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-bundleP over a smooth manifoldM is a particular type of connection which is compatible with the action of the group G.
Let π:P→M be a smooth principal G-bundle over a smooth manifoldM. Then a principal G-connection on P is a differential 1-form on Pwith values in the Lie algebra of G which is G-equivariant and reproduces the Lie algebra generators of the fundamental vector fields on P.
An affine bundle is a fiber bundle with a general affinestructure group of affine transformations of its typical fiber of dimension . Therefore, an affine connection is associated to a principal connection. It always exists.
For any affine connection , the corresponding linear derivative of an affine morphism defines a
unique linear connection on a vector bundle . With respect to linear bundle
coordinates on , this connection reads
Since every vector bundle is an affine bundle, any linear connection on
a vector bundle also is an affine connection.
If is a vector bundle, both an affine connection
and an associated linear connection are
connections on the same vector bundle , and their
difference is a basic soldering form on . Thus, every affine
connection on a vector bundle is a sum of a linear
connection and a basic soldering form on .
"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.
Ash was the ancient Egyptian god of oases, as well as the vineyards of the western Nile Delta and thus was viewed as a benign deity. Flinders Petrie in his 1923 expedition to the Saqqara (also spelt Sakkara) found several references to Ash in Old Kingdom wine jar seals: "I am refreshed by this Ash" was a common inscription.
In particular, he was identified by the Ancient Egyptians as the god of the Libu and Tinhu tribes, known as the "people of the oasis". Consequently Ash was known as the "lord of Libya", the western border areas occupied by the Libu and Tinhu tribes, corresponds roughly with the area of modern Libya. It is also possible that he was worshiped in Ombos, as their original chief deity.
In Egyptian mythology, as god of the oases, Ash was associated with Set, who was originally god of the desert, and was seen as protector of the Sahara. The first known reference to Ash dates to the Protodynastic Period, but by the late 2nd Dynasty, his importance had grown, and he was seen as protector of the royal estates, since the related god Set, in Lower Egypt, was regarded as the patron deity of royalty itself. Ash's importance was such that he was mentioned even until the 26th Dynasty.
Put differently, critics and haters either don’t have a basic understanding of Ramadan or the desire to connect with those involved in it ...Council of Britain also celebrated the connection by posting.
“Ashes to Flame... Ashes to Flame (ISBN ... Each chapter reveals the transformative process of healing and self-discovery, touching on the importance of embracing nature, finding solace in creativity, and connecting with a community.
Monoray, £22, pp332 ... He discovers new and often surprising connections everywhere from Hastings (the Ashes to Ashes video location) to, inevitably, Bowie’s birthplace in Brixton ... BoroughPress, £16.99, pp288 ... Eye, £9.99, pp414 (paperback) ... Share ... .
The festival is a beautiful reminder of the impermanence of life and the ultimate truth of mortality.It is celebrated by ascetics, Aghori sadhus, and Shiva devotees, who embrace the ashes as a form of purification and connection to the divine.
On ‘Hot’, the track ‘Ash’ most explicitly connects to that idea. Co-written by member Huh Yunjin, the song depicts new life rising from the ashes and discovering beauty by embracing pain.
The abundance of Potters with former Rovers connections would have Rovers fans quaking. Of the four players available, Ash Phillips and Lewis Baker started with AndrewMoran and Sam Gallagher in reserve ... As it was, it did not matter ... .
... protect their properties and damaged connections spewed water into the street ... To fill the pressure void, experts theorized, the open connections began to suck toxic ash, soot and smoke into the pipes.
... on Ash Wednesday, March 5. The service was held in Goggins Fieldhouse, led by Smela who discussed the connection between death, the meaning of Ash Wednesday, and the Lent season during his sermon.
In both wildfires, houses of worship fell to ash ... Ash Wednesday services at St ... Hillary McCarthy of Santa Monica noted the metaphoric connection of the fire as it relates to ash and loss of earthly possessions.
Ash Wednesday marks the start of the 40-day season of Lent in the church calendar and ConnectionChristian Church marked the occasion by offering Ashes to Go for the tenth consecutive year ... Ashes to Go ...