[{"user_id":"31496","_id":"53316","language":[{"iso":"eng"}],"article_number":"26","keyword":["Mathematics (miscellaneous)"],"type":"journal_article","publication":"Journal of Evolution Equations","status":"public","abstract":[{"lang":"eng","text":"AbstractThe quasilinear Keller–Segel system $$\\begin{aligned} \\left\\{ \\begin{array}{l} u_t=\\nabla \\cdot (D(u)\\nabla u) - \\nabla \\cdot (S(u)\\nabla v), \\\\ v_t=\\Delta v-v+u, \\end{array}\\right. \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n =\r\n ∇\r\n ·\r\n \r\n (\r\n D\r\n \r\n (\r\n u\r\n )\r\n \r\n ∇\r\n u\r\n )\r\n \r\n -\r\n ∇\r\n ·\r\n \r\n (\r\n S\r\n \r\n (\r\n u\r\n )\r\n \r\n ∇\r\n v\r\n )\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n v\r\n t\r\n \r\n =\r\n Δ\r\n v\r\n -\r\n v\r\n +\r\n u\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n endowed with homogeneous Neumann boundary conditions is considered in a bounded domain $$\\Omega \\subset {\\mathbb {R}}^n$$\r\n \r\n Ω\r\n ⊂\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n \r\n , $$n \\ge 3$$\r\n \r\n n\r\n ≥\r\n 3\r\n \r\n , with smooth boundary for sufficiently regular functions D and S satisfying $$D>0$$\r\n \r\n D\r\n >\r\n 0\r\n \r\n on $$[0,\\infty )$$\r\n \r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n , $$S>0$$\r\n \r\n S\r\n >\r\n 0\r\n \r\n on $$(0,\\infty )$$\r\n \r\n (\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n and $$S(0)=0$$\r\n \r\n S\r\n (\r\n 0\r\n )\r\n =\r\n 0\r\n \r\n . On the one hand, it is shown that if $$\\frac{S}{D}$$\r\n \r\n S\r\n D\r\n \r\n satisfies the subcritical growth condition $$\\begin{aligned} \\frac{S(s)}{D(s)} \\le C s^\\alpha \\qquad \\text{ for } \\text{ all } s\\ge 1 \\qquad \\text{ with } \\text{ some } \\alpha < \\frac{2}{n} \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n S\r\n (\r\n s\r\n )\r\n \r\n \r\n D\r\n (\r\n s\r\n )\r\n \r\n \r\n ≤\r\n C\r\n \r\n s\r\n α\r\n \r\n \r\n \r\n for\r\n \r\n \r\n all\r\n \r\n s\r\n ≥\r\n 1\r\n \r\n \r\n with\r\n \r\n \r\n some\r\n \r\n α\r\n <\r\n \r\n 2\r\n n\r\n \r\n \r\n \r\n \r\n \r\n \r\n and $$C>0$$\r\n \r\n C\r\n >\r\n 0\r\n \r\n , then for any sufficiently regular initial data there exists a global weak energy solution such that $${ \\mathrm{{ess}}} \\sup _{t>0} \\Vert u(t) \\Vert _{L^p(\\Omega )}<\\infty $$\r\n \r\n ess\r\n \r\n sup\r\n \r\n t\r\n >\r\n 0\r\n \r\n \r\n \r\n \r\n ‖\r\n u\r\n \r\n (\r\n t\r\n )\r\n \r\n ‖\r\n \r\n \r\n \r\n L\r\n p\r\n \r\n \r\n (\r\n Ω\r\n )\r\n \r\n \r\n \r\n <\r\n ∞\r\n \r\n for some $$p > \\frac{2n}{n+2}$$\r\n \r\n p\r\n >\r\n \r\n \r\n 2\r\n n\r\n \r\n \r\n n\r\n +\r\n 2\r\n \r\n \r\n \r\n . On the other hand, if $$\\frac{S}{D}$$\r\n \r\n S\r\n D\r\n \r\n satisfies the supercritical growth condition $$\\begin{aligned} \\frac{S(s)}{D(s)} \\ge c s^\\alpha \\qquad \\text{ for } \\text{ all } s\\ge 1 \\qquad \\text{ with } \\text{ some } \\alpha > \\frac{2}{n} \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n S\r\n (\r\n s\r\n )\r\n \r\n \r\n D\r\n (\r\n s\r\n )\r\n \r\n \r\n ≥\r\n c\r\n \r\n s\r\n α\r\n \r\n \r\n \r\n for\r\n \r\n \r\n all\r\n \r\n s\r\n ≥\r\n 1\r\n \r\n \r\n with\r\n \r\n \r\n some\r\n \r\n α\r\n >\r\n \r\n 2\r\n n\r\n \r\n \r\n \r\n \r\n \r\n \r\n and $$c>0$$\r\n \r\n c\r\n >\r\n 0\r\n \r\n , then the nonexistence of a global weak energy solution having the boundedness property stated above is shown for some initial data in the radial setting. This establishes some criticality of the value $$\\alpha = \\frac{2}{n}$$\r\n \r\n α\r\n =\r\n \r\n 2\r\n n\r\n \r\n \r\n for $$n \\ge 3$$\r\n \r\n n\r\n ≥\r\n 3\r\n \r\n , without any additional assumption on the behavior of D(s) as $$s \\rightarrow \\infty $$\r\n \r\n s\r\n →\r\n ∞\r\n \r\n , in particular without requiring any algebraic lower bound for D. When applied to the Keller–Segel system with volume-filling effect for probability distribution functions of the type $$Q(s) = \\exp (-s^\\beta )$$\r\n \r\n Q\r\n \r\n (\r\n s\r\n )\r\n \r\n =\r\n exp\r\n \r\n (\r\n -\r\n \r\n s\r\n β\r\n \r\n )\r\n \r\n \r\n , $$s \\ge 0$$\r\n \r\n s\r\n ≥\r\n 0\r\n \r\n , for global solvability the exponent $$\\beta = \\frac{n-2}{n}$$\r\n \r\n β\r\n =\r\n \r\n \r\n n\r\n -\r\n 2\r\n \r\n n\r\n \r\n \r\n is seen to be critical.\r\n"}],"author":[{"first_name":"Christian","last_name":"Stinner","full_name":"Stinner, Christian"},{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"date_created":"2024-04-07T12:29:25Z","volume":24,"publisher":"Springer Science and Business Media LLC","date_updated":"2024-04-07T12:36:21Z","doi":"10.1007/s00028-024-00954-x","title":"A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects","issue":"2","publication_status":"published","publication_identifier":{"issn":["1424-3199","1424-3202"]},"citation":{"chicago":"Stinner, Christian, and Michael Winkler. “A Critical Exponent in a Quasilinear Keller–Segel System with Arbitrarily Fast Decaying Diffusivities Accounting for Volume-Filling Effects.” Journal of Evolution Equations 24, no. 2 (2024). https://doi.org/10.1007/s00028-024-00954-x.","ieee":"C. Stinner and M. Winkler, “A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects,” Journal of Evolution Equations, vol. 24, no. 2, Art. no. 26, 2024, doi: 10.1007/s00028-024-00954-x.","ama":"Stinner C, Winkler M. A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects. Journal of Evolution Equations. 2024;24(2). doi:10.1007/s00028-024-00954-x","apa":"Stinner, C., & Winkler, M. (2024). A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects. Journal of Evolution Equations, 24(2), Article 26. https://doi.org/10.1007/s00028-024-00954-x","short":"C. Stinner, M. Winkler, Journal of Evolution Equations 24 (2024).","mla":"Stinner, Christian, and Michael Winkler. “A Critical Exponent in a Quasilinear Keller–Segel System with Arbitrarily Fast Decaying Diffusivities Accounting for Volume-Filling Effects.” Journal of Evolution Equations, vol. 24, no. 2, 26, Springer Science and Business Media LLC, 2024, doi:10.1007/s00028-024-00954-x.","bibtex":"@article{Stinner_Winkler_2024, title={A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects}, volume={24}, DOI={10.1007/s00028-024-00954-x}, number={226}, journal={Journal of Evolution Equations}, publisher={Springer Science and Business Media LLC}, author={Stinner, Christian and Winkler, Michael}, year={2024} }"},"intvolume":" 24","year":"2024"},{"type":"journal_article","status":"public","department":[{"_id":"555"}],"user_id":"100325","_id":"53542","article_number":"34","publication_identifier":{"issn":["1424-3199","1424-3202"]},"publication_status":"published","intvolume":" 24","citation":{"apa":"Papageorgiou, E. (2024). Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces. Journal of Evolution Equations, 24(2), Article 34. https://doi.org/10.1007/s00028-024-00959-6","short":"E. Papageorgiou, Journal of Evolution Equations 24 (2024).","mla":"Papageorgiou, Efthymia. “Asymptotic Behavior of Solutions to the Extension Problem for the Fractional Laplacian on Noncompact Symmetric Spaces.” Journal of Evolution Equations, vol. 24, no. 2, 34, Springer Science and Business Media LLC, 2024, doi:10.1007/s00028-024-00959-6.","bibtex":"@article{Papageorgiou_2024, title={Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces}, volume={24}, DOI={10.1007/s00028-024-00959-6}, number={234}, journal={Journal of Evolution Equations}, publisher={Springer Science and Business Media LLC}, author={Papageorgiou, Efthymia}, year={2024} }","ama":"Papageorgiou E. Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces. Journal of Evolution Equations. 2024;24(2). doi:10.1007/s00028-024-00959-6","chicago":"Papageorgiou, Efthymia. “Asymptotic Behavior of Solutions to the Extension Problem for the Fractional Laplacian on Noncompact Symmetric Spaces.” Journal of Evolution Equations 24, no. 2 (2024). https://doi.org/10.1007/s00028-024-00959-6.","ieee":"E. Papageorgiou, “Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces,” Journal of Evolution Equations, vol. 24, no. 2, Art. no. 34, 2024, doi: 10.1007/s00028-024-00959-6."},"volume":24,"author":[{"first_name":"Efthymia","last_name":"Papageorgiou","id":"100325","full_name":"Papageorgiou, Efthymia"}],"date_updated":"2024-04-17T13:20:29Z","doi":"10.1007/s00028-024-00959-6","publication":"Journal of Evolution Equations","abstract":[{"lang":"eng","text":"AbstractThis work deals with the extension problem for the fractional Laplacian on Riemannian symmetric spaces G/K of noncompact type and of general rank, which gives rise to a family of convolution operators, including the Poisson operator. More precisely, motivated by Euclidean results for the Poisson semigroup, we study the long-time asymptotic behavior of solutions to the extension problem for $$L^1$$\r\n \r\n L\r\n 1\r\n \r\n initial data. In the case of the Laplace–Beltrami operator, we show that if the initial data are bi-K-invariant, then the solution to the extension problem behaves asymptotically as the mass times the fundamental solution, but this convergence may break down in the non-bi-K-invariant case. In the second part, we investigate the long-time asymptotic behavior of the extension problem associated with the so-called distinguished Laplacian on G/K. In this case, we observe phenomena which are similar to the Euclidean setting for the Poisson semigroup, such as $$L^1$$\r\n \r\n L\r\n 1\r\n \r\n asymptotic convergence without the assumption of bi-K-invariance."}],"language":[{"iso":"eng"}],"keyword":["Mathematics (miscellaneous)"],"issue":"2","year":"2024","date_created":"2024-04-17T13:18:30Z","publisher":"Springer Science and Business Media LLC","title":"Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces"},{"date_updated":"2024-03-25T10:09:21Z","publisher":"Informa UK Limited","author":[{"first_name":"H.","last_name":"Gilbert","full_name":"Gilbert, H."},{"full_name":"Schürmann, M.","last_name":"Schürmann","first_name":"M."},{"first_name":"M.","full_name":"Liebendörfer, M.","last_name":"Liebendörfer"},{"last_name":"Lawson","full_name":"Lawson, D.","first_name":"D."},{"last_name":"Hodds","full_name":"Hodds, M.","first_name":"M."}],"date_created":"2024-03-25T10:02:09Z","title":"Post-pandemic online mathematics and statistics support: Practitioners’ opinions in Germany and Great Britain & Ireland","doi":"10.1080/0020739x.2023.2184282","publication_status":"published","publication_identifier":{"issn":["0020-739X","1464-5211"]},"year":"2023","citation":{"apa":"Gilbert, H., Schürmann, M., Liebendörfer, M., Lawson, D., & Hodds, M. (2023). Post-pandemic online mathematics and statistics support: Practitioners’ opinions in Germany and Great Britain & Ireland. International Journal of Mathematical Education in Science and Technology, 1–26. https://doi.org/10.1080/0020739x.2023.2184282","bibtex":"@article{Gilbert_Schürmann_Liebendörfer_Lawson_Hodds_2023, title={Post-pandemic online mathematics and statistics support: Practitioners’ opinions in Germany and Great Britain & Ireland}, DOI={10.1080/0020739x.2023.2184282}, journal={International Journal of Mathematical Education in Science and Technology}, publisher={Informa UK Limited}, author={Gilbert, H. and Schürmann, M. and Liebendörfer, M. and Lawson, D. and Hodds, M.}, year={2023}, pages={1–26} }","mla":"Gilbert, H., et al. “Post-Pandemic Online Mathematics and Statistics Support: Practitioners’ Opinions in Germany and Great Britain & Ireland.” International Journal of Mathematical Education in Science and Technology, Informa UK Limited, 2023, pp. 1–26, doi:10.1080/0020739x.2023.2184282.","short":"H. Gilbert, M. Schürmann, M. Liebendörfer, D. Lawson, M. Hodds, International Journal of Mathematical Education in Science and Technology (2023) 1–26.","ama":"Gilbert H, Schürmann M, Liebendörfer M, Lawson D, Hodds M. Post-pandemic online mathematics and statistics support: Practitioners’ opinions in Germany and Great Britain & Ireland. International Journal of Mathematical Education in Science and Technology. Published online 2023:1-26. doi:10.1080/0020739x.2023.2184282","ieee":"H. Gilbert, M. Schürmann, M. Liebendörfer, D. Lawson, and M. Hodds, “Post-pandemic online mathematics and statistics support: Practitioners’ opinions in Germany and Great Britain & Ireland,” International Journal of Mathematical Education in Science and Technology, pp. 1–26, 2023, doi: 10.1080/0020739x.2023.2184282.","chicago":"Gilbert, H., M. Schürmann, M. Liebendörfer, D. Lawson, and M. Hodds. “Post-Pandemic Online Mathematics and Statistics Support: Practitioners’ Opinions in Germany and Great Britain & Ireland.” International Journal of Mathematical Education in Science and Technology, 2023, 1–26. https://doi.org/10.1080/0020739x.2023.2184282."},"page":"1-26","_id":"52806","user_id":"30933","department":[{"_id":"10"},{"_id":"625"},{"_id":"34"},{"_id":"97"},{"_id":"98"}],"keyword":["Applied Mathematics","Education","Mathematics (miscellaneous)"],"language":[{"iso":"eng"}],"type":"journal_article","publication":"International Journal of Mathematical Education in Science and Technology","status":"public"},{"publication_identifier":{"issn":["0020-739X","1464-5211"]},"publication_status":"published","page":"1133-1152","intvolume":" 53","citation":{"mla":"Liebendörfer, Michael, et al. “The Role of Learning Strategies for Performance in Mathematics Courses for Engineers.” International Journal of Mathematical Education in Science and Technology, vol. 53, no. 5, Informa UK Limited, 2022, pp. 1133–52, doi:10.1080/0020739x.2021.2023772.","bibtex":"@article{Liebendörfer_Göller_Gildehaus_Kortemeyer_Biehler_Hochmuth_Ostsieker_Rode_Schaper_2022, title={The role of learning strategies for performance in mathematics courses for engineers}, volume={53}, DOI={10.1080/0020739x.2021.2023772}, number={5}, journal={International Journal of Mathematical Education in Science and Technology}, publisher={Informa UK Limited}, author={Liebendörfer, Michael and Göller, Robin and Gildehaus, Lara and Kortemeyer, Jörg and Biehler, Rolf and Hochmuth, Reinhard and Ostsieker, Laura and Rode, Jana and Schaper, Niclas}, year={2022}, pages={1133–1152} }","short":"M. Liebendörfer, R. Göller, L. Gildehaus, J. Kortemeyer, R. Biehler, R. Hochmuth, L. Ostsieker, J. Rode, N. Schaper, International Journal of Mathematical Education in Science and Technology 53 (2022) 1133–1152.","apa":"Liebendörfer, M., Göller, R., Gildehaus, L., Kortemeyer, J., Biehler, R., Hochmuth, R., Ostsieker, L., Rode, J., & Schaper, N. (2022). The role of learning strategies for performance in mathematics courses for engineers. International Journal of Mathematical Education in Science and Technology, 53(5), 1133–1152. https://doi.org/10.1080/0020739x.2021.2023772","ama":"Liebendörfer M, Göller R, Gildehaus L, et al. The role of learning strategies for performance in mathematics courses for engineers. International Journal of Mathematical Education in Science and Technology. 2022;53(5):1133-1152. doi:10.1080/0020739x.2021.2023772","ieee":"M. Liebendörfer et al., “The role of learning strategies for performance in mathematics courses for engineers,” International Journal of Mathematical Education in Science and Technology, vol. 53, no. 5, pp. 1133–1152, 2022, doi: 10.1080/0020739x.2021.2023772.","chicago":"Liebendörfer, Michael, Robin Göller, Lara Gildehaus, Jörg Kortemeyer, Rolf Biehler, Reinhard Hochmuth, Laura Ostsieker, Jana Rode, and Niclas Schaper. “The Role of Learning Strategies for Performance in Mathematics Courses for Engineers.” International Journal of Mathematical Education in Science and Technology 53, no. 5 (2022): 1133–52. https://doi.org/10.1080/0020739x.2021.2023772."},"volume":53,"author":[{"first_name":"Michael","orcid":"0000-0001-9887-2074","last_name":"Liebendörfer","full_name":"Liebendörfer, Michael","id":"30933"},{"last_name":"Göller","full_name":"Göller, Robin","first_name":"Robin"},{"full_name":"Gildehaus, Lara","last_name":"Gildehaus","first_name":"Lara"},{"first_name":"Jörg","full_name":"Kortemeyer, Jörg","last_name":"Kortemeyer"},{"first_name":"Rolf","last_name":"Biehler","id":"16274","full_name":"Biehler, Rolf"},{"full_name":"Hochmuth, Reinhard","last_name":"Hochmuth","first_name":"Reinhard"},{"last_name":"Ostsieker","full_name":"Ostsieker, Laura","first_name":"Laura"},{"full_name":"Rode, Jana","last_name":"Rode","first_name":"Jana"},{"first_name":"Niclas","last_name":"Schaper","full_name":"Schaper, Niclas"}],"date_updated":"2024-04-18T10:08:30Z","doi":"10.1080/0020739x.2021.2023772","type":"journal_article","status":"public","department":[{"_id":"363"},{"_id":"625"}],"user_id":"37888","_id":"35685","issue":"5","year":"2022","date_created":"2023-01-10T08:56:30Z","publisher":"Informa UK Limited","title":"The role of learning strategies for performance in mathematics courses for engineers","publication":"International Journal of Mathematical Education in Science and Technology","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Education","Mathematics (miscellaneous)"]},{"title":"Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students","doi":"10.1007/s40753-022-00188-7","date_updated":"2023-01-18T22:43:43Z","publisher":"Springer Science and Business Media LLC","author":[{"first_name":"Christiane","last_name":"Büdenbender-Kuklinski","full_name":"Büdenbender-Kuklinski, Christiane"},{"last_name":"Hochmuth","full_name":"Hochmuth, Reinhard","first_name":"Reinhard"},{"first_name":"Michael","full_name":"Liebendörfer, Michael","last_name":"Liebendörfer"}],"date_created":"2023-01-18T22:22:49Z","year":"2022","citation":{"ama":"Büdenbender-Kuklinski C, Hochmuth R, Liebendörfer M. Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students. International Journal of Research in Undergraduate Mathematics Education. Published online 2022. doi:10.1007/s40753-022-00188-7","chicago":"Büdenbender-Kuklinski, Christiane, Reinhard Hochmuth, and Michael Liebendörfer. “Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students.” International Journal of Research in Undergraduate Mathematics Education, 2022. https://doi.org/10.1007/s40753-022-00188-7.","ieee":"C. Büdenbender-Kuklinski, R. Hochmuth, and M. Liebendörfer, “Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students,” International Journal of Research in Undergraduate Mathematics Education, 2022, doi: 10.1007/s40753-022-00188-7.","apa":"Büdenbender-Kuklinski, C., Hochmuth, R., & Liebendörfer, M. (2022). Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students. International Journal of Research in Undergraduate Mathematics Education. https://doi.org/10.1007/s40753-022-00188-7","bibtex":"@article{Büdenbender-Kuklinski_Hochmuth_Liebendörfer_2022, title={Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students}, DOI={10.1007/s40753-022-00188-7}, journal={International Journal of Research in Undergraduate Mathematics Education}, publisher={Springer Science and Business Media LLC}, author={Büdenbender-Kuklinski, Christiane and Hochmuth, Reinhard and Liebendörfer, Michael}, year={2022} }","mla":"Büdenbender-Kuklinski, Christiane, et al. “Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students.” International Journal of Research in Undergraduate Mathematics Education, Springer Science and Business Media LLC, 2022, doi:10.1007/s40753-022-00188-7.","short":"C. Büdenbender-Kuklinski, R. Hochmuth, M. Liebendörfer, International Journal of Research in Undergraduate Mathematics Education (2022)."},"publication_identifier":{"issn":["2198-9745","2198-9753"]},"publication_status":"published","keyword":["Education","Mathematics (miscellaneous)"],"language":[{"iso":"eng"}],"_id":"37472","department":[{"_id":"10"}],"user_id":"30933","abstract":[{"text":"AbstractAs earlier research results suggest that many mathematics teaching students criticize a missing relevance in their studies, we explore explanations and interrelationships of their relevance assessments. We aim at finding out how one could support the students in attributing relevance to their study programs. A two-fold model for relevance assessments in mathematics teacher education is proposed, consisting of relevance content and relevance reasons. We investigate students' relevance perceptions of mathematical topics and of topics’ complexities, as well as their rating of individual and societal/ vocational relevance reasons, all in relation to their perception of the relevance of their overall program of study. Contrary to earlier research findings, our results suggest that mathematics teaching students already do attribute relevance to many content areas and that a preparation for the teaching profession is not the only reason for them to assign relevance. There also seem to be many students who would attribute relevance if they could develop as individuals and pursue their interests. We suggest that giving students opportunities to set individual priorities in their studies could hence support their relevance assessments. As low relevance assessments seem to be connected to students’ motivational problems, students might profit from motivational support, as well.","lang":"eng"}],"status":"public","publication":"International Journal of Research in Undergraduate Mathematics Education","type":"journal_article"},{"publication_identifier":{"issn":["2198-9745","2198-9753"]},"publication_status":"published","page":"163-188","intvolume":" 7","citation":{"chicago":"Pepin, Birgit, Rolf Biehler, and Ghislaine Gueudet. “Mathematics in Engineering Education: A Review of the Recent Literature with a View towards Innovative Practices.” International Journal of Research in Undergraduate Mathematics Education 7, no. 2 (2021): 163–88. https://doi.org/10.1007/s40753-021-00139-8.","ieee":"B. Pepin, R. Biehler, and G. Gueudet, “Mathematics in Engineering Education: a Review of the Recent Literature with a View towards Innovative Practices,” International Journal of Research in Undergraduate Mathematics Education, vol. 7, no. 2, pp. 163–188, 2021, doi: 10.1007/s40753-021-00139-8.","ama":"Pepin B, Biehler R, Gueudet G. Mathematics in Engineering Education: a Review of the Recent Literature with a View towards Innovative Practices. International Journal of Research in Undergraduate Mathematics Education. 2021;7(2):163-188. doi:10.1007/s40753-021-00139-8","mla":"Pepin, Birgit, et al. “Mathematics in Engineering Education: A Review of the Recent Literature with a View towards Innovative Practices.” International Journal of Research in Undergraduate Mathematics Education, vol. 7, no. 2, Springer Science and Business Media LLC, 2021, pp. 163–88, doi:10.1007/s40753-021-00139-8.","bibtex":"@article{Pepin_Biehler_Gueudet_2021, title={Mathematics in Engineering Education: a Review of the Recent Literature with a View towards Innovative Practices}, volume={7}, DOI={10.1007/s40753-021-00139-8}, number={2}, journal={International Journal of Research in Undergraduate Mathematics Education}, publisher={Springer Science and Business Media LLC}, author={Pepin, Birgit and Biehler, Rolf and Gueudet, Ghislaine}, year={2021}, pages={163–188} }","short":"B. Pepin, R. Biehler, G. Gueudet, International Journal of Research in Undergraduate Mathematics Education 7 (2021) 163–188.","apa":"Pepin, B., Biehler, R., & Gueudet, G. (2021). Mathematics in Engineering Education: a Review of the Recent Literature with a View towards Innovative Practices. International Journal of Research in Undergraduate Mathematics Education, 7(2), 163–188. https://doi.org/10.1007/s40753-021-00139-8"},"date_updated":"2024-04-18T09:48:52Z","volume":7,"author":[{"first_name":"Birgit","last_name":"Pepin","full_name":"Pepin, Birgit"},{"last_name":"Biehler","full_name":"Biehler, Rolf","id":"16274","first_name":"Rolf"},{"last_name":"Gueudet","full_name":"Gueudet, Ghislaine","first_name":"Ghislaine"}],"doi":"10.1007/s40753-021-00139-8","type":"journal_article","status":"public","_id":"35778","department":[{"_id":"363"}],"user_id":"37888","issue":"2","year":"2021","publisher":"Springer Science and Business Media LLC","date_created":"2023-01-10T10:43:08Z","title":"Mathematics in Engineering Education: a Review of the Recent Literature with a View towards Innovative Practices","publication":"International Journal of Research in Undergraduate Mathematics Education","abstract":[{"text":"AbstractThe aim of the special issue is to bring together important current international research on innovative teaching and learning practices in mathematics in engineering education, and to develop deeper understandings of the characteristics of current teaching and learning practices that can inform the design and implementation of future innovative practice. The focus of this review paper is to provide a state-of-the-art overview of this emerging field at the cross-roads between mathematics and engineering education, in addition to introducing the papers of this special issue. To guide this paper, we posed three review questions: (1) How can current (teaching/learning/study) practices of mathematics in engineering education be characterized with a view towards innovation?; (2) What are the ‘resources’ (cognitive, material, digital, social) used, and what are those that appear also well suited for innovative courses?; (3) What are promising innovative practices in mathematics in engineering education, and what are the implications for curriculum reform? Looking back across the studies we summarized in the review, we conclude that they are lagging behind the more fundamental changes that are happening in engineering education, whilst addressing selected aspects of innovative changes within the current system of engineering education. At the same time, the nine papers of this special issue contribute new perspectives for innovative practices in mathematics in engineering education, for a better understanding of current practices and for future research.","lang":"eng"}],"keyword":["Education","Mathematics (miscellaneous)"],"language":[{"iso":"eng"}]},{"publisher":"Springer Science and Business Media LLC","date_updated":"2024-04-18T10:09:08Z","volume":8,"author":[{"orcid":"0000-0003-2646-085X","last_name":"Schürmann","id":"59707","full_name":"Schürmann, Mirko","first_name":"Mirko"},{"full_name":"Panse, Anja","last_name":"Panse","first_name":"Anja"},{"last_name":"Shaikh","full_name":"Shaikh, Zain","first_name":"Zain"},{"full_name":"Biehler, Rolf","id":"16274","last_name":"Biehler","first_name":"Rolf"},{"first_name":"Niclas","full_name":"Schaper, Niclas","last_name":"Schaper"},{"first_name":"Michael","last_name":"Liebendörfer","orcid":"0000-0001-9887-2074","full_name":"Liebendörfer, Michael","id":"30933"},{"id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert","first_name":"Joachim"}],"date_created":"2023-01-10T09:09:23Z","title":"Consultation Phases in Mathematics Learning and Support Centres","doi":"10.1007/s40753-021-00154-9","publication_identifier":{"issn":["2198-9745","2198-9753"]},"publication_status":"published","issue":"1","year":"2021","page":"94-120","intvolume":" 8","citation":{"mla":"Schürmann, Mirko, et al. “Consultation Phases in Mathematics Learning and Support Centres.” International Journal of Research in Undergraduate Mathematics Education, vol. 8, no. 1, Springer Science and Business Media LLC, 2021, pp. 94–120, doi:10.1007/s40753-021-00154-9.","short":"M. Schürmann, A. Panse, Z. Shaikh, R. Biehler, N. Schaper, M. Liebendörfer, J. Hilgert, International Journal of Research in Undergraduate Mathematics Education 8 (2021) 94–120.","bibtex":"@article{Schürmann_Panse_Shaikh_Biehler_Schaper_Liebendörfer_Hilgert_2021, title={Consultation Phases in Mathematics Learning and Support Centres}, volume={8}, DOI={10.1007/s40753-021-00154-9}, number={1}, journal={International Journal of Research in Undergraduate Mathematics Education}, publisher={Springer Science and Business Media LLC}, author={Schürmann, Mirko and Panse, Anja and Shaikh, Zain and Biehler, Rolf and Schaper, Niclas and Liebendörfer, Michael and Hilgert, Joachim}, year={2021}, pages={94–120} }","apa":"Schürmann, M., Panse, A., Shaikh, Z., Biehler, R., Schaper, N., Liebendörfer, M., & Hilgert, J. (2021). Consultation Phases in Mathematics Learning and Support Centres. International Journal of Research in Undergraduate Mathematics Education, 8(1), 94–120. https://doi.org/10.1007/s40753-021-00154-9","ieee":"M. Schürmann et al., “Consultation Phases in Mathematics Learning and Support Centres,” International Journal of Research in Undergraduate Mathematics Education, vol. 8, no. 1, pp. 94–120, 2021, doi: 10.1007/s40753-021-00154-9.","chicago":"Schürmann, Mirko, Anja Panse, Zain Shaikh, Rolf Biehler, Niclas Schaper, Michael Liebendörfer, and Joachim Hilgert. “Consultation Phases in Mathematics Learning and Support Centres.” International Journal of Research in Undergraduate Mathematics Education 8, no. 1 (2021): 94–120. https://doi.org/10.1007/s40753-021-00154-9.","ama":"Schürmann M, Panse A, Shaikh Z, et al. Consultation Phases in Mathematics Learning and Support Centres. International Journal of Research in Undergraduate Mathematics Education. 2021;8(1):94-120. doi:10.1007/s40753-021-00154-9"},"_id":"35702","department":[{"_id":"363"},{"_id":"423"},{"_id":"91"},{"_id":"625"}],"user_id":"37888","keyword":["Education","Mathematics (miscellaneous)"],"language":[{"iso":"eng"}],"publication":"International Journal of Research in Undergraduate Mathematics Education","type":"journal_article","abstract":[{"text":"AbstractMathematics Learning Support Centres are becoming more and more common in higher education both internationally and in Germany. Whereas it is clear that their quality largely depends on a functioning interaction in consultations, little is known about how such consultations proceed in detail. On the basis of models from the literature and recorded support sessions (N = 36), we constructed a process model that divides consultations into four ideal–typical phases. In the individual consultations, forward or backward leaps occur, but overall the model seems to describe the data well. A high intercoder reliability shows that it can be applied consistently on real data by different researchers. An analysis of the consultations between students and tutors shows that both mainly work on past attempts or thoughts of the students to solve the exercise or problems and on concrete strategies to solve a problem within the session. In contrast, very little time is dedicated to summarizing and reflecting the solution. The data allows for a more in-depth discussion of what constitutes quality in advising processes and how it might be further explored. Practically, the model may structure support sessions and help in focussing on different goals in different phases.","lang":"eng"}],"status":"public"},{"language":[{"iso":"eng"}],"keyword":["Computer Science Applications","Human-Computer Interaction","Education","Mathematics (miscellaneous)"],"abstract":[{"lang":"eng","text":"AbstractThe range of teaching materials now available is becoming increasingly diverse. Despite this, however, the use and influence of textbooks in teaching still remains very high. When instructing reading comprehension, teachers often use textbooks as the basis for teaching in language lessons. Establishing a good match between textbooks and the skills to be acquired is therefore essential. In this paper, I investigate whether textbooks used in Austrian schools can adequately support the teaching of reading comprehension skills. Since reading comprehension is the basis for acquiring knowledge in all subjects, science textbooks are examined in addition to (German) language lesson textbooks. Thus, the content pages of four language textbooks and four science textbooks for fourth and sixth grade were analysed in terms of five different categories, i.e. general structural setup, learning goals, text types, text structures, and activities. The results reveal clear variations with respect to learning goals in language textbooks. For example, the extent to which reading comprehension is addressed ranges from 13.64 to 69.70%, depending on the book used. Although not addressed as a learning goal in the science textbooks, reading comprehension is often presupposed, especially in sixth grade. While the instruction of reading comprehension ought to entail coverage of reading strategies, this is often neglected, or only dealt with indirectly. Given the diversity of textbooks analysed, it seems all the more important to stress that teachers should: 1) clarify the goals and teaching strategies of a book before using it, 2) become aware of strategies that support the development of students' reading comprehension, and 3) use textbooks as a complementary (and not sole) tool to support reading comprehension in all subjects."}],"publication":"Technology, Knowledge and Learning","title":"Is Reading Comprehension Taken for Granted? An Analysis of Austrian Textbooks in Fourth and Sixth Grade","date_created":"2023-01-18T16:10:52Z","publisher":"Springer Science and Business Media LLC","year":"2021","issue":"2","department":[{"_id":"645"}],"user_id":"97270","_id":"37443","status":"public","type":"journal_article","doi":"10.1007/s10758-021-09490-w","volume":26,"author":[{"first_name":"Susanne","id":"97270","full_name":"Seifert, Susanne","last_name":"Seifert"}],"date_updated":"2023-01-18T16:45:42Z","page":"383-405","intvolume":" 26","citation":{"chicago":"Seifert, Susanne. “Is Reading Comprehension Taken for Granted? An Analysis of Austrian Textbooks in Fourth and Sixth Grade.” Technology, Knowledge and Learning 26, no. 2 (2021): 383–405. https://doi.org/10.1007/s10758-021-09490-w.","ieee":"S. Seifert, “Is Reading Comprehension Taken for Granted? An Analysis of Austrian Textbooks in Fourth and Sixth Grade,” Technology, Knowledge and Learning, vol. 26, no. 2, pp. 383–405, 2021, doi: 10.1007/s10758-021-09490-w.","ama":"Seifert S. Is Reading Comprehension Taken for Granted? An Analysis of Austrian Textbooks in Fourth and Sixth Grade. Technology, Knowledge and Learning. 2021;26(2):383-405. doi:10.1007/s10758-021-09490-w","mla":"Seifert, Susanne. “Is Reading Comprehension Taken for Granted? An Analysis of Austrian Textbooks in Fourth and Sixth Grade.” Technology, Knowledge and Learning, vol. 26, no. 2, Springer Science and Business Media LLC, 2021, pp. 383–405, doi:10.1007/s10758-021-09490-w.","bibtex":"@article{Seifert_2021, title={Is Reading Comprehension Taken for Granted? An Analysis of Austrian Textbooks in Fourth and Sixth Grade}, volume={26}, DOI={10.1007/s10758-021-09490-w}, number={2}, journal={Technology, Knowledge and Learning}, publisher={Springer Science and Business Media LLC}, author={Seifert, Susanne}, year={2021}, pages={383–405} }","short":"S. Seifert, Technology, Knowledge and Learning 26 (2021) 383–405.","apa":"Seifert, S. (2021). Is Reading Comprehension Taken for Granted? An Analysis of Austrian Textbooks in Fourth and Sixth Grade. Technology, Knowledge and Learning, 26(2), 383–405. https://doi.org/10.1007/s10758-021-09490-w"},"publication_identifier":{"issn":["2211-1662","2211-1670"]},"publication_status":"published"},{"user_id":"31496","_id":"53333","language":[{"iso":"eng"}],"keyword":["Mathematics (miscellaneous)","Theoretical Computer Science"],"publication":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","type":"journal_article","status":"public","date_created":"2024-04-07T12:45:49Z","author":[{"first_name":"Michael","full_name":"Winkler, Michael","id":"31496","last_name":"Winkler"}],"publisher":"Scuola Normale Superiore - Edizioni della Normale","date_updated":"2025-12-18T20:15:27Z","doi":"10.2422/2036-2145.202005_016","title":"$L^1$ solutions to parabolic Keller-Segel systems involving arbitrary superlinear degradation","publication_identifier":{"issn":["2036-2145","0391-173X"]},"publication_status":"published","page":"141-172","citation":{"ieee":"M. Winkler, “$L^1$ solutions to parabolic Keller-Segel systems involving arbitrary superlinear degradation,” ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, pp. 141–172, 2021, doi: 10.2422/2036-2145.202005_016.","chicago":"Winkler, Michael. “$L^1$ Solutions to Parabolic Keller-Segel Systems Involving Arbitrary Superlinear Degradation.” ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2021, 141–72. https://doi.org/10.2422/2036-2145.202005_016.","ama":"Winkler M. $L^1$ solutions to parabolic Keller-Segel systems involving arbitrary superlinear degradation. ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE. Published online 2021:141-172. doi:10.2422/2036-2145.202005_016","short":"M. Winkler, ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (2021) 141–172.","bibtex":"@article{Winkler_2021, title={$L^1$ solutions to parabolic Keller-Segel systems involving arbitrary superlinear degradation}, DOI={10.2422/2036-2145.202005_016}, journal={ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE}, publisher={Scuola Normale Superiore - Edizioni della Normale}, author={Winkler, Michael}, year={2021}, pages={141–172} }","mla":"Winkler, Michael. “$L^1$ Solutions to Parabolic Keller-Segel Systems Involving Arbitrary Superlinear Degradation.” ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, Scuola Normale Superiore - Edizioni della Normale, 2021, pp. 141–72, doi:10.2422/2036-2145.202005_016.","apa":"Winkler, M. (2021). $L^1$ solutions to parabolic Keller-Segel systems involving arbitrary superlinear degradation. ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 141–172. https://doi.org/10.2422/2036-2145.202005_016"},"year":"2021"},{"user_id":"23686","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"_id":"34665","type":"journal_article","status":"public","author":[{"id":"23686","full_name":"Black, Tobias","orcid":"0000-0001-9963-0800","last_name":"Black","first_name":"Tobias"},{"first_name":"Johannes","full_name":"Lankeit, Johannes","last_name":"Lankeit"},{"first_name":"Masaaki","full_name":"Mizukami, Masaaki","last_name":"Mizukami"}],"volume":18,"date_updated":"2022-12-21T10:05:25Z","doi":"10.1007/s00028-017-0411-5","publication_status":"published","publication_identifier":{"issn":["1424-3199","1424-3202"]},"citation":{"ama":"Black T, Lankeit J, Mizukami M. Singular sensitivity in a Keller–Segel-fluid system. Journal of Evolution Equations. 2017;18(2):561-581. doi:10.1007/s00028-017-0411-5","ieee":"T. Black, J. Lankeit, and M. Mizukami, “Singular sensitivity in a Keller–Segel-fluid system,” Journal of Evolution Equations, vol. 18, no. 2, pp. 561–581, 2017, doi: 10.1007/s00028-017-0411-5.","chicago":"Black, Tobias, Johannes Lankeit, and Masaaki Mizukami. “Singular Sensitivity in a Keller–Segel-Fluid System.” Journal of Evolution Equations 18, no. 2 (2017): 561–81. https://doi.org/10.1007/s00028-017-0411-5.","mla":"Black, Tobias, et al. “Singular Sensitivity in a Keller–Segel-Fluid System.” Journal of Evolution Equations, vol. 18, no. 2, Springer Science and Business Media LLC, 2017, pp. 561–81, doi:10.1007/s00028-017-0411-5.","short":"T. Black, J. Lankeit, M. Mizukami, Journal of Evolution Equations 18 (2017) 561–581.","bibtex":"@article{Black_Lankeit_Mizukami_2017, title={Singular sensitivity in a Keller–Segel-fluid system}, volume={18}, DOI={10.1007/s00028-017-0411-5}, number={2}, journal={Journal of Evolution Equations}, publisher={Springer Science and Business Media LLC}, author={Black, Tobias and Lankeit, Johannes and Mizukami, Masaaki}, year={2017}, pages={561–581} }","apa":"Black, T., Lankeit, J., & Mizukami, M. (2017). Singular sensitivity in a Keller–Segel-fluid system. Journal of Evolution Equations, 18(2), 561–581. https://doi.org/10.1007/s00028-017-0411-5"},"page":"561-581","intvolume":" 18","language":[{"iso":"eng"}],"keyword":["Mathematics (miscellaneous)"],"publication":"Journal of Evolution Equations","date_created":"2022-12-21T09:47:13Z","publisher":"Springer Science and Business Media LLC","title":"Singular sensitivity in a Keller–Segel-fluid system","issue":"2","year":"2017"},{"_id":"34886","user_id":"93826","department":[{"_id":"102"}],"type":"journal_article","status":"public","date_updated":"2023-03-06T09:50:37Z","author":[{"last_name":"Fouvry","full_name":"Fouvry, Étienne","first_name":"Étienne"},{"id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners","first_name":"Jürgen"}],"volume":172,"doi":"10.4007/annals.2010.172.2035","publication_status":"published","publication_identifier":{"issn":["0003-486X"]},"citation":{"chicago":"Fouvry, Étienne, and Jürgen Klüners. “On the Negative Pell Equation.” Annals of Mathematics 172, no. 3 (2010): 2035–2104. https://doi.org/10.4007/annals.2010.172.2035.","ieee":"É. Fouvry and J. Klüners, “On the negative Pell equation,” Annals of Mathematics, vol. 172, no. 3, pp. 2035–2104, 2010, doi: 10.4007/annals.2010.172.2035.","ama":"Fouvry É, Klüners J. On the negative Pell equation. Annals of Mathematics. 2010;172(3):2035-2104. doi:10.4007/annals.2010.172.2035","bibtex":"@article{Fouvry_Klüners_2010, title={On the negative Pell equation}, volume={172}, DOI={10.4007/annals.2010.172.2035}, number={3}, journal={Annals of Mathematics}, publisher={Annals of Mathematics}, author={Fouvry, Étienne and Klüners, Jürgen}, year={2010}, pages={2035–2104} }","short":"É. Fouvry, J. Klüners, Annals of Mathematics 172 (2010) 2035–2104.","mla":"Fouvry, Étienne, and Jürgen Klüners. “On the Negative Pell Equation.” Annals of Mathematics, vol. 172, no. 3, Annals of Mathematics, 2010, pp. 2035–104, doi:10.4007/annals.2010.172.2035.","apa":"Fouvry, É., & Klüners, J. (2010). On the negative Pell equation. Annals of Mathematics, 172(3), 2035–2104. https://doi.org/10.4007/annals.2010.172.2035"},"intvolume":" 172","page":"2035-2104","keyword":["Statistics","Probability and Uncertainty","Mathematics (miscellaneous)"],"language":[{"iso":"eng"}],"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"}],"publisher":"Annals of Mathematics","date_created":"2022-12-23T09:09:02Z","title":"On the negative Pell equation","issue":"3","year":"2010"}]