Line–sphere intersection - Revision history

199.46.196.231: Reformatted equations. You cannot square a vector!!!!

2014-05-09T20:15:56Z

Reformatted equations. You cannot square a vector!!!!

← Older revision		Revision as of 22:15, 9 May 2014
Line 1:		Line 1:
	Nice to meet you, I am Marvella Shryock. ~~Body developing~~ is ~~one~~ of ~~the issues I adore most~~. ~~My working day occupation~~ is a ~~meter reader~~. ~~California is exactly where~~ I've ~~usually~~ been ~~living and I adore every working day residing here~~.<br><br>~~Also visit my webpage ::~~ [http://www.~~gaysphere~~.~~net~~/~~blog~~/~~167593 home~~ std test ~~kit~~]		Nice to meet you, I am Marvella Shryock. California is where her home is but she requirements to transfer because of her family members. To collect coins is a factor that I'm completely addicted to. For many years I've been operating as a payroll clerk.<br><br>My site [http://www.breda.nl/users/noeliadfebdftijfsdnt over the counter std test]

92.200.60.101: Added reference to case 3

2014-02-08T13:09:48Z

Added reference to case 3

← Older revision		Revision as of 15:09, 8 February 2014
Line 1:		Line 1:
	~~[[File:O. B. Firsov~~, c.~~1940.jpg\|thumb\|right\|200px\|Oleg Firsov, c.1940]]~~		Nice to meet you, I am Marvella Shryock. Body developing is one of the issues I adore most. My working day occupation is a meter reader. California is exactly where I've usually been living and I adore every working day residing here.<br><br>Also visit my webpage :: [http://www.gaysphere.net/blog/167593 home std test kit]

	'''Oleg Borisovich Firsov''' ({{lang-ru\|Олег Борисович Фирсов}}, June 13 [OS May 31] 1915, [[St Petersburg\|Petrograd]] – April 2, 1998, [[Moscow]]) – was a [[Russian people\|Russian]] [[Soviet Union\|Soviet]] [[physicist]]-theorist known for his work on atomic interaction.<ref>{{cite journal\|author=Chibisov, Mikhail; Martynenko, Yurii; Sigmund, Peter; Yurasova, Vera\|title=Obituary: Oleg Borisovich Firsov\|journal=Physics Today\|date=October 1998\|volume=51\|issue=10\|pages=104\|url=http://www.physicstoday.org/resource/1/phtoad/v51/i10/p104_s1?bypassSSO=1\|doi=10.1063/1.882426}}</ref> He was awarded the [[Lenin Prize]] in 1972 for a series of work titled "Elementary processes and non-elastic scattering at nuclear collisions".

	~~==Biography==~~
	~~Firsov was the son of Boris Nilovich Firsov (1888–1920),~~ one of the ~~first Russian pilots, and Olga Vladimirovna von Walden (by mother Golitsyn, 1892–1920). He lost his parents at the age of 4, and grew up in an [[orphanage]]~~.

	He graduated with an undergraduate degree in physics from [[Leningrad State University]] in 1938, and remained there until the end of [[World War II]]. Staying in the city, he then moved to the [[Ioffe Physico-Technical Institute]] in [[Saint Petersburg\|Leningrad]], where he obtained his [[PhD]] in 1947 under [[Yakov Frenkel]]'s supervision. In 1955, he was invited by [[Igor Kurchatov]] to [[Moscow]]. He joined the [[Kurchatov Institute of Atomic Energy]] where worked until 1994, when he became severely ill.

	~~He was married to the physicist Victoria Yevgenyevna Lichko (1915–2004). Their daughter is the [[composer]] [[Elena Firsova]] (b. 1950).~~

	~~==Work==~~
	[[File:Oleg Firsov photo©DSmirnov.jpg\|thumb\|200px\|left\|Oleg Borisovich Firsov, 1982]]Firsov's PhD thesis and first publications were devoted to gas discharges and yielded a model of spark formation and propagation, which is ~~still used to describe both natural lightning and laboratory discharges. He returned to this topic in the 1970s to develop~~ a ~~more accurate theory~~.

	~~Firsov~~ is known among physicists for his studies of the quasi-molecular approach in the [[Quantum mechanics\|quantum mechanical]] theory of atomic collisions. In a 1951 paper, he presented an elegant analytical solution to the complicated problem of resonant charge exchange during hydrogen-hydrogen collisions. Since then, the quasi-molecular approach has been ~~used in many other fields related to the physics of atomic collisions.~~

	~~In 1953, Firsov devised the solution to the so-called inverse collision problem in which a scattering potential is inferred from known values of the scattering cross-section.~~

	At the beginning of the 1950s, when work on controlled fusion reactions had just started at Kurchatov, solving the problem of charge exchange for the confinement of a plasma in a magnetic system was crucial. Accordingly, Firsov was invited to tackle the problem. Applying his gift for discerning the root of a problem, he considered plasma permeation through a picket fence magnetic system and~~, in 1957, was the first to theoretically determine the width of a magnetic gap for a cusp system. His approach is still used.~~

	Around the same time, Firsov also carried out two of his best-known works. In 1957, he found the exact upper and lower limits of the interaction potential between two atoms in the Thomas-Fermi approximation. Since these limits turned out to be close to each other, the potential could be determined accurately. Firsov suggested a simple approximation of this potential that is convenient to use and is now referred to as the Firsov potential. In 1959, he proposed a formula for inelastic energy losses in an atomic collision on the basis of a very clear physical picture in which a number of electrons are exchanged between the colliding atoms. This formula has not only found a wide range of application in the physics of ion beams and radiation effects, but has also stimulated considerable theoretical activity.

	~~In 1966 and 1970, Firsov published two papers on the reflection of particles from a solid surface.~~

	During the last few years of his life, Firsov investigated one of the most fundamental cosmological problems-identifying the nature of [[dark matter]]. He proposed that the invisible mass in the universe is dust of ordinary matter.

	Among his pupils were physicists Mikhail Chibisov, Yuri Martynenko, Boris Smirnov and Edward Lozansky. He had particularly close scientific links with the [[experimentalist]] [[Vera Yurasova]], with whom he also worked in the [[Russian Academy of Sciences]] Council for [[Plasma Physics]].

	~~==Inverse collision problem==~~
	~~Let us consider the [[scattering]] of particles with energy <math>E</math> in a repulsive field <math>U(r)</math>~~
	~~and introduce the quantity~~
	~~:<math>w=\sqrt{1-\frac{U}{E}}~~.<~~/math~~>
	~~Firsov proved that this quantity is implicitly related to the angle of scattering~~ <~~math~~>~~\theta(b)</math>~~
	~~(<math>b</math> is the [[impact parameter]]) by the formula~~
	~~:<math>w=\exp \left(-\frac{1}{\pi}\int_{rw}^\infty \frac{\theta(b)\,db}{\sqrt{b^2-r^2w^2}}\right).</math>~~

	~~==Bibliography==~~
	*Lozansky, E.D. and Firsov O.B.: ''THE Theory of the Initial Stage of Streamer Propagation''
	*Firsov O.B.: in ''Fizika Plazmy i Problema Upravlyaemykh Termoyadernykh Reaktsiî'' Vol. 3 (Plasma Physics and Thermonuclear Research) (Ed. M A Leontovich) (Moscow: Izd. AN SSSR, 1958) p. 327
	*Lozansky, E.D. and Firsov O.B.: ~~The Theory of the Spark, 1975 (Лозанский Э.Д., Фирсов О.Б. Теория искры. 1975. 272 с.)~~

	~~==References==~~
	~~{{reflist}}~~

	~~==External links==~~
	~~{{commonscat\|Oleg Firsov}}~~
	*[http:~~//www.turpion.org/php/paper.phtml?journal_id=pu&paper_id=436 Uspekhi]~~
	*[http://www.kiae.ru/eng/str/nsi/l_nsi.htm Lenin prize]
	*[http://www.iop.org/EJ/toc/0022-3727/6/8 Article]
	*[http://www.~~srim.org/SRIM/History/HISTORY.htm Historical Review]~~
	*[http://homepage.ntlworld.com/dmitrismirnov/FirsovOB.html Obituary]
	*[http://website.lineone.net/~~~dmitrismirnov~~/~~Room21a.html Photo]~~

	~~{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->~~
	~~\| NAME = Firsov, Oleg~~
	~~\| ALTERNATIVE NAMES =~~
	~~\| SHORT DESCRIPTION = Russian physicist~~
	~~\| DATE OF BIRTH = 1915~~
	~~\| PLACE OF BIRTH =~~
	~~\| DATE OF DEATH = April 2, 1998~~
	~~\| PLACE OF DEATH =~~
	}}
	~~{{DEFAULTSORT:Firsov, Oleg}}~~
	~~[[Category:Russian physicists]]~~
	~~[[Category:Russian nuclear physicists]]~~
	~~[[Category:Soviet physicists]]~~
	~~[[Category:Soviet nuclear physicists]]~~
	~~[[Category:1915 births]]~~
	~~[[Category:1998 deaths]]~~
	~~[[Category:People from Saint Petersburg]~~]

en>ChrisGualtieri: /* References */Remove stub template(s). Page is start class or higher. Also check for and do General Fixes + Checkwiki fixes using AWB

2013-12-16T13:28:10Z

References: Remove stub template(s). Page is start class or higher. Also check for and do General Fixes + Checkwiki fixes using AWB

← Older revision		Revision as of 15:28, 16 December 2013
Line 1:		Line 1:
	~~The~~ author ~~is known by over the counter std test~~, [http://www.~~gaysphere~~.~~net~~/~~blog~~/~~297540 visit~~ the ~~next internet site~~], ~~title~~ of ~~Figures Lint~~. ~~North Dakota~~ is ~~her~~ beginning ~~place but she will have~~ to ~~transfer one day or another~~. ~~One~~ of the ~~things she enjoys most~~ is to ~~read comics and she'll~~ be ~~starting some thing else alongside with it~~. ~~She~~ is a ~~librarian~~ but ~~she~~'~~s always needed her personal business~~.		[[File:O. B. Firsov, c.1940.jpg\|thumb\|right\|200px\|Oleg Firsov, c.1940]]

			'''Oleg Borisovich Firsov''' ({{lang-ru\|Олег Борисович Фирсов}}, June 13 [OS May 31] 1915, [[St Petersburg\|Petrograd]] – April 2, 1998, [[Moscow]]) – was a [[Russian people\|Russian]] [[Soviet Union\|Soviet]] [[physicist]]-theorist known for his work on atomic interaction.<ref>{{cite journal\|author=Chibisov, Mikhail; Martynenko, Yurii; Sigmund, Peter; Yurasova, Vera\|title=Obituary: Oleg Borisovich Firsov\|journal=Physics Today\|date=October 1998\|volume=51\|issue=10\|pages=104\|url=http://www.physicstoday.org/resource/1/phtoad/v51/i10/p104_s1?bypassSSO=1\|doi=10.1063/1.882426}}</ref> He was awarded the [[Lenin Prize]] in 1972 for a series of work titled "Elementary processes and non-elastic scattering at nuclear collisions".

			==Biography==
			Firsov was the son of Boris Nilovich Firsov (1888–1920), one of the first Russian pilots, and Olga Vladimirovna von Walden (by mother Golitsyn, 1892–1920). He lost his parents at the age of 4, and grew up in an [[orphanage]].

			He graduated with an undergraduate degree in physics from [[Leningrad State University]] in 1938, and remained there until the end of [[World War II]]. Staying in the city, he then moved to the [[Ioffe Physico-Technical Institute]] in [[Saint Petersburg\|Leningrad]], where he obtained his [[PhD]] in 1947 under [[Yakov Frenkel]]'s supervision. In 1955, he was invited by [[Igor Kurchatov]] to [[Moscow]]. He joined the [[Kurchatov Institute of Atomic Energy]] where worked until 1994, when he became severely ill.

			He was married to the physicist Victoria Yevgenyevna Lichko (1915–2004). Their daughter is the [[composer]] [[Elena Firsova]] (b. 1950).

			==Work==
			[[File:Oleg Firsov photo©DSmirnov.jpg\|thumb\|200px\|left\|Oleg Borisovich Firsov, 1982]]Firsov's PhD thesis and first publications were devoted to gas discharges and yielded a model of spark formation and propagation, which is still used to describe both natural lightning and laboratory discharges. He returned to this topic in the 1970s to develop a more accurate theory.

			Firsov is known among physicists for his studies of the quasi-molecular approach in the [[Quantum mechanics\|quantum mechanical]] theory of atomic collisions. In a 1951 paper, he presented an elegant analytical solution to the complicated problem of resonant charge exchange during hydrogen-hydrogen collisions. Since then, the quasi-molecular approach has been used in many other fields related to the physics of atomic collisions.

			In 1953, Firsov devised the solution to the so-called inverse collision problem in which a scattering potential is inferred from known values of the scattering cross-section.

			At the beginning of the 1950s, when work on controlled fusion reactions had just started at Kurchatov, solving the problem of charge exchange for the confinement of a plasma in a magnetic system was crucial. Accordingly, Firsov was invited to tackle the problem. Applying his gift for discerning the root of a problem, he considered plasma permeation through a picket fence magnetic system and, in 1957, was the first to theoretically determine the width of a magnetic gap for a cusp system. His approach is still used.

			Around the same time, Firsov also carried out two of his best-known works. In 1957, he found the exact upper and lower limits of the interaction potential between two atoms in the Thomas-Fermi approximation. Since these limits turned out to be close to each other, the potential could be determined accurately. Firsov suggested a simple approximation of this potential that is convenient to use and is now referred to as the Firsov potential. In 1959, he proposed a formula for inelastic energy losses in an atomic collision on the basis of a very clear physical picture in which a number of electrons are exchanged between the colliding atoms. This formula has not only found a wide range of application in the physics of ion beams and radiation effects, but has also stimulated considerable theoretical activity.

			In 1966 and 1970, Firsov published two papers on the reflection of particles from a solid surface.

			During the last few years of his life, Firsov investigated one of the most fundamental cosmological problems-identifying the nature of [[dark matter]]. He proposed that the invisible mass in the universe is dust of ordinary matter.

			Among his pupils were physicists Mikhail Chibisov, Yuri Martynenko, Boris Smirnov and Edward Lozansky. He had particularly close scientific links with the [[experimentalist]] [[Vera Yurasova]], with whom he also worked in the [[Russian Academy of Sciences]] Council for [[Plasma Physics]].

			==Inverse collision problem==
			Let us consider the [[scattering]] of particles with energy <math>E</math> in a repulsive field <math>U(r)</math>
			and introduce the quantity
			:<math>w=\sqrt{1-\frac{U}{E}}.</math>
			Firsov proved that this quantity is implicitly related to the angle of scattering <math>\theta(b)</math>
			(<math>b</math> is the [[impact parameter]]) by the formula
			:<math>w=\exp \left(-\frac{1}{\pi}\int_{rw}^\infty \frac{\theta(b)\,db}{\sqrt{b^2-r^2w^2}}\right).</math>

			==Bibliography==
			*Lozansky, E.D. and Firsov O.B.: ''THE Theory of the Initial Stage of Streamer Propagation''
			*Firsov O.B.: in ''Fizika Plazmy i Problema Upravlyaemykh Termoyadernykh Reaktsiî'' Vol. 3 (Plasma Physics and Thermonuclear Research) (Ed. M A Leontovich) (Moscow: Izd. AN SSSR, 1958) p. 327
			*Lozansky, E.D. and Firsov O.B.: The Theory of the Spark, 1975 (Лозанский Э.Д., Фирсов О.Б. Теория искры. 1975. 272 с.)

			==References==
			{{reflist}}

			==External links==
			{{commonscat\|Oleg Firsov}}
			*[http://www.turpion.org/php/paper.phtml?journal_id=pu&paper_id=436 Uspekhi]
			*[http://www.kiae.ru/eng/str/nsi/l_nsi.htm Lenin prize]
			*[http://www.iop.org/EJ/toc/0022-3727/6/8 Article]
			*[http://www.srim.org/SRIM/History/HISTORY.htm Historical Review]
			*[http://homepage.ntlworld.com/dmitrismirnov/FirsovOB.html Obituary]
			*[http://website.lineone.net/~dmitrismirnov/Room21a.html Photo]

			{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
			\| NAME = Firsov, Oleg
			\| ALTERNATIVE NAMES =
			\| SHORT DESCRIPTION = Russian physicist
			\| DATE OF BIRTH = 1915
			\| PLACE OF BIRTH =
			\| DATE OF DEATH = April 2, 1998
			\| PLACE OF DEATH =
			}}
			{{DEFAULTSORT:Firsov, Oleg}}
			[[Category:Russian physicists]]
			[[Category:Russian nuclear physicists]]
			[[Category:Soviet physicists]]
			[[Category:Soviet nuclear physicists]]
			[[Category:1915 births]]
			[[Category:1998 deaths]]
			[[Category:People from Saint Petersburg]]

en>David Eppstein: /* References */ stub sort

2012-09-02T01:07:26Z

References: stub sort

New page

The author is known by over the counter std test, [http://www.gaysphere.net/blog/297540 visit the next internet site], title of Figures Lint. North Dakota is her beginning place but she will have to transfer one day or another. One of the things she enjoys most is to read comics and she'll be starting some thing else alongside with it. She is a librarian but she's always needed her personal business.