John Hilton Grace
John Hilton Grace (21 May 1873 - 4 March 1958) was a British mathematician.
Early life
He was born in Halewood, near Liverpool, the eldest of the six children of a farmer. He was educated at the village school and the Liverpool Institute. From there in 1892 he went up to Peterhouse College, Cambridge to study mathematics.[1]
Career
He was made a Fellow of Peterhouse in 1897 and became a Lecturer of Mathematics at Peterhouse and Pembroke colleges. An example of his work was his 1902 paper on the The Zeros of a Polynomial. In 1903 he collaborated with Alfred Young on their book Algebra of Invariants.[1]
He was elected a Fellow of the Royal Society in 1908.[1]
He spent 1916-1917 as Visiting Professor in Lahore and deputised for Professor MacDonald at Aberdeen University during the latter part of the war.[2]
In 1922 a breakdown in health forced his retirement from academic life and he spent the next part of his life in Norfolk.[1]
He died in Huntingdon in 1958 and was buried in the family grave at St. Nicholas Church, Halewood.
Theorem on zeros of a polynomial
If
- ,
are two polynomials that satisfy the apolarity condition, i.e. , then every neighborhood that includes all zeros of one polynomial also includes at least one zero of the other.[3][4]
Corollary
Let and be defined as in the above theorem. If the zeros of both polynomials lie in the unit disk, then the zeros of the "composition" of the two, , also lie in the unit disk.[3]
Publications
- Grace, J. H. (January 1936). "The actual irreducibility of some finite systems of invariant forms". Journal of the London Mathematical Society s1-11 (1): 20–21. doi:10.1112/jlms/s1-11.1.20. JFM 62.0075.02. Zbl 0013.14601. http://jlms.oxfordjournals.org/cgi/reprint/s1-11/1/20.
- Grace, J. H. (April 1930). "Two contract theorems". Journal of the London Mathematical Society s1-5 (2): 121–124. doi:10.1112/jlms/s1-5.2.121. http://jlms.oxfordjournals.org/cgi/reprint/s1-5/2/121.
- Grace, J. H. (January 1930). "The algebraic expression of projective properties". Journal of the London Mathematical Society s1-5 (1): 62–67. doi:10.1112/jlms/s1-5.1.62. http://jlms.oxfordjournals.org/cgi/reprint/s1-5/1/62.
- Grace, J. H. (1928). "Binary and ternary forms with prescribed polar systems". Proceedings of the London Mathematical Society s2-28 (1): 421–430. doi:10.1112/plms/s2-28.1.421. JFM 54.0133.03. http://plms.oxfordjournals.org/cgi/reprint/s2-28/1/421.
- Grace, J. H. (January 1928). "Surfaces related to a rational normal curve". Journal of the London Mathematical Society s1-3 (1): 34–38. doi:10.1112/jlms/s1-3.1.34. http://jlms.oxfordjournals.org/cgi/reprint/s1-3/1/34.
- Grace, J. H. (July 1927). "Note on ternary forms". Journal of the London Mathematical Society s1-2 (3): 182–185. doi:10.1112/jlms/s1-2.3.182. http://jlms.oxfordjournals.org/cgi/reprint/s1-2/3/182.
- Grace, J. H. (January 1927). "The four square theorem". Journal of the London Mathematical Society s1-2 (1): 3–8. doi:10.1112/jlms/s1-2.1.3. http://jlms.oxfordjournals.org/cgi/reprint/s1-2/1/3.
- Grace, J. H. (July 1926). "A point in enumerative geometry". Journal of the London Mathematical Society s1-1 (3): 167–170. doi:10.1112/jlms/s1-1.3.167. http://jlms.oxfordjournals.org/cgi/reprint/s1-1/3/167.
- Grace, J. H. (1918). "Note on a Diophantine approximation". Proceedings of the London Mathematical Society s2-17 (1): 316–319. doi:10.1112/plms/s2-17.1.316. http://plms.oxfordjournals.org/cgi/reprint/s2-17/1/316.
- Grace, J. H. (1918). "Tetrahedra in relation to spheres and quadrics". Proceedings of the London Mathematical Society s2-17 (1): 259–271. doi:10.1112/plms/s2-17.1.259. JFM 47.0612.01. http://plms.oxfordjournals.org/cgi/reprint/s2-17/1/259.
- Grace, J. H. (1918). "The classification of rational approximations". Proceedings of the London Mathematical Society s2-17 (1): 247–258. doi:10.1112/plms/s2-17.1.247. JFM 47.0166.01. http://plms.oxfordjournals.org/cgi/reprint/s2-17/1/247.
- Grace, J. H. (1904). "Note on the foregoing paper". Proceedings of the London Mathematical Society s2-1 (1): 208–209. doi:10.1112/plms/s2-1.1.208. http://plms.oxfordjournals.org/cgi/reprint/s2-1/1/208.
- Grace, J. H. (1904). "Extension of two theorems on covariants". Proceedings of the London Mathematical Society s2-1 (1): 151–153. doi:10.1112/plms/s2-1.1.151. JFM 34.0120.03. http://plms.oxfordjournals.org/cgi/reprint/s2-1/1/151.
- Grace, J. H.; A. Young (1903). The Algebra of Invariants. Cambridge University Press. http://books.google.com/?id=TrAAAAAAMAAJ.
- Grace, J. H.. "On the zeros of a polynomial". Proceedings of the Cambridge Philosophical Society 11: 352–357.
- Grace, J. H. (May 1902). "On perpetuants". Proceedings of the London Mathematical Society s1-35 (1): 319–331. doi:10.1112/plms/s1-35.1.319. http://plms.oxfordjournals.org/cgi/reprint/s1-35/1/319.
- Grace, J. H. (May 1902). "Types of perpetuants". Proceedings of the London Mathematical Society s1-35 (1): 107–114. doi:10.1112/plms/s1-35.1.107. http://plms.oxfordjournals.org/cgi/reprint/s1-35/1/107.
- Grace, J. H. (March 4, 1901). "A theorem on curves in a linear complex". Proceedings of the Cambridge Philosophical Society 11: 132–133. http://books.google.com/?id=IJ81AAAAIAAJ&pg=PA132.
- Grace, J. H. (March 1901). "Linear null systems of binary forms". Proceedings of the London Mathematical Society s1-34 (1): 168–172. doi:10.1112/plms/s1-34.1.168. JFM 33.0126.02. http://plms.oxfordjournals.org/cgi/reprint/s1-34/1/168.
- Grace, J. H. (November 1900). "On a class of plane curves". Proceedings of the London Mathematical Society s1-33 (1): 193–196. doi:10.1112/plms/s1-33.1.193. http://plms.oxfordjournals.org/cgi/reprint/s1-33/1/193.
- Grace, J. H. (1898). "Circles, spheres, and linear complexes". Transactions of the Cambridge Philosophical Society 16: 153–190.
References
Further reading
External links
- Works written by or about John Hilton Grace at Wikisource
Persondata |
Name |
Grace, John Hilton |
Alternative names |
|
Short description |
British mathematician |
Date of birth |
1873 May 21 |
Place of birth |
Halewood |
Date of death |
1958 March 4 |
Place of death |
|