ジョン・ヒルトン・グレース

ジョン・ヒルトン・グレース John Hilton Grace
生誕	(1873-05-21) 1873年 5月21日ランカシャー、ヘイルウッド（英語版）
死没	1958年 3月4日(1958-03-04)（84歳没）
国籍	GBR
研究分野	数学
主な業績	グレース–ウォルシュ–セゲーの定理（英語版）
主な受賞歴	FRS^[1]
プロジェクト:人物伝
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ジョン・ヒルトン・グレース（英: John Hilton Grace、 (1873-05-21) 1873年 5月21日 – 1958年 3月4日(1958-03-04) ) はイギリスの数学者。グレース–ウォルシュ–セゲーの定理（英語版）などで知られる^[2]。

生い立ち

リヴァプール近郊のヘイルウッド（英語版）で、農家ウィリアム・グレース（William Grace）とエリザベス・ヒルトン（Elizabeth Hilton）の6人の子の長男に生まれた。村の学校とリヴァプール・インスティテュートで学んだ。1892年から、ケンブリッジ大学ピーターハウス・カレッジ（英語版）に通い、数学を学んだ^[1]。妹の息子は動物遺伝学者のアラン・ロバートソン（Alan Robertson）。

学業

1897年にピーターハウス・カレッジのフェローに選ばれ、ピーターハウス・カレッジとペンブローク・カレッジの数学講師になった。彼の作品に、1902年の The Zeros of a Polynomial がある。1903年、アルフレッド・ヤング（英語版）と共同して書籍 Algebra of Invariants を書いた^[1]。

1908年王立協会フェロー選出^[1]。

1916-1917年の間はラホールの客員研究員として過ごし、戦争後半の間はアバディーン大学のマクドナルド教授の代理を務めた^[3]。

1922年、病気を患い学者から引退し、余生をノーフォークで過ごした^[1]。

1958年、ハンティンドンで死没。ヘイルウッドのセント・ニコラス教会の家族墓地に埋葬された。

多項式の零点に関する定理

a(z)=a_{0}+{\tbinom {n}{1}}a_{1}z+{\tbinom {n}{2}}a_{2}z^{2}+\dots +a_{n}z^{n}

,

b(z)=b_{0}+{\tbinom {n}{1}}b_{1}z+{\tbinom {n}{2}}b_{2}z^{2}+\dots +b_{n}z^{n}

を $a_{0}b_{n}-{\tbinom {n}{1}}a_{1}b_{n-1}+{\tbinom {n}{2}}a_{2}b_{n-2}-\cdots +(-1)^{n}a_{n}b_{0}=0$ を満たす多項式としたとき、一方の多項式の零点を含むすべての近傍は、少なくとももう一方の多項式の零点を1つ含む^[4]^[5]。

系

$a(z)$ と $b(z)$ を上記と同様に定義する。双方の零点がすべて単位円板上にあるとき、多項式を"合成"した関数 $c(z)=a_{0}b_{0}+{\tbinom {n}{1}}a_{1}b_{1}z+{\tbinom {n}{2}}a_{2}b_{2}z^{2}+\cdots +a_{n}b_{n}z^{n}$ の零点も単位円板にある^[4]。

出版物

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.
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.
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.
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.
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.
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.
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.
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.
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. https://zenodo.org/record/1433519.
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. https://zenodo.org/record/1447786.
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. https://zenodo.org/record/1433509.
Grace, J. H. (1917-06-01). “On Feuerbach's Theorem”. The Journal of the Indian Mathematical Society. doi:10.18311/jims/1917/17604.
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. https://zenodo.org/record/1433457.
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. https://zenodo.org/record/1447766.
Grace, J. H.; A. Young (1903). The Algebra of Invariants. Cambridge University Press
Grace, J. H. (11 November 1901). “On the zeros of a polynomial”. Mathematical 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. https://zenodo.org/record/1447752.
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. https://zenodo.org/record/1433431.
Grace, J. H. (4 March 1901). “A theorem on curves in a linear complex”. Mathematical Proceedings of the Cambridge Philosophical Society 11: 132–133.
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. https://zenodo.org/record/1447748.
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. https://zenodo.org/record/1433421.
Grace, J. H. (1898). “Circles, spheres, and linear complexes”. Transactions of the Cambridge Philosophical Society 16: 153–190.

出典

^ ^a ^b ^c ^d ^e Todd, J. A. (1958). “John Hilton Grace 1873-1958”. Biographical Memoirs of Fellows of the Royal Society 4: 92–97. doi:10.1098/rsbm.1958.0008. JSTOR 769502.
^ Hörmander, Erling (1954). “On a theorem of Grace”. Mathematica Scandinavica 2: 55–64. doi:10.7146/math.scand.a-10395.
^ Todd, J. A. (1959). “John Hilton Grace”. Journal of the London Mathematical Society: 113–117. doi:10.1112/jlms/s1-34.1.113.
^ ^a ^b Szegő, Gábor (1922). “Bemerkungen zu einem Satz von J H Grace über die Wurzeln algebraischer Gleichungen” (ドイツ語). Mathematische Zeitschrift 13: 28–55. doi:10.1007/BF01485280.
^ Rahman, Qazi I.; Gerhard Schmeisser (2002). “Grace's theorem and equivalent forms”. Analytic Theory of Polynomials. Oxford University Press. pp. 107. ISBN 0-19-853493-0

外部リンク

英語版ウィキソースにはJohn Hilton Grace著の原文があります。

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