Breathe
Breathe may refer to:
Books
Film
Music
Bands
Albums
Songs
Breathe (Nickelback song)
"Breathe" is a song recorded by Canadian rock band Nickelback. It was released on November 20, 2000, as the third single from the album The State. It was the second multi-format rock hit from the album in the United States, peaking at number ten on the Mainstream Rock Tracks chart and number 21 on the Modern Rock Tracks chart. The song is also featured on MuchMusic's Big Shiny Tunes 5 compilation album and is also featured in the 2002 fantasy film, Clockstoppers.
Track listing
Charts
References
External links
Breathe (Télépopmusik song)
"Breathe" is the title of the debut single by the French dance music group Télépopmusik. It features guest vocals by singer Angela McCluskey and appears on the group's 2001 album Genetic World.
Released as a single throughout 2002, "Breathe" reached #42 on the UK Singles Chart in March of that year. The single was released late in the year in the US, and it reached its peak chart positions on the Billboard Hot Dance Club Play chart (#9) and the Hot 100 chart (#78) in February 2003.
"Breathe" was nominated for a Grammy Award in the category Best Dance Recording at the ceremony held in February 2004, losing out to "Come into My World" by Kylie Minogue.
The song was reviewed favorably by Chris Long at the BBC, who described McCluskey's vocals as "breathless" and said the single was "a deliciously silky track that lolls by a holiday pool and enjoys the sunshine."
"Breathe" was featured in an advertising campaign by the automobile company Mitsubishi in 2003 to promote its Outlander model, and in the UK by Peugeot in 2002 to promote the 307. "Breathe" was also featured in the advertising campaign by Visa Europe in their "Love Every Day" campaign.
Cycle (album)
Cycle is an album by the Japanese noise musician Merzbow. It features recordings of Masami Akita's pet chickens. Material from this album was performed live at Radio Nova in Oslo, which was released as Mini Cycle / Yoshino Tamago / Yonos Bigfoot.
Track listing
All music composed by Masami Akita.
Personnel
References
Chain (algebraic topology)
In algebraic topology, a simplicial k-chain is a formal linear combination of k-simplices.
Integration on chains
Integration is defined on chains by taking the linear combination of integrals over the simplices in the chain with coefficients typically integers. The set of all k-chains forms a group and the sequence of these groups is called a chain complex.
Boundary operator on chains
The boundary of a chain is the linear combination of boundaries of the simplices in the chain. The boundary of a k-chain is a (k−1)-chain. Note that the boundary of a simplex is not a simplex, but a chain with coefficients 1 or −1 – thus chains are the closure of simplices under the boundary operator.
Example 1: The boundary of a path is the formal difference of its endpoints: it is a telescoping sum. To illustrate, if the 1-chain 
is a path from point 
to point 
, where
![t_{1}=[v_{1},v_{2}]\,](http://assets.wn.com/wiki/en/d/7b/b6e7d3ecaef478651e0d8-462f82.png)
,
![t_{2}=[v_{2},v_{3}]\,](http://assets.wn.com/wiki/en/5/43/5ee705b1ad0e6ff83958b-3e5558.png)
and
![t_{3}=[v_{3},v_{4}]\,](http://assets.wn.com/wiki/en/8/c8/09108c28ba3db9561bd33-758664.png)
are its constituent 1-simplices, then
![{\begin{aligned}\partial _{1}c&=\partial _{1}(t_{1}+t_{2}+t_{3})\\&=\partial _{1}(t_{1})+\partial _{1}(t_{2})+\partial _{1}(t_{3})\\&=\partial _{1}([v_{1},v_{2}])+\partial _{1}([v_{2},v_{3}])+\partial _{1}([v_{3},v_{4}])\\&=([v_{2}]-[v_{1}])+([v_{3}]-[v_{2}])+([v_{4}]-[v_{3}])\\&=[v_{4}]-[v_{1}].\end{aligned}}](http://assets.wn.com/wiki/en/b/b0/183536d07b946501af8c5-48538c.png)
Example 2: The boundary of the triangle is a formal sum of its edges with signs arranged to make the traversal of the boundary counterclockwise.
Cycle (music)
Cycle has several meanings in the field of music. Acoustically, it refers to one complete vibration, the base unit of Hertz being one cycle per second. Theoretically, an interval cycle is a collection of pitch classes created by a sequence of identical intervals. Individual pieces that aggregate into larger works are considered cycles, for example, the movements of a suite, symphony, sonata, or string quartet. This definition can apply to everything from settings of the Mass or a song cycle to an opera cycle. Cycle also applies to the complete performance of an individual composer's work in one genre.
Harmonic cycles—repeated sequences of a harmonic progression—are at the root of many musical genres, such as the twelve-bar blues. In compositions of this genre, the chord progression may be repeated indefinitely, with melodic and lyrical variation forming the musical interest. The form theme and variations is essentially of this type, but generally on a larger scale.
Composition using a tone row is another example of a cycle of pitch material, although it may be more difficult to hear because the variations are more diverse.
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