Kuzmin, Rodion Osievich

Rodion Osievich Kuzmin
Rodion Osievich Kuzmin
Date of Birth
Place of Birth	village Rippled, Gorodok district , Vitebsk province , Russian Empire
Date of death
A place of death	Leningrad , RSFSR , USSR
A country	; ;
Scientific field	maths
Place of work	; ; ;
Alma mater	Petrograd University
Academic degree	( 1935 )
supervisor	J. V. Uspensky

Rodion Osievich Kuzmin ( 1891 - 1949 ) - Russian and Soviet mathematician, dean of the technical faculty of Perm University (1921), doctor of physical and mathematical sciences (1935), corresponding member of the USSR Academy of Sciences (1946).

Content

1 Biography
2 Contribution to Mathematics
3 notes
4 References and Sources

Biography

He graduated from the Faculty of Physics and Mathematics of Petrograd University in 1916 . He was left at the department to prepare for the professorship.

From August 1918 to 1921 he was a senior assistant at the Department of Mechanics at Perm University , a teacher at Tomsk Institute of Technology and Tomsk University ^[2] (1919–1920), where he lectured on the course of analysis of infinitesimal quantities. Since 1921 - professor at the Department of Mathematics and Deputy Dean of the Physics and Mathematics Faculty of Perm University .

At the same time since 1921 he was dean of the technical faculty of Perm University ^[3] .

Since 1922 - professor at the Petrograd Polytechnic Institute (later - the University) and other universities in Petrograd . Doctor of physico-mathematical sciences ( 1935 ), corresponding member of the USSR Academy of Sciences ( 1946 ).

Russian politician Mikhail Ivanovich Amosov is the grandson of R. O. Kuzmin.

The main works relate to number theory and mathematical analysis .

In the 1930s, together with N. M. Gunther, he published the “Collection of Problems in Higher Mathematics” in three volumes, which was translated into German and withstood more than ten editions.

Contribution to Math

In 1928, Kuzmin solved ^{[4] the} following Gauss problem (see Gauss – Kuzmin statistics ):

Let be

x

{\ displaystyle x}

- random variable uniformly distributed over the interval

(0,1)

{\ displaystyle (0,1)}

let it go

x={\cfrac {1}{k_{1}+{\cfrac {1}{k_{2}+\cdots }}}}

{\ displaystyle x = {\ cfrac {1} {k_ {1} + {\ cfrac {1} {k_ {2} + \ cdots}}}}}

is a representation of the number x as a continued fraction . Need to evaluate the expression

\Delta _{n}(s)=\mathbb {P} \left\{{\cfrac {1}{k_{n+1}+{\cfrac {1}{k_{n+2}+\cdots }}}}\leqslant s\right\}-\log _{2}(1+s)~.

{\ displaystyle \ Delta _ {n} (s) = \ mathbb {P} \ left \ {{\ cfrac {1} {k_ {n + 1} + {\ cfrac {1} {k_ {n + 2} + \ cdots}}}} \ leqslant s \ right \} - \ log _ {2} (1 + s) ~.}

Gauss proved that

\Delta _{n}\to 0

{\ displaystyle \ Delta _ {n} \ to 0}

tends to zero when

n\to \infty

{\ displaystyle n \ to \ infty}

but failed to give an explicit assessment. R.O. Kuzmin proved that

|\Delta _{n}(s)|\leqslant C\cdot e^{-\alpha {\sqrt {n}}}~,

{\ displaystyle | \ Delta _ {n} (s) | \ leqslant C \ cdot e ^ {- \ alpha {\ sqrt {n}}} ~,}

Where

C

{\ displaystyle C}

and

\alpha

{\ displaystyle \ alpha}

- some positive constants. In 1929, Paul Levy proved a stronger assessment.

C\cdot 0{,}7^{n}

{\ displaystyle C \ cdot 0 {,} 7 ^ {n}}

.

In 1930, R. O. Kuzmin proved ^[5] that if $a$ ${\ displaystyle a}$ is an algebraic number , and $b$ ${\ displaystyle b}$ - real quadratic irrationality , then the number $a^{b}$ ${\ displaystyle a ^ {b}}$ transcendentally . For example, it follows that the number

2^{\sqrt {2}}=2{,}6651441426902251886502972498731\ldots

{\ displaystyle 2 ^ {\ sqrt {2}} = 2 {,} 6651441426902251886502972498731 \ ldots}

is transcendental. For further results in this direction, see the Gelfond – Schneider theorem .

Notes

↑ German National Library , Berlin State Library , Bavarian State Library , etc. Record # 1043036008 // General regulatory control (GND) - 2012—2016.
<a href=" https://wikidata.org/wiki/Track:Q27302 "> </a> <a href=" https://wikidata.org/wiki/Track:Q304037 "> </a> <a href = " https://wikidata.org/wiki/Track:Q256507 "> </a> <a href=" https://wikidata.org/wiki/Track:Q170109 "> </a> <a href = " https://wikidata.org/wiki/Track:Q36578 "> </a>
↑ [vital.lib.tsu.ru/vital/access/services/Download/vtls:000314916/SOURCE1 Physicists about physics and physicists]. Tomsk: Tomsk State University, 1998.S. 31.
↑ Romashova L. A. Technical Faculty of Perm State University (1920–1922) // Club "Perm Local History".
↑ R.O. Kuzmin. On one Gauss problem // Reports of the USSR Academy of Sciences. - 1928. - S. 375-380 .
↑ R.O. Kuzmin. About a new class of transcendental numbers // News of the USSR Academy of Sciences. VII series. Department of Physical and Mathematical Sciences. - 1930. - No. 6 . - S. 585-597 .

References and Sources

Kuzmin Rodion Osievich // Great Soviet Encyclopedia : [in 30 vol.] / Ch. ed. A.M. Prokhorov . - 3rd ed. - M .: Soviet Encyclopedia, 1969-1978.
Venkov B.A., Natanson I.P. Rodion Osievich Kuzmin (1891–1949) (obituary) // Uspekhi Matematicheskikh Nauk . - 1949. - T. 4 , No. 4 (32) . - S. 148–155 .
Oshurkova R. A. Rodion Osievich Kuzmin // Professors of Perm State University (1963–2001) / Ch. Ed .: V.V. Malanin . Perm: Publishing house Perm. University, 2001.419 s. S. 113–114.
Profile of Rodion Osievich Kuzmin on the official website of the RAS .
Sviderskaya G. E. 110th Birth Anniversary: Rodion Osievich Kuzmin (1891–1949) // Mathematics at the University (Public Scientific and Methodical Internet Journal of St. Petersburg State Technical University). - 2001-2002. - No. 2 . - ISSN 1819–6616 . Archived on April 13, 2014.

[_fecaaee43607bd98-1] German National Library , Berlin State Library , Bavarian State Library , etc. Record # 1043036008 // General regulatory control (GND) - 2012—2016.
<a href=" https://wikidata.org/wiki/Track:Q27302 "> </a> <a href=" https://wikidata.org/wiki/Track:Q304037 "> </a> <a href = " https://wikidata.org/wiki/Track:Q256507 "> </a> <a href=" https://wikidata.org/wiki/Track:Q170109 "> </a> <a href = " https://wikidata.org/wiki/Track:Q36578 "> </a>

[2] [vital.lib.tsu.ru/vital/access/services/Download/vtls:000314916/SOURCE1 Physicists about physics and physicists]. Tomsk: Tomsk State University, 1998.S. 31.

[3] Romashova L. A. Technical Faculty of Perm State University (1920–1922) // Club "Perm Local History".

[4] R.O. Kuzmin. On one Gauss problem // Reports of the USSR Academy of Sciences. - 1928. - S. 375-380 .

[5] R.O. Kuzmin. About a new class of transcendental numbers // News of the USSR Academy of Sciences. VII series. Department of Physical and Mathematical Sciences. - 1930. - No. 6 . - S. 585-597 .