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	Fiber bundle - Wikipedia, the free encyclopedia
		Fiber bundles generalize vector bundles, where the main example is the tangent bundle of a manifold.
		A sphere bundle is a fiber bundle whose fiber is an n-sphere.
		In the smooth category, a G-bundle is a smooth fiber bundle where G is a Lie group and the corresponding action on F is smooth and the transition functions are all smooth maps.
	en.wikipedia.org /wiki/Fiber_bundle (1166 words)

	Fibre Bundle
		faisceau fibreux (bundle of fibres), faisceau de fibres (bundle of fibres), paquet de fibres (bundle of fibres), bundle (bundle of fibres).
		fascio di fibre (bast bundle, bundle, bundle of fibres), fascetto di fibre (bast bundle, bundle, bundle of fibres), mazzetta di fibre (bast bundle, bundle, bundle of fibres), bundle (bast bundle, bundle, bundle of fibres).
		feixe fibroso (bast bundle, bundle, bundle of fibres), feixe de fibras (bast bundle, bundle, bundle of fibres, reed, staple), tubo de fibras (bast bundle, bundle, bundle of fibres).
	www.websters-online-dictionary.org /fi/fibre+bundle.html (397 words)

	Method of and apparatus for producing a glass fibre bundle for use in optical communications systems - Patent 4204852
		To reduce breakage of fibres in optical glass fibre bundles during manufacture caused by formation of loops in the fibre during sheathing, a twist is imparted to the fibre bundle during its formation.
		The greater the number of fibres in the bundle, the greater is the problem created by the loops due to an increase in the difference in length introduced between different fibres in the bundle.
		Whilst we prefer to impart a twist to the fibre bundle by rotation of the glass rods as the fibre bundle is drawn, it is also, of course, possible to impart a twist by maintaining the rods stationary and rotating the winding drum.
	www.freepatentsonline.com /4204852.html (2586 words)

	Fiber bundle -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-18)
		Fiber bundles generalize (Click link for more info and facts about vector bundle) vector bundles of which the main example is the (Click link for more info and facts about tangent bundle) tangent bundle of a (A pipe that has several lateral outlets to or from other pipes) manifold.
		A similar nontrivial bundle is the (A closed surface with only one side; formed by passing one end of a tube through the side of the tube and joining it with the other end) Klein bottle which can be viewed as a "twisted" circle bundle over another circle.
		Fiber bundles often come with a ((chemistry) two or more atoms bound together as a single unit and forming part of a molecule) group of symmetries which describe the matching conditions between overlapping local trivialization charts.
	www.absoluteastronomy.com /encyclopedia/f/fi/fiber_bundle.htm (1581 words)

	PlanetMath: fiber bundle
		Some examples of fiber bundles are vector bundles and covering spaces.
		Thus we have a category of fiber bundles over a fixed base with fixed structure group.
		This is version 7 of fiber bundle, born on 2002-10-31, modified 2003-06-24.
	planetmath.org /encyclopedia/FiberBundle.html (158 words)

	Illuminating device having optical light guide formed as fibre bundle - Patent 4483585
		These fibres are bundled, end rings are fitted at both ends of the bundle, and both ends are suitably ground to form a fibre bundle of flexible, semi-rigid or rigid conduit.
		MgF.sub.2 is applied on a glass base plate having substantially the same refractive index as that of the fibre bundle and the glass base plates are adhered on the input and output end surfaces of the fibre bundle by a transparent adhesive having substantially the same refractive index as that of the fibre bundle.
		The illuminating device having the fibre bundle according to the present invention comprises an optical reflecting body having a peripheral reflecting surface attached to the incidence end surface of the fibre bundle.
	www.freepatentsonline.com /4483585.html (3987 words)

	Apparatus for removing the wrapper from a wrapped fibre bundle - Patent 4746259
		It is generally known that fibres are transported in the form of fibre bundles from the fibre manufacturer to the brush manufacturer, such fibre bundles consisting of a bundle of loose fibres being held together by a wrapper which mainly consists of a paper strip or the like.
		Obviously, gripping fibre bundle 1 at its wrapper 2 can occur in still other ways, e.g., by allowing a number of short pins, that are distributed along the periphery of fibre bundle 1, to act radially with respect to the latter in wrapper 2.
		In a preferred variant the semicircular cut-outs 27-28 are replaced by angular cut-outs so that fibre bundle 1 upon being applied between the protruding parts 25-26 of the slides is pressed in the form of a polygon, the number of sides of this polygon corresponding with the number of arms 7.
	freepatentsonline.com /4746259.html (2888 words)

	CMMT(MN)063 Environmental and Fatigue Testing of Fibre Bundles and Impregnated Strands (Site not responding. Last check: 2007-10-18)
		It is important when feeding the fibre bundle through the resin bath that the speed and tension is sufficient to produce a uniformly impregnated test specimen.
		This is because the load capacity of the fibre bundle gradually deteriorates as the weaker fibres fail with increasing load.
		E-glass fibre strands were observed to degrade steadily in deionised water with the rate of degradation being temperature independent over the temperature range 23°C to 70°C (Figure 5).
	midas.npl.co.uk /midas/content/mn063.html (4419 words)

	Fibre-optics bundles (from optics) -- Encyclopædia Britannica
		An ordered bundle of rods or fibres is thus capable of taking an image projected upon one end of the bundle and reproducing it at the other end.
		Fibre optics is also the basis of the fibrescopes used in examining internal parts of...
		In the eye, the nerve forms from the convergence of visual nerve fibres in the optic disk at the rear of the eyeball.
	www.britannica.com /eb/article-37969 (941 words)

	Sculpture Maths - - Fibre Bundles (Site not responding. Last check: 2007-10-18)
		The structure of a fibre bundle consists of a base, which for the Möbius Band and other of John's sculptures, is a circle.
		The notion of a fibre bundle is so general that it describes new kinds of objects which are difficult to visualise as they may be realised properly only in a space of many dimensions, or have to be constructed as a concatenation of given forms and data.
		The fibre could also be, not a triangle or square, but one of the five Platonic solids, for example a tetrahedron or a cube.
	www.popmath.org.uk /sculpmath/pagesm/fibundle.html (791 words)

	Steve's place - Plant Growth
		Vascular bundles are composed of four main tissues: xylem conducts water to leaves; the vascular cambium between xylem and phloem can produce new cells; phloem conducts sugars from sources to sinks such as growing leaves, roots, storage parenchyma in the trunk and specialised storage organs; and sclerenchyma fibres protect the bundle from mechanical damage.
		It is a low density fibre composite formed from fibres (cells), which themselves are formed mostly from polymeric cellulose strands, embedded in a lignin matrix.
		Fibres (cells) are glued together by a lignified middle lamella.
	www.steve.gb.com /science/plant_growth.html (1882 words)

	Fibre bundles (Site not responding. Last check: 2007-10-18)
		A typical fibre bundle associated to any manifold M is the tangent bundle TM, which is the bundle formed by all the tangent vectors.
		is the bundle of all covectors, that is the fibres of this bundle are dual to the fibres of the tangent bundle.
		A principal fibre bundle P with structure group G is defined as a fibre bundle with a free and transitive right G-action on the fibres.
	www.phys.uu.nl /~hofman/scriptie/duality/node50.html (738 words)

	Sirolan Tensor (Site not responding. Last check: 2007-10-18)
		Average fibre strength, or fibre bundle strength, is particularly important for quantifying damage in dyed wools.
		A 10% drop in bundle tenacity reduces spinning performance by an amount similar to that caused by a 6-9 mm reduction in Hauteur.
		Bundle tenacity is an important component in predicting yarn strength and spinning performance.
	www.tft.csiro.au /achievements/sirolantensor.html (549 words)

	Amazon.com: The Topology of Fibre Bundles. (PMS-14): Books (Site not responding. Last check: 2007-10-18)
		Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory.
		A fibre bundle consists, at least, of the following: (i) a topological space B called the bundle space (or, simply, bundle), (ii) a topological space X called the base space, (iii) a continuous map p: B X of B onto X called the projection, and (iv) a space Y called the fibre.
		Fiber bundles are now ubiquitous in differential topology, algebraic topology, differential geometry, and algebraic geometry, and have also found a place in theoretical physics, thanks to the success of gauge field theories.
	www.amazon.com /exec/obidos/tg/detail/-/0691005486?v=glance (1438 words)

	Let There Be Light. Scoping with fibre optics.
		With fibre optics it is the "active" fibre tip, not the filament, that is imaged in the focal plane of the objective (picture 1).
		In cross section, a fibre optic light transfer cable consists of a central core made up of hundreds of very fine glass filaments cemented together to form a bundle which is wrapped in a flexible protective outer jacket or cable.
		The ends of the bundle are polished to optical flatness and embedded in an aluminium or brass casing.
	www.microscopy-uk.org.uk /mag/artmar04/rnfibre.html (1364 words)

	Method and arrangement for producing a basic element of a multi-element optical cable - US Patent 5938987 (Site not responding. Last check: 2007-10-18)
		The fibre tension control device 4 is as shown the FIGURE a device consisting of two successive wheels 4a, 4b, described in greater detail in Finnish patent application 953,338 filed simultaneously with the present application and corresponding U.S. application Ser.
		From the pulling device 8 the unit consisting of the pipe and the fibres is passed via a relaxation zone 11 and a final cooling zone 12 to a receiving spooler 13.
		The operation of the invention is thus based on the controlled tension of the fibre(s) and on the sliding of the fibre(s) inside the protective pipe during the manufacture, which aims at providing a controlled excess length for the fibre.
	www.patentstorm.us /patents/5938987.html (1774 words)

	PlanetMath: jet bundle
		This concept has much in common with that of the germ of a smooth function on a manifold: it contains not only the value of a function at a point, but also some information about the behaviour of the function near that point.
		Instead of defining all the jet bundles at once, we may choose to define only the first jet bundle in the way described above.
		This is version 3 of jet bundle, born on 2005-08-18, modified 2005-08-30.
	planetmath.org /encyclopedia/JetBundle.html (341 words)

	[No title]
		In this second part we turn to submersions between manifolds, establish a ne* cessary and sufficient condition for such a map to be a (locally trivial fibre) bundle* (theorem B belo* *w), and apply it to several typical situations.
		In the fibre Et, we have three domains,(t)(X),,0(t)(X0),,00(t)(X00) ; an* d since ß is a fibration, the second one can be pushed into the third one by a homotopy relative to the first * one.
		B is a submersion-fibration and that a group ac* ts freely, cocompactly and properly discontinuously on E and permutes the fibres*.
	hopf.math.purdue.edu /Meigniez/sfb.txt (4981 words)

	Graduiertenkolleg Analytische Topologie und Metageometrie (Site not responding. Last check: 2007-10-18)
		The purpose of the course is to provide an introduction to basic fibre bundle theory for mathematics and physics students with a minimum of background.
		The gauge group of a fibre bundle and its classifing space is discussed.
		An effort is made to show the unifying character of fibre bundle theory as it is used to relate notions of topology and geometry to algebra, arithmetic, analysis, and mathematical physics.
	wwwmath.uni-muenster.de /math/metageo/vorlesung0001-husemoeller.html (248 words)

	Fast muscle in squid (Loligo pealei): contractile properties of a specialized muscle fibre type -- Kier and Curtin 205 ...
		The muscle fibre bundle preparations (shaded) were obtained by cutting a small section from a transverse slice of the arm or tentacle.
		The extensive sarcoplasmic reticulum (SR) of the cross-striated tentacle fibres is visible.
		The slopes of the dashed lines on the length recordings give the velocity of shortening, and the vertical lines are the same times at which force was measured and mark the centre of the section from which the slopes were measured.
	jeb.biologists.org /cgi/content/figsonly/205/13/1907 (734 words)

	Effects of fibre bundle size and stitch pattern on the static properties of unidirectional carbon-fibre non-crimp ...
		Effects of fibre bundle size and stitch pattern on the static properties of unidirectional carbon-fibre non-crimp fabric composites
		In the present report, the variation in static (tension and compression) properties of unidirectional carbon-fibre NCF composites was studied as a function of stitch pattern and fibre bundle size.
		By studying the effects of stitch pattern and bundle size on the static properties, the aim was to be able to determine the most important stitch parameters to obtain good mechanical properties.
	epubl.luth.se /1402-1617/2002/269 (225 words)

	Isometric and isovelocity contractile performance of red musle fibres from the dogfish Scyliorhinus canicula -- Lou et ...
		was found for each fibre bundle by fitting a hyperbola to its force/velocity data as described in the text.
		by the fibre bundles during stretch is shown in Fig.
		Black lines (white fibres) and red lines (red fibres) were calculated from Hill's equation using the mean values of the fitted constants in Table 3A (means for seven white fibre preparations and seven red fibre preparations).
	jeb.biologists.org /cgi/content/full/205/11/1585 (5142 words)

	Re: principle fibre bundle (Site not responding. Last check: 2007-10-18)
		I can "see" a normal fibre bundle but the I'm not an expert, but as I didn't see anyone else respond: For a principal bundle, the example to keep in mind is the frame bundle.
		Note, a "point" in the frame bundle is a basis set, that is, an ordered n-tuple of vectors.
		Now, if you take the frame bundle, and use a copy of the original vector space from the original vector bundle, the associated bundle is the original vector bundle.
	www.lns.cornell.edu /spr/2002-04/msg0040908.html (232 words)

	IngentaConnect Fibre bundle formulation of nonrelativistic quantum mechanics: I.... (Site not responding. Last check: 2007-10-18)
		Fibre bundle formulation of nonrelativistic quantum mechanics: I. Introduction.
		The new form of the theory is equivalent to the usual one and is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions.
		The present, first, part of this investigation is devoted to the introduction of basic concepts on which the fibre bundle approach to quantum mechanics rests.
	api.ingentaconnect.com /content/iop/jphysa/2001/00000034/00000023/art00308 (286 words)

	"Lie algebroid of a principal fibre bundle" (Site not responding. Last check: 2007-10-18)
		Three natural constructions of the Lie algebroid for a given principal fiber bundle are repeated from the paper [12].
		The most if G is semisimple: two principal fibre bundles with semisimple structural Lie groups are locally isomorphic if and only if their associated Lie algebra bundles are isomorphic.
		In consequence, two arbitrary principal fibre bundles with semisimple structural Lie groups and isomorphic associated Lie algebra bundles have isomorphic Lie algebroids, so they are then locally isomorphic.
	im0.p.lodz.pl /~kubarski/forum/abs15.html (358 words)

	Fiber bundle
		B is called the base space of the fiber bundle and E the total space, and for any
		A section of a fiber bundle is a continuous map,
		, for x in B. Since bundles do not in general have sections, one of the purposes of the theory is to account for their existence.
	www.sciencedaily.com /encyclopedia/fiber_bundle (533 words)

	"Lie algebroid of a principal fibre bundle – three equivalent definitions" (Site not responding. Last check: 2007-10-18)
		Starting with some Atiyah's construction (1957) we define the so-called Lie functor for principal fibre bundles.
		This functor assigns some Lie algebroid (Pradines 1967) to each principal fibre bundle and plays an analogous role as the Lie functor for Lie groups.
		of a principal fibre bundle P(M,G) is constructed by using the Lie algebra X
	im0.p.lodz.pl /~kubarski/forum/abs12.html (150 words)

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