1. Pontryagin Biography of Lev Pontryagin (19081988) http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

2. The Drex Blog Lev Pontryagin And His Magical Maximum Principle Lev Pontryagin and his magical maximum principle http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

3. Encyclopedia Lev Pontryagin Biography of L.S. Pontryagin Pontryagin, Lev Semenovich Pontryagin, Lev Semenovich Pontryagin, Lev Semenovich CategoryRussian scientists http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

4. Lev Semenovich Pontryagin - Definition Of Lev Semenovich Lev Semenovich Pontryagin (Russian 1051; 1077; 1074; 1057; 1077; 1084; 1105; 1085; 1086; 1074; 1080; 1095; 1055; 1086; 1085; 1090; 1088; 1103; 1075; 1080; 1085;) (3 Sept http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

5. Lev Semenovich Pontryagin Informational resource on Lev Semenovich Pontryagin http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

6. Lev Semenovich Pontryagin: Information From Answers.com Lev Semenovich pontryagin lev Semenovich Pontryagin ( Russian ? ?. http://www.answers.com/topic/lev-semenovich-pontryagin

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping Lev Semenovich Pontryagin Wikipedia Lev Semenovich Pontryagin Lev Semenovich Pontryagin Russian: 3 September 3 May ) was a Soviet Russian mathematician . He was born in Moscow and lost his eyesight in a primus stove explosion when he was 14. Despite his blindness he was able to become a mathematician due to the help of his mother Tatyana Andreevna who read mathematical books to him. He made major discoveries in a number of fields of mathematics, including the more geometric parts of topology He worked on duality theory for homology while still a student. He went on to lay foundations for the abstract theory of the Fourier transform , now called Pontryagin duality . In topology he posed the basic problem of cobordism theory . This led to the introduction around 1940 of a theory of characteristic classes , now called Pontryagin classes , designed to vanish on a manifold that is a boundary Later in his career he worked in optimal control theory. His

7. BookFinder.com Current Problems Of Mathematics. Differential Equations, Mathematical Analysis, and Their Applications Collection of Papers Dedicated to Akademician Sic Lev Semenovich Pontryagin on http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

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9. Lev Semenovich Pontryagin - Wikipedia, The Free Encyclopedia Lev Semenovich Pontryagin (Russian ? ? ?) (3 September 1908 –3 May 1988) was a Soviet Russian mathematician. http://en.wikipedia.org/wiki/Lev_Semenovich_Pontryagin

Wikimedia needs your help in the final days of its fund drive. See our fundraising page The Red Cross and other charities also need your help. Lev Semenovich Pontryagin From Wikipedia, the free encyclopedia. Lev Semenovich Pontryagin Russian: 3 September 3 May ) was a Soviet Russian mathematician . He was born in Moscow and lost his eyesight in a primus stove explosion when he was 14. Despite his blindness he was able to become a mathematician due to the help of his mother Tatyana Andreevna who read mathematical books to him. He made major discoveries in a number of fields of mathematics, including the more geometric parts of topology He worked on duality theory for homology while still a student. He went on to lay foundations for the abstract theory of the Fourier transform , now called Pontryagin duality . In topology he posed the basic problem of cobordism theory . This led to the introduction around 1940 of a theory of characteristic classes , now called Pontryagin classes , designed to vanish on a manifold that is a boundary Later in his career he worked in optimal control theory. His

10. Lev Semenovich Pontryagin Lev Semenovich Pontryagin (Russian Лев Семёнович ПонÑ?рягин) (3September 1908 – 3 May 1988) was a Soviet Russian mathematician. http://www.algebra.com/algebra/about/history/Lev-Semenovich-Pontryagin.wikipedia

Lev Semenovich Pontryagin Regular View Dictionary View (all words explained) Algebra Help my dictionary with pronunciation , wikipedia etc Wikimedia needs your help in the final days of its fund drive. See our fundraising page The Red Cross and other charities also need your help. Lev Semenovich Pontryagin Lev Semenovich Pontryagin Russian: 3 September 3 May ) was a Soviet Russian mathematician . He was born in Moscow and lost his eyesight in a primus stove explosion when he was 14. Despite his blindness he was able to become a mathematician due to the help of his mother Tatyana Andreevna who read mathematical books to him. He made major discoveries in a number of fields of mathematics, including the more geometric parts of topology He worked on duality theory for homology while still a student. He went on to lay foundations for the abstract theory of the Fourier transform , now called Pontryagin duality . In topology he posed the basic problem of cobordism theory . This led to the introduction around 1940 of a theory of characteristic classes , now called Pontryagin classes , designed to vanish on a manifold that is a boundary Later in his career he worked in optimal control theory. His

11. Lev Semenovich Pontryagin - Enpsychlopedia It uses material from the Wikipedia article Lev Semenovich Pontryagin .Via Personal Open Wikipedia (beta) open source software by J Grohol and Psych http://psychcentral.com/psypsych/Lev_Semenovich_Pontryagin

home resource directory disorders quizzes ... support forums Lev Semenovich Pontryagin Lev Semenovich Pontryagin Russian: 3 September 3 May ) was a Soviet Russian mathematician . He was born in Moscow and lost his eyesight in a primus stove explosion when he was 14. Despite his blindness he was able to become a mathematician due to the help of his mother Tatyana Andreevna who read mathematical books to him. He made major discoveries in a number of fields of mathematics, including the more geometric parts of topology He worked on duality theory for homology while still a student. He went on to lay foundations for the abstract theory of the Fourier transform , now called Pontryagin duality . In topology he posed the basic problem of cobordism theory . This led to the introduction around 1940 of a theory of characteristic classes , now called Pontryagin classes , designed to vanish on a manifold that is a boundary Later in his career he worked in optimal control theory. His minimum principle is fundamental to modern theory on the subject. He also introduced there the idea of a bang-bang principle , to describe situations where either the maximum 'steer' should be applied to a system, or none.

12. Lev Semenovich Pontryagin - Wikipedia, The Free Encyclopedia Lev Semenovich Pontryagin. From Wikipedia, the free encyclopedia. Lev SemenovichPontryagin (Russian ? ? ?) (3 September 1908 – 3 May http://www.voyager.in/Lev_Semenovich_Pontryagin

Main Page Recent changes Edit this page Page history ... Printable version Not logged in Log in Help / Contact us Lev Semenovich Pontryagin From Wikipedia, the free encyclopedia. Categories 1908 births 1988 deaths Russian mathematicians ... Soviet mathematicians Lev Semenovich Pontryagin Russian: 3 September 3 May ) was a Soviet Russian mathematician . He was born in Moscow and lost his eyesight in a primus stove explosion when he was 14. Despite his blindness he was able to become a mathematician due to the help of his mother Tatyana Andreevna who read mathematical books to him. He made major discoveries in a number of fields of mathematics, including the more geometric parts of topology He worked on duality theory for homology while still a student. He went on to lay foundations for the abstract theory of the Fourier transform , now called Pontryagin duality . In topology he posed the basic problem of cobordism theory . This led to the introduction around 1940 of a theory of characteristic classes , now called Pontryagin classes , designed to vanish on a manifold that is a boundary Later in his career he worked in optimal control theory. His

13. Pontryagin Biography of lev pontryagin (19081988) lev Semenovich pontryagin s father,Semen Akimovich pontryagin was a civil servant. pontryagin s mother http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pontryagin.html

Lev Semenovich Pontryagin Born: 3 Sept 1908 in Moscow, Russia Died: 3 May 1988 Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Lev Semenovich Pontryagin 's father, Semen Akimovich Pontryagin was a civil servant. Pontryagin's mother, Tat'yana Andreevna Pontryagina, was 29 years old when he was born and she was a remarkable woman who played a crucial role in his path to becoming a mathematician. Perhaps the description of 'civil servant', although accurate, gives the wrong impression that the family were reasonably well off. In fact Semen Akimovich's job left the family without enough money to allow them to give their son a good education and Tat'yana Andreevna worked using her sewing skills to help out the family finances. Pontryagin attended the town school where the standard of education was well below that of the better schools but the family's poor circumstances put these well out of reach financially. At the age of 14 years Pontryagin suffered an accident and an explosion left him blind. This might have meant an end to his education and career but his mother had other ideas and devoted herself to help him succeed despite the almost impossible difficulties of being blind. The help that she gave Pontryagin is described in [1] and [2]:- From this moment Tat'yana Andreevna assumed complete responsibility for ministering to the needs of her son in all aspects of his life. In spite of the great difficulties with which she had to contend, she was so successful in her self-appointed task that she truly deserves the gratitude ... of science throughout the world. For many years she worked, in effect, as Pontryagin's secretary, reading scientific works aloud to him, writing in the formulas in his manuscripts, correcting his work and so on. In order to do this she had, in particular, to learn to read foreign languages. Tat'yana Andreevna helped Pontryagin in all other respects, seeing to his needs and taking very great care of him.

14. Pontryagin Portraits Portraits of lev pontryagin. The URL of this page is, © Copyright information.http//wwwhistory.mcs.st-andrews.ac.uk/history/PictDisplay/pontryagin.html. http://www-groups.dcs.st-and.ac.uk/~history/PictDisplay/Pontryagin.html

Lev Pontryagin JOC/EFR August 2005 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/PictDisplay/Pontryagin.html

15. Pontryagin, Lev Semyonovich --  Encyclopædia Britannica pontryagin, lev Semyonovich Russian mathematician, noted for contributions totopology, algebra, and dynamical systems. http://www.britannica.com/eb/article?tocId=9126343

16. Kamenev, Lev Borisovich --  Encyclopædia Britannica pontryagin, lev Semyonovich Russian mathematician, noted for contributions totopology, algebra, lev Semenovich pontryagin University of St.Andrews http://www.britannica.com/eb/article-9044475?&query=kamenev&ct=

17. Allmath.com - Math Site For Kids! Home Of Flashcards, Math pontryagin, lev Semyonovich. pontryahgin. (190888). Mathematician, born inMoscow, Russia. The loss of his sight in an accident at the age of 14 did not http://www.allmath.com/biosearch.php?QMeth=ID&ID=25596

18. Allmath.com - Math Site For Kids! Home Of Flashcards, Math Plücker, Julius Playfair, John Poincaré, (Jules) Henri Poisson, Siméon Denis pontryagin, lev Semyonovich Purbach or Peuerbach, Georg von http://www.allmath.com/biosearch.php?QMeth=range&start=O&end=Q

19. Wikipedia Topics From Answers.com lev Nussimbaum lev Oborin lev Semenovich pontryagin lev Shestov lev Vygotsky lev Yashin lev s disease levack Station, Ontario http://www.answers.com/library/Wikipedia-letter-1L-first-10901

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20. Pontryagin Duality - Wikipedia, The Free Encyclopedia The theory, introduced by lev pontryagin and combined with Haar measure introducedby John von Neumann, André Weil and others depends on the theory of the http://en.wikipedia.org/wiki/Dual_group

Wikimedia needs your help in the final days of its fund drive. See our fundraising page The Red Cross and other charities also need your help. Pontryagin duality From Wikipedia, the free encyclopedia. (Redirected from Dual group In mathematics , in particular in harmonic analysis and the theory of topological groups Pontryagin duality explains the general properties of the Fourier transform . It places in a unified context a number of observations about functions on the real line or on finite abelian groups: Suitably regular complex-valued periodic functions on the real line have Fourier series and that these functions can be recovered from their Fourier series; Suitably regular complex-valued functions on the real line have Fourier transforms that are also functions on the real line and, just as for periodic functions, these functions can be recovered from their Fourier transforms; and Complex-valued functions on a finite abelian group have discrete Fourier transforms which are functions on the dual group , which is a (non-canonically) isomorphic group. Moreover any function on a finite group can be recovered from its discrete Fourier transform. The theory, introduced by

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