{{short description|Japanese mathematician}} {{Infobox scientist | name = Mitio Nagumo | image = | alt = | caption = | birth_date = {{Birth date|df=yes|1905|5|7}} | birth_place = [[Yamagata Prefecture]], [[Japan]] | death_date = {{Death date and age|df=yes|1995|2|6|1905|5|7}} | death_place = [[Koganei, Tokyo]], [[Japan]] | fields = [[Mathematics]] | workplaces = [[Osaka University|University of Osaka]] | alma_mater = [[University of Tokyo]] | doctoral_advisor = [[Takuji Yosie]]<ref name=collectedworks/> | notable_students = [[Jin Akiyama]] | awards = | known_for = [[Bony-Brezis theorem|Nagumo theorem]]<br/> [[Nagumo’s uniqueness theorem]] <br/> {{no wrap|[[Quasi-arithmetic mean|Kolmogorov-Nagumo-de Finetti mean]]}}}}

'''Mitio (Michio) Nagumo''' ({{langx|ja|南雲 道夫}}; May 7, 1905 &ndash; February 6, 1995) was a [[Japanese people|Japanese]] [[mathematician]], who specialized in the theory of [[differential equation]]s. He gave the first [[necessary and sufficient condition]] for [[Positive invariant set|positive invariance]] of [[closed set]]s under the flow induced by ordinary differential equations ([[Bony-Brezis theorem|Nagumo/Bony-Brezis theorem]]).<ref name=blanchini>{{citation|title=Survey paper: Set invariance in control|first=Franco|last= Blanchini|journal=Automatica |volume= 35 |number=11 |year= 1999|pages= 1747–1767| doi=10.1016/S0005-1098(99)00113-2}}</ref>

== Biography == Mitio Nagumo graduated from the Department of Mathematics at the [[Imperial University of Tokyo]] in March 1928. In March 1931 he was appointed Lecturer in the Faculty of Technology at the [[Kyushu University|Imperial University of Kyushu]]. In February 1932 he left [[Japan]] for an academic visit to [[University of Göttingen|Göttingen]], where he remained for two years. Upon his return from [[Göttingen]] in March 1934, he was appointed Lecturer in the Department of Mathematics at the [[Osaka University|Imperial University of Osaka]],<ref name=bio>{{citation|title=Mitio Nagumo|first=K|last= Yosida| journal=Funkcialaj Ekvacioj|volume= 6 |year= 1966| url=http://fe.math.kobe-u.ac.jp/FE/Free/vol09/fe09-3.pdf}} {{in lang|eo}}</ref> and was promoted to Associate Professor in September that year, becoming Professor in the Faculty of Science in March 1936. In March 1937 Nagumo received a [[Doctor of Science]] degree from the [[Imperial University of Tokyo]]. In the 1960s he made a number of academic visits abroad, spending time at the [[Courant Institute of Mathematical Sciences]] (where he visited [[Kurt Otto Friedrichs|Kurt Friedrichs]] and other old acquaintances from his time at [[University of Göttingen|Göttingen]]) and the [[Federal University of Rio Grande do Sul]] in 1960, followed by a visit to the [[National Tsing Hua University]] in 1963-64. He retired from [[Osaka University]] in December 1966, after which he was granted the title of Honorary Professor. He was subsequently appointed Professor at [[Sophia University]], from which he retired in March 1976, having reached [[mandatory retirement]] age.<ref name=collectedworks>{{cite book |last1= Yamaguti |first1= Masaya |last2= Nirenberg |first2= Louis |author2-link=Louis Nirenberg |last3= Mizohata |first3= Sigeru |last4= Sibuya |first4=Yasutaka |date= 1993 |title= Mitio Nagumo Collected Papers |publisher= Springer Japan |pages= 462–465 |isbn=978-4431549338}}</ref>

Much of Nagumo's original work was published in [[Japanese language|Japanese]] and [[German language|German]],<ref name=collectedworks/> however his research and teaching have influenced numerous mathematicians (especially in [[Japan]]) who have since made many of his results available in [[English language|English]].<ref name=hsieh-subiya>{{cite book |last1= Hsieh |first1= Po-Fang |last2= Sibuya |first2= Yasutaka |date= June 1999 |title= Basic Theory of Ordinary Differential Equations |publisher= Springer |isbn=9781461215066}}</ref>

==Works== *{{citation|title=Über die Differentialgleichung y"= ƒ (x, y, y')|first=Mitio|last= Nagumo| journal=Nippon Sugaku-Buturigakkwai Kizi Dai 3 Ki |volume= 19 |year= 1937|pages= 861–866| url=https://www.jstage.jst.go.jp/article/ppmsj1919/19/0/19_0_861/_article}} {{in lang|de}} *{{citation|title=Über die Lage der Integralkurven gewöhnlicher Differentialgleichungen|first=Mitio|last= Nagumo| journal=Nippon Sugaku-Buturigakkwai Kizi Dai 3 Ki |volume= 24 |year= 1942|pages= 551–559| url=https://www.jstage.jst.go.jp/article/ppmsj1919/24/0/24_0_551/_article}} {{in lang|de}} *{{citation|title=Über das Anfangswertproblem Partieller Differentialgleichungen|first=Mitio|last= Nagumo| journal= Japanese Journal of Mathematics: Transactions and Abstracts |volume= 8 |number=10 |year= 1941 |publisher= Mathematical Society of Japan| url=https://www.jstage.jst.go.jp/article/jjm1924/18/0/18_0_41/_article}} {{in lang|de}} *{{citation|title=Quantities and real numbers|first=Mitio|last= Nagumo| journal=Osaka J. Math |volume= 14 |year= 1977|pages= 1–10| url=https://projecteuclid.org/download/pdf_1/euclid.ojm/1200770204}} *{{citation|title=On a condition of stability for a differential equation|first1=Mitio|last1= Nagumo| first2=Masuo |last2=Fukuhara | journal=Proceedings of the Imperial Academy |volume= 6 |number=4 |year= 1930|pages= 131–132|doi=10.3792/pia/1195581383| url=http://projecteuclid.org/download/pdf_1/euclid.pja/1195581383|doi-access=free}} *{{citation|title=On the periodic solution of an ordinary differential equation of second order|first1=Mitio|last1= Nagumo| journal=Zenkoku Shijou Suugaku Danwakai |year= 1944|pages= 54–61}} *{{cite book |last=Nagumo |first=Mitio |date=1961 |title=Introduction to the theory of Banach space |volume=1 |publisher=Editôra Meridional-"Emma" }}

==Literature== *{{cite book |last1= Yamaguti |first1= Masaya |last2= Nirenberg |first2= Louis |last3= Mizohata |first3= Sigeru |last4= Sibuya |first4=Yasutaka |date= 1993 |title= Mitio Nagumo Collected Papers |publisher= Springer Japan |isbn=978-4431549338}} *{{cite book |last1= Hsieh |first1= Po-Fang |last2= Sibuya |first2= Yasutaka |date= June 1999 |title= Basic Theory of Ordinary Differential Equations |publisher= Springer |isbn=9781461215066}}

==References== {{Reflist}} {{Authority control}}

{{DEFAULTSORT:Nagumo, Mitio}} [[Category:1905 births]] [[Category:1995 deaths]] [[Category:20th-century Japanese mathematicians]] [[Category:University of Tokyo alumni]] [[Category:Academic staff of Kyushu University]] [[Category:Academic staff of the University of Osaka]] [[Category:Academic staff of Sophia University]] [[Category:Scientists from Yamagata Prefecture]]