What is "connection"

Connection \Con*nec"tion\, n. [Cf. Connexion.]

1. The act of connecting, or the state of being connected; the act or process of bringing two things into contact; junction; union; as, the connection between church and state is inescapable; the connection of pipes of different diameters requires an adapter.

   Syn: link, connectedness.

2. That which connects or joins together; bond; tie.

3. any relationship between things or events; association; alliance; as, a causal connection between interest rates and stock prices.

   Syn: relation.

   He [Algazel] denied the possibility of a known connection between cause and effect.
   --Whewell.

   The eternal and inseparable connection between virtue and happiness.
   --Atterbury.

   Any sort of connection which is perceived or imagined between two or more things.
   --I. Taylor.

4. A relation; esp. a person connected with another by marriage rather than by blood; -- used in a loose and indefinite, and sometimes a comprehensive, sense.

   4. The persons or things that are connected; as, a business connection; the Methodist connection.

   Men elevated by powerful connection.
   --Motley.

   At the head of a strong parliamentary connection.
   --Macaulay.

   Whose names, forces, connections, and characters were perfectly known to him.
   --Macaulay.

5. something that connects other objects.

   Syn: connexion, connector, connecter, connective.

6. (usually plural) an acquaintance or acquaintances who are influential or in a position of power and to whom you are connected in some way (as by family or friendship); as, he has powerful connections.

7. a communications channel; as, my cell phone had a bad connection.

8. (Transportation) a vehicle in which one may continue a journey after debarking from another vehicle; the departing vehicle of a connection[9]; as, my connection leaves four hours after my arrival; I missed my connection.

   Note: A connection may be more specifically referred to as a connecting flight, a connecting train, etc.

9. (Transportation) the scheduled arrival of one vehicle and departure of a second, sufficiently close in time and place to allow the departing vehicle serve as a means of continuing a journey begun or continued in the first vehicle; as, we can get a connection at Newark to continue on to Paris; -- most commonly used of airplanes, trains, and buses arriving and departing at the same terminal.

10. (Transportation) the transfer of a passenger from one vehicle to another to continue a journey; as, the connection was made in Copenhagen; -- most commonly of scheduled transportation on common carriers.

11. (Commerce) a vendor who can supply desired materials at a favorable price, or under conditions when other sources are unavailable; as, to get a bargain from one's connection in the jewelry trade; to have connections for the purchase of marijuana; -- often used in the pl..

12. (Psychol.) the process of bringing ideas or events together in memory or imagination.

    Syn: association, connection, connexion.

    In this connection, in connection with this subject.

    Note: [A phrase objected to by some writers.]

    Note: This word was formerly written, as by Milton, with x instead of t in the termination, connexion, and the same thing is true of the kindred words inflexion, reflexion, and the like. But the general usage at present is to spell them connection, inflection, reflection, etc.

    Syn: Union; coherence; continuity; junction; association; dependence; intercourse; commerce; communication; affinity; relationship.

late 14c., conneccion, later connexioun (mid-15c.), from Old French connexion, from Latin connexionem (nominative connexio) "a binding or joining together," from *connexare, frequentative of conectere "to fasten together, to tie, join together," from com- "together" (see com-) + nectere "to bind, tie" (see nexus).\n

\nSpelling shifted from connexion to connection (especially in American English) mid-18c. under influence of connect, abetted by affection, direction, etc. See -xion.

n. 1 (context uncountable English) The act of connecting. 2 The point at which two or more things are connected.

1. n. a relation between things or events (as in the case of one causing the other or sharing features with it); "there was a connection between eating that pickle and having that nightmare" [syn: connexion, connectedness] [ant: unconnectedness]

2. the state of being connected; "the connection between church and state is inescapable" [syn: link, connectedness] [ant: disjunction]

3. an instrumentality that connects; "he soldered the connection"; "he didn't have the right connector between the amplifier and the speakers" [syn: connexion, connector, connecter, connective]

4. (usually plural) a person who is influential and to whom you are connected in some way (as by family or friendship); "he has powerful connections"

5. the process of bringing ideas or events together in memory or imagination; "conditioning is a form of learning by association" [syn: association, connexion]

6. a connecting shape [syn: connexion, link]

7. a supplier (especially of narcotics)

8. shifting from one form of transportation to another; "the plane was late and he missed his connection in Atlanta" [syn: connexion]

9. the act of bringing two things into contact (especially for communication); "the joining of hands around the table"; "there was a connection via the internet" [syn: joining, connexion]

Connection may refer to:

Connection is a split EP by the Orange County, California, rock bands Home Grown and Limbeck, released in 2000 by Utility Records. It resulted from a tour the previous year on which the two bands played together and became friends.

The EP was Home Grown's final recording with guitarist Justin Poyser and drummer Bob Herco, who both left the band in 2000.

Geometry of quantum systems (e.g., noncommutative geometry and supergeometry) is mainly phrased in algebraic terms of modules and algebras. Connections on modules are generalization of a linear connection on a smooth vector bundle E → X written as a Koszul connection on the C(X)-module of sections of E → X.

In differential geometry, a fibered manifold is surjective submersion of smooth manifolds Y → X. Locally trivial fibered manifolds are fiber bundles. Therefore, a notion of connection on fibered manifolds provides a general framework of a connection on fiber bundles.

Composite bundles Y → Σ → X play a prominent role in gauge theory with symmetry breaking, e.g., gauge gravitation theory, non-autonomous mechanics where $X=\mathbb R$ is the time axis, e.g., mechanics with time-dependent parameters, and so on. There are the important relations between connections on fiber bundles Y → X, Y → Σ and Σ → X.

In partner dancing, connection is a physical communication method used by a pair of dancers to facilitate synchronized dance movement, in which one dancer (the "lead") directs the movements of the other dancer (the "follower") by means of non-verbal directions conveyed through a physical connection between the dancers. It is an essential technique in many types of partner dancing and is used extensively in partner dances that feature significant physical contact between the dancers, including the Argentine Tango, Lindy Hop, Balboa, East Coast Swing, West Coast Swing, Salsa, and Modern Jive.

Other forms of communication, such as visual cues or spoken cues, sometimes aid in connecting with one's partner, but are often used in specific circumstances (e.g., practicing figures, or figures which are purposely danced without physical connection). Connection can be used to transmit power and energy as well as information and signals; some dance forms (and some dancers) primarily emphasize power or signaling, but most are probably a mixture of both.

Following and leading in a partner dance is accomplished by maintaining a physical connection called the frame that allows the leader to transmit body movement to the follower, and for the follower to suggest ideas to the leader. A frame is a stable structural combination of both bodies maintained through the dancers' arms and/or legs.

Connection occurs in both open and closed dance positions (also called "open frame" and "closed frame").

In closed position with body contact, connection is achieved by maintaining the frame. The follower moves to match the leader, maintaining the pressure between the two bodies as well as the position.

When creating frame, tension is the primary means of establishing communication. Changes in tension are made to create rhythmic variations in moves and movements, and are communicated through points of contact. In an open position or a closed position without body contact, the hands and arms alone provide the connection, which may be one of three forms: tension, compression or neutral.

• During tension or leverage connection, the dancers are pulling away from each other with an equal and opposite force. The arms do not originate this force alone: they are often assisted by tension in trunk musculature, through body weight or by momentum.
• During compression connection, the dancers are pushing towards each other.
• In a neutral position, the hands do not impart any force other than the touch of the follower's hands in the leader's.

In swing dances, tension and compression may be maintained for a significant period of time. In other dances, such as Latin, tension and compression may be used as indications of upcoming movement. However, in both styles, tension and compression do not signal immediate movement: the follow must be careful not to move prior to actual movement by the lead. Until then, the dancers must match pressures without moving their hands. In some styles of Lindy Hop, the tension may become quite high without initiating movement.

The general rule for open connections is that moves of the leader's hands back, forth, left or right are originated through moves of the entire body. Accordingly, for the follower, a move of the connected hand is immediately transformed into the corresponding move of the body. Tensing the muscles and locking the arm achieves this effect but is neither comfortable nor correct. Such tension eliminates the subtler communication in the connection, and eliminates free movement up and down, such as is required to initiate many turns.

Instead of just tensing the arms, connection is achieved by engaging the shoulder, upper body and torso muscles. Movement originates in the body's core. A leader leads by moving himself and maintaining frame and connection. Different forms of dance and different movements within each dance may call for differences in the connection. In some dances the separation distance between the partners remains pretty constant. In others e.g. Modern Jive moving closer together and further apart are fundamental to the dance, requiring flexion and extension of the arms, alternating compression and tension.

The connection between two partners has a different feel in every dance and with every partner. Good social dancers adapt to the conventions of the dance and the responses of their partners.

Connection (2013) is the third studio album by European musical duo The Green Children. As with their previous albums, a percentage of the proceeds were donated to The Green Children Foundation, their charity, which benefits orphaned children and animals in need. Supporters who pre-ordered the album received an autographed copy. This album also marks the first time Milla Sunde recorded a song in her native Norwegian tongue.

Connection is an album by trumpeter/bandleader Don Ellis recorded in 1972 and released on the Columbia label. The album features big band arrangements of pop hits of the day along with Ellis' "Theme from The French Connection" which won him a Grammy Award for Best Instrumental Arrangement in 1973

In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner. There are a variety of kinds of connections in modern geometry, depending on what sort of data one wants to transport. For instance, an affine connection, the most elementary type of connection, gives a means for transporting tangent vectors to a manifold from one point to another along a curve. An affine connection is typically given in the form of a covariant derivative, which gives a means for taking directional derivatives of vector fields: the infinitesimal transport of a vector field in a given direction.

Connections are of central importance in modern geometry in large part because they allow a comparison between the local geometry at one point and the local geometry at another point. Differential geometry embraces several variations on the connection theme, which fall into two major groups: the infinitesimal and the local theory. The local theory concerns itself primarily with notions of parallel transport and holonomy. The infinitesimal theory concerns itself with the differentiation of geometric data. Thus a covariant derivative is a way of specifying a derivative of a vector field along another vector field on a manifold. A Cartan connection is a way of formulating some aspects of connection theory using differential forms and Lie groups. An Ehresmann connection is a connection in a fibre bundle or a principal bundle by specifying the allowed directions of motion of the field. A Koszul connection is a connection generalizing the derivative in a vector bundle.

Connections also lead to convenient formulations of geometric invariants, such as the curvature (see also curvature tensor and curvature form), and torsion tensor.

In mathematics, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. If the fiber bundle is a vector bundle, then the notion of parallel transport must be linear. Such a connection is equivalently specified by a covariant derivative, which is an operator that can differentiate sections of that bundle along tangent directions in the base manifold. Connections in this sense generalize, to arbitrary vector bundles, the concept of a linear connection on the tangent bundle of a smooth manifold, and are sometimes known as linear connections. Nonlinear connections are connections that are not necessarily linear in this sense.

Connections on vector bundles are also sometimes called Koszul connections after Jean-Louis Koszul, who gave an algebraic framework for describing them .

In mathematics, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. A principal G-connection on a principal G-bundle P over a smooth manifold M is a particular type of connection which is compatible with the action of the group G.

A principal connection can be viewed as a special case of the notion of an Ehresmann connection, and is sometimes called a principal Ehresmann connection. It gives rise to (Ehresmann) connections on any fiber bundle associated to P via the associated bundle construction. In particular, on any associated vector bundle the principal connection induces a covariant derivative, an operator that can differentiate sections of that bundle along tangent directions in the base manifold. Principal connections generalize to arbitrary principal bundles the concept of a linear connection on the frame bundle of a smooth manifold.

"Connection" is a song released by the Britpop group Elastica. It was originally released in 1994 as a single and the album version was not released until 1995 on their self-titled debut.

The song was the subject of controversy, due to its overt similarity to another band's work. The intro synthesizer part (later repeated as a guitar figure) is lifted from the guitar riff in Wire's " Three Girl Rhumba" and transposed down a semitone. A judgment resulted in an out-of-court settlement and the credits were rewritten.

The song is the theme to the UK television programme Trigger Happy TV. A live version of the song was featured on the MuchMusic live compilation album, Much at Edgefest '99.

The song was covered by Elastica's label-mates Collapsed Lung and released as a seven-inch vinyl single in 1995.

"Connection" is a song by British rock and roll band The Rolling Stones, featured on their 1967 album Between the Buttons. It was written by Mick Jagger and Keith Richards (but mostly Richards), features vocals by both of them and is said to be about the long hours the band spent in airports. The lyrics contain much rhyming based on the word connection. The lyrics also reflect very heavily the pressures the band was under by 1967:

The song was written before Jagger, Richards and fellow Rolling Stone Brian Jones were arrested by the police for drugs.

Although it was never released as a single, it is a popular live song. The song itself is built on a very simple chord progression featuring a repetitive drum pattern, Chuck Berry-like lead guitar from Richards, the piano of Jack Nitzsche, tambourine and organ pedals by multi-instrumentalist Jones, and bass by Wyman. Jagger, Jones, and Wyman later overdubbed handclaps. Jagger said in 1967, "That's me beating my hands on the bass drum."

Let Y → X,  be an affine bundle modelled over a vector bundle $\overline Y\to X$. A connection Γ on Y → X is called the affine connection if it as a section Γ : Y → JY of the jet bundle JY → Y of Y is an affine bundle morphism over X. In particular, this is the case of an affine connection on the tangent bundle TX of a smooth manifold X.

With respect to affine bundle coordinates (x, y) on Y, an affine connection Γ on Y → X is given by the tangent-valued connection form

\Gamma_\lambda^i=\Gamma_\lambda{}^i{}_j(x^\nu) y^j + \sigma_\lambda^i(x^\nu).

An affine bundle is a fiber bundle with a general affine structure group $GA(m,\mathbb R)$ of affine transformations of its typical fiber V of dimension m. Therefore, an affine connection is associated to a principal connection. It always exists.

For any affine connection Γ : Y → JY, the corresponding linear derivative $\overline\Gamma:\overline Y\to J^1\overline Y$ of an affine morphism Γ defines a unique linear connection on a vector bundle $\overline Y\to X$. With respect to linear bundle coordinates $(x^\lambda,\overline y^i)$ on $\overline Y$, this connection reads

Since every vector bundle is an affine bundle, any linear connection on a vector bundle also is an affine connection.

If Y → X is a vector bundle, both an affine connection Γ and an associated linear connection $\overline\Gamma$ are connections on the same vector bundle Y → X, and their difference is a basic soldering form on σ = σ(x)dx ⊗ ∂. Thus, every affine connection on a vector bundle Y → X is a sum of a linear connection and a basic soldering form on Y → X.

It should be noted that, due to the canonical vertical splitting VY = Y × Y, this soldering form is brought into a vector-valued form σ = σ(x)dx ⊗ e where e is a fiber basis for Y.

Given an affine connection Γ on a vector bundle Y → X, let R and $\overline R$ be the curvatures of a connection Γ and the associated linear connection $\overline \Gamma$, respectively. It is readily observed that $R = \overline R + T$, where

\mu}^i dx^\lambda\wedge dx^\mu\otimes \partial_i, \qquad T_{\lambda \mu}^i = \partial_\lambda\sigma_\mu^i - \partial_\mu\sigma_\lambda^i + \sigma_\lambda^h \Gamma_\mu{}^i{}_h - \sigma_\mu^h \Gamma_\lambda{}^i{}_h,

is the torsion of Γ with respect to the basic soldering form σ.

In particular, let us consider the tangent bundle TX of a manifold X coordinated by $(x^\mu,\dot x^\mu)$. There is the canonical soldering form $\theta=dx^\mu\otimes \dot\partial_\mu$ on TX which coincides with the tautological one-form θ = dx ⊗ ∂ on X due to the canonical vertical splitting VTX = TX × TX. Given an arbitrary linear connection Γ on TX, the corresponding affine connection

A_\lambda^\mu=\Gamma_\lambda{}^\mu{}_\nu \dot x^\nu +\delta^\mu_\lambda,

on TX is the Cartan connection. The torsion of the Cartan connection A with respect to the soldering form θ coincides with the torsion of a linear connection Γ, and its curvature is a sum R + T of the curvature and the torsion of Γ.