Τροπική γεωμετρία (Greek Wikipedia)

Analysis of information sources in references of the Wikipedia article "Τροπική γεωμετρία" in Greek language version.

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15wikipedia.org

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ams.org

Mikhalkin, Grigory (2005). «Enumerative tropical algebraic geometry in R²». Journal of the American Mathematical Society 18 (2): 313–377. doi:10.1090/S0894-0347-05-00477-7. http://www.ams.org/journals/jams/2005-18-02/S0894-0347-05-00477-7/S0894-0347-05-00477-7.pdf.
Katz, Eric (2017), «What is Tropical Geometry?», Notices of the American Mathematical Society 64 (4): 380–382, doi:10.1090/noti1507, https://www.ams.org/publications/journals/notices/201704/rnoti-p380.pdf

archives-ouvertes.fr

hal.archives-ouvertes.fr

Pin, Jean-Eric (1998). «Tropical semirings» (PDF). Στο: Gunawardena, J. Idempotency. Publications of the Newton Institute. 11. Cambridge University Press. σελίδες 50–69. doi:10.1017/CBO9780511662508.004. ISBN 9780511662508.

arxiv.org

Kontsevich, Maxim; Soibelman, Yan (2000-11-07). «Homological mirror symmetry and torus fibrations».
arXiv:math/0011041
.
Chan, Melody· Sturmfels, Bernd (2013). «Elliptic curves in honeycomb form». Στο: Brugallé, Erwan. Algebraic and combinatorial aspects of tropical geometry. Proceedings based on the CIEM workshop on tropical geometry, International Centre for Mathematical Meetings (CIEM), Castro Urdiales, Spain, December 12–16, 2011. Contemporary Mathematics. 589. Providence, RI: American Mathematical Society. σελίδες 87–107. arXiv:1203.2356 . Bibcode:2012arXiv1203.2356C. ISBN 978-0-8218-9146-9. Zbl 1312.14142.
Krivulin, Nikolai (2014). «Tropical optimization problems». Στο: Leon A. Petrosyan· David W. K. Yeung· Joseph V. Romanovsky. Advances in Economics and Optimization: Collected Scientific Studies Dedicated to the Memory of L. V. Kantorovich. New York: Nova Science Publishers. σελίδες 195–214. arXiv:1408.0313 . ISBN 978-1-63117-073-7.

berkeley.edu

math.berkeley.edu

Speyer, David; Sturmfels, Bernd (2009), «Tropical mathematics», Mathematics Magazine 82 (3): 163–173, doi:10.1080/0025570X.2009.11953615, https://math.berkeley.edu/~bernd/mathmag.pdf

doi.org

dx.doi.org

Maslov, Victor (1987). «On a new superposition principle for optimization problems». Russian Mathematical Surveys 42 (3): 43–54. doi:10.1070/RM1987v042n03ABEH001439. Bibcode: 1987RuMaS..42...43M.
Mikhalkin, Grigory (2005). «Enumerative tropical algebraic geometry in R²». Journal of the American Mathematical Society 18 (2): 313–377. doi:10.1090/S0894-0347-05-00477-7. http://www.ams.org/journals/jams/2005-18-02/S0894-0347-05-00477-7/S0894-0347-05-00477-7.pdf.
Speyer, David; Sturmfels, Bernd (2009), «Tropical mathematics», Mathematics Magazine 82 (3): 163–173, doi:10.1080/0025570X.2009.11953615, https://math.berkeley.edu/~bernd/mathmag.pdf
Katz, Eric (2017), «What is Tropical Geometry?», Notices of the American Mathematical Society 64 (4): 380–382, doi:10.1090/noti1507, https://www.ams.org/publications/journals/notices/201704/rnoti-p380.pdf
Cartwright, Dustin; Payne, Sam (2012), «Connectivity of tropicalizations», Mathematical Research Letters 19 (5): 1089–1095, doi:10.4310/MRL.2012.v19.n5.a10
Tabera, Luis Felipe (2005-01-01). «Tropical constructive Pappus' theorem» (στα αγγλικά). International Mathematics Research Notices 2005 (39): 2373–2389. doi:10.1155/IMRN.2005.2373. ISSN 1073-7928.
Kerber, Michael; Gathmann, Andreas (2008-05-01). «A Riemann–Roch theorem in tropical geometry» (στα αγγλικά). Mathematische Zeitschrift 259 (1): 217–230. doi:10.1007/s00209-007-0222-4. ISSN 1432-1823.
Shiozawa, Yoshinori (2015). «International trade theory and exotic algebras». Evolutionary and Institutional Economics Review 12: 177–212. doi:10.1007/s40844-015-0012-3. https://www.researchgate.net/publication/280646264. This is a digest of Y. Shiozawa, "Subtropical Convex Geometry as the Ricardian Theory of International Trade" draft paper.
Kalinin, N.; Guzmán-Sáenz, A.; Prieto, Y.; Shkolnikov, M.; Kalinina, V.; Lupercio, E. (2018-08-15). «Self-organized criticality and pattern emergence through the lens of tropical geometry» (στα αγγλικά). Proceedings of the National Academy of Sciences of the United States of America 115 (35): E8135–E8142. doi:10.1073/pnas.1805847115. ISSN 0027-8424. PMID 30111541. Bibcode: 2018PNAS..115E8135K.

doi.org

Pin, Jean-Eric (1998). «Tropical semirings» (PDF). Στο: Gunawardena, J. Idempotency. Publications of the Newton Institute. 11. Cambridge University Press. σελίδες 50–69. doi:10.1017/CBO9780511662508.004. ISBN 9780511662508.
Simon, Imre (1988). «Recognizable sets with multiplicities in the tropical semiring». Mathematical Foundations of Computer Science 1988. Lecture Notes in Computer Science. 324. σελίδες 107–120. doi:10.1007/BFb0017135. ISBN 978-3-540-50110-7.

harvard.edu

adsabs.harvard.edu

Maslov, Victor (1987). «On a new superposition principle for optimization problems». Russian Mathematical Surveys 42 (3): 43–54. doi:10.1070/RM1987v042n03ABEH001439. Bibcode: 1987RuMaS..42...43M.
Chan, Melody· Sturmfels, Bernd (2013). «Elliptic curves in honeycomb form». Στο: Brugallé, Erwan. Algebraic and combinatorial aspects of tropical geometry. Proceedings based on the CIEM workshop on tropical geometry, International Centre for Mathematical Meetings (CIEM), Castro Urdiales, Spain, December 12–16, 2011. Contemporary Mathematics. 589. Providence, RI: American Mathematical Society. σελίδες 87–107. arXiv:1203.2356 . Bibcode:2012arXiv1203.2356C. ISBN 978-0-8218-9146-9. Zbl 1312.14142.
Kalinin, N.; Guzmán-Sáenz, A.; Prieto, Y.; Shkolnikov, M.; Kalinina, V.; Lupercio, E. (2018-08-15). «Self-organized criticality and pattern emergence through the lens of tropical geometry» (στα αγγλικά). Proceedings of the National Academy of Sciences of the United States of America 115 (35): E8135–E8142. doi:10.1073/pnas.1805847115. ISSN 0027-8424. PMID 30111541. Bibcode: 2018PNAS..115E8135K.

mlr.press

proceedings.mlr.press

Zhang, Liwen; Naitzat, Gregory; Lim, Lek-Heng (2018). «Tropical Geometry of Deep Neural Networks». 35th International Conference on Machine Learning, pp. 5824–5832. http://proceedings.mlr.press/v80/zhang18i.html.

nih.gov

pubmedcentral.nih.gov

Kalinin, N.; Guzmán-Sáenz, A.; Prieto, Y.; Shkolnikov, M.; Kalinina, V.; Lupercio, E. (2018-08-15). «Self-organized criticality and pattern emergence through the lens of tropical geometry» (στα αγγλικά). Proceedings of the National Academy of Sciences of the United States of America 115 (35): E8135–E8142. doi:10.1073/pnas.1805847115. ISSN 0027-8424. PMID 30111541. Bibcode: 2018PNAS..115E8135K.

ncbi.nlm.nih.gov

Kalinin, N.; Guzmán-Sáenz, A.; Prieto, Y.; Shkolnikov, M.; Kalinina, V.; Lupercio, E. (2018-08-15). «Self-organized criticality and pattern emergence through the lens of tropical geometry» (στα αγγλικά). Proceedings of the National Academy of Sciences of the United States of America 115 (35): E8135–E8142. doi:10.1073/pnas.1805847115. ISSN 0027-8424. PMID 30111541. Bibcode: 2018PNAS..115E8135K.

ox.ac.uk

economics.ox.ac.uk

«How geometry came to the rescue during the banking crisis». Department of Economics, University of Oxford. Αρχειοθετήθηκε από το πρωτότυπο στις 24 Νοεμβρίου 2018. Ανακτήθηκε στις 24 Μαρτίου 2014.

quantamagazine.org

Hartnett, Kevin (5 Σεπτεμβρίου 2018). «Tinkertoy Models Produce New Geometric Insights». Quanta Magazine. Ανακτήθηκε στις 12 Δεκεμβρίου 2018.

researchgate.net

Shiozawa, Yoshinori (2015). «International trade theory and exotic algebras». Evolutionary and Institutional Economics Review 12: 177–212. doi:10.1007/s40844-015-0012-3. https://www.researchgate.net/publication/280646264. This is a digest of Y. Shiozawa, "Subtropical Convex Geometry as the Ricardian Theory of International Trade" draft paper.

web.archive.org

«How geometry came to the rescue during the banking crisis». Department of Economics, University of Oxford. Αρχειοθετήθηκε από το πρωτότυπο στις 24 Νοεμβρίου 2018. Ανακτήθηκε στις 24 Μαρτίου 2014.

wikipedia.org

en.wikipedia.org

Hartnett, Kevin (5 Σεπτεμβρίου 2018). «Tinkertoy Models Produce New Geometric Insights». Quanta Magazine. Ανακτήθηκε στις 12 Δεκεμβρίου 2018.
Maslov, Victor (1987). «On a new superposition principle for optimization problems». Russian Mathematical Surveys 42 (3): 43–54. doi:10.1070/RM1987v042n03ABEH001439. Bibcode: 1987RuMaS..42...43M.
Kontsevich, Maxim; Soibelman, Yan (2000-11-07). «Homological mirror symmetry and torus fibrations».
arXiv:math/0011041
.
Mikhalkin, Grigory (2005). «Enumerative tropical algebraic geometry in R²». Journal of the American Mathematical Society 18 (2): 313–377. doi:10.1090/S0894-0347-05-00477-7. http://www.ams.org/journals/jams/2005-18-02/S0894-0347-05-00477-7/S0894-0347-05-00477-7.pdf.
Simon, Imre (1988). «Recognizable sets with multiplicities in the tropical semiring». Mathematical Foundations of Computer Science 1988. Lecture Notes in Computer Science. 324. σελίδες 107–120. doi:10.1007/BFb0017135. ISBN 978-3-540-50110-7.
Speyer, David; Sturmfels, Bernd (2009), «Tropical mathematics», Mathematics Magazine 82 (3): 163–173, doi:10.1080/0025570X.2009.11953615, https://math.berkeley.edu/~bernd/mathmag.pdf
Maclagan, Diane· Sturmfels, Bernd (2015). Introduction to Tropical Geometry. American Mathematical Society. ISBN 9780821851982.
Mikhalkin, Grigory (2004). «Amoebas of algebraic varieties and tropical geometry». Στο: Donaldson, Simon· Eliashberg, Yakov· Gromov, Mikhael. Different faces of geometry. International Mathematical Series. 3. New York, NY: Kluwer Academic/Plenum Publishers. σελίδες 257–300. ISBN 978-0-306-48657-9. Zbl 1072.14013.
Katz, Eric (2017), «What is Tropical Geometry?», Notices of the American Mathematical Society 64 (4): 380–382, doi:10.1090/noti1507, https://www.ams.org/publications/journals/notices/201704/rnoti-p380.pdf
Tabera, Luis Felipe (2005-01-01). «Tropical constructive Pappus' theorem» (στα αγγλικά). International Mathematics Research Notices 2005 (39): 2373–2389. doi:10.1155/IMRN.2005.2373. ISSN 1073-7928.
Kerber, Michael; Gathmann, Andreas (2008-05-01). «A Riemann–Roch theorem in tropical geometry» (στα αγγλικά). Mathematische Zeitschrift 259 (1): 217–230. doi:10.1007/s00209-007-0222-4. ISSN 1432-1823.
Chan, Melody· Sturmfels, Bernd (2013). «Elliptic curves in honeycomb form». Στο: Brugallé, Erwan. Algebraic and combinatorial aspects of tropical geometry. Proceedings based on the CIEM workshop on tropical geometry, International Centre for Mathematical Meetings (CIEM), Castro Urdiales, Spain, December 12–16, 2011. Contemporary Mathematics. 589. Providence, RI: American Mathematical Society. σελίδες 87–107. arXiv:1203.2356 . Bibcode:2012arXiv1203.2356C. ISBN 978-0-8218-9146-9. Zbl 1312.14142.
Zhang, Liwen; Naitzat, Gregory; Lim, Lek-Heng (2018). «Tropical Geometry of Deep Neural Networks». 35th International Conference on Machine Learning, pp. 5824–5832. http://proceedings.mlr.press/v80/zhang18i.html.
Sunada, T. (2012). Topological Crystallography: With a View Towards Discrete Geometric Analysis. Surveys and Tutorials in the Applied Mathematical Sciences. 6. Springer Japan. ISBN 9784431541769.
Kalinin, N.; Guzmán-Sáenz, A.; Prieto, Y.; Shkolnikov, M.; Kalinina, V.; Lupercio, E. (2018-08-15). «Self-organized criticality and pattern emergence through the lens of tropical geometry» (στα αγγλικά). Proceedings of the National Academy of Sciences of the United States of America 115 (35): E8135–E8142. doi:10.1073/pnas.1805847115. ISSN 0027-8424. PMID 30111541. Bibcode: 2018PNAS..115E8135K.

worldcat.org

Tabera, Luis Felipe (2005-01-01). «Tropical constructive Pappus' theorem» (στα αγγλικά). International Mathematics Research Notices 2005 (39): 2373–2389. doi:10.1155/IMRN.2005.2373. ISSN 1073-7928.
Kerber, Michael; Gathmann, Andreas (2008-05-01). «A Riemann–Roch theorem in tropical geometry» (στα αγγλικά). Mathematische Zeitschrift 259 (1): 217–230. doi:10.1007/s00209-007-0222-4. ISSN 1432-1823.
Kalinin, N.; Guzmán-Sáenz, A.; Prieto, Y.; Shkolnikov, M.; Kalinina, V.; Lupercio, E. (2018-08-15). «Self-organized criticality and pattern emergence through the lens of tropical geometry» (στα αγγλικά). Proceedings of the National Academy of Sciences of the United States of America 115 (35): E8135–E8142. doi:10.1073/pnas.1805847115. ISSN 0027-8424. PMID 30111541. Bibcode: 2018PNAS..115E8135K.

zbmath.org

Mikhalkin, Grigory (2004). «Amoebas of algebraic varieties and tropical geometry». Στο: Donaldson, Simon· Eliashberg, Yakov· Gromov, Mikhael. Different faces of geometry. International Mathematical Series. 3. New York, NY: Kluwer Academic/Plenum Publishers. σελίδες 257–300. ISBN 978-0-306-48657-9. Zbl 1072.14013.
Chan, Melody· Sturmfels, Bernd (2013). «Elliptic curves in honeycomb form». Στο: Brugallé, Erwan. Algebraic and combinatorial aspects of tropical geometry. Proceedings based on the CIEM workshop on tropical geometry, International Centre for Mathematical Meetings (CIEM), Castro Urdiales, Spain, December 12–16, 2011. Contemporary Mathematics. 589. Providence, RI: American Mathematical Society. σελίδες 87–107. arXiv:1203.2356 . Bibcode:2012arXiv1203.2356C. ISBN 978-0-8218-9146-9. Zbl 1312.14142.