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Topic: Integrable system

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	Neil Southall, Mathematical Sciences, Loughborough University (Site not responding. Last check: 2007-10-01)
		Integrable systems are significant in that they combine tractability with nonlinearity.
		Most general methods for solving integrable systems begin with forming a linear system, whose compatibility conditions (requirement that mixed second derivatives commute) happens to be the original integrable system.
		Integrability in discrete-time systems is related to the existence of confined (movable) singularities.
	www-staff.lboro.ac.uk /~manjs2/index.htm (1269 words)

	Mathematics - Wikipedia, the free encyclopedia
		As the number system is further developed, the integers are recognised as a subset of the rational numbers ("fractions").
		The structural properties of these objects are investigated in the study of groups, rings, fields and other abstract systems, which are themselves such objects.
		Many phenomena in nature can be described by dynamical systems; chaos theory makes precise the ways in which many of these systems exhibit unpredictable yet still deterministic behavior.
	en.wikipedia.org /wiki/Mathematics (3876 words)

	Color (Site not responding. Last check: 2007-10-01)
		The rod system (which vision in very low light relies on exclusively) does not by itself sense differences in wavelength; therefore it is not normally implicated in Color vision.
		In one system, red is considered to motivate action; orange and purple are related to spirituality; yellow cheers; green creates cosiness and warmth; blue relaxes; and white is associated with either purity or death.
		The Munsell Color system is a famous classification that organises various colors into a Color solid based on hue, saturation and value.
	color.iqnaut.net (4962 words)

	ScienceDaily: Mathematics
		Further steps need writing or some other system for recording numbers such as tallies or the knotted strings called khipu used by the Inca empire to store numerical data.
		It was the goal of Hilbert's program to put all of mathematics on a firm axiomatic basis, but according to Gödel's incompleteness theorem every (sufficiently powerful) axiomatic system has undecidable formulas; and so a final axiomatization of mathematics is unavailable.
		The deeper structural properties of numbers are studied in abstract algebra and the investigation of groups, rings, fields and other abstract number systems.
	www.sciencedaily.com /encyclopedia/mathematics (4227 words)

	[No title] (Site not responding. Last check: 2007-10-01)
		When an integrable Hamiltonian system, possessing an m-resonant lower dimensional normally parabolic torus is perturbed, a parabolic m-resonance occurs.
		When in addition the iso-energetic non-degeneracy condition fails for the integrable system, the near integrable Hamiltonian exhibits a flat parabolic m-resonance.
		Analytical and numerical study of a phenomenological model of a 3 degrees of freedom (d.o.f.) near integrable Hamiltonian system reveals several types of parabolic resonances.
	www.wisdom.weizmann.ac.il /~/litvak/abs_eng.html (188 words)

	geometric quantization and non-integrable systems
		There are quite a few restrictions\nthough, but for the novice it\'s hard to see precisely what are the\ntypical results to expect in a given situation.\n\nI want to keep things at the level of ordinary QM, i.e.
		Now, in\nmath/9904046 Tyurin says that a mechanical system has a real\npolarization iff it is integrable.
		There are quite a few restrictions\nandgt; though, but for the novice it\'s hard to see precisely what are the\nandgt; typical results to expect in a given situation.\nandgt;\nandgt; I want to keep things at the level of ordinary QM, i.e.
	www.physicsforums.com /showthread.php?p=467738 (687 words)

	QUANTUM UNIVERSE AS ALGEBRA
		T(n) represents an extension or degree of freedom of any quantum system, and one which is Fourier related to a local concept of energy, by a specific Ansatz in the local FCCR model of quantum theory.
		At least one sense of a local Newtonian microtime of a system of 3 particles could be attached to measures of separation of the points of this 3-simplex.
		That concept of spatial dimension is contained within the structure of the algebra of linear operators generated by fundamental "observables" of the system that acts on the Hilbert space.
	graham.main.nc.us /~bhammel/PHYS/algu.html (11267 words)

	The Principal chiral model as an integrable system - nas (ResearchIndex) (Site not responding. Last check: 2007-10-01)
		The Principal chiral model as an integrable system
		Ma~nas, The principal chiral model as an integrable system, this volume.
		1 the integrability of classical spinor models in two--dimensi..
	citeseer.ist.psu.edu /426204.html (613 words)

	What is Complete Integrability?
		The phase space\nwill be a 2N dimensional space, and each eigenfrequancy\nwill have a bunch of concentric circles (each circle depicting\nthe time evolution of a solution) and each bunch of concentric\ncircles is lying in its own 2D plane of 2N-space.\n\nThe set of all lines that trace out solutions will look\nlike a kind of bunch of\nconcentric hyper-tori.
		In other words, you can get\nandgt; andgt; lots of completely integrable systems by taking linear systems\nandgt; andgt; and "warping" them.\n\nandgt;Yes, this is what I meant!\n\nActually from what you say below, my guess is not what\nyou meant.
		This is presumably what you mean by\n\'a discretised KdV equation which is integrable in terms of solitons\'.\n\nI find it quite extraordinary and hugely encouraging that solitons turn\nup naturally in the basic equations of QM and am enthused that work in\nthis area continues apace.
	www.physicsforums.com /showthread.php?p=288407 (3222 words)

	Dissipative System (Site not responding. Last check: 2007-10-01)
		Global-Rent-a-scope, an international telescope time rental service, based in Mayhill, New Mexico, USA announces, for the first time in recorded history, a new, spectacular service available anywhere in the world with an Internet connection.
		Another meaning of "dissipative system" is one that dissipates heat, see heat dissipation.
		A piecewise-conserved constant of motion for a dissipative system..
	www.dissipativesystem.info (389 words)

	Determinant structure of RI type discrete integrable system
		type discrete integrable system by Vinet–Zhedanov on a semi-infinite lattice is studied using the bilinear method.
		type discrete integrable system are derived by applying appropriate dependent variable transformations.
		It is shown that a particular solution for the bilinear equations on a semi-infinite lattice is given in terms of Casorati-type determinants.
	stacks.iop.org /0305-4470/37/4557 (226 words)

	Symplectic geometry seminar (Site not responding. Last check: 2007-10-01)
		Guillemin and Sternberg constructed in the 1980s the Gel'fand-Cetlin integrable system on the coadjoint orbits of $U(n,\C)$, which is the symplectic geometric version, via geometric quantization, of the Gel'fand-Cetlin basis.
		In this talk we show how deformation theory give rise to the analogous symplectic-geometric results for the case of $U(n,\H)$, i.e.
		we construct a completely integrable system on the coadjoint orbits of $U(n,\H)$.
	www.math.toronto.edu /symplec/fall03/sem092203.html (145 words)

	BEATRICE's Home Page (Site not responding. Last check: 2007-10-01)
		The numerical solution of a class of systems modelling two-way long wave propagation, with V.A. Dougalis, J. Math.
		Integrable evolution PDE's in time-dependent domains, with A. Fokas, Inv.
		Well-posed boundary value problem for integrable evolution equations on a finite interval Theor.
	www.personal.reading.ac.uk /~sms00bp (243 words)

	Learning in Neural Networks and an Integrable System (ResearchIndex) (Site not responding. Last check: 2007-10-01)
		Learning in Neural Networks and an Integrable System (ResearchIndex)
		Learning in Neural Networks and an Integrable System
		29 Optimization and Dynamical Systems (context) - Helmke, Moore - 1994
	citeseer.ist.psu.edu /23273.html (438 words)

	Vladimir Bazhanov at MSRI - Conformal Field Theory as a completely integrable quantum system (Site not responding. Last check: 2007-10-01)
		Vladimir Bazhanov at MSRI - Conformal Field Theory as a completely integrable quantum system
		Vladimir Bazhanov - Conformal Field Theory as a completely integrable quantum system
		A PDF version of the lecture notes is available here.
	www.msri.org /publications/ln/msri/2002/ssymmetry/bazhanov/1 (36 words)

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