Descriptivist theory of names - Revision history

163.1.230.48: Forgot to change second instance of Santa being called an elf

2014-11-19T02:55:59Z

Forgot to change second instance of Santa being called an elf

← Older revision		Revision as of 04:55, 19 November 2014
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	~~[[Maxwell's Equations]], when converted to [[cylindrical coordinates]],~~ and ~~with the boundary conditions for an [[optical fiber]] while including [[birefringence]]~~ as ~~an effect taken into account, will yield the coupled [[nonlinear Schrödinger equation]]s. After employing the [[Inverse scattering transform]] (~~a ~~procedure analogous to the [[Fourier Transform]] and [[Laplace Transform]]) on the resulting equations, the Manakov system is then obtained~~. ~~The most general form of the Manakov system is as follows:~~		The individual who wrote the article is called Jayson Hirano and he completely digs that title. He functions as a bookkeeper. I've always loved living in Mississippi. To perform lacross is the thing I love most of all.<br><br>Here is my homepage :: accurate psychic readings - [http://si.dgmensa.org/xe/index.php?document_srl=48014&mid=c0102 find out here],

	~~:<math>v_{1}~~'~~=-i\,\xi\,v_{1}+q_{1}\,v_{2}+q_{2}\,v_{3}</math>~~
	~~:<math>v_{2}'=-q_{1}^{*}\,v_{1}+i\,\xi\,v_{2}</math>~~
	~~:<math>v_{3}'=-q_{2}^{*}\,v_{1}+i\,\xi\,v_{3}~~.~~</math>~~

	It is ~~a coupled system~~ of ~~linear [[ordinary differential equations]]~~. ~~The functions~~ <~~math~~>~~q_{1}, q_{2}~~<~~/math~~> ~~represent the envelope of the electromagnetic field as an initial condition.~~

	~~For theoretical purposes, the [[integral equation]] version is often very useful. It~~ is ~~as follows~~:

	:~~<math>\lim_{x\to a}e^{i\xi x}v_{1}~~-~~\lim_{x\to b}e^{i\xi x}v_{1}=\int_{a}^{b}~~[~~e^{i\xi x}\,q_{1}\,v_{2}+e^{i\xi x}\,q_{2}\,v_{3}]\,dx</math>~~
	:~~<math>\lim_{x\to a}e^{-i\xi x}v_{2}-\lim_{x\to b}e^{-i\xi x}v_{2}=-\int_{a}^{b}e^{-i\xi x}\,q_{1}^{*}\,v_{1}\,dx<~~/~~math>~~
	~~:<math>\lim_{x\to a}e^{-i\xi x}v_{3}-\lim_{x\to b}e^{-i\xi x}v_{3}=-\int_{a}^{b}e^{-i\xi x}\,q_{2}^{*}\,v_{1}\,dx<~~/~~math>~~

	~~One may make further substitutions and simplifications, depending on the limits used and the assumptions about boundary or initial conditions~~. ~~One important concept is that <math>\xi<~~/math> is complex; assumptions must be made about this [[eigenvalue]] parameter. If a non-zero solution is desired, the imaginary part of the eigenvalue cannot change [[Sign (mathematics)\|sign]]; accordingly, most researchers take the imaginary part to be [[Positive number\|positive]].

	==~~References==~~
	*C. Menyuk, ''Application of multiple-length-scale methods to the study of optical fiber transmission'', ~~Journal of Engineering Mathematics 36: 113-136, 1999, Kluwer Academic Publishers, Netherlands.~~
	*D. Kaup, B. Malomed, ''Soliton Trapping and Daughter Waves in the Manakov Model'', Physical Review A, Vol. 48, No. 1, July 1993.
	*S. V. Manakov, ''Remarks on the Integrals of the Euler Equations of the n-dimensional Heavy Top'', Functional Anal. Appl., Vol. 10, pp. 93–94, 1976.

	~~[[Category:Fiber optics]]~~
	~~[[Category:Ordinary differential equations]]~~

93.5.162.23: /* See also */ added onomastics link

2013-10-13T18:31:18Z

See also: added onomastics link

← Older revision		Revision as of 20:31, 13 October 2013
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	The ~~writer~~ is ~~called Wilber Pegues~~. ~~Mississippi~~ is ~~the only place I've been residing in but I will have to transfer in~~ a ~~year or two~~. ~~Distributing production has been his occupation for some time~~. ~~To climb~~ is ~~something I truly appreciate performing~~.<br><br>~~Stop by my web blog~~: ~~[http~~://~~kpupf~~.~~com/xe/talk/735373 phone psychic readings~~]		[[Maxwell's Equations]], when converted to [[cylindrical coordinates]], and with the boundary conditions for an [[optical fiber]] while including [[birefringence]] as an effect taken into account, will yield the coupled [[nonlinear Schrödinger equation]]s. After employing the [[Inverse scattering transform]] (a procedure analogous to the [[Fourier Transform]] and [[Laplace Transform]]) on the resulting equations, the Manakov system is then obtained. The most general form of the Manakov system is as follows:

			:<math>v_{1}'=-i\,\xi\,v_{1}+q_{1}\,v_{2}+q_{2}\,v_{3}</math>
			:<math>v_{2}'=-q_{1}^{*}\,v_{1}+i\,\xi\,v_{2}</math>
			:<math>v_{3}'=-q_{2}^{*}\,v_{1}+i\,\xi\,v_{3}.</math>

			It is a coupled system of linear [[ordinary differential equations]]. The functions <math>q_{1}, q_{2}</math> represent the envelope of the electromagnetic field as an initial condition.

			For theoretical purposes, the [[integral equation]] version is often very useful. It is as follows:

			:<math>\lim_{x\to a}e^{i\xi x}v_{1}-\lim_{x\to b}e^{i\xi x}v_{1}=\int_{a}^{b}[e^{i\xi x}\,q_{1}\,v_{2}+e^{i\xi x}\,q_{2}\,v_{3}]\,dx</math>
			:<math>\lim_{x\to a}e^{-i\xi x}v_{2}-\lim_{x\to b}e^{-i\xi x}v_{2}=-\int_{a}^{b}e^{-i\xi x}\,q_{1}^{*}\,v_{1}\,dx</math>
			:<math>\lim_{x\to a}e^{-i\xi x}v_{3}-\lim_{x\to b}e^{-i\xi x}v_{3}=-\int_{a}^{b}e^{-i\xi x}\,q_{2}^{*}\,v_{1}\,dx</math>

			One may make further substitutions and simplifications, depending on the limits used and the assumptions about boundary or initial conditions. One important concept is that <math>\xi</math> is complex; assumptions must be made about this [[eigenvalue]] parameter. If a non-zero solution is desired, the imaginary part of the eigenvalue cannot change [[Sign (mathematics)\|sign]]; accordingly, most researchers take the imaginary part to be [[Positive number\|positive]].

			==References==
			*C. Menyuk, ''Application of multiple-length-scale methods to the study of optical fiber transmission'', Journal of Engineering Mathematics 36: 113-136, 1999, Kluwer Academic Publishers, Netherlands.
			*D. Kaup, B. Malomed, ''Soliton Trapping and Daughter Waves in the Manakov Model'', Physical Review A, Vol. 48, No. 1, July 1993.
			*S. V. Manakov, ''Remarks on the Integrals of the Euler Equations of the n-dimensional Heavy Top'', Functional Anal. Appl., Vol. 10, pp. 93–94, 1976.

			[[Category:Fiber optics]]
			[[Category:Ordinary differential equations]]

en>Hmainsbot1: /* Kripke’s objections and the causal theory */AWB general fixes and, delink dates per :WP:DATELINK, :WP:YEARLINK and :MOS:UNLINKYEARS using AWB (8097)

2012-07-20T23:43:51Z

Kripke’s objections and the causal theory: AWB general fixes and, delink dates per WP:DATELINK, WP:YEARLINK and MOS:UNLINKYEARS using AWB (8097)

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The writer is called Wilber Pegues. Mississippi is the only place I've been residing in but I will have to transfer in a year or two. Distributing production has been his occupation for some time. To climb is something I truly appreciate performing.<br><br>Stop by my web blog: [http://kpupf.com/xe/talk/735373 phone psychic readings]