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Topic: Loop space

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	PlanetMath: loop space
		be a topological space, and give the space of continuous maps
		Cross-references: relative topology, loops, subset, open, compact, collection, subbasis, compact-open topology, continuous maps, topological space
		This is version 4 of loop space, born on 2002-02-02, modified 2003-07-25.
	planetmath.org /encyclopedia/LoopSpace.html (62 words)

	Space Station - MSN Encarta
		Space stations are used as laboratories where scientific and engineering experiments are conducted and as servicing centers where spacecraft can be repaired, upgraded, or even constructed.
		Space stations are expected to one day act as spaceports where spacecraft can pick up and deliver people, cargo, and fuel on the way to or returning from distant destinations, such as Mars.
		A space station was first proposed by Russian scientist Konstantin Tsiolkovsky at the beginning of the 20th century.
	encarta.msn.com /encyclopedia_761587628/Space_Station.html (963 words)

	Reference.com/Encyclopedia/Loop space
		In mathematics, the space of loops or loop space of a topological space X is the space of continuous maps from the unit circle S
		If we consider the quotient of the loop space with respect to the equivalence relation of pointed homotopy, then we obtain a group, the well-known fundamental group.
		The loop space construction is right adjoint to the suspension functor, and the version for pointed spaces to the reduced suspension.
	www.reference.com /browse/wiki/Infinite_loop_space (205 words)

	The Reference Frame: Objections to loop quantum gravity
		In theoretical physics, loop quantum gravity is one speculative approach to quantum gravity, sometimes cited as a competitor theory to string theory.
		It is not surprising; if loop quantum gravity cannot predict the existence of space itself, it is even more difficult to decide whether it predicts the existence of gravitons and their interactions.
		Loop quantum gravity, on the other hand, says that geometry is a good variable at all distance scales, and the areas etc. have discrete spectrum, which contradicts Lorentz invariance in any theory with local excitations.
	motls.blogspot.com /2004/10/objections-to-loop-quantum-gravity.html (5350 words)

	ARCH'IT architetture / BASE 4. Loop.space
		Close up view of the nest-like spaces of the loop machine, a closed box in which 50 m of film is inserted.
		The pavilion relies on spontaneous crowd congregation to propose a new radical way of perceiving a given sporting event, and each looped space is perceived as an immersive environment in which the relationship of scale and proportion between the viewer and projection are radically modified.
		Internal view of a looped space within which the spatial configuration and the media information displayed maintain the crowd in a focused and united state.
	architettura.supereva.com /architetture/20060513/index.htm (950 words)

	BioMed Central \| Full text \| Saturating representation of loop conformational fragments in structure databanks
		These loops are involved in the recognition of the antigen molecules and have been shown that for five of the six CDR loops (also known as the hypervariable regions) there are few different main-chain conformations (canonical forms)[29].
		For instance, for loop length 8 a 62.5% cutoff is required to guarantee similar conformations but in case of 12 residue loops 41.6% cutoff is already enough to ensure structural similarity (Figure 2a and Table 3 and 4).
		Almost all loop fragments in 2005 can be matched sequentially to a fragment already known in 2001 with 40% of greater sequence identity, and 25% of all loop sequences in 2005 have a 100% sequence identity to loop sequences in 2001 (Figure 4).
	www.biomedcentral.com /1472-6807/6/15 (5569 words)

	3.3 Fermat’s principle and Morse theory in globally hyperbolic spacetimes
		(The loop space of a connected topological space is the space of all continuous curves joining any two fixed points.) On this Hilbert manifold, the energy functional is always bounded from below, and its critical points are exactly the geodesics between the given end-points.
		is necessary for relating the space of trial paths (i.e., of past-oriented lightlike curves from
		) to the loop space of the spacetime manifold or, equivalently, to the loop space of a Cauchy surface.
	www.emis.de /journals/LRG/Articles/lrr-2004-9/articlesu12.html (1205 words)

	Loop Page
		The loop should be mechanically stable (wires not flopping loose) The distributed capacitance between turns should be kept low by proper design to allow for wide tuning range, but not too wide to degrade the length to diameter ratio of the coil.
		To mount it to the loop head, I used a hole in the crossover of the loop to attach to the alt-azimuth mount.
		Prior to this, loops were of the transformer variety, with the signal being coupled to the receiver via a link turn, wound amongst, but not attached to the windings of the main tank coil.
	www.frontiernet.net /~jadale/Loop.htm (6432 words)

	The Single Turn Magnetic Loop Antenna
		So if you have the space, and even if you don't have alot of extra space, you might consider the loop to be a very good alternative to the dipole, or even a (Yagi) beam.
		Larger loops are rarely seen these days in full view since they usually blend in so well with their surroundings.
		A horizontal loop is similar to a vertical radiator in that its propagation is omni-directional.
	ka1fsb.home.att.net /loopants.html (4099 words)

	Art: Loop space \| VRoot.org (Site not responding. Last check: 2007-10-29)
		Inside the pavilion, each looped space is perceived as an immersive environment in which the relationship of scale and proportion between the viewer and projection are modified.
		The pavilion can unfold itself as needed into a network of spaces which are defined by parameters of time, boundary, crowd density and program; the structure is able to continuously adapt itself to any kind of boundary condition.
		There are 3 structural deformations: tilting (vertical deformation), loop formation (horizontal curvature) and twisting (diagonal deformation), and each space can perform them singularly or in combination to achieve the spatial quality requested by the programme and the user.
	vroot.org /node/517 (258 words)

	Loops of Space - - science news articles online technology magazine articles Loops of Space (Site not responding. Last check: 2007-10-29)
		By applying the loop formulation of quantum theory to the problem, they were the first to derive discrete units of space directly from the equations of general relativity.
		Now space joins the quantum party, but only at an amazingly small scale; the diameter of a quantum loop is a minuscule 10-33 centimeter (a million-billion-billion- billionths of a centimeter).
		According to Smolin, it is difficult to talk about the properties of one loop of space, just as you can’t talk about the temperature or density of a single atom.
	www.discover.com /issues/apr-93/features/loopsofspace199 (5616 words)

	Loop group - Wikipedia, the free encyclopedia
		In mathematics, a loop group is a group of loops in a topological group G with multiplication defined pointwise.
		An element of LG is called a loop in G. Pointwise multiplication of such loops gives LG the structure of a topological group.
		The space LG is called the free loop group on G.
	en.wikipedia.org /wiki/Loop_group (253 words)

	[No title]
		The closed-loop-antifreeze space heating system consists of two loops; the heat collection loop and the heat delivery loop.
		The drain-back space heating system consists of two loops; the heat collection loop and the heat delivery loop.
		The air can then either be directed into a room for space heating or into a heat storage bin for use at a later time.
	www.coseia.org /SolarSpaceHeating.html (1606 words)

	Open problems in homotopy theory of Lie groups
		For instance this has been used to show in [3] that every finite loop space is homotopy equivalent to a smooth parallelizable manifold.
		It has also been used in [1] to produce an exotic finite loop space which is not rationally homotopy equivalent to any compact Lie group, resolving an old conjecture in the negative.
		A finite loop space not rationally equivalent to a compact lie group.
	www.lehigh.edu /~dlj0/Grodal-problemsession.html (694 words)

	Loop space
		Inside the pavilion, each looped space is perceived as an immersive environment in which the relationship of scale and proportion between the viewer and projection are modified.
		The pavilion can unfold itself as needed into a network of spaces which are defined by parameters of time, boundary, crowd density and program; the structure is able to continuously adapt itself to any kind of boundary condition.
		There are 3 structural deformations: tilting (vertical deformation), loop formation (horizontal curvature) and twisting (diagonal deformation), and each space can perform them singularly or in combination to achieve the spatial quality requested by the programme and the user.
	www.we-make-money-not-art.com /archives/008492.php (578 words)

	Interceptive Orthodontics and Space Maintenance
		The premature loss of primary molars may require the placement of a space maintainer to prevent the migration of the adjacent teeth, depending upon the teeth present and the arch length.
		A space maintainer is usually not necessary if there is a sufficient amount of space present to allow for eruption of permanent tooth/teeth.
		A space maintainer may not be recommended if severe crowding exists, such that space maintenance is of minimal effect and subsequent orthodontic intervention is indicated.
	www1.umn.edu /dental/courses/dent_5501/orthohts.htm (1341 words)

	freesound :: view tag :: loop space
		convoluted back to back loop 60 bpm 1a.wav :: (0:02) :: This is loop 1 in a series of 40 loops that...
		convoluted back to back loop 60 bpm 1b.wav :: (0:02) :: This is loop 2 in a series of 40 loops that...
		convoluted back to back loop 60 bpm 1c.wav :: (0:02) :: This is loop 3 in a series of 40 loops that...
	freesound.iua.upf.edu /tagsViewSingle.php?id=98_155 (390 words)

	Chicago West Loop Commercial Loft Office Rental Space For Rent Or Lease
		The location of this west loop rental loft office building is becoming the city's most sought after area, placing you steps away from Greek Town, UIC, Civic Opera House, Chicago theatres, as well as Michigan Avenue and State Street shopping.
		This chicago office space puts your business within walking distance of public transportation and gives you easy access to major expressways as well as availability of a T-3 LINE IN OUR BUILDING.
		This chicago office building offers extremely unique west loop commercial space for rent, lease, or sublease that is hard to find.
	www.730randolph.com (177 words)

	Space, NASA and astronomy news \| Chron.com - Houston Chronicle
		Astronaut's love of movies out of this world— Each week he has been in space, Lopez-Alegria has picked a "movie of the week." He sends down snippets of music or dialogue from the space station's DVD collection and sends clues in e-mails or radio transmissions until flight controllers correctly guess the film.
		NASA jostles space station to try to fix solar panel—Two tries to jar the half-retracted wing into place fail, setting up a possible, unplanned fourth spacewalk.
		Problem — Kinks that occurred while retracting the solar array aboard the international space station forced Discovery astronauts to stop for the day.
	www.chron.com /news/space (539 words)

	Loop Space (Site not responding. Last check: 2007-10-29)
		bookings for the Loop can be sent by e mail (provisionally, please only when the dates are listed below) otherwise by post see "booking information"
		Loop dates - 01 October to 14 March
		Annual WW event on the Dart Loop 17/18 Feb 07
	www.dartaccess.co.uk /currentLoopinfo.html (60 words)

	Transactions of the American Mathematical Society
		On the equivariant Morse complex of the free loop space of a surface
		Abstract: We prove two theorems about the equivariant topology of the free loop space of a surface.
		G. Lodder, Dihedral homology and the free loop space, Proc.
	www.ams.org /tran/1998-350-03/S0002-9947-98-02097-2/home.html (289 words)

	Chicago spa: Spa Space Downtown Chicago
		Located in the West Loop, Spa Space is considered the most progressive Chicago spa downtown for men and women.
		About Us - Located on the west edge of Chicago's Loop, Spa Space was formed from the idea that corrective, therapeutic and highly effective treatments need not be performed in a cold, medical environment.
		Our Space - Every inch of Spa Space is designed to make you feel indulged, relaxed and confident that you're in good, caring hands.
	www.spaspace.com /chicago_spa.htm (880 words)

	Classifying Spaces Made Easy
		It follows that each space E(n) is an infinite loop space: a space of loops in a space of loops in a space of loops in...
		If G is any topological group, there is a topological space BG with a basepoint such that the space of loops in BG starting and ending at this point is homotopy equivalent to G. This space BG is unique up to homotopy equivalence.
		The quotient space BG = EG/G is thus the space of all nordered n-tuples of distinct points in an infinite-dimensional Hilbert space.
	math.ucr.edu /home/baez/calgary/BG.html (6059 words)

	String Propagator: a Loop Space Representation
		The string quantum kernel is normally written as a functional sum over the string coordinates and the world-sheet metrics.
		As an alternative to this quantum field-inspired approach, we study the closed bosonic string propagation amplitude in the functional space of loop configurations.
		This functional theory is based entirely on the Jacobi variational formulation of quantum mechanics, without the use of a lattice approximation.
	www-dft.ts.infn.it /~ansoldi/Research/StringPropagator/HTML/index.html (128 words)

	Math Forum Discussions
		> that infinite loop spaces can be viewed like sheaves of spaces.
		You proved that any n-fold loop space is an n-fold
		homotopy-algebraic structures on loop spaces: indeed, much of the theory was
	www.mathforum.org /kb/message.jspa?messageID=1690195&tstart=0 (403 words)

	LOOP — Loop Bar, Melbourne Bar — Art Space & Venue
		Buff Diss will be performing his own style of masking tape art all over loop which needs to be seen to be believed.
		Luxxe has now reformed on Aussie shores with pair Duotone travelling far from their space station in Aotearoa to rock Melbourne-ites for the first time.
		Duotone has interfaced with Luke Mac D and Sdzeit to slam it out at Melbournes esteemed Loop Venue on Saturday the 4th of August.
	www.looponline.com.au (872 words)

	Math Forum Discussions
		that infinite loop spaces can be viewed like sheaves of spaces.
		shows that the category of n-fold loop spaces is a category of sheaves
		n-fold loop spaces can be characterized by homotopy C-algebras.
	www.mathforum.org /kb/message.jspa?messageID=1690194&tstart=0 (511 words)

	Léandre: Diffeomorphisms of the circle and the based stochastic loop space
		Léandre: Diffeomorphisms of the circle and the based stochastic loop space
		Diffeomorphisms of the circle and the based stochastic loop space.
		: Invariant Sobolev Calculus on the free loop space.
	www.numdam.org /numdam-bin/item?id=SPS_1997__31__322_0 (97 words)

	Transactions of the American Mathematical Society
		Algebraic structure in the loop space homology Bockstein spectral sequence
		Stephen Halperin, Universal enveloping algebras and loop space homology, J. Pure Appl.
		Keywords: Loop space homology, Bockstein spectral sequence, universal enveloping algebra
	www.ams.org /tran/2002-354-08/S0002-9947-02-02971-9/home.html (190 words)

	sysidhl
		Shown are actual experimental excitation and response data collected from the Hubble Space Telescope in orbit.
		From this set of data, a special set parameters called Observer Markov Parameters, which are linearly related to input-output data, are computed.
		In addition to recovering the system open-loop state space model, OCID also identifies the system existing state feedback controller gain, and an optimal observer gain associated with the process and measurement noise embedded in the experimental data.
	www.dartmouth.edu /~mqphan/sidhlights.html (2992 words)

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