(√d) are equal. In a prior work we fully described the asymptotics of the 4-ranks of those class groups. Here we get the first non-trivial results about the asymptotic behavior of the 8-rank of the narrow class group. For example, we show that more than 76% of the quadratic fields ℚ(√d), where d is special, have the property that the 8-rank of the narrow class group is zero.","lang":"eng"}],"language":[{"iso":"eng"}],"doi":"10.1112/plms/pdp057","author":[{"full_name":"Fouvry, Étienne","first_name":"Étienne","last_name":"Fouvry"},{"full_name":"Klüners, Jürgen","last_name":"Klüners","first_name":"Jürgen","id":"21202"}],"publication_identifier":{"issn":["0024-6115"]},"year":"2010","title":"The parity of the period of the continued fraction of d","intvolume":"       101","publication_status":"published","date_updated":"2023-03-06T10:16:54Z","citation":{"short":"É. Fouvry, J. Klüners, Proceedings of the London Mathematical Society 101 (2010) 337–391.","chicago":"Fouvry, Étienne, and Jürgen Klüners. “The Parity of the Period of the Continued Fraction of d.” <i>Proceedings of the London Mathematical Society</i> 101, no. 2 (2010): 337–91. <a href=\"https://doi.org/10.1112/plms/pdp057\">https://doi.org/10.1112/plms/pdp057</a>.","apa":"Fouvry, É., &#38; Klüners, J. (2010). The parity of the period of the continued fraction of d. <i>Proceedings of the London Mathematical Society</i>, <i>101</i>(2), 337–391. <a href=\"https://doi.org/10.1112/plms/pdp057\">https://doi.org/10.1112/plms/pdp057</a>","ieee":"É. Fouvry and J. Klüners, “The parity of the period of the continued fraction of d,” <i>Proceedings of the London Mathematical Society</i>, vol. 101, no. 2, pp. 337–391, 2010, doi: <a href=\"https://doi.org/10.1112/plms/pdp057\">10.1112/plms/pdp057</a>.","ama":"Fouvry É, Klüners J. The parity of the period of the continued fraction of d. <i>Proceedings of the London Mathematical Society</i>. 2010;101(2):337-391. doi:<a href=\"https://doi.org/10.1112/plms/pdp057\">10.1112/plms/pdp057</a>","bibtex":"@article{Fouvry_Klüners_2010, title={The parity of the period of the continued fraction of d}, volume={101}, DOI={<a href=\"https://doi.org/10.1112/plms/pdp057\">10.1112/plms/pdp057</a>}, number={2}, journal={Proceedings of the London Mathematical Society}, publisher={Wiley}, author={Fouvry, Étienne and Klüners, Jürgen}, year={2010}, pages={337–391} }","mla":"Fouvry, Étienne, and Jürgen Klüners. “The Parity of the Period of the Continued Fraction of d.” <i>Proceedings of the London Mathematical Society</i>, vol. 101, no. 2, Wiley, 2010, pp. 337–91, doi:<a href=\"https://doi.org/10.1112/plms/pdp057\">10.1112/plms/pdp057</a>."},"publisher":"Wiley","_id":"34888","page":"337-391","volume":101,"user_id":"93826","status":"public"},{"page":"493-508","publisher":"Mathematical Sciences Publishers","_id":"34887","user_id":"93826","volume":4,"status":"public","citation":{"chicago":"Fouvry, Étienne, and Jürgen Klüners. “On the Spiegelungssatz for the 4-Rank.” <i>Algebra &#38;amp; Number Theory</i> 4, no. 5 (2010): 493–508. <a href=\"https://doi.org/10.2140/ant.2010.4.493\">https://doi.org/10.2140/ant.2010.4.493</a>.","short":"É. Fouvry, J. Klüners, Algebra &#38;amp; Number Theory 4 (2010) 493–508.","ieee":"É. Fouvry and J. Klüners, “On the Spiegelungssatz for the 4-rank,” <i>Algebra &#38;amp; Number Theory</i>, vol. 4, no. 5, pp. 493–508, 2010, doi: <a href=\"https://doi.org/10.2140/ant.2010.4.493\">10.2140/ant.2010.4.493</a>.","apa":"Fouvry, É., &#38; Klüners, J. (2010). On the Spiegelungssatz for the 4-rank. <i>Algebra &#38;amp; Number Theory</i>, <i>4</i>(5), 493–508. <a href=\"https://doi.org/10.2140/ant.2010.4.493\">https://doi.org/10.2140/ant.2010.4.493</a>","bibtex":"@article{Fouvry_Klüners_2010, title={On the Spiegelungssatz for the 4-rank}, volume={4}, DOI={<a href=\"https://doi.org/10.2140/ant.2010.4.493\">10.2140/ant.2010.4.493</a>}, number={5}, journal={Algebra &#38;amp; Number Theory}, publisher={Mathematical Sciences Publishers}, author={Fouvry, Étienne and Klüners, Jürgen}, year={2010}, pages={493–508} }","ama":"Fouvry É, Klüners J. On the Spiegelungssatz for the 4-rank. <i>Algebra &#38;amp; Number Theory</i>. 2010;4(5):493-508. doi:<a href=\"https://doi.org/10.2140/ant.2010.4.493\">10.2140/ant.2010.4.493</a>","mla":"Fouvry, Étienne, and Jürgen Klüners. “On the Spiegelungssatz for the 4-Rank.” <i>Algebra &#38;amp; Number Theory</i>, vol. 4, no. 5, Mathematical Sciences Publishers, 2010, pp. 493–508, doi:<a href=\"https://doi.org/10.2140/ant.2010.4.493\">10.2140/ant.2010.4.493</a>."},"language":[{"iso":"eng"}],"doi":"10.2140/ant.2010.4.493","year":"2010","title":"On the Spiegelungssatz for the 4-rank","author":[{"full_name":"Fouvry, Étienne","last_name":"Fouvry","first_name":"Étienne"},{"id":"21202","first_name":"Jürgen","last_name":"Klüners","full_name":"Klüners, Jürgen"}],"publication_identifier":{"issn":["1937-0652"]},"publication_status":"published","date_updated":"2023-03-06T10:18:14Z","intvolume":"         4","date_created":"2022-12-23T09:10:12Z","keyword":["Algebra and Number Theory"],"type":"journal_article","department":[{"_id":"102"}],"issue":"5","publication":"Algebra &amp; Number Theory","abstract":[{"text":"Let d be a nonsquare positive integer. We give the value of the natural probability that the narrow ideal class groups of the quadratic fields ℚ(√d) and ℚ(√−d) have the same 4-ranks. ","lang":"eng"}]},{"language":[{"iso":"eng"}],"doi":"10.1137/080734467","year":"2010","title":"Algorithmic Enumeration of Ideal Classes for Quaternion Orders","author":[{"first_name":"Markus","last_name":"Kirschmer","full_name":"Kirschmer, Markus","id":"82258"},{"full_name":"Voight, John","first_name":"John","last_name":"Voight"}],"publication_identifier":{"issn":["0097-5397","1095-7111"]},"publication_status":"published","date_updated":"2023-04-04T09:25:08Z","intvolume":"        39","date_created":"2023-03-07T08:49:35Z","keyword":["General Mathematics","General Computer Science"],"type":"journal_article","department":[{"_id":"102"}],"publication":"SIAM Journal on Computing","issue":"5","extern":"1","abstract":[{"text":"We provide algorithms to count and enumerate representatives of the (right) ideal classes of an Eichler order in a quaternion algebra defined over a number field. We analyze the run time of these algorithms and consider several related problems, including the computation of two-sided ideal classes, isomorphism classes of orders, connecting ideals for orders, and ideal principalization. We conclude by giving the complete list of definite Eichler orders with class number at most 2.","lang":"eng"}],"page":"1714-1747","publisher":"Society for Industrial & Applied Mathematics (SIAM)","_id":"42803","user_id":"93826","volume":39,"status":"public","citation":{"chicago":"Kirschmer, Markus, and John Voight. “Algorithmic Enumeration of Ideal Classes for Quaternion Orders.” <i>SIAM Journal on Computing</i> 39, no. 5 (2010): 1714–47. <a href=\"https://doi.org/10.1137/080734467\">https://doi.org/10.1137/080734467</a>.","short":"M. Kirschmer, J. Voight, SIAM Journal on Computing 39 (2010) 1714–1747.","apa":"Kirschmer, M., &#38; Voight, J. (2010). 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Statistik online lernen - Ein Modell für Lehrerkompetenz als Basis einer Online-Lehrerfortbildung für Statistik in der Sekundarstufe I. In: Lindmeier A, Ufer St, eds. <i>Beiträge zum Mathematikunterricht 2010</i>. WTM-Verlag; 2010:915-918.","bibtex":"@inbook{Wassong_Biehler_2010, place={Münster}, title={Statistik online lernen - Ein Modell für Lehrerkompetenz als Basis einer Online-Lehrerfortbildung für Statistik in der Sekundarstufe I}, booktitle={Beiträge zum Mathematikunterricht 2010}, publisher={WTM-Verlag}, author={Wassong, Thomas and Biehler, Rolf}, editor={Lindmeier, A. and Ufer, St.}, year={2010}, pages={915–918} }","mla":"Wassong, Thomas, and Rolf Biehler. “Statistik online lernen - Ein Modell für Lehrerkompetenz als Basis einer Online-Lehrerfortbildung für Statistik in der Sekundarstufe I.” <i>Beiträge zum Mathematikunterricht 2010</i>, edited by A. 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Biehler, “Statistik online lernen - Ein Modell für Lehrerkompetenz als Basis einer Online-Lehrerfortbildung für Statistik in der Sekundarstufe I,” in <i>Beiträge zum Mathematikunterricht 2010</i>, A. Lindmeier and St. Ufer, Eds. Münster: WTM-Verlag, 2010, pp. 915–918."}},{"user_id":"37888","volume":31,"page":"1-3","_id":"56968","publisher":"Springer Science and Business Media LLC","status":"public","citation":{"bibtex":"@article{Biehler_Peter-Koop_Sträßer_Weigand_2010, title={JMD ab 2010 bei Springer}, volume={31}, DOI={<a href=\"https://doi.org/10.1007/s13138-010-0002-2\">10.1007/s13138-010-0002-2</a>}, number={1}, journal={Journal für Mathematik-Didaktik}, publisher={Springer Science and Business Media LLC}, author={Biehler, Rolf and Peter-Koop, Andrea and Sträßer, Rudolf and Weigand, Hans-Georg}, year={2010}, pages={1–3} }","ama":"Biehler R, Peter-Koop A, Sträßer R, Weigand H-G. 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Prömmel, “Developing students’ computer-supported simulation and modelling competencies by means of carefully designed working environments,” in <i>Proceedings of ICoTS 8, Ljubljana, July 2010</i>, C. Reading, Ed. Voorburg, The Netherlands: IASE, 2010.","apa":"Biehler, R., &#38; Prömmel, A. (2010). Developing students’ computer-supported simulation and modelling competencies by means of carefully designed working environments. In C. Reading (Ed.), <i>Proceedings of ICoTS 8, Ljubljana, July 2010</i>. 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