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Topic: Line bundle

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	Bundle Gerbes: General Idea and Definition \| The n-Category Café
		A bundle gerbe is a categorification of a transition function of a fiber bundle.
		For that reason, bundle gerbes are sometimes addressed as a “geometric realization of third integral cohomology”, in the same sense that complex line bundles are a “geometric realization of second integral cohomology”.
		For complex line bundle gerbes the above definition can be understood as obtained from the definition of a transition function of a line bundle by replacing the monoid of complex numbers by the monoidal category of 1-dimensional complex vector spaces; and by replacing equations between numbers by coherent (here: associative) isomorphisms of vector spaces.
	golem.ph.utexas.edu /category/2006/10/bundle_gerbes.html (860 words)

	Line bundle - Wikipedia, the free encyclopedia
		For example a curve in the plane having a tangent line at each point determines a varying line: the tangent bundle is a way of organising these.
		This reminds one of the orientation double cover on a differential manifold: indeed that's a special case in which the line bundle is the determinant bundle (top exterior power) of the tangent bundle.
		In the case of the complex line bundle, we are looking in fact also for circle bundles.
	en.wikipedia.org /wiki/Line_bundle (680 words)

	eGenome Help
		Bundles are collections of individual elements that share identical database identifiers and compatible genomic positions, and so presumably represent the same genomic feature.
		The top of the page is a bundle data section displaying general information about the bundle and its position in the genome.
		In some instances a bundle min cannot be defined, in which case the minimal position is listed as "none" and only the max position is shown with a value.
	egenome.chop.edu /access/pages/help/viewbundle.html (1855 words)

	Springer Online Reference Works
		The study of line bundles on projective varieties is a classical problem in algebraic geometry (cf.
		vector bundles on a compact complex algebraic surface was shown to be isomorphic to the moduli space of instanton unitary vector bundles on the corresponding
		An instanton vector bundle on a Riemannian manifold is a differential bundle together with a connection whose curvature form satisfies a certain system of non-linear differential equations.
	eom.springer.de /v/v096390.htm (1313 words)

	Institute for Healthcare Improvement: Central Line Bundle Compliance
		The percentage of intensive care unit (ICU) patients with central lines for whom all five elements of the Central Line Bundle are documented on the daily goals sheet and/or central line insertion checklist or patient's medical record.
		If a bundle element is contraindicated for a particular patient and this is documented appropriately on the checklist, then the patient can still be considered compliant with regard to this measure.
		Incorporating the five elements of the Central Line Bundle into a central line insertion checklist and a daily goals sheet, and reviewing lines daily during multidisciplinary rounds, allows for easy review of bundle compliance.
	www.ihi.org /IHI/Topics/CriticalCare/IntensiveCare/Measures/CentralLineBundleComplianceRate.htm (463 words)

	PlanetMath: line bundle
		In algebraic geometry, the term line bundle refers to a locally free coherent sheaf of rank 1, also called an invertible sheaf.
		Cross-references: point, stalk, map, obvious, dimension, continuous functions, topology, sections, holomorphic, sheaf, variety, algebraic, non-singular, equivalent, vector bundle, complex, real, theory, manifold, invertible sheaf, rank, coherent sheaf, locally free, term, algebraic geometry
		This is version 2 of line bundle, born on 2003-03-13, modified 2003-08-22.
	planetmath.org /encyclopedia/LineBundle.html (137 words)

	Geometrical Objects
		Line segment bundles probably have some applications in computer vision algorithms, but the primary reason for including them is to provide an efficient way to draw a large number of line segments (cf.
		Line segment bundles are created (accessed) using the same function as to create (access) a line segment but the inputs (outputs) are sheets rather than single points.
		However, it is not an error to create polygon bundles in which the domain is continuous: this represents a filled region whose shape is interpolated between the explicitly specified polygons.
	www.cs.hmc.edu /~fleck/envision/user-manual/geometrical-objects.html (1453 words)

	Resource Bundles in Depth (Site not responding. Last check: 2007-11-03)
		Resource bundles are searched by changing all the dots to slashes, then appending the changed name to each path in the class path.
		Bundles names occuring earlier in the string have their corresponding bundles checked before bundles specified later in the string.
		The text2gui library's resource bundle factories also cache resource bundles, but they allow the bundle cache to be invalidated, so that the next load of a bundle re-reads the file backing the bundle.
	www.tacosoftware.com /products/text2gui/docs/Resource_Bundle.html (2062 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		>They define a canonical line bundle over >a real projective space Pn as the subset >of Pn x Rn+1 consisting of all pairs ((-x,+x),v) >such that v is a multiple of x.
		> They define a canonical line bundle over > a real projective space Pn as the subset > of Pn x Rn+1 consisting of all pairs ((-x,+x),v) > such that v is a multiple of x.
		Anyhow, what that means is that you know pretty much everything there is to know about line bundles, once you get a good mental picture of the canonical line bundles over real projective spaces.
	www.math.niu.edu /~rusin/known-math/99/bundle (461 words)

	Tracepak Bundles for Sample Transport and Conditioning (Site not responding. Last check: 2007-11-03)
		Some form of external heating must be provided to the sample line to maintain the sample integrity and prevent components in the sample from condensing out as the temperature drops below their respective dew points.
		To avoid failed sample lines, a thorough design with proper tubing such as PFA Teflon and a temperature controller is needed.
		In dry extractive systems, after the sample is extracted from the flue and conditioned to remove particulates and moisture, the gaseous sample is transported in a heat traced line to an environmental enclosure where the analyzer is located.
	www.obcorp.com /WebPages/TubingBundles/TXsample.htm (891 words)

	Atlas: Canonical Representations of Orthogonal Groups of Line-Bundle-Valued Ternary Quadratic Bundles over Schemes with ...
		Given a line-bundle-valued ternary quadratic bundle over any scheme, there is a functorial representation of its group of orthogonal similitudes in the Witt-invariant, which by definition is the degree zero part of the associated generalised Clifford algebra bundle.
		The various orthogonal groups of a quadratic bundle are canonically determined in terms of the automorphisms of its even Clifford algebra.
		Hence the self-duality of the underlying bundle of the even Clifford algebra implies that the quadratic bundle is semiregular everywhere if it is semiregular even at a single point.
	atlas-conferences.com /cgi-bin/abstract/caoz-56 (625 words)

	NurseZone - On the job - Nursing news - Archive
		While they are often lifesavers, these “central lines” are also dangerous infection risks, responsible for as many as 28,000 deaths each year, due to the introduction of lethal pathogens during insertion or the growth of the patient’s own bacteria on the catheter line.
		Since implementing the five elements in the Central Line Bundle, which was created in the mid-1990s, hospitals across the nation have seen results in lowering the incidence of central line infections.
		As with any initiative, preventing central line infections is an ongoing effort, and the staff at Community Hospital South will continue to look for ways to improve, looking to the IHI collaborative and its network of hospitals to share ideas on what has been successful.
	www.nursezone.com /job/MedicalNewsAlerts.asp?articleID=15082 (1309 words)

	Flex Line Bundles (Site not responding. Last check: 2007-11-03)
		A Flex Line Bundle delivers both voice and data over a high capacity customizing the voice/data allocation to meet the needs of your business.
		Minute Bundles offer a great per-minute rate while providing a level of predictability to your monthly invoice.
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	www.telepacific.com /products/flexLineBundle.asp (597 words)

	Canonical line bundle - Wikipedia, the free encyclopedia
		The canonical or tautological line bundle on a projective space appears frequently in mathematics, often in the study of characteristic classes.
		Note that there is possible confusion with the theory of the canonical class in algebraic geometry; for which reason the name tautological is preferred in some contexts.
		In fact, it is straightforward to show that, for n = 1, the canonical line bundle is none other than the well-known bundle whose total space is the Möbius band.
	en.wikipedia.org /wiki/Canonical_line_bundle (175 words)

	Line 6 - TonePort
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	www.line6.com /toneport (379 words)

	The Official Step By Step Guide - 2
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	startingaclothingline.com /html/the_official_step_by_step_guid.html (715 words)

	DATA Step Graphics Interface Dictionary : LINREP
		ERROR: A representation for the specified line type index has not been defined on this workstation.
		numeric variable name; returns the line width (in pixels) associated with the bundle.
		Refer to Line Types for representations of the line types.
	www.asu.edu /sas/sasdoc/sashtml/gref/z1060769.htm (209 words)

	week125
		Locally a section of a complex line bundle looks a lot like a complex-valued function, but this isn't true globally unless your line bundle is trivial.
		This is actually an abelian group, since when we tensor two line bundles we get another line bundle, and when you tensor any line bundle with its dual, you get the trivial line bundle, which plays the role of the multiplicative identity for tensor products.
		It was recently shown that the renormalization of quantum field theory is organized by the Hopf algebra of decorated rooted trees, whose coproduct identifies the divergences requiring subtraction and whose antipode achieves this.
	math.ucr.edu /home/baez/week125.html (2712 words)

	Projective Lines
		Projective lines are not very interesting from the viewpoint of axiomatic projective geometry, since they have only one line on which all the points lie.
		is the line through the origin corresponding to this point.
		These bundles play an important role in topology, so it is good to understand them in a number of ways.
	math.ucr.edu /home/baez/octonions/node9.html (1085 words)

	34a
		We define a tropical line bundle to be an element of
		We saw how sections of tropical line bundles over tori are tropical theta functions.
		This carries a complex structure which interchanges horizontal and vertical directions in the tangent bundle.
	www.aimath.org /WWN/amoebas/articles/html/34a (594 words)

	Ample cone
		That is, a line bundle is very ample if it can be obtained by pulling back
		The tensor product of two very ample line bundles is again very ample.
		A line bundle on a projective variety is ample if some tensor power of it is very ample.
	www.aimath.org /WWN/modspacecurves/glossary/node1.html (93 words)

	$L^{2}$ extension for jets of holomorphic sections of a hermitian line bundle, Dan Popovici
		Let $(X, \omega)$ be a weakly pseudoconvex Kähler manifold, $Y \subset X$ a closed submanifold defined by some holomorphic section of a vector bundle over $X$, and $L$ a Hermitian line bundle satisfying certain positivity conditions.
		In particular, if $Y$ is merely a point, this gives the existence of a global holomorphic function with an $L^{2}$ norm under control and with prescribed values for all its derivatives up to order $k$ at that point.
		This result generalizes the $L^{2}$ extension theorems of Ohsawa-Takegoshi and of Manivel to the case of jets of sections of a line bundle.
	projecteuclid.org /getRecord?id=euclid.nmj/1134569893 (609 words)

	Line 6 GearBox Gold Bundle \| Sweetwater.com
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	www.sweetwater.com /store/detail/GearBoxGold (502 words)

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	www.creativepro.com /story/news/5049.html (826 words)

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	Auto FX Product Line Bundle (Site not responding. Last check: 2007-11-03)
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	www.thepowerxchange.com /product_2025_detailed.html (162 words)

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