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Vojtěch Jarník (22. prosince 1897 - 22. září 1970) se narodil v Praze, kde také absolvoval na Univerzitě Karlově. Po absolutoriu nastoupil na Univerzitě jako asistent. V letech 1923-1927 a 1927-1928 hostoval na Göttingenské univerzitě jako spolupracovník Edmunda Georga Hermanna Landaua. Jarník byl jmenován šéfem matematické sekce UK roku 1928. Tento post si udržel až do roku 1968, kdy odešel do důchodu. V roce 1952 se na jeho popud vyčlenila matematicko-fyzikální fakulta z fakulty přírodovědecké, takže jej bezesporu můžeme považovat za zakladatele MFF. Řada dnešních trendů ve vědeckém výzkumu i ve výuce navazuje na dílo profesora Jarníka, mimo jiné je i autorem dodnes užívaných učebnic matematické analýzy. následující text existuje pouze v anglické verzi The main topic of Jarnik's research was number theory. One of the problems which he worked on extensively was related to the Gauss circle problem. Let R(r) denote the number of points (m, n) with m, n [belongs] Z contained in a circle centre O, radius r. There exists a constant C and a number k with
Let d be the minimal value of k. Gauss proved in 1837 that d <= 1. Sierpinski improved the inequality to d <= 2/3 in 1904. Landau also made important contributions and in 1915 Hardy and Landau proved that d > 1/2. In 1923 it was proved that d < 2/3. Jarnik and Landau studied the same problem for curves and surfaces other than circles. Here one is interested in the difference between the number of lattice points within the closed surface and the volume enclosed by the surface. Jarnik showed that for certain closed curves the error term does have d = 2/3. He studied the problem for the particular case of the ellipsoid in a series of papers. | |
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Another area of number theory which interested Jarnik was Diophantine approximation. He wrote papers on this topic spanning the years 1928 to 1969. During the decade 1939-49 he wrote a series of papers dealing with the geometry of numbers, in particular dealing with Minkowski's inequality for convex bodies. Around 60 of Jarnik's 90 papers were written on number theory. Many of the others were written on functions of a real variable, particularly during the years 1933-36, where he studied Dini derivatives and approximate derivatives of continuous functions. He also wrote on rearrangement of infinite series, trigonometric series and other areas of analysis. Jarnik's character is described in Acta Arithmetica:-
As well as being an editor of Acta Arithmetica from the
beginning of the journal, Jarnik was active in organising university education
and scientific research throughout Czechoslovakia. He was honoured by many
scientific societies, in particular being elected to the Czechoslovak Academy of
Sciences. |
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11. července 2003
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