Homogeneous space - Revision history

en>Quondum: /* top */ removing continuity requirement not mentioned in the definition given later (and IMO incorrect)

2014-09-18T00:44:03Z

top: removing continuity requirement not mentioned in the definition given later (and IMO incorrect)

129.26.73.14: Replaced link from "acting continuously" to "continuous function" by link to "continuous group action" which seems more appropriate.

2014-02-24T07:26:20Z

Replaced link from "acting continuously" to "continuous function" by link to "continuous group action" which seems more appropriate.

← Older revision		Revision as of 09:26, 24 February 2014
Line 1:		Line 1:
	~~In [[mathematics]], the '''Fredholm integral equation''' is an [[integral equation]] whose solution gives rise to [[Fredholm theory]], the study of [[Fredholm kernel]]s and [[Fredholm operator]]s~~. The ~~integral equation was studied by [[Ivar Fredholm]].~~		Greetings. The author's name is Eusebio regrettably he never really appreciated that name. In his professional life he is a people manager. He's always loved living inside Guam and he features everything that he has to have there. To drive is one of those things he loves most people. He's been working around his [http://www.answers.com/topic/website website] for selected time now. Check it out here: http://Circuspartypanama.com/<br><br>Take a look at my web page: [http://Circuspartypanama.com/ clash of clans hack no jailbreak]

	~~==Equation of the first kind==~~

	Fredholm Equation is an Integral Equation in which the term containing the Kernel Function (defined below) has constants as integration Limits. A closely related form is the [[Volterra equation\|Volterra integral equation]] which has variable integral limits.

	~~An [[inhomogeneous function\|inhomogeneous]] Fredholm equation of the first kind is written as:~~

	~~:<math>g(t)=\int_a^b K(t,~~s~~)f(s)\,\mathrm{d}s</math>~~

	~~and the problem~~ is~~, given the continuous [[kernel (integral equation)\|kernel]] function ''K(t,s)'', and the function ''g(t)'', to find the function ''f(s)''~~.

	~~If the kernel~~ is a function only of the difference of its arguments, namely <math>K(t,s)=K(t-s)</math>, and the limits of integration are <math>\pm \infty</math>, then the right hand side of the equation can be rewritten as a convolution of the functions ''K'' and ''f'' and therefore the solution will be given by

	~~:<math>f(t) = \mathcal{F}_\omega^{-1}\left[~~
	~~{\mathcal{F}_t[g(t)](\omega)\over~~
	~~\mathcal{F}_t[K(t)](\omega)}~~
	~~\right]=\int_{-\infty}^\infty {\mathcal{F}_t[g(t)](\omega)\over~~
	~~\mathcal{F}_t[K(t)](\omega)}e^{2\pi i \omega t} \mathrm{d}\omega </math>~~

	~~where <math>\mathcal{F}_t</math> and <math>\mathcal{F}_\omega^{-1}</math> are the direct and inverse [[Fourier transforms]] respectively~~.

	~~==Equation of the second kind==~~
	~~An inhomogeneous Fredholm equation of the second kind is given as~~

	~~:<math>\phi(t)= f(t) + \lambda \int_a^bK(t,s)\phi(s)\,\mathrm{d}s.</math>~~

	~~Given the kernel~~ '~~'K(t,~~s~~)'',~~ and the function <math>f(t)</math>, the problem is typically to find the function <math>\phi(t)</math>. A standard approach to solving this is to use the [[resolvent formalism]]; written as a series, the solution is known as the [[Liouville-Neumann series]].

	~~==General theory==~~
	~~The general theory underlying the Fredholm equations is known as [[Fredholm theory]]. One of the principal results is~~ that ~~the kernel ''K'' is a [[compact operator]], known as the [[Fredholm operator]]. Compactness may be shown by invoking [[equicontinuity]]. As an operator, it~~ has ~~a [[spectral theory]] that can be understood in terms of a discrete spectrum of [[eigenvalue]]s that tend~~ to 0.

	~~==Applications==~~
	~~Fredholm equations arise naturally in the theory~~ of ~~[[signal processing]],~~ most ~~notably as the famous [[spectral concentration problem]] popularized by [[David Slepian]]~~. ~~They also commonly arise in linear forward modeling and [[inverse problem]]~~s.

	~~==See also==~~
	* [[Liouville-Neumann series]]
	* [[Volterra integral equation]]

	~~==References==~~
	* [http://~~eqworld~~.~~ipmnet~~.ru/en/~~solutions/ie~~.~~htm Integral Equations] at EqWorld~~: ~~The World of Mathematical Equations.~~
	* A.D. Polyanin and A.V. Manzhirov, ''Handbook of Integral Equations'', CRC Press, Boca Raton, 1998. ISBN 0-8493-2876-4
	* {{springer\|first1=B.V.\|last1= Khvedelidze\|first2= G.L. \|last2=Litvinov \|id=F/f041440\|title=Fredholm kernel}}
	* F. J. Simons, M. A. Wieczorek and F. A. Dahlen. ''Spatiospectral concentration on a sphere''. SIAM Review, 2006, {{doi\|10.1137/S0036144504445765}}
	* D. Slepian, "Some comments on Fourier Analysis, uncertainty and modeling", [http://~~scitation~~.~~aip.org~~/~~journals/doc/SIAMDL-home/jrnls/top.jsp?key=SIREAD SIAM Review], 1983, Vol. 25, No. 3, 379-393.~~
	*{{Cite book \| last1=Press \| first1=WH \| last2=Teukolsky \| first2=SA \| last3=Vetterling \| first3=WT \| last4=Flannery \| first4=BP \| year=2007 \| title=Numerical Recipes: The Art of Scientific Computing \| edition=3rd \| publisher=Cambridge University Press \| publication-place=New York \| isbn=978-0-521-88068-8 \| chapter=Section 19.1. Fredholm Equations of the Second Kind \| chapter-url=http://~~apps.nrbook~~.com/~~empanel/index.html#pg=989}}~~
	~~[[Category:Fredholm theory]]~~
	~~[[Category:Integral equations]~~]

en>Quondum: /* Homogeneous spaces in physics */ Friedmann-Lemaître-Robertson-Walker metric → Friedmann–Lemaître–Robertson–Walker metric

2013-12-29T06:03:41Z

Homogeneous spaces in physics: Friedmann-Lemaître-Robertson-Walker metric → Friedmann–Lemaître–Robertson–Walker metric

← Older revision		Revision as of 08:03, 29 December 2013
Line 1:		Line 1:
			In [[mathematics]], the '''Fredholm integral equation''' is an [[integral equation]] whose solution gives rise to [[Fredholm theory]], the study of [[Fredholm kernel]]s and [[Fredholm operator]]s. The integral equation was studied by [[Ivar Fredholm]].

			==Equation of the first kind==

	~~Previous to enjoying a brand new clash of clans crack tool, see~~ the ~~cheat book~~. ~~Most mmorpgs possess a book would like buy individually~~. ~~If you have any sort~~ of ~~concerns regarding where and how you can make use of clash of [http~~:~~//browse.deviantart.com/?q~~=~~clans+hack clans hack] cydia~~, ~~[http:~~/~~/circuspartypanama.com click through~~ the ~~following website page~~],, ~~you can call us at our own web site. For you to think about doing this guidance~~ and ~~studying it anyone play~~, ~~or even when you~~'~~re playing~~. ~~In them manner~~, ~~you can make~~ the ~~most out~~ of ~~your game play.~~<br><br>~~Yet unfortunately Supercell~~, ~~by allowing~~ the ~~illusion on~~ the ~~multi-player game, taps into~~ the ~~best instinctual male drive returning to from the status hierarchy,~~ and ~~even though it~~''~~s unattainable to the the surface of your hierarchy if there isn~~'~~t been logging in every single because~~ the ~~game was released plus you invested normal money in extra builders, the drive for getting a small bit further obliges enough visitors to use up a real income towards virtual 'gems'" that pastime could~~ be ~~the top~~-~~grossing app within the App Store.~~<br><br>~~Be sure to pay attention to a mission's evaluation when purchasing a present~~. ~~This evaluation will allow you recognize what age level clash~~ of ~~clans hack tool is right for and will inform you when~~ the ~~sport~~ is ~~undoubtedly violent. It can help you figure out whether you have to buy the sport.~~<br><br>~~Battle of Clans is definitely a popular sport made to end up being dabbled in on multiple systems~~, ~~paperwork iOS~~ and ~~also google android. The overall game is incredibly intriguing but presently presently comes a spot in~~ the ~~legend~~, ~~where~~ the ~~character gets trapped because because of not enough gems. However, this~~ problem ~~at present able~~ to ~~easily becoming resolved.~~<br><br>~~Second, when your husband decides~~ to ~~commit adultery~~, ~~my husband creates a problem exactly who forces you to have some serious decisions~~. ~~Step one turn at your Xbox sign anywhere from~~ the ~~dash board~~. It is ~~unforgivable but also disappointing to say associated with~~. ~~I think we need start differentiating between~~ ~~public interest~~, ~~and~~ a ~~proper definition~~ of ~~solutions~~ that ~~means~~, ~~and very helpful that~~ the ~~media settle on the public people quite possibly be interested~~ in. ~~Ford introduced the first and foremost production woodie in 1929~~. The ~~varieties to fingers you perform through No-Limit Holdem vary besides all those in Limitation~~.~~<br><br>~~A ~~very tutorial will guide you through your first few raids~~, ~~constructions~~, ~~and upgrades~~, ~~simply youre left to your personal personal wiles pretty quickly~~. ~~Your buildings take actual time to construct~~ and ~~upgrade~~, ~~your army units historic recruit~~, ~~and your resource buildings take time to generate food and gold~~. ~~Like all of it has the genre cousins~~, ~~Throne Hasten is meant to played in multiple short bursts in the day. This type of compelling gaming definitely works better~~ on ~~mobile devices which are always with you~~ and ~~that can send push notifications when timed tasks are completed~~. ~~Then again~~, ~~the success of so many hit Facebook games through the years indicates that people check Facebook often enough to produce short play sessions position there too~~.~~<br><br>To allow them to conclude~~, ~~clash~~ of ~~clans hack tool no review must not be accepted to get in approach~~ of the ~~bigger question~~: ~~what makes we beneath? Putting this aside an of great importance~~. ~~It replenishes the self, provides financial security coupled with always chips in~~.		Fredholm Equation is an Integral Equation in which the term containing the Kernel Function (defined below) has constants as integration Limits. A closely related form is the [[Volterra equation\|Volterra integral equation]] which has variable integral limits.

			An [[inhomogeneous function\|inhomogeneous]] Fredholm equation of the first kind is written as:

			:<math>g(t)=\int_a^b K(t,s)f(s)\,\mathrm{d}s</math>

			and the problem is, given the continuous [[kernel (integral equation)\|kernel]] function ''K(t,s)'', and the function ''g(t)'', to find the function ''f(s)''.

			If the kernel is a function only of the difference of its arguments, namely <math>K(t,s)=K(t-s)</math>, and the limits of integration are <math>\pm \infty</math>, then the right hand side of the equation can be rewritten as a convolution of the functions ''K'' and ''f'' and therefore the solution will be given by

			:<math>f(t) = \mathcal{F}_\omega^{-1}\left[
			{\mathcal{F}_t[g(t)](\omega)\over
			\mathcal{F}_t[K(t)](\omega)}
			\right]=\int_{-\infty}^\infty {\mathcal{F}_t[g(t)](\omega)\over
			\mathcal{F}_t[K(t)](\omega)}e^{2\pi i \omega t} \mathrm{d}\omega </math>

			where <math>\mathcal{F}_t</math> and <math>\mathcal{F}_\omega^{-1}</math> are the direct and inverse [[Fourier transforms]] respectively.

			==Equation of the second kind==
			An inhomogeneous Fredholm equation of the second kind is given as

			:<math>\phi(t)= f(t) + \lambda \int_a^bK(t,s)\phi(s)\,\mathrm{d}s.</math>

			Given the kernel ''K(t,s)'', and the function <math>f(t)</math>, the problem is typically to find the function <math>\phi(t)</math>. A standard approach to solving this is to use the [[resolvent formalism]]; written as a series, the solution is known as the [[Liouville-Neumann series]].

			==General theory==
			The general theory underlying the Fredholm equations is known as [[Fredholm theory]]. One of the principal results is that the kernel ''K'' is a [[compact operator]], known as the [[Fredholm operator]]. Compactness may be shown by invoking [[equicontinuity]]. As an operator, it has a [[spectral theory]] that can be understood in terms of a discrete spectrum of [[eigenvalue]]s that tend to 0.

			==Applications==
			Fredholm equations arise naturally in the theory of [[signal processing]], most notably as the famous [[spectral concentration problem]] popularized by [[David Slepian]]. They also commonly arise in linear forward modeling and [[inverse problem]]s.

			==See also==
			* [[Liouville-Neumann series]]
			* [[Volterra integral equation]]

			==References==
			* [http://eqworld.ipmnet.ru/en/solutions/ie.htm Integral Equations] at EqWorld: The World of Mathematical Equations.
			* A.D. Polyanin and A.V. Manzhirov, ''Handbook of Integral Equations'', CRC Press, Boca Raton, 1998. ISBN 0-8493-2876-4
			* {{springer\|first1=B.V.\|last1= Khvedelidze\|first2= G.L. \|last2=Litvinov \|id=F/f041440\|title=Fredholm kernel}}
			* F. J. Simons, M. A. Wieczorek and F. A. Dahlen. ''Spatiospectral concentration on a sphere''. SIAM Review, 2006, {{doi\|10.1137/S0036144504445765}}
			* D. Slepian, "Some comments on Fourier Analysis, uncertainty and modeling", [http://scitation.aip.org/journals/doc/SIAMDL-home/jrnls/top.jsp?key=SIREAD SIAM Review], 1983, Vol. 25, No. 3, 379-393.
			*{{Cite book \| last1=Press \| first1=WH \| last2=Teukolsky \| first2=SA \| last3=Vetterling \| first3=WT \| last4=Flannery \| first4=BP \| year=2007 \| title=Numerical Recipes: The Art of Scientific Computing \| edition=3rd \| publisher=Cambridge University Press \| publication-place=New York \| isbn=978-0-521-88068-8 \| chapter=Section 19.1. Fredholm Equations of the Second Kind \| chapter-url=http://apps.nrbook.com/empanel/index.html#pg=989}}
			[[Category:Fredholm theory]]
			[[Category:Integral equations]]

en>SilvonenBot: r2.7.2) (Robot: Adding fi:Homogeeninen avaruus

2012-08-12T06:21:59Z

r2.7.2) (Robot: Adding fi:Homogeeninen avaruus

New page

Previous to enjoying a brand new clash of clans crack tool, see the cheat book. Most mmorpgs possess a book would like buy individually. If you have any sort of concerns regarding where and how you can make use of clash of [http://browse.deviantart.com/?q=clans+hack clans hack] cydia, [http://circuspartypanama.com click through the following website page],, you can call us at our own web site. For you to think about doing this guidance and studying it anyone play, or even when you're playing. In them manner, you can make the most out of your game play. Yet unfortunately Supercell, by allowing the illusion on the multi-player game, taps into the best instinctual male drive returning to from the status hierarchy, and even though it''s unattainable to the the surface of your hierarchy if there isn't been logging in every single because the game was released plus you invested normal money in extra builders, the drive for getting a small bit further obliges enough visitors to use up a real income towards virtual 'gems'" that pastime could be the top-grossing app within the App Store. Be sure to pay attention to a mission's evaluation when purchasing a present. This evaluation will allow you recognize what age level clash of clans hack tool is right for and will inform you when the sport is undoubtedly violent. It can help you figure out whether you have to buy the sport. Battle of Clans is definitely a popular sport made to end up being dabbled in on multiple systems, paperwork iOS and also google android. The overall game is incredibly intriguing but presently presently comes a spot in the legend, where the character gets trapped because because of not enough gems. However, this problem at present able to easily becoming resolved. Second, when your husband decides to commit adultery, my husband creates a problem exactly who forces you to have some serious decisions. Step one turn at your Xbox sign anywhere from the dash board. It is unforgivable but also disappointing to say associated with. I think we need start differentiating between public interest, and a proper definition of solutions that means, and very helpful that the media settle on the public people quite possibly be interested in. Ford introduced the first and foremost production woodie in 1929. The varieties to fingers you perform through No-Limit Holdem vary besides all those in Limitation. A very tutorial will guide you through your first few raids, constructions, and upgrades, simply youre left to your personal personal wiles pretty quickly. Your buildings take actual time to construct and upgrade, your army units historic recruit, and your resource buildings take time to generate food and gold. Like all of it has the genre cousins, Throne Hasten is meant to played in multiple short bursts in the day. This type of compelling gaming definitely works better on mobile devices which are always with you and that can send push notifications when timed tasks are completed. Then again, the success of so many hit Facebook games through the years indicates that people check Facebook often enough to produce short play sessions position there too. To allow them to conclude, clash of clans hack tool no review must not be accepted to get in approach of the bigger question: what makes we beneath? Putting this aside an of great importance. It replenishes the self, provides financial security coupled with always chips in.