Tatjana van Aardenne Honor Festival

Tatjana van Aardenne-Ehrenfest 1977 in Leiden

Tatjana van Aardenne-Ehrenfest , born as Tatjana Pawlowna Ehrenfest, (born October 28, 1905 in Vienna , † November 29, 1984 in Dordrecht ) was a Dutch mathematician.

Life

Tatjana van Aardenne-Ehrenfest grew up in Saint Petersburg before her parents Paul Ehrenfest and Tatjana Ehrenfest-Afanassjewa moved to Leiden with her in 1912 . Paul Ehrenfest was a well-known theoretical physicist and successor to the chair of Hendrik Antoon Lorentz in Leiden, her mother also known as a mathematician and theoretical physicist. Until 1917 she received home schooling from her parents. After graduating from the municipal high school in Leiden in 1922, she studied at the University of Leiden , where she received her doctorate in 1931 under Willem van der Woude ( Oppervlakken met scharen van gesloten geodetic lijnen ). In 1928, after completing her doctoral examination in Leiden, she studied for a semester in Göttingen with, among others, Harald Bohr and Max Born , whose assistant she was for a while. After completing her doctorate, she was a housewife, never had an academic position and did not work as a mathematician, but regularly took part in mathematical events of the Dutch Mathematical Society, frequently asking questions after the obituary by Nicolaas Govert de Bruijn . She initiated this with the request to ask a stupid question, but, according to de Bruijn, often came across the core of the problem under discussion and put her finger on the sore point of the solution presented. After de Bruijn, she showed a depth and sagacity that, under other circumstances, would have helped her to an impressive career.

She married the surgeon van Aardenne. Her son Gijs van Aardenne was a manager, politician (Minister of Economic Affairs) and in the Dutch parliament.

plant

With Nicolaas Govert de Bruijn, she published an essay on De Bruijn episodes in 1951 , in which they were not discovered, but which made these episodes known, which were named after De Bruijn. This also specifies the BEST formula, a product formula for the number of Euler circles in directed, connected Euler graphs , which is also named after Cedric Smith and William Thomas Tutte in the name of BEST or deBruijn-van Aardenne Ehrenfest-Smith-Tutte's sentence . The BEST formula is: ${\ displaystyle EK (G)}$ ${\ displaystyle G}$

{\ displaystyle \ operatorname {EK} (G) = t_ {w} (G) \ prod _ {v \ in V} {\ bigl (} \ deg (v) -1 {\ bigr)}!}

Here, the amount of the node , the input level of a node and the number Rooted tree of the graph , that is, and for Euler graph at each node is equal so that a constant for the respective graphs. ${\ displaystyle V}$ ${\ displaystyle \ deg (v)}$ ${\ displaystyle t_ {w} (G)}$ ${\ displaystyle G}$

She also found a lower bound for the discrepancy in sequences of low discrepancy (also called quasi-random sequences) in the 1940s. These are sequences in which each sub-sequence has a lower bound for the discrepancy. With this, she answered a question from Johannes van der Corput about the existence of such sequences with a discrepancy of zero, which are therefore as evenly distributed as possible in their respective interval, negative in 1945: there is a lower bound for the discrepancy. The discrepancy of a sequence in the interval is formally defined as ${\ displaystyle M}$ ${\ displaystyle D_ {N}}$ ${\ displaystyle x_ {1}, x_ {2}, \ cdots, x_ {N}}$ ${\ displaystyle [a, b]}$

{\ displaystyle D_ {N} = \ sup _ {a \ leq c \ leq d \ leq b} \ left \ vert {\ frac {\ left | \ {\, s_ {1}, \ dots, s_ {N} \, \} \ cap [c, d] \ right |} {N}} - {\ frac {dc} {ba}} \ right \ vert}

The border crossing is chosen for the infinite sequence . Their lower bound, published in 1949, was of the order of magnitude . Wolfgang M. Schmidt found the best possible lower bound in 1972 . ${\ displaystyle N \ to \ infty}$ ${\ displaystyle {\ frac {\ ln \ ln N} {\ ln \ ln \ ln N}}}$ ${\ displaystyle \ ln N}$

Fonts

with J. Wolff : On the borders of the simply connected areas , Comm. Math. Helv., Volume 16, 1944, pp. 321-323
Proof of the impossibility of a just distribution over an infinite sequence of points over an interval , Proc. Con. Ned. Akad. Wetensch., Volume 48, 1945, pp. 3–8 (= Indagationes Mathematicae, Volume 7, 1945, pp. 71-76)
On the impossibility of just distribution , Proc. Con. Ned. Akad. Wetensch., Volume 52, 1949, pp. 734–739 (= Indagationes Mathematicae, Volume 11, 1949, pp. 264–269)
with J. Korevaar , NG de Bruijn: A note on slowly oscillating functions , Nieuw Archief voor Wiskunde, Series 2, Volume 23, 1949, pp. 77-86
with NG de Bruijn: Circuits and trees in oriented linear graphs , Simon Stevin, Volume 28, 1951, pp. 203-217.

literature

NG de Bruijn: In memoriam T. van Aardenne-Ehrenfest, 1905-1984 , Nieuw Archief voor Wiskunde, Series 4, Volume 3, 1985, pp. 235-236.

Individual evidence

↑ Tatjana van Aardenne-Ehrenfest in the Mathematics Genealogy Project (English) . German translation of the title of the dissertation: Surfaces with multitudes of closed geodetic lines.
↑ Entry at planetmath
^ WT Tutte, CA Smith: On unicursal paths in a network of degree 4 , American Mathematical Monthly, Volume 48, 1951, pp. 233-237
^ Discrepancy Theorem , Mathworld
↑ Schmidt, Acta Arithmetica, Volume 21, 1972, pp. 45-50

personal data
SURNAME	Aardenne-Ehrenfest, Tatjana van
ALTERNATIVE NAMES	Celebration of Honor, Tatiana Pavlovna
BRIEF DESCRIPTION	Dutch mathematician
DATE OF BIRTH	October 28, 1905
PLACE OF BIRTH	Vienna
DATE OF DEATH	November 29, 1984
Place of death	Dordrecht

[1] Tatjana van Aardenne-Ehrenfest in the Mathematics Genealogy Project (English) . German translation of the title of the dissertation: Surfaces with multitudes of closed geodetic lines.

[2] Entry at planetmath

[3] WT Tutte, CA Smith: On unicursal paths in a network of degree 4 , American Mathematical Monthly, Volume 48, 1951, pp. 233-237

[4] Discrepancy Theorem , Mathworld

[5] Schmidt, Acta Arithmetica, Volume 21, 1972, pp. 45-50