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# Vector bundles: In a manner similar to the previous examples the projections ( p: V → S ) of real ( complex ) vector bundles to their base spaces form a category Vect < sub > R </ sub > ( Vect < sub > C </ sub >) over Top ( morphisms of vector bundles respecting the vector space structure of the fibres ).
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# and Vector
# Vector fields on any smooth manifold M can be thought of as derivations X of the ring of smooth functions on the manifold, and therefore form a Lie algebra under the Lie bracket = XY − YX, because the Lie bracket of any two derivations is a derivation.
See the Jones_calculus # Jones_vectors | Jones Vector for a detailed list of the 6 common polarization types.
# Tab at top of page: When viewing a page, click the star symbol File: Vector skin-page not in the watchlist. png between the ' View history ' tab and the search box at the very top of the page, to respectively add or remove the page from your watchlist.
# and bundles
# the cortex, which contains the keratin bundles in cell structures that remain roughly rod-like ; and in some cases,
To show that this definition is equivalent to the others above, one must introduce a suitable notion of a moving frame for the bundle E. In general, this is possible for any G-connection on a fibre bundle with structure group G. See Ehresmann connection # Associated bundles for more details.
# Fibre bundles: Fibre products exist in the category Top of topological spaces and thus by the previous example A ( Top ) is fibred over Top.
# and manner
# Direct contempt is that which occurs in the presence of the presiding judge ( in facie curiae ) and may be dealt with summarily: the judge notifies the offending party that he or she has acted in a manner which disrupts the tribunal and prejudices the administration of justice.
# Ensuring that substantive support is provided in a timely manner to the human rights treaty body concerned, drawing on the appropriate resources of the human rights programme ;
# Allow for any manner of traversal of document ( beginning to end, end to beginning, alphabetical order, etc.
# A form of coherent interference that affects two or more elements of a network in a similar manner ( i. e., highly coupled ) as distinct from locally generated noise or interference that is statistically independent between pairs of network elements.
# The quality of an AIS when it performs its intended function in an unimpaired manner, free from deliberate or inadvertent unauthorized manipulation of the system.
# Best known of all, Pickens riding a dropped H-bomb to a certain death, whooping and waving his cowboy hat ( in the manner of a rodeo performer bronc riding or bull riding ), not knowing its detonation will trigger a Russian doomsday device.
# All Members shall settle their international disputes by peaceful means in such a manner that international peace and security, and justice, are not endangered.
# All Members shall refrain in their international relations from the threat or use of force against the territorial integrity or political independence of any state, or in any other manner inconsistent with the Purposes of the United Nations.
# " Based, as we said, on the quantity and constitution of the underlying objects, meaning generally by " constitution " the manner of composition.
# it must be executed by both parties ( not their attorneys ) " in the manner required for a deed to be recorded ", known as an acknowledgment, before a notary public.
# Communities of transaction emphasize the importance of buying and selling products in a social online manner where people must interact in order to complete the transaction.
# Susceptibility to teratogenesis depends on the genotype of the conceptus and the manner in which this interacts with adverse environmental factors.
# Subject to full public assessment and use without constraints in a manner equally available to all parties ;
# None shall strike another on board the ship, but every man's quarrel shall be ended on shore by sword or pistol in this manner.
# The Commentaries of Sir W. Blackstone, Knight, on the Law and Constitution of England, carefully abridged in a new manner, and continued down to the present time ... By Wm.
# The rule is susceptible to tactical voting, in the sense that there are conditions under which a voter with full knowledge of how the other voters are to vote and of the rule being used would have an incentive to vote in a manner that does not reflect his preferences.
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