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Poster auf der Fachtagung: BKL Workshop Klinische Linguistik ","citation":{"apa":"Rilling, E., Wilken, R., Wismann, K., Glandorf, B., Hoffmann, H., Hinnenkamp, C., Rohlmann, I., Ludewigt, J., Bittner, C., Orlov, T., Claus, K., Grosser, C., &#38; Winnecken, A. (2010). <i>Alltagsorientierte Therapie: Ein interdisziplinäres, gruppentherapeutisches Angebot von Sprach- und Ergotherapie im Aphasie-Zentrum, Vechta-Langförden. Poster auf der Fachtagung: BKL Workshop Klinische Linguistik </i>.","mla":"Rilling, Eva, et al. <i>Alltagsorientierte Therapie: Ein Interdisziplinäres, Gruppentherapeutisches Angebot von Sprach- Und Ergotherapie Im Aphasie-Zentrum, Vechta-Langförden. Poster Auf Der Fachtagung: BKL Workshop Klinische Linguistik </i>. 2010.","bibtex":"@book{Rilling_Wilken_Wismann_Glandorf_Hoffmann_Hinnenkamp_Rohlmann_Ludewigt_Bittner_Orlov_et al._2010, place={Freiburg im Breisgau}, title={Alltagsorientierte Therapie: Ein interdisziplinäres, gruppentherapeutisches Angebot von Sprach- und Ergotherapie im Aphasie-Zentrum, Vechta-Langförden. Poster auf der Fachtagung: BKL Workshop Klinische Linguistik }, author={Rilling, Eva and Wilken, Rainer and Wismann, Kathrin and Glandorf, Birte and Hoffmann, Hannah and Hinnenkamp, Christiane and Rohlmann, Ines and Ludewigt, Jacqueline and Bittner, Christian and Orlov, Tatjana and et al.}, year={2010} }","short":"E. Rilling, R. Wilken, K. Wismann, B. Glandorf, H. Hoffmann, C. Hinnenkamp, I. Rohlmann, J. Ludewigt, C. Bittner, T. Orlov, K. Claus, C. Grosser, A. Winnecken, Alltagsorientierte Therapie: Ein Interdisziplinäres, Gruppentherapeutisches Angebot von Sprach- Und Ergotherapie Im Aphasie-Zentrum, Vechta-Langförden. Poster Auf Der Fachtagung: BKL Workshop Klinische Linguistik , Freiburg im Breisgau, 2010.","chicago":"Rilling, Eva, Rainer Wilken, Kathrin Wismann, Birte Glandorf, Hannah Hoffmann, Christiane Hinnenkamp, Ines Rohlmann, et al. <i>Alltagsorientierte Therapie: Ein Interdisziplinäres, Gruppentherapeutisches Angebot von Sprach- Und Ergotherapie Im Aphasie-Zentrum, Vechta-Langförden. Poster Auf Der Fachtagung: BKL Workshop Klinische Linguistik </i>. Freiburg im Breisgau, 2010.","ieee":"E. Rilling <i>et al.</i>, <i>Alltagsorientierte Therapie: Ein interdisziplinäres, gruppentherapeutisches Angebot von Sprach- und Ergotherapie im Aphasie-Zentrum, Vechta-Langförden. Poster auf der Fachtagung: BKL Workshop Klinische Linguistik </i>. Freiburg im Breisgau, 2010.","ama":"Rilling E, Wilken R, Wismann K, et al. <i>Alltagsorientierte Therapie: Ein Interdisziplinäres, Gruppentherapeutisches Angebot von Sprach- Und Ergotherapie Im Aphasie-Zentrum, Vechta-Langförden. Poster Auf Der Fachtagung: BKL Workshop Klinische Linguistik </i>.; 2010."},"place":"Freiburg im Breisgau","year":"2010"},{"publisher":"American Chemical Society (ACS)","date_updated":"2023-02-10T14:38:19Z","author":[{"first_name":"J.","last_name":"Liu","full_name":"Liu, J."},{"first_name":"S.","full_name":"Pancera, S.","last_name":"Pancera"},{"last_name":"Boyko","full_name":"Boyko, V.","first_name":"V."},{"first_name":"A.","full_name":"Shukla, A.","last_name":"Shukla"},{"first_name":"T.","full_name":"Narayanan, T.","last_name":"Narayanan"},{"last_name":"Huber","full_name":"Huber, Klaus","id":"237","first_name":"Klaus"}],"date_created":"2023-02-10T14:36:16Z","volume":26,"title":"Evaluation of the Particle Growth of Amorphous Calcium Carbonate in Water by Means of the Porod Invariant from SAXS","doi":"10.1021/la101888c","publication_status":"published","publication_identifier":{"issn":["0743-7463","1520-5827"]},"issue":"22","year":"2010","citation":{"bibtex":"@article{Liu_Pancera_Boyko_Shukla_Narayanan_Huber_2010, title={Evaluation of the Particle Growth of Amorphous Calcium Carbonate in Water by Means of the Porod Invariant from SAXS}, volume={26}, DOI={<a href=\"https://doi.org/10.1021/la101888c\">10.1021/la101888c</a>}, number={22}, journal={Langmuir}, publisher={American Chemical Society (ACS)}, author={Liu, J. and Pancera, S. and Boyko, V. and Shukla, A. and Narayanan, T. and Huber, Klaus}, year={2010}, pages={17405–17412} }","mla":"Liu, J., et al. “Evaluation of the Particle Growth of Amorphous Calcium Carbonate in Water by Means of the Porod Invariant from SAXS.” <i>Langmuir</i>, vol. 26, no. 22, American Chemical Society (ACS), 2010, pp. 17405–12, doi:<a href=\"https://doi.org/10.1021/la101888c\">10.1021/la101888c</a>.","short":"J. Liu, S. Pancera, V. Boyko, A. Shukla, T. Narayanan, K. Huber, Langmuir 26 (2010) 17405–17412.","apa":"Liu, J., Pancera, S., Boyko, V., Shukla, A., Narayanan, T., &#38; Huber, K. (2010). Evaluation of the Particle Growth of Amorphous Calcium Carbonate in Water by Means of the Porod Invariant from SAXS. <i>Langmuir</i>, <i>26</i>(22), 17405–17412. <a href=\"https://doi.org/10.1021/la101888c\">https://doi.org/10.1021/la101888c</a>","ieee":"J. Liu, S. Pancera, V. Boyko, A. Shukla, T. Narayanan, and K. Huber, “Evaluation of the Particle Growth of Amorphous Calcium Carbonate in Water by Means of the Porod Invariant from SAXS,” <i>Langmuir</i>, vol. 26, no. 22, pp. 17405–17412, 2010, doi: <a href=\"https://doi.org/10.1021/la101888c\">10.1021/la101888c</a>.","chicago":"Liu, J., S. Pancera, V. Boyko, A. Shukla, T. Narayanan, and Klaus Huber. “Evaluation of the Particle Growth of Amorphous Calcium Carbonate in Water by Means of the Porod Invariant from SAXS.” <i>Langmuir</i> 26, no. 22 (2010): 17405–12. <a href=\"https://doi.org/10.1021/la101888c\">https://doi.org/10.1021/la101888c</a>.","ama":"Liu J, Pancera S, Boyko V, Shukla A, Narayanan T, Huber K. Evaluation of the Particle Growth of Amorphous Calcium Carbonate in Water by Means of the Porod Invariant from SAXS. <i>Langmuir</i>. 2010;26(22):17405-17412. doi:<a href=\"https://doi.org/10.1021/la101888c\">10.1021/la101888c</a>"},"intvolume":"        26","page":"17405-17412","_id":"41992","user_id":"237","department":[{"_id":"314"}],"keyword":["Electrochemistry","Spectroscopy","Surfaces and Interfaces","Condensed Matter Physics","General Materials Science"],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Langmuir","status":"public"},{"status":"public","type":"journal_article","publication":"Langmuir","language":[{"iso":"eng"}],"keyword":["Electrochemistry","Spectroscopy","Surfaces and Interfaces","Condensed Matter Physics","General Materials Science"],"user_id":"237","department":[{"_id":"314"}],"_id":"41993","citation":{"ama":"Bayer FM, Hiltrop K, Huber K. 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Hydrogen-Bond-Induced Heteroassembly in Binary Colloidal Systems. <i>Langmuir</i>, <i>26</i>(17), 13815–13822. <a href=\"https://doi.org/10.1021/la101831x\">https://doi.org/10.1021/la101831x</a>","bibtex":"@article{Bayer_Hiltrop_Huber_2010, title={Hydrogen-Bond-Induced Heteroassembly in Binary Colloidal Systems}, volume={26}, DOI={<a href=\"https://doi.org/10.1021/la101831x\">10.1021/la101831x</a>}, number={17}, journal={Langmuir}, publisher={American Chemical Society (ACS)}, author={Bayer, Frank M. and Hiltrop, Karl and Huber, Klaus}, year={2010}, pages={13815–13822} }","mla":"Bayer, Frank M., et al. “Hydrogen-Bond-Induced Heteroassembly in Binary Colloidal Systems.” <i>Langmuir</i>, vol. 26, no. 17, American Chemical Society (ACS), 2010, pp. 13815–22, doi:<a href=\"https://doi.org/10.1021/la101831x\">10.1021/la101831x</a>.","short":"F.M. Bayer, K. Hiltrop, K. Huber, Langmuir 26 (2010) 13815–13822."},"intvolume":"        26","page":"13815-13822","year":"2010","issue":"17","publication_status":"published","publication_identifier":{"issn":["0743-7463","1520-5827"]},"doi":"10.1021/la101831x","title":"Hydrogen-Bond-Induced Heteroassembly in Binary Colloidal Systems","author":[{"first_name":"Frank M.","last_name":"Bayer","full_name":"Bayer, Frank M."},{"last_name":"Hiltrop","full_name":"Hiltrop, Karl","first_name":"Karl"},{"first_name":"Klaus","full_name":"Huber, Klaus","id":"237","last_name":"Huber"}],"date_created":"2023-02-10T14:37:27Z","volume":26,"date_updated":"2023-02-10T14:38:57Z","publisher":"American Chemical Society (ACS)"},{"volume":43,"author":[{"first_name":"S.","last_name":"Lages","full_name":"Lages, S."},{"first_name":"R.","last_name":"Michels","full_name":"Michels, R."},{"last_name":"Huber","full_name":"Huber, Klaus","id":"237","first_name":"Klaus"}],"date_created":"2023-02-10T14:39:34Z","publisher":"American Chemical Society (ACS)","date_updated":"2023-02-10T14:39:59Z","doi":"10.1021/ma9027239","title":"Coil-Collapse and Coil-Aggregation due to the Interaction of Cu<sup>2+</sup> and Ca<sup>2+</sup> Ions with Anionic Polyacylate Chains in Dilute Solution","issue":"6","publication_identifier":{"issn":["0024-9297","1520-5835"]},"publication_status":"published","intvolume":"        43","page":"3027-3035","citation":{"ama":"Lages S, Michels R, Huber K. Coil-Collapse and Coil-Aggregation due to the Interaction of Cu<sup>2+</sup> and Ca<sup>2+</sup> Ions with Anionic Polyacylate Chains in Dilute Solution. <i>Macromolecules</i>. 2010;43(6):3027-3035. doi:<a href=\"https://doi.org/10.1021/ma9027239\">10.1021/ma9027239</a>","ieee":"S. Lages, R. Michels, and K. Huber, “Coil-Collapse and Coil-Aggregation due to the Interaction of Cu<sup>2+</sup> and Ca<sup>2+</sup> Ions with Anionic Polyacylate Chains in Dilute Solution,” <i>Macromolecules</i>, vol. 43, no. 6, pp. 3027–3035, 2010, doi: <a href=\"https://doi.org/10.1021/ma9027239\">10.1021/ma9027239</a>.","chicago":"Lages, S., R. Michels, and Klaus Huber. “Coil-Collapse and Coil-Aggregation Due to the Interaction of Cu<sup>2+</sup> and Ca<sup>2+</sup> Ions with Anionic Polyacylate Chains in Dilute Solution.” <i>Macromolecules</i> 43, no. 6 (2010): 3027–35. <a href=\"https://doi.org/10.1021/ma9027239\">https://doi.org/10.1021/ma9027239</a>.","short":"S. Lages, R. Michels, K. Huber, Macromolecules 43 (2010) 3027–3035.","bibtex":"@article{Lages_Michels_Huber_2010, title={Coil-Collapse and Coil-Aggregation due to the Interaction of Cu<sup>2+</sup> and Ca<sup>2+</sup> Ions with Anionic Polyacylate Chains in Dilute Solution}, volume={43}, DOI={<a href=\"https://doi.org/10.1021/ma9027239\">10.1021/ma9027239</a>}, number={6}, journal={Macromolecules}, publisher={American Chemical Society (ACS)}, author={Lages, S. and Michels, R. and Huber, Klaus}, year={2010}, pages={3027–3035} }","mla":"Lages, S., et al. “Coil-Collapse and Coil-Aggregation Due to the Interaction of Cu<sup>2+</sup> and Ca<sup>2+</sup> Ions with Anionic Polyacylate Chains in Dilute Solution.” <i>Macromolecules</i>, vol. 43, no. 6, American Chemical Society (ACS), 2010, pp. 3027–35, doi:<a href=\"https://doi.org/10.1021/ma9027239\">10.1021/ma9027239</a>.","apa":"Lages, S., Michels, R., &#38; Huber, K. (2010). Coil-Collapse and Coil-Aggregation due to the Interaction of Cu<sup>2+</sup> and Ca<sup>2+</sup> Ions with Anionic Polyacylate Chains in Dilute Solution. <i>Macromolecules</i>, <i>43</i>(6), 3027–3035. <a href=\"https://doi.org/10.1021/ma9027239\">https://doi.org/10.1021/ma9027239</a>"},"year":"2010","department":[{"_id":"314"}],"user_id":"237","_id":"41995","language":[{"iso":"eng"}],"keyword":["Materials Chemistry","Inorganic Chemistry","Polymers and Plastics","Organic Chemistry"],"publication":"Macromolecules","type":"journal_article","status":"public"},{"language":[{"iso":"eng"}],"article_number":"125606 ","user_id":"71124","series_title":"Nanotechnology ","department":[{"_id":"623"}],"_id":"42030","status":"public","type":"conference","title":"Low-density MOVPE grown InGaAs QDs exhibiting ultra-narrow single exciton linewidths","author":[{"last_name":" Richter","full_name":" Richter, D","first_name":"D"},{"first_name":"R","full_name":"Hafenbrak, R","last_name":"Hafenbrak"},{"first_name":"Klaus D.","last_name":"Jöns","full_name":"Jöns, Klaus D.","id":"85353"},{"first_name":"W-M","full_name":"Schulz, W-M","last_name":"Schulz"},{"first_name":"M","full_name":"Eichfelder, M","last_name":"Eichfelder"},{"first_name":"M","full_name":"Heldmaier, M","last_name":"Heldmaier"},{"full_name":"Roßbach, R","last_name":"Roßbach","first_name":"R"},{"last_name":"Jetter","full_name":"Jetter, M","first_name":"M"},{"full_name":"Michler, P","last_name":"Michler","first_name":"P"}],"date_created":"2023-02-13T08:19:11Z","volume":21,"date_updated":"2023-02-13T08:44:48Z","citation":{"ieee":"D.  Richter <i>et al.</i>, “Low-density MOVPE grown InGaAs QDs exhibiting ultra-narrow single exciton linewidths,” vol. 21. 2010.","chicago":"Richter, D, R Hafenbrak, Klaus D. Jöns, W-M Schulz, M Eichfelder, M Heldmaier, R Roßbach, M Jetter, and P Michler. “Low-Density MOVPE Grown InGaAs QDs Exhibiting Ultra-Narrow Single Exciton Linewidths.” Nanotechnology , 2010.","ama":"Richter D, Hafenbrak R, Jöns KD, et al. Low-density MOVPE grown InGaAs QDs exhibiting ultra-narrow single exciton linewidths. 2010;21.","apa":"Richter, D., Hafenbrak, R., Jöns, K. D., Schulz, W.-M., Eichfelder, M., Heldmaier, M., Roßbach, R., Jetter, M., &#38; Michler, P. (2010). <i>Low-density MOVPE grown InGaAs QDs exhibiting ultra-narrow single exciton linewidths</i> (No. 125606; Vol. 21).","short":"D.  Richter, R. Hafenbrak, K.D. Jöns, W.-M. Schulz, M. Eichfelder, M. Heldmaier, R. Roßbach, M. Jetter, P. Michler, 21 (2010).","mla":"Richter, D., et al. <i>Low-Density MOVPE Grown InGaAs QDs Exhibiting Ultra-Narrow Single Exciton Linewidths</i>. 125606, 2010.","bibtex":"@article{ Richter_Hafenbrak_Jöns_Schulz_Eichfelder_Heldmaier_Roßbach_Jetter_Michler_2010, series={Nanotechnology }, title={Low-density MOVPE grown InGaAs QDs exhibiting ultra-narrow single exciton linewidths}, volume={21}, number={125606}, author={ Richter, D and Hafenbrak, R and Jöns, Klaus D. and Schulz, W-M and Eichfelder, M and Heldmaier, M and Roßbach, R and Jetter, M and Michler, P}, year={2010}, collection={Nanotechnology } }"},"intvolume":"        21","year":"2010"},{"type":"newspaper_article","publication":"Counterfire","status":"public","publication_date":"2010-04-24","_id":"42613","user_id":"49063","department":[{"_id":"136"}],"language":[{"iso":"eng"}],"extern":"1","year":"2010","citation":{"ama":"Fuchs C. The Internet – serving the revolution? <i>Counterfire</i>. 2010.","chicago":"Fuchs, Christian. “The Internet – Serving the Revolution?” <i>Counterfire</i>, 2010.","ieee":"C. Fuchs, “The Internet – serving the revolution?,” <i>Counterfire</i>, 2010.","bibtex":"@article{Fuchs_2010, title={The Internet – serving the revolution?}, journal={Counterfire}, author={Fuchs, Christian}, year={2010} }","short":"C. Fuchs, Counterfire (2010).","mla":"Fuchs, Christian. “The Internet – Serving the Revolution?” <i>Counterfire</i>, 2010.","apa":"Fuchs, C. (2010). The Internet – serving the revolution? <i>Counterfire</i>."},"date_updated":"2023-02-28T01:42:03Z","date_created":"2023-02-28T01:40:52Z","author":[{"first_name":"Christian","full_name":"Fuchs, Christian","id":"21863","last_name":"Fuchs","orcid":"0000-0003-0589-4579"}],"title":"The Internet – serving the revolution?"},{"status":"public","type":"journal_article","article_type":"original","extern":"1","_id":"8179","department":[{"_id":"623"},{"_id":"7"}],"user_id":"71541","intvolume":"        10","page":"343-360","citation":{"ieee":"S. Gharibian, “Strong NP-hardness of the quantum separability problem,” <i>Quantum Information &#38; Computation</i>, vol. 10, no. 3{\\ &#38; }4, pp. 343–360, 2010.","chicago":"Gharibian, Sevag. “Strong NP-Hardness of the Quantum Separability Problem.” <i>Quantum Information &#38; Computation</i> 10, no. 3{\\ &#38; }4 (2010): 343–60.","ama":"Gharibian S. Strong NP-hardness of the quantum separability problem. <i>Quantum Information &#38; Computation</i>. 2010;10(3{\\ &#38; }4):343-360.","mla":"Gharibian, Sevag. “Strong NP-Hardness of the Quantum Separability Problem.” <i>Quantum Information &#38; Computation</i>, vol. 10, no. 3{\\ &#38; }4, 2010, pp. 343–60.","bibtex":"@article{Gharibian_2010, title={Strong NP-hardness of the quantum separability problem}, volume={10}, number={3{\\ &#38; }4}, journal={Quantum Information &#38; Computation}, author={Gharibian, Sevag}, year={2010}, pages={343–360} }","short":"S. Gharibian, Quantum Information &#38; Computation 10 (2010) 343–360.","apa":"Gharibian, S. (2010). Strong NP-hardness of the quantum separability problem. <i>Quantum Information &#38; Computation</i>, <i>10</i>(3{\\ &#38; }4), 343–360."},"publication_status":"published","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/0810.4507"}],"oa":"1","date_updated":"2023-02-28T11:04:38Z","volume":10,"author":[{"first_name":"Sevag","last_name":"Gharibian","orcid":"0000-0002-9992-3379","id":"71541","full_name":"Gharibian, Sevag"}],"abstract":[{"lang":"eng","text":"Given the density matrix rho of a bipartite quantum state, the quantum separability problem asks whether rho is entangled or separable. In 2003, Gurvits showed that this problem is NP-hard if rho is located within an inverse exponential (with respect to dimension) distance from the border of the set of separable quantum states. In this paper, we extend this NP-hardness to an inverse polynomial distance from the separable set. The result follows from a simple combination of works by Gurvits, Ioannou, and Liu. We apply our result to show (1) an immediate lower bound on the maximum distance between a bound entangled state and the separable set (assuming P != NP), and (2) NP-hardness for the problem of determining whether a completely positive trace-preserving linear map is entanglement-breaking."}],"publication":"Quantum Information & Computation","language":[{"iso":"eng"}],"external_id":{"arxiv":["0810.4507"]},"year":"2010","issue":"3{\\&}4","title":"Strong NP-hardness of the quantum separability problem","date_created":"2019-03-01T12:09:59Z"},{"_id":"34886","user_id":"93826","department":[{"_id":"102"}],"status":"public","type":"journal_article","doi":"10.4007/annals.2010.172.2035","date_updated":"2023-03-06T09:50:37Z","author":[{"last_name":"Fouvry","full_name":"Fouvry, Étienne","first_name":"Étienne"},{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"}],"volume":172,"citation":{"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>.","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>.","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>","short":"É. Fouvry, J. Klüners, Annals of Mathematics 172 (2010) 2035–2104.","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>.","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} }","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>"},"page":"2035-2104","intvolume":"       172","publication_status":"published","publication_identifier":{"issn":["0003-486X"]},"keyword":["Statistics","Probability and Uncertainty","Mathematics (miscellaneous)"],"language":[{"iso":"eng"}],"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."}],"publication":"Annals of Mathematics","title":"On the negative Pell equation","publisher":"Annals of Mathematics","date_created":"2022-12-23T09:09:02Z","year":"2010","issue":"3"},{"abstract":[{"lang":"eng","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."}],"publication":"Proceedings of the London Mathematical Society","language":[{"iso":"eng"}],"keyword":["General Mathematics"],"year":"2010","issue":"2","title":"The parity of the period of the continued fraction of d","date_created":"2022-12-23T09:22:49Z","publisher":"Wiley","status":"public","type":"journal_article","department":[{"_id":"102"}],"user_id":"93826","_id":"34888","page":"337-391","intvolume":"       101","citation":{"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>.","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>.","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>","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>","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} }","short":"É. Fouvry, J. Klüners, Proceedings of the London Mathematical Society 101 (2010) 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>."},"related_material":{"link":[{"relation":"confirmation","url":"https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=fc7ab412993fd2bf0069de42fbef1ecc69137755"}]},"publication_identifier":{"issn":["0024-6115"]},"publication_status":"published","doi":"10.1112/plms/pdp057","volume":101,"author":[{"first_name":"Étienne","full_name":"Fouvry, Étienne","last_name":"Fouvry"},{"full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners","first_name":"Jürgen"}],"date_updated":"2023-03-06T10:16:54Z"},{"publication_status":"published","publication_identifier":{"issn":["1937-0652"]},"issue":"5","year":"2010","citation":{"short":"É. Fouvry, J. Klüners, Algebra &#38;amp; Number Theory 4 (2010) 493–508.","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>.","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} }","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>","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>.","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>.","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>"},"page":"493-508","intvolume":"         4","date_updated":"2023-03-06T10:18:14Z","publisher":"Mathematical Sciences Publishers","author":[{"full_name":"Fouvry, Étienne","last_name":"Fouvry","first_name":"Étienne"},{"first_name":"Jürgen","last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen"}],"date_created":"2022-12-23T09:10:12Z","volume":4,"title":"On the Spiegelungssatz for the 4-rank","doi":"10.2140/ant.2010.4.493","type":"journal_article","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"}],"status":"public","_id":"34887","user_id":"93826","department":[{"_id":"102"}],"keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}]},{"type":"book","status":"public","_id":"40145","user_id":"49063","department":[{"_id":"136"}],"extern":"1","language":[{"iso":"eng"}],"year":"2010","place":"New York","citation":{"short":"C. Fuchs, Internet and Society: Social Theory in the Information Age. Paperback, Routledge, New York, 2010.","bibtex":"@book{Fuchs_2010, place={New York}, title={Internet and Society: Social Theory in the Information Age. Paperback}, publisher={Routledge}, author={Fuchs, Christian}, year={2010} }","mla":"Fuchs, Christian. <i>Internet and Society: Social Theory in the Information Age. Paperback</i>. Routledge, 2010.","apa":"Fuchs, C. (2010). <i>Internet and Society: Social Theory in the Information Age. Paperback</i>. Routledge.","ama":"Fuchs C. <i>Internet and Society: Social Theory in the Information Age. Paperback</i>. Routledge; 2010.","chicago":"Fuchs, Christian. <i>Internet and Society: Social Theory in the Information Age. Paperback</i>. New York: Routledge, 2010.","ieee":"C. Fuchs, <i>Internet and Society: Social Theory in the Information Age. Paperback</i>. New York: Routledge, 2010."},"date_updated":"2023-03-08T02:13:26Z","publisher":"Routledge","date_created":"2023-01-26T02:20:21Z","author":[{"first_name":"Christian","full_name":"Fuchs, Christian","id":"21863","orcid":"0000-0003-0589-4579","last_name":"Fuchs"}],"title":"Internet and Society: Social Theory in the Information Age. Paperback"},{"extern":"1","language":[{"iso":"eng"}],"_id":"41660","user_id":"49063","department":[{"_id":"136"}],"status":"public","type":"journal_article","publication":"tripleC (cognition, communication, co-operation)","title":"Co-editor of the special issue “Capitalist crisis, communication & culture“","main_file_link":[{"url":"https://www.triple-c.at/index.php/tripleC/issue/view/20","open_access":"1"}],"oa":"1","date_updated":"2023-03-08T03:18:05Z","author":[{"orcid":"0000-0003-0589-4579","last_name":"Fuchs","full_name":"Fuchs, Christian","id":"21863","first_name":"Christian"},{"first_name":"Matthias","last_name":"Schafranek","full_name":"Schafranek, Matthias"},{"full_name":"Hakken, David","last_name":"Hakken","first_name":"David"},{"first_name":"Marcus","full_name":"Breen, Marcus","last_name":"Breen"}],"date_created":"2023-02-03T23:50:47Z","volume":8,"year":"2010","citation":{"chicago":"Fuchs, Christian, Matthias Schafranek, David Hakken, and Marcus Breen. “Co-Editor of the Special Issue “Capitalist Crisis, Communication &#38; Culture“.” <i>TripleC (Cognition, Communication, Co-Operation)</i> 8, no. 2 (2010): 193–309.","ieee":"C. Fuchs, M. Schafranek, D. Hakken, and M. Breen, “Co-editor of the special issue “Capitalist crisis, communication &#38; culture“,” <i>tripleC (cognition, communication, co-operation)</i>, vol. 8, no. 2, pp. 193–309, 2010.","ama":"Fuchs C, Schafranek M, Hakken D, Breen M. Co-editor of the special issue “Capitalist crisis, communication &#38; culture“. <i>tripleC (cognition, communication, co-operation)</i>. 2010;8(2):193-309.","apa":"Fuchs, C., Schafranek, M., Hakken, D., &#38; Breen, M. (2010). Co-editor of the special issue “Capitalist crisis, communication &#38; culture“. <i>TripleC (Cognition, Communication, Co-Operation)</i>, <i>8</i>(2), 193–309.","mla":"Fuchs, Christian, et al. “Co-Editor of the Special Issue “Capitalist Crisis, Communication &#38; Culture“.” <i>TripleC (Cognition, Communication, Co-Operation)</i>, vol. 8, no. 2, 2010, pp. 193–309.","short":"C. Fuchs, M. Schafranek, D. Hakken, M. Breen, TripleC (Cognition, Communication, Co-Operation) 8 (2010) 193–309.","bibtex":"@article{Fuchs_Schafranek_Hakken_Breen_2010, title={Co-editor of the special issue “Capitalist crisis, communication &#38; culture“}, volume={8}, number={2}, journal={tripleC (cognition, communication, co-operation)}, author={Fuchs, Christian and Schafranek, Matthias and Hakken, David and Breen, Marcus}, year={2010}, pages={193–309} }"},"page":"193-309","intvolume":"         8","issue":"2"}]