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词条 Joseph Miller Thomas
释义

  1. Selected publications

     Articles  Books 

  2. References

Joseph Miller Thomas (16 January 1898 – 1979) was an American mathematician, known for the Thomas decomposition of algebraic and differential systems.[1]

Thomas received his Ph.D., supervised by Frederick Wahn Beal, from the University of Pennsylvania with thesis Congruences of Circles, Studied with reference to the Surface of Centers.[2] He was a mathematics professor at Duke University for many years. His graduate students include Mabel Griffin (later married to L. B. Reavis) and Ruth W. Stokes.[3] In 1935 he was one of the founders of the Duke Mathematical Journal. For the academic year 1936–1937 was a visiting scholar at the Institute for Advanced Study.[4]

Based upon earlier work by Charles Riquier and Maurice Janet, Thomas's research was important for the introduction of involutive bases.[5][6]

Selected publications

Articles

  • with Oswald Veblen: {{cite journal|title=Projective Normal Coördinates for the Geometry of Paths|journal=Proceedings of the National Academy of Sciences|pmid=16576871 | volume=11|issue=4|pmc=1085921|year=1925|pages=204–7|doi=10.1073/pnas.11.4.204|last1=Veblen|first1=O.|last2=Thomas|first2=J. M.}}
  • Note on the projective geometry of paths. Proceedings of the National Academy of Sciences 11, no. 4 (1925): 207–209.
  • The number of even and odd absolute permutations of n letters. Bull. Amer. Math. Soc. 31 (1925) 303–304. {{mr|1561049}}
  • Conformal correspondence of Riemann spaces. Proceedings of the National Academy of Sciences 11, no. 5 (1925): 257–259.
  • Conformal invariants. Proceedings of the National Academy of Sciences 12, no. 6 (1926): 389–393.
  • Asymmetric displacement of a vector. Trans. Amer. Math. Soc. 28 (1926) 658–670. {{mr|1501370}}
  • with Oswald Veblen: Projective invariants of affine geometry of paths. Annals of Mathematics 27 (1926): 279–296. {{doi|10.2307/1967848}}
  • Riquier's existence theorems. Annals of Mathematics 30 (1928): 285–310. {{doi|10.2307/1968282}}
  • Matrices of integers ordering derivatives. Trans. Amer. Math. Soc. 33 (1931) 389–410. {{mr|1501594}}
  • The condition for an orthonomic differential system. Trans. Amer. Math. Soc. 34 (1932) 332–338. {{mr|1501640}}
  • Pfaffian systems of species one. Trans. Amer. Math. Soc. 35 (1933) 356–371. {{mr|1501689}}
  • Riquier's existence theorems. Annals of Mathematics 35 (1934): 306–311. {{doi|10.2307/1968434}} (addendum to 1928 publication in Annals of Mathematics)
  • An existence theorem for generalized pfaffian systems. Bull. Amer. Math. Soc. 40 (1934) 309–315. {{mr|1562842}}
  • The condition for a pfaffian system in involution. Bull. Amer. Math. Soc. 40 (1934) 316–320. {{mr|1562843}}
  • Sturm's theorem for multiple roots. National Mathematics Magazine 15, no. 8 (1941): 391-394. {{jstor|3028551}}
  • Equations equivalent to a linear differential equation. Proc. Amer. Math. Soc. 3 (1952) 899–903. {{mr|0052001}}

Books

  • {{cite book|title=Differential systems|year=1937}}[7]
  • {{cite book|title=Theory of equations|publisher=McGraw-Hill|year=1938|postscript=; 211 pages}}
  • {{cite book|title=Elementary mathematics in artillery fire, by Joseph Miller Thomas with tables prepared by Vincent H. Haag|publisher=McGraw-Hill|year=1942|postscript=; 256 pages}}
  • {{cite book|title=Systems and roots|publisher=William Byrd Press|year=1962|postscript=; 123 pages}}
  • {{cite book|title=A primer on roots|publisher=William Byrd Press|year=1974|postscript=; 106 pages}}

References

1. ^[https://arxiv.org/abs/1008.3767 Thomas Decomposition of Algebraic and Differential Systems by Thomas Bächler, Vladimir Gerdt, Markus Lange-Hegermann, Daniel Robertz, 2010]
2. ^{{MathGenealogy|id=36219}}
3. ^{{cite book | first1 = Judy | last1 = Green | author1-link = Judy Green (mathematician) | first2 = Jeanne | last2 = LaDuke | author2-link = Jeanne LaDuke|title=Pioneering Women in American Mathematics: The Pre-1940 PhD's |year=2009 |publisher=American Mathematical Society |url=https://books.google.com/books?id=IRbOAwAAQBAJ| isbn = 9780821843765 }} (Griffin) Reavis and Stokes biographies on p.513-515 and p.580-582 of the [https://www.ams.org/bookpages/hmath-34-PioneeringWomen.pdf Supplementary Material] at [https://www.ams.org/publications/authors/books/postpub/hmath-34 AMS], respectively.
4. ^[https://www.ias.edu/scholars/joseph-miller-thomas Joseph Miller Thomas | Institute for Advanced Study]
5. ^{{cite book|author=Kondratieva, M. V.|title=Differential and Difference Dimension Polynomials|url=https://books.google.com/books?id=mwu2JgtnbY0C|year=1998|publisher=Springer Science & Business Media|isbn=978-0-7923-5484-0|page=ix (preface)}}
6. ^{{cite journal|author=Astrelin, A. V.|author2=Golubitsky, O. D.|author3=Pankratiev, E. V.|year=2000|title=Involutive bases of ideals in the ring of polynomials|journal=Programming and Computer Software|volume=26|issue=1|pages=31–35|doi=10.1007/bf02759177}}
7. ^{{cite journal|author=Bochner, Salomon|authorlink=Salomon Bochner|title=Review: Differential systems by J. M. Thomas|journal=Bull. Amer. Math. Soc.|year=1938|volume=44|issue=5|pages=314–315|url=http://www.ams.org/journals/bull/1938-44-05/S0002-9904-1938-06724-9/S0002-9904-1938-06724-9.pdf|doi=10.1090/s0002-9904-1938-06724-9}}
{{Authority control}}{{DEFAULTSORT:Thomas, Joseph Miller}}

7 : 1898 births|1979 deaths|20th-century American mathematicians|PDE theorists|University of Pennsylvania alumni|Duke University faculty|Institute for Advanced Study visiting scholars
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