Determinant (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Determinant" in English language version.

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16doi.org

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8ams.org

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7arxiv.org

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5web.archive.org

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3jstor.org

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3semanticscholar.org

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2archive.org

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2archives-ouvertes.fr

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2tripod.com

549^th place

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2worldcat.org

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1gatech.edu

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1ic.ac.uk

low place

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1nova.edu

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1mathoverflow.net

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1harvard.edu

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1uoregon.edu

3,144^th place

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1zbmath.org

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1st-and.ac.uk

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1xaktly.com

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1books.google.com

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1handle.net

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1fu-berlin.de

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1ens-lyon.fr

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1academia.edu

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academia.edu (Global: 121^st place; English: 142^nd place)

Abeles, Francine F. (2008). "Dodgson condensation: The historical and mathematical development of an experimental method". Linear Algebra and Its Applications. 429 (2–3): 429–438. doi:10.1016/j.laa.2007.11.022.

ams.org (Global: 451^st place; English: 277^th place)

mathscinet.ams.org

Eves 1990, p. 405 Eves, Howard (1990), An introduction to the history of mathematics (6 ed.), Saunders College Publishing, ISBN 0-03-029558-0, MR 1104435
Kleiner 2007, p. 80 Kleiner, Israel (2007), Kleiner, Israel (ed.), A History of Abstract Algebra, Birkhäuser, doi:10.1007/978-0-8176-4685-1, ISBN 978-0-8176-4684-4, MR 2347309
Kleiner 2007, §5.2 Kleiner, Israel (2007), Kleiner, Israel (ed.), A History of Abstract Algebra, Birkhäuser, doi:10.1007/978-0-8176-4685-1, ISBN 978-0-8176-4684-4, MR 2347309
Eves 1990, p. 494 Eves, Howard (1990), An introduction to the history of mathematics (6 ed.), Saunders College Publishing, ISBN 0-03-029558-0, MR 1104435
Cajori 1993, Vol. II, p. 92, no. 462 Cajori, Florian (1993), A history of mathematical notations: Including Vol. I. Notations in elementary mathematics; Vol. II. Notations mainly in higher mathematics, Reprint of the 1928 and 1929 originals, Dover, ISBN 0-486-67766-4, MR 3363427
Garibaldi 2004 Garibaldi, Skip (2004), "The characteristic polynomial and determinant are not ad hoc constructions", American Mathematical Monthly, 111 (9): 761–778, arXiv:math/0203276, doi:10.2307/4145188, JSTOR 4145188, MR 2104048
Rote 2001 Rote, Günter (2001), "Division-free algorithms for the determinant and the Pfaffian: algebraic and combinatorial approaches" (PDF), Computational discrete mathematics, Lecture Notes in Comput. Sci., vol. 2122, Springer, pp. 119–135, doi:10.1007/3-540-45506-X_9, ISBN 978-3-540-42775-9, MR 1911585, archived from the original (PDF) on 2007-02-01, retrieved 2020-06-04

ams.org

Fisikopoulos & Peñaranda 2016, §1.1, Bareiss 1968 Fisikopoulos, Vissarion; Peñaranda, Luis (2016), "Faster geometric algorithms via dynamic determinant computation", Computational Geometry, 54: 1–16, arXiv:1206.7067, doi:10.1016/j.comgeo.2015.12.001 Bareiss, Erwin (1968), "Sylvester's Identity and Multistep Integer-Preserving Gaussian Elimination" (PDF), Mathematics of Computation, 22 (102): 565–578, doi:10.2307/2004533, JSTOR 2004533, archived (PDF) from the original on 2012-10-25

archive.org (Global: 6^th place; English: 6^th place)

McConnell (1957). Applications of Tensor Analysis. Dover Publications. pp. 10–17.
Cajori, F. A History of Mathematics p. 80

archives-ouvertes.fr (Global: 1,031^st place; English: 879^th place)

hal.archives-ouvertes.fr

Silvester, J. R. (2000). "Determinants of Block Matrices". Math. Gaz. 84 (501): 460–467. doi:10.2307/3620776. JSTOR 3620776. S2CID 41879675.
Habgood & Arel 2012 Habgood, Ken; Arel, Itamar (2012). "A condensation-based application of Cramer's rule for solving large-scale linear systems" (PDF). Journal of Discrete Algorithms. 10: 98–109. doi:10.1016/j.jda.2011.06.007. Archived (PDF) from the original on 2019-05-05.

arxiv.org (Global: 69^th place; English: 59^th place)

Sothanaphan, Nat (January 2017). "Determinants of block matrices with noncommuting blocks". Linear Algebra and Its Applications. 512: 202–218. arXiv:1805.06027. doi:10.1016/j.laa.2016.10.004. S2CID 119272194.
Lin, Minghua; Sra, Suvrit (2014). "Completely strong superadditivity of generalized matrix functions". arXiv:1410.1958 [math.FA].
Garibaldi 2004 Garibaldi, Skip (2004), "The characteristic polynomial and determinant are not ad hoc constructions", American Mathematical Monthly, 111 (9): 761–778, arXiv:math/0203276, doi:10.2307/4145188, JSTOR 4145188, MR 2104048
Fisikopoulos & Peñaranda 2016, §1.1, §4.3 Fisikopoulos, Vissarion; Peñaranda, Luis (2016), "Faster geometric algorithms via dynamic determinant computation", Computational Geometry, 54: 1–16, arXiv:1206.7067, doi:10.1016/j.comgeo.2015.12.001
Camarero, Cristóbal (2018-12-05). "Simple, Fast and Practicable Algorithms for Cholesky, LU and QR Decomposition Using Fast Rectangular Matrix Multiplication". arXiv:1812.02056 [cs.NA].
Fisikopoulos & Peñaranda 2016, §1.1 Fisikopoulos, Vissarion; Peñaranda, Luis (2016), "Faster geometric algorithms via dynamic determinant computation", Computational Geometry, 54: 1–16, arXiv:1206.7067, doi:10.1016/j.comgeo.2015.12.001
Fisikopoulos & Peñaranda 2016, §1.1, Bareiss 1968 Fisikopoulos, Vissarion; Peñaranda, Luis (2016), "Faster geometric algorithms via dynamic determinant computation", Computational Geometry, 54: 1–16, arXiv:1206.7067, doi:10.1016/j.comgeo.2015.12.001 Bareiss, Erwin (1968), "Sylvester's Identity and Multistep Integer-Preserving Gaussian Elimination" (PDF), Mathematics of Computation, 22 (102): 565–578, doi:10.2307/2004533, JSTOR 2004533, archived (PDF) from the original on 2012-10-25

books.google.com (Global: 3^rd place; English: 3^rd place)

Varadarajan, V. S (2004), Supersymmetry for mathematicians: An introduction, American Mathematical Soc., ISBN 978-0-8218-3574-6.

doi.org (Global: 2^nd place; English: 2^nd place)

Silvester, J. R. (2000). "Determinants of Block Matrices". Math. Gaz. 84 (501): 460–467. doi:10.2307/3620776. JSTOR 3620776. S2CID 41879675.
Sothanaphan, Nat (January 2017). "Determinants of block matrices with noncommuting blocks". Linear Algebra and Its Applications. 512: 202–218. arXiv:1805.06027. doi:10.1016/j.laa.2016.10.004. S2CID 119272194.
Paksoy; Turkmen; Zhang (2014). "Inequalities of Generalized Matrix Functions via Tensor Products". Electronic Journal of Linear Algebra. 27: 332–341. doi:10.13001/1081-3810.1622.
A proof can be found in the Appendix B of Kondratyuk, L. A.; Krivoruchenko, M. I. (1992). "Superconducting quark matter in SU(2) color group". Zeitschrift für Physik A. 344 (1): 99–115. Bibcode:1992ZPhyA.344...99K. doi:10.1007/BF01291027. S2CID 120467300.
Kleiner 2007, p. 80 Kleiner, Israel (2007), Kleiner, Israel (ed.), A History of Abstract Algebra, Birkhäuser, doi:10.1007/978-0-8176-4685-1, ISBN 978-0-8176-4684-4, MR 2347309
Bourbaki (1994, p. 59) Bourbaki, Nicolas (1994), Elements of the history of mathematics, translated by Meldrum, John, Springer, doi:10.1007/978-3-642-61693-8, ISBN 3-540-19376-6
Kleiner 2007, §5.2 Kleiner, Israel (2007), Kleiner, Israel (ed.), A History of Abstract Algebra, Birkhäuser, doi:10.1007/978-0-8176-4685-1, ISBN 978-0-8176-4684-4, MR 2347309
Habgood & Arel 2012 Habgood, Ken; Arel, Itamar (2012). "A condensation-based application of Cramer's rule for solving large-scale linear systems" (PDF). Journal of Discrete Algorithms. 10: 98–109. doi:10.1016/j.jda.2011.06.007. Archived (PDF) from the original on 2019-05-05.
Garibaldi 2004 Garibaldi, Skip (2004), "The characteristic polynomial and determinant are not ad hoc constructions", American Mathematical Monthly, 111 (9): 761–778, arXiv:math/0203276, doi:10.2307/4145188, JSTOR 4145188, MR 2104048
Fisikopoulos & Peñaranda 2016, §1.1, §4.3 Fisikopoulos, Vissarion; Peñaranda, Luis (2016), "Faster geometric algorithms via dynamic determinant computation", Computational Geometry, 54: 1–16, arXiv:1206.7067, doi:10.1016/j.comgeo.2015.12.001
Bunch & Hopcroft 1974 Bunch, J. R.; Hopcroft, J. E. (1974). "Triangular Factorization and Inversion by Fast Matrix Multiplication". Mathematics of Computation. 28 (125): 231–236. doi:10.1090/S0025-5718-1974-0331751-8. hdl:1813/6003.
Fisikopoulos & Peñaranda 2016, §1.1 Fisikopoulos, Vissarion; Peñaranda, Luis (2016), "Faster geometric algorithms via dynamic determinant computation", Computational Geometry, 54: 1–16, arXiv:1206.7067, doi:10.1016/j.comgeo.2015.12.001
Rote 2001 Rote, Günter (2001), "Division-free algorithms for the determinant and the Pfaffian: algebraic and combinatorial approaches" (PDF), Computational discrete mathematics, Lecture Notes in Comput. Sci., vol. 2122, Springer, pp. 119–135, doi:10.1007/3-540-45506-X_9, ISBN 978-3-540-42775-9, MR 1911585, archived from the original (PDF) on 2007-02-01, retrieved 2020-06-04
Fang, Xin Gui; Havas, George (1997). "On the worst-case complexity of integer Gaussian elimination" (PDF). Proceedings of the 1997 international symposium on Symbolic and algebraic computation. ISSAC '97. Kihei, Maui, Hawaii, United States: ACM. pp. 28–31. doi:10.1145/258726.258740. ISBN 0-89791-875-4. Archived from the original (PDF) on 2011-08-07. Retrieved 2011-01-22.
Fisikopoulos & Peñaranda 2016, §1.1, Bareiss 1968 Fisikopoulos, Vissarion; Peñaranda, Luis (2016), "Faster geometric algorithms via dynamic determinant computation", Computational Geometry, 54: 1–16, arXiv:1206.7067, doi:10.1016/j.comgeo.2015.12.001 Bareiss, Erwin (1968), "Sylvester's Identity and Multistep Integer-Preserving Gaussian Elimination" (PDF), Mathematics of Computation, 22 (102): 565–578, doi:10.2307/2004533, JSTOR 2004533, archived (PDF) from the original on 2012-10-25
Abeles, Francine F. (2008). "Dodgson condensation: The historical and mathematical development of an experimental method". Linear Algebra and Its Applications. 429 (2–3): 429–438. doi:10.1016/j.laa.2007.11.022.

ens-lyon.fr (Global: 6,599^th place; English: low place)

perso.ens-lyon.fr

Fang, Xin Gui; Havas, George (1997). "On the worst-case complexity of integer Gaussian elimination" (PDF). Proceedings of the 1997 international symposium on Symbolic and algebraic computation. ISSAC '97. Kihei, Maui, Hawaii, United States: ACM. pp. 28–31. doi:10.1145/258726.258740. ISBN 0-89791-875-4. Archived from the original (PDF) on 2011-08-07. Retrieved 2011-01-22.

fu-berlin.de (Global: 3,329^th place; English: 4,598^th place)

page.inf.fu-berlin.de

Rote 2001 Rote, Günter (2001), "Division-free algorithms for the determinant and the Pfaffian: algebraic and combinatorial approaches" (PDF), Computational discrete mathematics, Lecture Notes in Comput. Sci., vol. 2122, Springer, pp. 119–135, doi:10.1007/3-540-45506-X_9, ISBN 978-3-540-42775-9, MR 1911585, archived from the original (PDF) on 2007-02-01, retrieved 2020-06-04

gatech.edu (Global: 4,448^th place; English: 2,923^rd place)

textbooks.math.gatech.edu

"Determinants and Volumes". textbooks.math.gatech.edu. Retrieved 16 March 2018.

handle.net (Global: 102^nd place; English: 76^th place)

hdl.handle.net

Bunch & Hopcroft 1974 Bunch, J. R.; Hopcroft, J. E. (1974). "Triangular Factorization and Inversion by Fast Matrix Multiplication". Mathematics of Computation. 28 (125): 231–236. doi:10.1090/S0025-5718-1974-0331751-8. hdl:1813/6003.

harvard.edu (Global: 18^th place; English: 17^th place)

ui.adsabs.harvard.edu

A proof can be found in the Appendix B of Kondratyuk, L. A.; Krivoruchenko, M. I. (1992). "Superconducting quark matter in SU(2) color group". Zeitschrift für Physik A. 344 (1): 99–115. Bibcode:1992ZPhyA.344...99K. doi:10.1007/BF01291027. S2CID 120467300.

ic.ac.uk (Global: low place; English: 9,602^nd place)

ee.ic.ac.uk

Proofs can be found in http://www.ee.ic.ac.uk/hp/staff/dmb/matrix/proof003.html

jstor.org (Global: 26^th place; English: 20^th place)

Silvester, J. R. (2000). "Determinants of Block Matrices". Math. Gaz. 84 (501): 460–467. doi:10.2307/3620776. JSTOR 3620776. S2CID 41879675.
Garibaldi 2004 Garibaldi, Skip (2004), "The characteristic polynomial and determinant are not ad hoc constructions", American Mathematical Monthly, 111 (9): 761–778, arXiv:math/0203276, doi:10.2307/4145188, JSTOR 4145188, MR 2104048
Fisikopoulos & Peñaranda 2016, §1.1, Bareiss 1968 Fisikopoulos, Vissarion; Peñaranda, Luis (2016), "Faster geometric algorithms via dynamic determinant computation", Computational Geometry, 54: 1–16, arXiv:1206.7067, doi:10.1016/j.comgeo.2015.12.001 Bareiss, Erwin (1968), "Sylvester's Identity and Multistep Integer-Preserving Gaussian Elimination" (PDF), Mathematics of Computation, 22 (102): 565–578, doi:10.2307/2004533, JSTOR 2004533, archived (PDF) from the original on 2012-10-25

mathoverflow.net (Global: low place; English: low place)

Serre, Denis (Oct 18, 2010). "Concavity of det^¹/_n over HPD_n". MathOverflow.

nova.edu (Global: low place; English: low place)

nsuworks.nova.edu

Paksoy; Turkmen; Zhang (2014). "Inequalities of Generalized Matrix Functions via Tensor Products". Electronic Journal of Linear Algebra. 27: 332–341. doi:10.13001/1081-3810.1622.

semanticscholar.org (Global: 11^th place; English: 8^th place)

api.semanticscholar.org

Silvester, J. R. (2000). "Determinants of Block Matrices". Math. Gaz. 84 (501): 460–467. doi:10.2307/3620776. JSTOR 3620776. S2CID 41879675.
Sothanaphan, Nat (January 2017). "Determinants of block matrices with noncommuting blocks". Linear Algebra and Its Applications. 512: 202–218. arXiv:1805.06027. doi:10.1016/j.laa.2016.10.004. S2CID 119272194.
A proof can be found in the Appendix B of Kondratyuk, L. A.; Krivoruchenko, M. I. (1992). "Superconducting quark matter in SU(2) color group". Zeitschrift für Physik A. 344 (1): 99–115. Bibcode:1992ZPhyA.344...99K. doi:10.1007/BF01291027. S2CID 120467300.

st-and.ac.uk (Global: 3,503^rd place; English: 3,612^th place)

www-history.mcs.st-and.ac.uk

History of matrices and determinants: http://www-history.mcs.st-and.ac.uk/history/HistTopics/Matrices_and_determinants.html

tripod.com (Global: 549^th place; English: 491^st place)

jeff560.tripod.com

Origins of mathematical terms: http://jeff560.tripod.com/d.html
History of matrix notation: http://jeff560.tripod.com/matrices.html

uoregon.edu (Global: 3,144^th place; English: 2,101^st place)

darkwing.uoregon.edu

A Brief History of Linear Algebra and Matrix Theory at: "A Brief History of Linear Algebra and Matrix Theory". Archived from the original on 10 September 2012. Retrieved 24 January 2012.

web.archive.org (Global: 1^st place; English: 1^st place)

A Brief History of Linear Algebra and Matrix Theory at: "A Brief History of Linear Algebra and Matrix Theory". Archived from the original on 10 September 2012. Retrieved 24 January 2012.
Habgood & Arel 2012 Habgood, Ken; Arel, Itamar (2012). "A condensation-based application of Cramer's rule for solving large-scale linear systems" (PDF). Journal of Discrete Algorithms. 10: 98–109. doi:10.1016/j.jda.2011.06.007. Archived (PDF) from the original on 2019-05-05.
Rote 2001 Rote, Günter (2001), "Division-free algorithms for the determinant and the Pfaffian: algebraic and combinatorial approaches" (PDF), Computational discrete mathematics, Lecture Notes in Comput. Sci., vol. 2122, Springer, pp. 119–135, doi:10.1007/3-540-45506-X_9, ISBN 978-3-540-42775-9, MR 1911585, archived from the original (PDF) on 2007-02-01, retrieved 2020-06-04
Fang, Xin Gui; Havas, George (1997). "On the worst-case complexity of integer Gaussian elimination" (PDF). Proceedings of the 1997 international symposium on Symbolic and algebraic computation. ISSAC '97. Kihei, Maui, Hawaii, United States: ACM. pp. 28–31. doi:10.1145/258726.258740. ISBN 0-89791-875-4. Archived from the original (PDF) on 2011-08-07. Retrieved 2011-01-22.
Fisikopoulos & Peñaranda 2016, §1.1, Bareiss 1968 Fisikopoulos, Vissarion; Peñaranda, Luis (2016), "Faster geometric algorithms via dynamic determinant computation", Computational Geometry, 54: 1–16, arXiv:1206.7067, doi:10.1016/j.comgeo.2015.12.001 Bareiss, Erwin (1968), "Sylvester's Identity and Multistep Integer-Preserving Gaussian Elimination" (PDF), Mathematics of Computation, 22 (102): 565–578, doi:10.2307/2004533, JSTOR 2004533, archived (PDF) from the original on 2012-10-25

worldcat.org (Global: 5^th place; English: 5^th place)

search.worldcat.org

Dummit & Foote 2004, §11.4 Dummit, David S.; Foote, Richard M. (2004), Abstract algebra (3rd ed.), Hoboken, NJ: Wiley, ISBN 9780471452348, OCLC 248917264
Dummit & Foote 2004, §11.4, Theorem 30 Dummit, David S.; Foote, Richard M. (2004), Abstract algebra (3rd ed.), Hoboken, NJ: Wiley, ISBN 9780471452348, OCLC 248917264

xaktly.com (Global: low place; English: low place)

Dr. Jeff Cruza. "Triangle area".

zbmath.org (Global: 1,923^rd place; English: 1,068^th place)

Muir, Sir Thomas, The Theory of Determinants in the historical Order of Development [London, England: Macmillan and Co., Ltd., 1906]. JFM 37.0181.02

Determinant (English Wikipedia)

academia.edu (Global: 121st place; English: 142nd place)

ams.org (Global: 451st place; English: 277th place)

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ams.org

archive.org (Global: 6th place; English: 6th place)

archives-ouvertes.fr (Global: 1,031st place; English: 879th place)

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arxiv.org (Global: 69th place; English: 59th place)

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doi.org (Global: 2nd place; English: 2nd place)

ens-lyon.fr (Global: 6,599th place; English: low place)

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fu-berlin.de (Global: 3,329th place; English: 4,598th place)

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gatech.edu (Global: 4,448th place; English: 2,923rd place)

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handle.net (Global: 102nd place; English: 76th place)

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harvard.edu (Global: 18th place; English: 17th place)

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ic.ac.uk (Global: low place; English: 9,602nd place)

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jstor.org (Global: 26th place; English: 20th place)

mathoverflow.net (Global: low place; English: low place)

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semanticscholar.org (Global: 11th place; English: 8th place)

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st-and.ac.uk (Global: 3,503rd place; English: 3,612th place)

www-history.mcs.st-and.ac.uk

tripod.com (Global: 549th place; English: 491st place)

jeff560.tripod.com

uoregon.edu (Global: 3,144th place; English: 2,101st place)

darkwing.uoregon.edu

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worldcat.org (Global: 5th place; English: 5th place)

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zbmath.org (Global: 1,923rd place; English: 1,068th place)

academia.edu (Global: 121^st place; English: 142^nd place)

ams.org (Global: 451^st place; English: 277^th place)

archive.org (Global: 6^th place; English: 6^th place)

archives-ouvertes.fr (Global: 1,031^st place; English: 879^th place)

arxiv.org (Global: 69^th place; English: 59^th place)

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doi.org (Global: 2^nd place; English: 2^nd place)

ens-lyon.fr (Global: 6,599^th place; English: low place)

fu-berlin.de (Global: 3,329^th place; English: 4,598^th place)

gatech.edu (Global: 4,448^th place; English: 2,923^rd place)

handle.net (Global: 102^nd place; English: 76^th place)

harvard.edu (Global: 18^th place; English: 17^th place)

ic.ac.uk (Global: low place; English: 9,602^nd place)

jstor.org (Global: 26^th place; English: 20^th place)

semanticscholar.org (Global: 11^th place; English: 8^th place)

st-and.ac.uk (Global: 3,503^rd place; English: 3,612^th place)

tripod.com (Global: 549^th place; English: 491^st place)

uoregon.edu (Global: 3,144^th place; English: 2,101^st place)

web.archive.org (Global: 1^st place; English: 1^st place)

worldcat.org (Global: 5^th place; English: 5^th place)

zbmath.org (Global: 1,923^rd place; English: 1,068^th place)