[{"doi":"10.1137/030600210","title":"A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems","author":[{"full_name":"Day, S.","last_name":"Day","first_name":"S."},{"first_name":"O.","last_name":"Junge","full_name":"Junge, O."},{"first_name":"K.","last_name":"Mischaikow","full_name":"Mischaikow, K."}],"date_created":"2020-04-15T08:17:18Z","date_updated":"2022-01-06T06:52:52Z","page":"117-160","citation":{"bibtex":"@article{Day_Junge_Mischaikow_2004, title={A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems}, DOI={<a href=\"https://doi.org/10.1137/030600210\">10.1137/030600210</a>}, journal={SIAM Journal on Applied Dynamical Systems}, author={Day, S. and Junge, O. and Mischaikow, K.}, year={2004}, pages={117–160} }","mla":"Day, S., et al. “A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems.” <i>SIAM Journal on Applied Dynamical Systems</i>, 2004, pp. 117–60, doi:<a href=\"https://doi.org/10.1137/030600210\">10.1137/030600210</a>.","short":"S. Day, O. Junge, K. Mischaikow, SIAM Journal on Applied Dynamical Systems (2004) 117–160.","apa":"Day, S., Junge, O., &#38; Mischaikow, K. (2004). A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems. <i>SIAM Journal on Applied Dynamical Systems</i>, 117–160. <a href=\"https://doi.org/10.1137/030600210\">https://doi.org/10.1137/030600210</a>","ama":"Day S, Junge O, Mischaikow K. A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems. <i>SIAM Journal on Applied Dynamical Systems</i>. 2004:117-160. doi:<a href=\"https://doi.org/10.1137/030600210\">10.1137/030600210</a>","ieee":"S. Day, O. Junge, and K. Mischaikow, “A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems,” <i>SIAM Journal on Applied Dynamical Systems</i>, pp. 117–160, 2004.","chicago":"Day, S., O. Junge, and K. Mischaikow. “A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems.” <i>SIAM Journal on Applied Dynamical Systems</i>, 2004, 117–60. <a href=\"https://doi.org/10.1137/030600210\">https://doi.org/10.1137/030600210</a>."},"year":"2004","publication_identifier":{"issn":["1536-0040"]},"publication_status":"published","language":[{"iso":"eng"}],"department":[{"_id":"101"}],"user_id":"15701","_id":"16527","status":"public","publication":"SIAM Journal on Applied Dynamical Systems","type":"journal_article"},{"type":"journal_article","publication":"Parallel Processing Letters","abstract":[{"text":"<jats:p> We discuss nearest neighbor load balancing schemes on processor networks which are represented by a cartesian product of graphs and present a new optimal diffusion scheme for general graphs. In the first part of the paper, we introduce the Alternating-Direction load balancing scheme, which reduces the number of load balance iterations by a factor of 2 for cartesian products of graphs. The resulting flow is theoretically analyzed and can be very high for certain cases. Therefore, we further present the Mixed-Direction scheme which needs the same number of iterations but computes in most cases a much smaller flow. In the second part of the paper, we present a simple optimal diffusion scheme for general graphs, calculating a balancing flow which is minimal in the l<jats:sub>2</jats:sub> norm. It is based on the spectra of the graph representing the network and needs only m-1 iterations to balance the load with m being the number of distinct eigenvalues. Known optimal diffusion schemes have the same performance, however the optimal scheme presented in this paper can be implemented in a very simple manner. The number of iterations of optimal diffusion schemes is independent of the load scenario and, thus, they are practical for networks which represent graphs with known spectra. Finally, our experiments exhibit that the new optimal scheme can successfully be combined with the Alternating-Direction and Mixed-Direction schemes for efficient load balancing on product graphs. </jats:p>","lang":"eng"}],"status":"public","_id":"16587","user_id":"15701","department":[{"_id":"101"}],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0129-6264","1793-642X"]},"year":"2004","citation":{"ama":"Elsässer R, Monien B, Preis R, Frommer A. Optimal Diffusion Schemes and Load Balancing on Product Graphs. <i>Parallel Processing Letters</i>. 2004:61-73. doi:<a href=\"https://doi.org/10.1142/s0129626404001714\">10.1142/s0129626404001714</a>","ieee":"R. Elsässer, B. Monien, R. Preis, and A. Frommer, “Optimal Diffusion Schemes and Load Balancing on Product Graphs,” <i>Parallel Processing Letters</i>, pp. 61–73, 2004.","chicago":"Elsässer, Robert, Burkhard Monien, Robert Preis, and Andreas Frommer. “Optimal Diffusion Schemes and Load Balancing on Product Graphs.” <i>Parallel Processing Letters</i>, 2004, 61–73. <a href=\"https://doi.org/10.1142/s0129626404001714\">https://doi.org/10.1142/s0129626404001714</a>.","mla":"Elsässer, Robert, et al. “Optimal Diffusion Schemes and Load Balancing on Product Graphs.” <i>Parallel Processing Letters</i>, 2004, pp. 61–73, doi:<a href=\"https://doi.org/10.1142/s0129626404001714\">10.1142/s0129626404001714</a>.","bibtex":"@article{Elsässer_Monien_Preis_Frommer_2004, title={Optimal Diffusion Schemes and Load Balancing on Product Graphs}, DOI={<a href=\"https://doi.org/10.1142/s0129626404001714\">10.1142/s0129626404001714</a>}, journal={Parallel Processing Letters}, author={Elsässer, Robert and Monien, Burkhard and Preis, Robert and Frommer, Andreas}, year={2004}, pages={61–73} }","short":"R. Elsässer, B. Monien, R. Preis, A. Frommer, Parallel Processing Letters (2004) 61–73.","apa":"Elsässer, R., Monien, B., Preis, R., &#38; Frommer, A. (2004). Optimal Diffusion Schemes and Load Balancing on Product Graphs. <i>Parallel Processing Letters</i>, 61–73. <a href=\"https://doi.org/10.1142/s0129626404001714\">https://doi.org/10.1142/s0129626404001714</a>"},"page":"61-73","date_updated":"2022-01-06T06:52:52Z","date_created":"2020-04-16T05:46:56Z","author":[{"first_name":"Robert","last_name":"Elsässer","full_name":"Elsässer, Robert"},{"full_name":"Monien, Burkhard","last_name":"Monien","first_name":"Burkhard"},{"full_name":"Preis, Robert","last_name":"Preis","first_name":"Robert"},{"full_name":"Frommer, Andreas","last_name":"Frommer","first_name":"Andreas"}],"title":"Optimal Diffusion Schemes and Load Balancing on Product Graphs","doi":"10.1142/s0129626404001714"},{"date_created":"2020-04-16T08:11:16Z","author":[{"first_name":"Oliver","full_name":"Junge, Oliver","last_name":"Junge"},{"first_name":"Hinke M.","last_name":"Osinga","full_name":"Osinga, Hinke M."}],"date_updated":"2022-01-06T06:52:53Z","doi":"10.1051/cocv:2004006","title":"A set oriented approach to global optimal control","publication_status":"published","publication_identifier":{"issn":["1292-8119","1262-3377"]},"citation":{"ama":"Junge O, Osinga HM. A set oriented approach to global optimal control. <i>ESAIM: Control, Optimisation and Calculus of Variations</i>. 2004:259-270. doi:<a href=\"https://doi.org/10.1051/cocv:2004006\">10.1051/cocv:2004006</a>","chicago":"Junge, Oliver, and Hinke M. Osinga. “A Set Oriented Approach to Global Optimal Control.” <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, 2004, 259–70. <a href=\"https://doi.org/10.1051/cocv:2004006\">https://doi.org/10.1051/cocv:2004006</a>.","ieee":"O. Junge and H. M. Osinga, “A set oriented approach to global optimal control,” <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, pp. 259–270, 2004.","short":"O. Junge, H.M. Osinga, ESAIM: Control, Optimisation and Calculus of Variations (2004) 259–270.","mla":"Junge, Oliver, and Hinke M. Osinga. “A Set Oriented Approach to Global Optimal Control.” <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, 2004, pp. 259–70, doi:<a href=\"https://doi.org/10.1051/cocv:2004006\">10.1051/cocv:2004006</a>.","bibtex":"@article{Junge_Osinga_2004, title={A set oriented approach to global optimal control}, DOI={<a href=\"https://doi.org/10.1051/cocv:2004006\">10.1051/cocv:2004006</a>}, journal={ESAIM: Control, Optimisation and Calculus of Variations}, author={Junge, Oliver and Osinga, Hinke M.}, year={2004}, pages={259–270} }","apa":"Junge, O., &#38; Osinga, H. M. (2004). A set oriented approach to global optimal control. <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, 259–270. <a href=\"https://doi.org/10.1051/cocv:2004006\">https://doi.org/10.1051/cocv:2004006</a>"},"page":"259-270","year":"2004","user_id":"15701","department":[{"_id":"101"}],"_id":"16619","type":"journal_article","publication":"ESAIM: Control, Optimisation and Calculus of Variations","status":"public"},{"publication_identifier":{"isbn":["0780386825"]},"publication_status":"published","year":"2004","citation":{"apa":"Junge, O., Marsden, J. E., &#38; Mezic, I. (2004). Uncertainty in the dynamics of conservative maps. In <i>2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)</i>. <a href=\"https://doi.org/10.1109/cdc.2004.1430379\">https://doi.org/10.1109/cdc.2004.1430379</a>","bibtex":"@inproceedings{Junge_Marsden_Mezic_2004, title={Uncertainty in the dynamics of conservative maps}, DOI={<a href=\"https://doi.org/10.1109/cdc.2004.1430379\">10.1109/cdc.2004.1430379</a>}, booktitle={2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)}, author={Junge, O. and Marsden, J.E. and Mezic, I.}, year={2004} }","mla":"Junge, O., et al. “Uncertainty in the Dynamics of Conservative Maps.” <i>2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)</i>, 2004, doi:<a href=\"https://doi.org/10.1109/cdc.2004.1430379\">10.1109/cdc.2004.1430379</a>.","short":"O. Junge, J.E. Marsden, I. Mezic, in: 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), 2004.","ama":"Junge O, Marsden JE, Mezic I. Uncertainty in the dynamics of conservative maps. 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No.04CH37601)</i>, 2004. <a href=\"https://doi.org/10.1109/cdc.2004.1430379\">https://doi.org/10.1109/cdc.2004.1430379</a>."},"date_updated":"2022-01-06T06:52:53Z","date_created":"2020-04-16T08:12:31Z","author":[{"last_name":"Junge","full_name":"Junge, O.","first_name":"O."},{"full_name":"Marsden, J.E.","last_name":"Marsden","first_name":"J.E."},{"first_name":"I.","full_name":"Mezic, I.","last_name":"Mezic"}],"title":"Uncertainty in the dynamics of conservative maps","doi":"10.1109/cdc.2004.1430379","publication":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","type":"conference","status":"public","_id":"16620","department":[{"_id":"101"}],"user_id":"15701","language":[{"iso":"eng"}]},{"department":[{"_id":"101"}],"user_id":"47427","_id":"16498","language":[{"iso":"eng"}],"publication":"Proceedings of the Royal Society of London. 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Dellnitz, “Computation of the dominant Lyapunov exponent via spatial integration using matrix norms,” <i>Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences</i>, pp. 2933–2955, 2003.","chicago":"Aston, P. J., and M. Dellnitz. “Computation of the Dominant Lyapunov Exponent via Spatial Integration Using Matrix Norms.” <i>Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences</i>, 2003, 2933–55. <a href=\"https://doi.org/10.1098/rspa.2003.1143\">https://doi.org/10.1098/rspa.2003.1143</a>.","apa":"Aston, P. J., &#38; Dellnitz, M. (2003). Computation of the dominant Lyapunov exponent via spatial integration using matrix norms. <i>Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences</i>, 2933–2955. <a href=\"https://doi.org/10.1098/rspa.2003.1143\">https://doi.org/10.1098/rspa.2003.1143</a>","bibtex":"@article{Aston_Dellnitz_2003, title={Computation of the dominant Lyapunov exponent via spatial integration using matrix norms}, DOI={<a href=\"https://doi.org/10.1098/rspa.2003.1143\">10.1098/rspa.2003.1143</a>}, journal={Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences}, author={Aston, P. J. and Dellnitz, M.}, year={2003}, pages={2933–2955} }","short":"P.J. Aston, M. Dellnitz, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences (2003) 2933–2955.","mla":"Aston, P. J., and M. Dellnitz. “Computation of the Dominant Lyapunov Exponent via Spatial Integration Using Matrix Norms.” <i>Proceedings of the Royal Society of London. 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Schütze, S. Mostaghim, M. Dellnitz, J. Teich, in: Lecture Notes in Computer Science, Berlin, Heidelberg, 2003.","apa":"Schütze, O., Mostaghim, S., Dellnitz, M., &#38; Teich, J. (2003). Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques. In <i>Lecture Notes in Computer Science</i>. Berlin, Heidelberg. <a href=\"https://doi.org/10.1007/3-540-36970-8_9\">https://doi.org/10.1007/3-540-36970-8_9</a>","chicago":"Schütze, Oliver, Sanaz Mostaghim, Michael Dellnitz, and Jürgen Teich. “Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques.” In <i>Lecture Notes in Computer Science</i>. Berlin, Heidelberg, 2003. <a href=\"https://doi.org/10.1007/3-540-36970-8_9\">https://doi.org/10.1007/3-540-36970-8_9</a>.","ieee":"O. Schütze, S. Mostaghim, M. Dellnitz, and J. 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Berlin, Heidelberg; 2003. doi:<a href=\"https://doi.org/10.1007/3-540-36970-8_9\">10.1007/3-540-36970-8_9</a>"},"date_updated":"2022-01-06T06:52:54Z","date_created":"2020-04-16T09:58:10Z","author":[{"first_name":"Oliver","full_name":"Schütze, Oliver","last_name":"Schütze"},{"full_name":"Mostaghim, Sanaz","last_name":"Mostaghim","first_name":"Sanaz"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"full_name":"Teich, Jürgen","last_name":"Teich","first_name":"Jürgen"}],"title":"Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques","doi":"10.1007/3-540-36970-8_9"},{"date_created":"2022-12-23T09:53:23Z","publisher":"Elsevier BV","title":"Minimal discriminants for fields with small Frobenius groups as Galois groups","issue":"2","year":"2003","language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"publication":"Journal of Number Theory","abstract":[{"lang":"eng","text":"We apply class field theory to the computation of the minimal discriminants for certain solvable groups. In particular, we apply our techniques to small Frobenius groups and all imprimitive degree 8 groups such that the corresponding fields have only a degree 2 and no degree 4 subfield."}],"author":[{"first_name":"Claus","last_name":"Fieker","full_name":"Fieker, Claus"},{"id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners","first_name":"Jürgen"}],"volume":99,"date_updated":"2023-03-06T09:19:16Z","doi":"10.1016/s0022-314x(02)00071-9","publication_status":"published","publication_identifier":{"issn":["0022-314X"]},"citation":{"short":"C. Fieker, J. Klüners, Journal of Number Theory 99 (2003) 318–337.","bibtex":"@article{Fieker_Klüners_2003, title={Minimal discriminants for fields with small Frobenius groups as Galois groups}, volume={99}, DOI={<a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">10.1016/s0022-314x(02)00071-9</a>}, number={2}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Fieker, Claus and Klüners, Jürgen}, year={2003}, pages={318–337} }","mla":"Fieker, Claus, and Jürgen Klüners. “Minimal Discriminants for Fields with Small Frobenius Groups as Galois Groups.” <i>Journal of Number Theory</i>, vol. 99, no. 2, Elsevier BV, 2003, pp. 318–37, doi:<a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">10.1016/s0022-314x(02)00071-9</a>.","apa":"Fieker, C., &#38; Klüners, J. (2003). Minimal discriminants for fields with small Frobenius groups as Galois groups. <i>Journal of Number Theory</i>, <i>99</i>(2), 318–337. <a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">https://doi.org/10.1016/s0022-314x(02)00071-9</a>","ama":"Fieker C, Klüners J. Minimal discriminants for fields with small Frobenius groups as Galois groups. <i>Journal of Number Theory</i>. 2003;99(2):318-337. doi:<a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">10.1016/s0022-314x(02)00071-9</a>","ieee":"C. Fieker and J. Klüners, “Minimal discriminants for fields with small Frobenius groups as Galois groups,” <i>Journal of Number Theory</i>, vol. 99, no. 2, pp. 318–337, 2003, doi: <a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">10.1016/s0022-314x(02)00071-9</a>.","chicago":"Fieker, Claus, and Jürgen Klüners. “Minimal Discriminants for Fields with Small Frobenius Groups as Galois Groups.” <i>Journal of Number Theory</i> 99, no. 2 (2003): 318–37. <a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">https://doi.org/10.1016/s0022-314x(02)00071-9</a>."},"intvolume":"        99","page":"318-337","user_id":"93826","department":[{"_id":"102"}],"_id":"34896","type":"journal_article","status":"public"},{"language":[{"iso":"eng"}],"_id":"16538","department":[{"_id":"101"}],"user_id":"15701","status":"public","publication":"Handbook of Dynamical Systems","type":"book_chapter","title":"Set Oriented Numerical Methods for Dynamical Systems","doi":"10.1016/s1874-575x(02)80026-1","date_updated":"2022-01-06T06:52:52Z","date_created":"2020-04-15T08:37:59Z","author":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"full_name":"Junge, Oliver","last_name":"Junge","first_name":"Oliver"}],"year":"2002","citation":{"mla":"Dellnitz, Michael, and Oliver Junge. “Set Oriented Numerical Methods for Dynamical Systems.” <i>Handbook of Dynamical Systems</i>, 2002, doi:<a href=\"https://doi.org/10.1016/s1874-575x(02)80026-1\">10.1016/s1874-575x(02)80026-1</a>.","short":"M. Dellnitz, O. Junge, in: Handbook of Dynamical Systems, 2002.","bibtex":"@inbook{Dellnitz_Junge_2002, title={Set Oriented Numerical Methods for Dynamical Systems}, DOI={<a href=\"https://doi.org/10.1016/s1874-575x(02)80026-1\">10.1016/s1874-575x(02)80026-1</a>}, booktitle={Handbook of Dynamical Systems}, author={Dellnitz, Michael and Junge, Oliver}, year={2002} }","apa":"Dellnitz, M., &#38; Junge, O. (2002). Set Oriented Numerical Methods for Dynamical Systems. In <i>Handbook of Dynamical Systems</i>. <a href=\"https://doi.org/10.1016/s1874-575x(02)80026-1\">https://doi.org/10.1016/s1874-575x(02)80026-1</a>","ama":"Dellnitz M, Junge O. Set Oriented Numerical Methods for Dynamical Systems. 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Finding zeros by multilevel subdivision techniques. <i>IMA Journal of Numerical Analysis</i>, 167–185. <a href=\"https://doi.org/10.1093/imanum/22.2.167\">https://doi.org/10.1093/imanum/22.2.167</a>","bibtex":"@article{Dellnitz_2002, title={Finding zeros by multilevel subdivision techniques}, DOI={<a href=\"https://doi.org/10.1093/imanum/22.2.167\">10.1093/imanum/22.2.167</a>}, journal={IMA Journal of Numerical Analysis}, author={Dellnitz, M.}, year={2002}, pages={167–185} }","mla":"Dellnitz, M. “Finding Zeros by Multilevel Subdivision Techniques.” <i>IMA Journal of Numerical Analysis</i>, 2002, pp. 167–85, doi:<a href=\"https://doi.org/10.1093/imanum/22.2.167\">10.1093/imanum/22.2.167</a>.","short":"M. Dellnitz, IMA Journal of Numerical Analysis (2002) 167–185.","chicago":"Dellnitz, M. “Finding Zeros by Multilevel Subdivision Techniques.” <i>IMA Journal of Numerical Analysis</i>, 2002, 167–85. <a href=\"https://doi.org/10.1093/imanum/22.2.167\">https://doi.org/10.1093/imanum/22.2.167</a>.","ieee":"M. Dellnitz, “Finding zeros by multilevel subdivision techniques,” <i>IMA Journal of Numerical Analysis</i>, pp. 167–185, 2002.","ama":"Dellnitz M. 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Preis, “Diffusion Schemes for Load Balancing on Heterogeneous Networks,” <i>Theory of Computing Systems</i>, pp. 305–320, 2002.","chicago":"Elsässer, Robert, Burkhard Monien, and Robert Preis. “Diffusion Schemes for Load Balancing on Heterogeneous Networks.” <i>Theory of Computing Systems</i>, 2002, 305–20. <a href=\"https://doi.org/10.1007/s00224-002-1056-4\">https://doi.org/10.1007/s00224-002-1056-4</a>.","ama":"Elsässer R, Monien B, Preis R. Diffusion Schemes for Load Balancing on Heterogeneous Networks. <i>Theory of Computing Systems</i>. 2002:305-320. doi:<a href=\"https://doi.org/10.1007/s00224-002-1056-4\">10.1007/s00224-002-1056-4</a>","apa":"Elsässer, R., Monien, B., &#38; Preis, R. (2002). Diffusion Schemes for Load Balancing on Heterogeneous Networks. <i>Theory of Computing Systems</i>, 305–320. <a href=\"https://doi.org/10.1007/s00224-002-1056-4\">https://doi.org/10.1007/s00224-002-1056-4</a>","short":"R. Elsässer, B. Monien, R. Preis, Theory of Computing Systems (2002) 305–320.","bibtex":"@article{Elsässer_Monien_Preis_2002, title={Diffusion Schemes for Load Balancing on Heterogeneous Networks}, DOI={<a href=\"https://doi.org/10.1007/s00224-002-1056-4\">10.1007/s00224-002-1056-4</a>}, journal={Theory of Computing Systems}, author={Elsässer, Robert and Monien, Burkhard and Preis, Robert}, year={2002}, pages={305–320} }","mla":"Elsässer, Robert, et al. “Diffusion Schemes for Load Balancing on Heterogeneous Networks.” <i>Theory of Computing Systems</i>, 2002, pp. 305–20, doi:<a href=\"https://doi.org/10.1007/s00224-002-1056-4\">10.1007/s00224-002-1056-4</a>."},"publication_identifier":{"issn":["1432-4350","1433-0490"]},"publication_status":"published","title":"Diffusion Schemes for Load Balancing on Heterogeneous Networks","doi":"10.1007/s00224-002-1056-4","date_updated":"2022-01-06T06:52:52Z","author":[{"full_name":"Elsässer, Robert","last_name":"Elsässer","first_name":"Robert"},{"last_name":"Monien","full_name":"Monien, Burkhard","first_name":"Burkhard"},{"first_name":"Robert","full_name":"Preis, Robert","last_name":"Preis"}],"date_created":"2020-04-16T05:45:42Z"},{"date_updated":"2023-03-06T10:26:58Z","volume":11,"author":[{"full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners","first_name":"Jürgen"}],"publication_status":"published","related_material":{"link":[{"relation":"confirmation","url":"https://projecteuclid.org/journals/experimental-mathematics/volume-11/issue-2/Algorithms-for-function-fields/em/1062621213.full"}]},"intvolume":"        11","page":"171-181","citation":{"ieee":"J. Klüners, “Algorithms for function fields,” <i>Experiment. Math. </i>, vol. 11, no. 2, pp. 171–181, 2002.","chicago":"Klüners, Jürgen. “Algorithms for Function Fields.” <i>Experiment. Math. </i> 11, no. 2 (2002): 171–81.","ama":"Klüners J. Algorithms for function fields. <i>Experiment Math </i>. 2002;11(2):171-181.","apa":"Klüners, J. (2002). Algorithms for function fields. <i>Experiment. Math. </i>, <i>11</i>(2), 171–181.","bibtex":"@article{Klüners_2002, title={Algorithms for function fields}, volume={11}, number={2}, journal={Experiment. Math. }, publisher={Elsevier BV}, author={Klüners, Jürgen}, year={2002}, pages={171–181} }","short":"J. Klüners, Experiment. Math.  11 (2002) 171–181.","mla":"Klüners, Jürgen. “Algorithms for Function Fields.” <i>Experiment. Math. </i>, vol. 11, no. 2, Elsevier BV, 2002, pp. 171–81."},"_id":"35954","department":[{"_id":"102"}],"user_id":"93826","type":"journal_article","status":"public","publisher":"Elsevier BV","date_created":"2023-01-11T09:45:40Z","title":"Algorithms for function fields","issue":"2","year":"2002","keyword":["algorithms","decompositions","Galois groups","subfields"],"language":[{"iso":"eng"}],"publication":"Experiment. Math. ","abstract":[{"text":"Let {\\ASIE K}\\,/{\\small \\ℚ}({\\ASIE t \\!}) be a finite extension. We describe algorithms for computing subfields and automorphisms of {\\ASIE K}\\,/{\\small \\ℚ}({\\ASIE t }\\!). As an application we give an algorithm for finding decompositions of rational functions in {\\small \\ℚ(α)}. We also present an algorithm which decides if an extension {\\ASIE L}\\,/{\\small \\ℚ}({\\ASIE t \\!}) is a subfield of {\\ASIE K}. In case [{\\ASIE K : \\;}{\\small\\ℚ}({\\ASIE t \\!})] = [{\\ASIE L : \\;}{\\small \\ℚ}({\\ASIE t \\!})] we obtain a {\\small \\ℚ}({\\ASIE t \\!})-isomorphism test. Furthermore, we describe an algorithm which computes subfields of the normal closure of {\\ASIE K}\\,/{\\small \\ℚ}({\\ASIE t \\!}).","lang":"eng"}]},{"department":[{"_id":"101"}],"user_id":"15701","_id":"16555","language":[{"iso":"eng"}],"publication":"Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems","type":"book_chapter","status":"public","date_created":"2020-04-15T09:10:54Z","author":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"first_name":"Gary","full_name":"Froyland, Gary","last_name":"Froyland"},{"full_name":"Junge, Oliver","last_name":"Junge","first_name":"Oliver"}],"date_updated":"2022-01-06T06:52:52Z","doi":"10.1007/978-3-642-56589-2_7","title":"The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems","publication_identifier":{"isbn":["9783642625244","9783642565892"]},"publication_status":"published","citation":{"chicago":"Dellnitz, Michael, Gary Froyland, and Oliver Junge. “The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems.” In <i>Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems</i>. Berlin, Heidelberg, 2001. <a href=\"https://doi.org/10.1007/978-3-642-56589-2_7\">https://doi.org/10.1007/978-3-642-56589-2_7</a>.","ieee":"M. Dellnitz, G. Froyland, and O. Junge, “The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems,” in <i>Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems</i>, Berlin, Heidelberg, 2001.","ama":"Dellnitz M, Froyland G, Junge O. The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems. In: <i>Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems</i>. Berlin, Heidelberg; 2001. doi:<a href=\"https://doi.org/10.1007/978-3-642-56589-2_7\">10.1007/978-3-642-56589-2_7</a>","short":"M. Dellnitz, G. Froyland, O. 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In <i>Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems</i>. Berlin, Heidelberg. <a href=\"https://doi.org/10.1007/978-3-642-56589-2_7\">https://doi.org/10.1007/978-3-642-56589-2_7</a>"},"place":"Berlin, Heidelberg","year":"2001"},{"status":"public","publication":"Nonlinear Dynamics and Statistics","type":"book_chapter","language":[{"iso":"eng"}],"_id":"16598","department":[{"_id":"101"}],"user_id":"15701","year":"2001","place":"Boston, MA","citation":{"bibtex":"@inbook{Froyland_2001, place={Boston, MA}, title={Extracting Dynamical Behavior via Markov Models}, DOI={<a href=\"https://doi.org/10.1007/978-1-4612-0177-9_12\">10.1007/978-1-4612-0177-9_12</a>}, booktitle={Nonlinear Dynamics and Statistics}, author={Froyland, Gary}, year={2001} }","mla":"Froyland, Gary. “Extracting Dynamical Behavior via Markov Models.” <i>Nonlinear Dynamics and Statistics</i>, 2001, doi:<a href=\"https://doi.org/10.1007/978-1-4612-0177-9_12\">10.1007/978-1-4612-0177-9_12</a>.","short":"G. 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An adaptive subdivision technique for the approximation of attractors and invariant measures: proof of convergence. <i>Dynamical Systems</i>, 213–222. <a href=\"https://doi.org/10.1080/14689360109696233\">https://doi.org/10.1080/14689360109696233</a>","mla":"Junge, Oliver. “An Adaptive Subdivision Technique for the Approximation of Attractors and Invariant Measures: Proof of Convergence.” <i>Dynamical Systems</i>, 2001, pp. 213–22, doi:<a href=\"https://doi.org/10.1080/14689360109696233\">10.1080/14689360109696233</a>.","bibtex":"@article{Junge_2001, title={An adaptive subdivision technique for the approximation of attractors and invariant measures: proof of convergence}, DOI={<a href=\"https://doi.org/10.1080/14689360109696233\">10.1080/14689360109696233</a>}, journal={Dynamical Systems}, author={Junge, Oliver}, year={2001}, pages={213–222} }","short":"O. 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Malle, “A Database for Field Extensions of the Rationals,” <i>LMS Journal of Computation and Mathematics</i>, vol. 4, pp. 182–196, 2001, doi: <a href=\"https://doi.org/10.1112/s1461157000000851\">10.1112/s1461157000000851</a>.","chicago":"Klüners, Jürgen, and Gunter Malle. “A Database for Field Extensions of the Rationals.” <i>LMS Journal of Computation and Mathematics</i> 4 (2001): 182–96. <a href=\"https://doi.org/10.1112/s1461157000000851\">https://doi.org/10.1112/s1461157000000851</a>.","ama":"Klüners J, Malle G. A Database for Field Extensions of the Rationals. <i>LMS Journal of Computation and Mathematics</i>. 2001;4:182-196. doi:<a href=\"https://doi.org/10.1112/s1461157000000851\">10.1112/s1461157000000851</a>","apa":"Klüners, J., &#38; Malle, G. (2001). A Database for Field Extensions of the Rationals. <i>LMS Journal of Computation and Mathematics</i>, <i>4</i>, 182–196. <a href=\"https://doi.org/10.1112/s1461157000000851\">https://doi.org/10.1112/s1461157000000851</a>","bibtex":"@article{Klüners_Malle_2001, title={A Database for Field Extensions of the Rationals}, volume={4}, DOI={<a href=\"https://doi.org/10.1112/s1461157000000851\">10.1112/s1461157000000851</a>}, journal={LMS Journal of Computation and Mathematics}, publisher={Wiley}, author={Klüners, Jürgen and Malle, Gunter}, year={2001}, pages={182–196} }","short":"J. Klüners, G. Malle, LMS Journal of Computation and Mathematics 4 (2001) 182–196.","mla":"Klüners, Jürgen, and Gunter Malle. “A Database for Field Extensions of the Rationals.” <i>LMS Journal of Computation and Mathematics</i>, vol. 4, Wiley, 2001, pp. 182–96, doi:<a href=\"https://doi.org/10.1112/s1461157000000851\">10.1112/s1461157000000851</a>."},"intvolume":"         4","page":"182-196","author":[{"full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners","first_name":"Jürgen"},{"first_name":"Gunter","full_name":"Malle, Gunter","last_name":"Malle"}],"volume":4,"date_updated":"2023-03-02T09:53:08Z","doi":"10.1112/s1461157000000851","type":"journal_article","status":"public","user_id":"93826","department":[{"_id":"102"}],"_id":"34897","year":"2001","date_created":"2022-12-23T09:56:22Z","publisher":"Wiley","title":"A Database for Field Extensions of the Rationals","publication":"LMS Journal of Computation and Mathematics","abstract":[{"text":"This paper announces the creation of a database for number fields. It describes the contents and the methods of access, indicates the origin of the polynomials, and formulates the aims of this collection of fields.","lang":"eng"}],"external_id":{"arxiv":["math/0102232"]},"language":[{"iso":"eng"}],"keyword":["Computational Theory and Mathematics","General Mathematics"]},{"publication":"Equadiff 99","type":"book_chapter","status":"public","department":[{"_id":"101"}],"user_id":"15701","_id":"16513","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9789810243593","9789812792617"]},"publication_status":"published","citation":{"ama":"Aston PJ, Dellnitz M. The Computation of Lyapunov Exponents via Spatial Integration Using Vector Norms. In: <i>Equadiff 99</i>. ; 2000. doi:<a href=\"https://doi.org/10.1142/9789812792617_0196\">10.1142/9789812792617_0196</a>","ieee":"P. J. Aston and M. Dellnitz, “The Computation of Lyapunov Exponents via Spatial Integration Using Vector Norms,” in <i>Equadiff 99</i>, 2000.","chicago":"Aston, P. J., and M. Dellnitz. “The Computation of Lyapunov Exponents via Spatial Integration Using Vector Norms.” In <i>Equadiff 99</i>, 2000. <a href=\"https://doi.org/10.1142/9789812792617_0196\">https://doi.org/10.1142/9789812792617_0196</a>.","short":"P.J. Aston, M. Dellnitz, in: Equadiff 99, 2000.","mla":"Aston, P. J., and M. Dellnitz. “The Computation of Lyapunov Exponents via Spatial Integration Using Vector Norms.” <i>Equadiff 99</i>, 2000, doi:<a href=\"https://doi.org/10.1142/9789812792617_0196\">10.1142/9789812792617_0196</a>.","bibtex":"@inbook{Aston_Dellnitz_2000, title={The Computation of Lyapunov Exponents via Spatial Integration Using Vector Norms}, DOI={<a href=\"https://doi.org/10.1142/9789812792617_0196\">10.1142/9789812792617_0196</a>}, booktitle={Equadiff 99}, author={Aston, P. J. and Dellnitz, M.}, year={2000} }","apa":"Aston, P. J., &#38; Dellnitz, M. (2000). The Computation of Lyapunov Exponents via Spatial Integration Using Vector Norms. In <i>Equadiff 99</i>. <a href=\"https://doi.org/10.1142/9789812792617_0196\">https://doi.org/10.1142/9789812792617_0196</a>"},"year":"2000","author":[{"first_name":"P. J.","full_name":"Aston, P. J.","last_name":"Aston"},{"first_name":"M.","last_name":"Dellnitz","full_name":"Dellnitz, M."}],"date_created":"2020-04-15T07:53:09Z","date_updated":"2022-01-06T06:52:52Z","doi":"10.1142/9789812792617_0196","title":"The Computation of Lyapunov Exponents via Spatial Integration Using Vector Norms"}]