# Mitio Nagumo

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Japanese mathematician

Mitio Nagumo Born (1905-05-07)7 May 1905 Yamagata Prefecture, Japan Died 6 February 1995(1995-02-06) (aged 89) Koganei, Tokyo, Japan Alma mater University of Tokyo Known for Nagumo theorem Nagumo’s uniqueness theorem Kolmogorov-Nagumo-de Finetti mean Scientific career Fields Mathematics Institutions University of Osaka Doctoral advisor Takuji Yosie[1] Notable students Jin Akiyama

**Mitio (Michio) Nagumo** ([Japanese](/source/Japanese_language): 南雲 道夫; May 7, 1905 – February 6, 1995) was a [Japanese](/source/Japanese_people) [mathematician](/source/Mathematician), who specialized in the theory of [differential equations](/source/Differential_equation). He gave the first [necessary and sufficient condition](/source/Necessary_and_sufficient_condition) for [positive invariance](/source/Positive_invariant_set) of [closed sets](/source/Closed_set) under the flow induced by ordinary differential equations ([Nagumo/Bony-Brezis theorem](/source/Bony-Brezis_theorem)).[2]

## Biography

Mitio Nagumo graduated from the Department of Mathematics at the [Imperial University of Tokyo](/source/Imperial_University_of_Tokyo) in March 1928. In March 1931 he was appointed Lecturer in the Faculty of Technology at the [Imperial University of Kyushu](/source/Kyushu_University). In February 1932 he left [Japan](/source/Japan) for an academic visit to [Göttingen](/source/University_of_G%C3%B6ttingen), where he remained for two years. Upon his return from [Göttingen](/source/G%C3%B6ttingen) in March 1934, he was appointed Lecturer in the Department of Mathematics at the [Imperial University of Osaka](/source/Osaka_University),[3] 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](/source/Doctor_of_Science) degree from the [Imperial University of Tokyo](/source/Imperial_University_of_Tokyo). In the 1960s he made a number of academic visits abroad, spending time at the [Courant Institute of Mathematical Sciences](/source/Courant_Institute_of_Mathematical_Sciences) (where he visited [Kurt Friedrichs](/source/Kurt_Otto_Friedrichs) and other old acquaintances from his time at [Göttingen](/source/University_of_G%C3%B6ttingen)) and the [Federal University of Rio Grande do Sul](/source/Federal_University_of_Rio_Grande_do_Sul) in 1960, followed by a visit to the [National Tsing Hua University](/source/National_Tsing_Hua_University) in 1963-64. He retired from [Osaka University](/source/Osaka_University) in December 1966, after which he was granted the title of Honorary Professor. He was subsequently appointed Professor at [Sophia University](/source/Sophia_University), from which he retired in March 1976, having reached [mandatory retirement](/source/Mandatory_retirement) age.[1]

Much of Nagumo's original work was published in [Japanese](/source/Japanese_language) and [German](/source/German_language),[1] however his research and teaching have influenced numerous mathematicians (especially in [Japan](/source/Japan)) who have since made many of his results available in [English](/source/English_language).[4]

## Works

- Nagumo, Mitio (1937), ["Über die Differentialgleichung y"= ƒ (x, y, y')"](https://www.jstage.jst.go.jp/article/ppmsj1919/19/0/19_0_861/_article), *Nippon Sugaku-Buturigakkwai Kizi Dai 3 Ki*, **19**: 861–866 (in German)

- Nagumo, Mitio (1942), ["Über die Lage der Integralkurven gewöhnlicher Differentialgleichungen"](https://www.jstage.jst.go.jp/article/ppmsj1919/24/0/24_0_551/_article), *Nippon Sugaku-Buturigakkwai Kizi Dai 3 Ki*, **24**: 551–559 (in German)

- Nagumo, Mitio (1941), ["Über das Anfangswertproblem Partieller Differentialgleichungen"](https://www.jstage.jst.go.jp/article/jjm1924/18/0/18_0_41/_article), *Japanese Journal of Mathematics: Transactions and Abstracts*, **8** (10), Mathematical Society of Japan (in German)

- Nagumo, Mitio (1977), ["Quantities and real numbers"](https://projecteuclid.org/download/pdf_1/euclid.ojm/1200770204), *Osaka J. Math*, **14**: 1–10

- Nagumo, Mitio; Fukuhara, Masuo (1930), ["On a condition of stability for a differential equation"](http://projecteuclid.org/download/pdf_1/euclid.pja/1195581383), *Proceedings of the Imperial Academy*, **6** (4): 131–132, [doi](/source/Doi_(identifier)):[10.3792/pia/1195581383](https://doi.org/10.3792%2Fpia%2F1195581383)

- Nagumo, Mitio (1944), "On the periodic solution of an ordinary differential equation of second order", *Zenkoku Shijou Suugaku Danwakai*: 54–61

- Nagumo, Mitio (1961). *Introduction to the theory of Banach space*. Vol. 1. Editôra Meridional-"Emma".

## Literature

- Yamaguti, Masaya; Nirenberg, Louis; Mizohata, Sigeru; Sibuya, Yasutaka (1993). *Mitio Nagumo Collected Papers*. Springer Japan. [ISBN](/source/ISBN_(identifier)) [978-4431549338](https://en.wikipedia.org/wiki/Special:BookSources/978-4431549338).

- Hsieh, Po-Fang; Sibuya, Yasutaka (June 1999). *Basic Theory of Ordinary Differential Equations*. Springer. [ISBN](/source/ISBN_(identifier)) [9781461215066](https://en.wikipedia.org/wiki/Special:BookSources/9781461215066).

## References

1. ^ [***a***](#cite_ref-collectedworks_1-0) [***b***](#cite_ref-collectedworks_1-1) [***c***](#cite_ref-collectedworks_1-2) Yamaguti, Masaya; [Nirenberg, Louis](/source/Louis_Nirenberg); Mizohata, Sigeru; Sibuya, Yasutaka (1993). *Mitio Nagumo Collected Papers*. Springer Japan. pp. 462–465. [ISBN](/source/ISBN_(identifier)) [978-4431549338](https://en.wikipedia.org/wiki/Special:BookSources/978-4431549338).

1. **[^](#cite_ref-blanchini_2-0)** Blanchini, Franco (1999), "Survey paper: Set invariance in control", *Automatica*, **35** (11): 1747–1767, [doi](/source/Doi_(identifier)):[10.1016/S0005-1098(99)00113-2](https://doi.org/10.1016%2FS0005-1098%2899%2900113-2)

1. **[^](#cite_ref-bio_3-0)** Yosida, K (1966), ["Mitio Nagumo"](http://fe.math.kobe-u.ac.jp/FE/Free/vol09/fe09-3.pdf) (PDF), *Funkcialaj Ekvacioj*, **6** (in Esperanto)

1. **[^](#cite_ref-hsieh-subiya_4-0)** Hsieh, Po-Fang; Sibuya, Yasutaka (June 1999). *Basic Theory of Ordinary Differential Equations*. Springer. [ISBN](/source/ISBN_(identifier)) [9781461215066](https://en.wikipedia.org/wiki/Special:BookSources/9781461215066).

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