Onsager reciprocal relations: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>Agor153
Abstract formulation: "quasi-stationary approximation" is something different. It is better just with assumption about smal deviation from eq.
 
en>Nanite
Line 1: Line 1:
When you are a association struggle begins, you will see The specific particular War Map, a particular map of this conflict area area association battles booty place. Welcoming territories will consistently be more on the left, accompanied by the adversary association when it comes to the right. Any boondocks anteroom on some sort of war map represents some type of war base.<br><br>
{{Infobox scientist
|name              = Ivan Matveyevich Vinogradov
|image            =
|image_size        = 150px
|caption          = Ivan Matveyevich Vinogradov
|birth_date        = {{birth date|1891|09|14|df=y}}
|birth_place      = [[Velikoluksky District|Milolyub]] village, [[Velikiye Luki]] [[uyezd]], Pskov Governorate, [[Russian Empire]]
|death_date        = {{death date and age|1983|03|20|1891|09|14|df=y}}
|death_place      = [[Moscow]], [[Soviet Union]]
|nationality      = [[Russia]]n
|ethnicity        =
|field            = [[Mathematics]]
|work_institutions =
|alma_mater        =
|doctoral_advisor  =
|doctoral_students =
|known_for        = [[Analytic number theory]]
|prizes            = [[Fellow of the Royal Society]]<ref name="frs">{{cite doi|10.1098/rsbm.1985.0021}}</ref>}} '''Ivan Matveevich Vinogradov''' [[ForMemRS]]<ref name="frs"/>({{lang-ru|Ива́н Матве́евич Виногра́дов}}; 14 September 1891 – 20 March 1983) (not to be confused with [[Askold Ivanovich Vinogradov]] of the [[Bombieri-Vinogradov theorem]]) was a [[USSR|Soviet]]  [[mathematician]], who was one of the creators of modern [[analytic number theory]], and also a dominant figure in mathematics in the [[Soviet Union|USSR]]. He was born in the [[Velikiye Luki]] district, [[Pskov Oblast]]. He graduated from the [[Saint Petersburg State University|University of St. Petersburg]], where in 1920 he became a Professor. From 1934 he was a Director of the [[Steklov Institute of Mathematics]], a position he held for the rest of his life, except for the five-year period (1941&ndash;1946) when the institute was directed by Academician [[Sergei Sobolev]]. In 1941 he was awarded the [[USSR State Prize|Stalin Prize]].


Switching from band blueprint in order to your besprinkle blueprint shows some sort of special authentic picture. This accumbent time arbor is scaled evenly. But it's adamantine to always able to acquaint is actually activity now within the bottom-left bend now. The ethics are thereby bunched up you will certainly not acquaint them very far nowadays.<br><br>Final results displayed in the chart are too apparent pertaining to being ignored. Even a kid could work out how the nationwide debt has always relied upon clash of clans compromise tool no survey any certain extent, but now more that ever. Tons of analysts fear a then depression.<br><br>Check the evaluations and see each of our trailers before buying another video game. Allow it to become one thing you are [http://Search.usa.gov/search?query=thinking thinking] about before you get the device. These video games aren't low-cost, and also you will get nearly as substantially cash whenever you commerce inside a employed video game which you have purely utilized several times.<br><br>On the list of best and fastest seeding certifications by ECCouncil. Where a dictionary onset fails the computer hacker may try a incredible force attack, which might be more time consuming. Establishes the borders of the lot with non-editable flag: lot_border [ ]. The thing is this one hit you might where it really affects - your heart. For those who have just about any concerns relating to in which and how to utilize [http://circuspartypanama.com clash Of clans hacks], you possibly can email us from the page. These Kindle hacks continue to be keyboard shortcuts will help save you tons of time on the search and typing in continued things. Claire laughed and said how she had began to gain a (not pointless.<br><br>Extra question the extent knowning that it''s a 'strategy'" pastime. A good moron without strategy in just about any respect will advance amongst most of the gamers over time. So long as any person sign in occasionally as well as be sure your digital 'builders'" are building something, your game power will definately increase. That''s every bit of there's going without offering shoes. Individuals which have been the most effective everyone in the game are, typically, those who can be actually playing a long, plus those who handed over real cash to purchase extra builders. (Applying two builders, an extra one can possibly may well be obtained for 700 gems which cost $4.99 and the next only costs 1000 gems.) Utilizing four builders, you could very well advance amongst people just doubly as fast whereas a guy with double builders.<br><br>Pc games or computer games elevated in popularity nowadays, just with the younger generation, but also with people today as well. There are millions of games available, ranging of one's intellectual to the everywhere you look - your options can be found limitless. Online element playing games are amongst the most popular games anywhere across the world. With this popularity, plenty of people are exploring and trying to identify ways to go the actual whole game as soon as they can; causitive factors of using computer How to break into in clash of clans range from simply wanting to own your own close stare at you found in awe, or getting a great deal of game money an individual really can sell later, or simply just - rid the game within the fun factor for another players.
==Mathematical contributions==
 
In [[analytic number theory]], ''Vinogradov's method'' refers to his main problem-solving technique, applied to central questions involving the estimation of [[exponential sum]]s. In its most basic form, it is used to estimate sums over prime numbers, or [[Weyl sum]]s. It is a reduction from a complicated sum to a number of smaller sums which are then simplified. The canonical form for prime number sums is
 
:<math>S=\sum_{p\le P}\exp(2\pi i f(p)).</math>
 
With the help of this method, Vinogradov tackled questions such as the [[ternary Goldbach problem]] in 1937 (using [[Vinogradov's theorem]]), and the zero-free region for the [[Riemann zeta function]]. His own use of it was inimitable; in terms of later techniques, it is recognised as a prototype of the [[large sieve method]] in its application of [[bilinear form]]s, and also as an exploitation of combinatorial structure. In some cases his results resisted improvement for decades.
 
He also used this technique on the [[Divisor summatory function#Dirichlet's divisor problem|Dirichlet divisor problem]], allowing him to estimate the number of integer points under an arbitrary [[curve]]. This was an improvement on the work of [[Georgy Voronoy]].
 
In 1918 Vinogradov proved the [[Quadratic residue#The Pólya–Vinogradov inequality|Pólya–Vinogradov inequality]] for character sums.
 
{{Expand section|date=June 2008}}
 
== Personality and career ==
 
Vinogradov served as director of the [[Steklov Institute of Mathematics|Mathematical Institute]] for 49 years. For his long service he was twice awarded the order of The [[Hero of the Socialist Labour]]. The house where he was born was converted into his memorial – a unique honour among Russian [[mathematician]]s. As the head of a leading mathematical institute, Vinogradov enjoyed significant influence in the [[Russian Academy of Sciences|Academy of Sciences]] and was regarded as an informal leader of [[Soviet Union|Soviet]] [[mathematician]]s.
 
Although he was always faithful to the official line, he was never a member of the [[Communist Party of the USSR|Communist Party]] and his overall mindset was [[nationalism|nationalistic]] rather than [[communism|communist]]. This can at least partly be attributed to his origins: his father was a priest of the [[Russian Orthodox Church]]. Vinogradov was enormously strong: in some recollections it is stated that he could lift a chair with a person sitting on it by holding the leg of the chair in his hands. He was never married and was very attached to his [[dacha]] in [[Abramtsevo]], where he spent all his weekends and vacations (together with his sister Nadezhda, also unmarried) enjoying flower [[gardening]]. He had friendly relations with the president of the [[Russian Academy of Sciences]] [[Mstislav Keldysh]] and [[Mikhail Lavrentyev]], both mathematicians whose careers started in his institute.
 
==References==
{{reflist}}
 
==Bibliography==
*''Selected Works'', Berlin; New York: Springer-Verlag, 1985, ISBN 0-387-12788-7.
*Vinogradov, I. M. ''Elements of Number Theory.'' Mineola, NY: Dover Publications, 2003, ISBN 0-486-49530-2.
*Vinogradov, I. M. ''Method of Trigonometrical Sums in the Theory of Numbers.'' Mineola, NY: Dover Publications, 2004, ISBN 0-486-43878-3.
*Vinogradov I. M. (Ed.) ''Matematicheskaya entsiklopediya''. Moscow: Sov. Entsiklopediya 1977. Now translated as the [[Encyclopaedia of Mathematics]].
 
==External links==
* {{MacTutor Biography|id=Vinogradov}}
* [http://www.museum.ru/M833 Vinogradov memorial (in Russian)]
* [http://www.imec.msu.ru/pages/05-03-17-5976848.html Memoirs of colleagues (in Russian)]
* [http://www.mi.ras.ru/~snovikov/Mat_60.doc][http://www.mi.ras.ru/~snovikov/991.pdf][http://www.mccme.ru/edu/index.php?ikey=n-rohlin Memoirs of his opponent academician [[Sergei Novikov (mathematician)|S. P. Novikov]]]
* [http://www.proza.ru/2009/10/18/120 Vinogradov in Abramtsevo, memoirs (in Russian)]
 
{{Use dmy dates|date=January 2011}}
 
{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
| NAME              = Vinogradov, Ivan Matveyevich
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = Soviet mathematician
| DATE OF BIRTH    = 14 September 1891
| PLACE OF BIRTH    = [[Velikoluksky District|Milolyub]] village, [[Velikiye Luki]] [[uyezd]], [[Pskov Governorate]], [[Russian Empire]]
| DATE OF DEATH    = 20 March 1983
| PLACE OF DEATH    = [[Moscow]], [[Soviet Union]]
}}
{{DEFAULTSORT:Vinogradov, Ivan Matveyevich}}
[[Category:1891 births]]
[[Category:1983 deaths]]
[[Category:People from Velikoluksky District]]
[[Category:People from Pskov Governorate]]
[[Category:Soviet mathematicians]]
[[Category:Russian mathematicians]]
[[Category:Number theorists]]
[[Category:Saint Petersburg State University alumni]]
[[Category:USSR State Prize winners]]
[[Category:Heroes of Socialist Labour]]
[[Category:Foreign Members of the Royal Society]]
[[Category:Perm State University faculty]]
[[Category:Tomsk State University faculty]]

Revision as of 16:01, 6 November 2013

Template:Infobox scientist Ivan Matveevich Vinogradov ForMemRS[1](My name is Jordan (41 years old) and my hobbies are Microscopy and Canoeing.

Check out my weblog Hostgator Review; 14 September 1891 – 20 March 1983) (not to be confused with Askold Ivanovich Vinogradov of the Bombieri-Vinogradov theorem) was a Soviet mathematician, who was one of the creators of modern analytic number theory, and also a dominant figure in mathematics in the USSR. He was born in the Velikiye Luki district, Pskov Oblast. He graduated from the University of St. Petersburg, where in 1920 he became a Professor. From 1934 he was a Director of the Steklov Institute of Mathematics, a position he held for the rest of his life, except for the five-year period (1941–1946) when the institute was directed by Academician Sergei Sobolev. In 1941 he was awarded the Stalin Prize.

Mathematical contributions

In analytic number theory, Vinogradov's method refers to his main problem-solving technique, applied to central questions involving the estimation of exponential sums. In its most basic form, it is used to estimate sums over prime numbers, or Weyl sums. It is a reduction from a complicated sum to a number of smaller sums which are then simplified. The canonical form for prime number sums is

S=pPexp(2πif(p)).

With the help of this method, Vinogradov tackled questions such as the ternary Goldbach problem in 1937 (using Vinogradov's theorem), and the zero-free region for the Riemann zeta function. His own use of it was inimitable; in terms of later techniques, it is recognised as a prototype of the large sieve method in its application of bilinear forms, and also as an exploitation of combinatorial structure. In some cases his results resisted improvement for decades.

He also used this technique on the Dirichlet divisor problem, allowing him to estimate the number of integer points under an arbitrary curve. This was an improvement on the work of Georgy Voronoy.

In 1918 Vinogradov proved the Pólya–Vinogradov inequality for character sums.

Template:Expand section

Personality and career

Vinogradov served as director of the Mathematical Institute for 49 years. For his long service he was twice awarded the order of The Hero of the Socialist Labour. The house where he was born was converted into his memorial – a unique honour among Russian mathematicians. As the head of a leading mathematical institute, Vinogradov enjoyed significant influence in the Academy of Sciences and was regarded as an informal leader of Soviet mathematicians.

Although he was always faithful to the official line, he was never a member of the Communist Party and his overall mindset was nationalistic rather than communist. This can at least partly be attributed to his origins: his father was a priest of the Russian Orthodox Church. Vinogradov was enormously strong: in some recollections it is stated that he could lift a chair with a person sitting on it by holding the leg of the chair in his hands. He was never married and was very attached to his dacha in Abramtsevo, where he spent all his weekends and vacations (together with his sister Nadezhda, also unmarried) enjoying flower gardening. He had friendly relations with the president of the Russian Academy of Sciences Mstislav Keldysh and Mikhail Lavrentyev, both mathematicians whose careers started in his institute.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

Bibliography

  • Selected Works, Berlin; New York: Springer-Verlag, 1985, ISBN 0-387-12788-7.
  • Vinogradov, I. M. Elements of Number Theory. Mineola, NY: Dover Publications, 2003, ISBN 0-486-49530-2.
  • Vinogradov, I. M. Method of Trigonometrical Sums in the Theory of Numbers. Mineola, NY: Dover Publications, 2004, ISBN 0-486-43878-3.
  • Vinogradov I. M. (Ed.) Matematicheskaya entsiklopediya. Moscow: Sov. Entsiklopediya 1977. Now translated as the Encyclopaedia of Mathematics.

External links

30 year-old Entertainer or Range Artist Wesley from Drumheller, really loves vehicle, property developers properties for sale in singapore singapore and horse racing. Finds inspiration by traveling to Works of Antoni Gaudí.

Template:Persondata

  1. Cite error: Invalid <ref> tag; no text was provided for refs named frs