Labyrinth

In Greek mythology, the Labyrinth (Greek λαβύρινθος labyrinthos) was an elaborate structure designed and built by the legendary artificer Daedalus for King Minos of Crete at Knossos. Its function was to hold the Minotaur eventually killed by the hero Theseus. Daedalus had so cunningly made the Labyrinth that he could barely escape it after he built it.

Although early Cretan coins occasionally exhibit branching (multicursal) patterns, the single-path (unicursal) seven-course "Classical" design without branching or dead ends became associated with the Labyrinth on coins as early as 430 BC, and similar non-branching patterns became widely used as visual representations of the Labyrinth – even though both logic and literary descriptions make it clear that the Minotaur was trapped in a complex branching maze. Even as the designs became more elaborate, visual depictions of the mythological Labyrinth from Roman times until the Renaissance are almost invariably unicursal. Branching mazes were reintroduced only when garden mazes became popular during the Renaissance.

Bony labyrinth

The bony labyrinth (also osseous labyrinth or otic capsule) is the rigid, bony outer wall of the inner ear in the temporal bone. It consists of three parts: the vestibule, semicircular canals, and cochlea. These are cavities hollowed out of the substance of the bone, and lined by periosteum. They contain a clear fluid, the perilymph, in which the membranous labyrinth is situated.

A fracture classification system in which temporal bone fractures detected on CT are delineated based on disruption of the otic capsule has been found to be predictive for complications of temporal bone trauma such as facial nerve injury, sensorineural deafness and cerebrospinal fluid otorrhea. On radiographic images, the otic capsule is the most dense portion of the temporal bone.

In otospongiosis, a leading cause of adult-onset hearing loss, the otic capsule is exclusively affected. This area normally undergoes no remodeling in adult life, and is extremely dense. With otospongiosis, the normally dense enchondral bone is replaced by haversian bone, a spongy and vascular matrix that results in sensorineural hearing loss due to compromise of the conductive capacity of the inner ear ossicles. This results in hypodensity on CT, with the portion first affected usually being the fissula ante fenestram.

Labyrinth (artwork)

Labyrinth is a 2013 artwork by the British artist Mark Wallinger that marks the 150th anniversary of the London Underground. The artwork consists of 270 enamel plaques of unique unicursal labyrinth designs, one for every London tube station, each will be numbered according to its position in the route taken by the contestants in the 2009 Guinness World Record Tube Challenge. In October 2014, Art/Books published Labyrinth: A Journey Through London's Underground by Mark Wallinger, a comprehensive photographic book of all 270 labyrinth designs in situ in the Underground stations.

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References

Associator

In abstract algebra, the term associator is used in different ways as a measure of the nonassociativity of an algebraic structure.

Ring theory

For a nonassociative ring or algebra , the associator is the multilinear map given by

Just as the commutator measures the degree of noncommutativity, the associator measures the degree of nonassociativity of . It is identically zero for an associative ring or algebra.

The associator in any ring obeys the identity

The associator is alternating precisely when is an alternative ring.

The associator is symmetric in its two rightmost arguments when is a pre-Lie algebra.

The nucleus is the set of elements that associate with all others: that is, the n in R such that

It turns out that any two of being implies that the third is also the zero set.

Quasigroup theory

A quasigroup Q is a set with a binary operation such that for each a,b in Q, the equations and have unique solutions x,y in Q. In a quasigroup Q, the associator is the map defined by the equation

Nucleus (order theory)

In mathematics, and especially in order theory, a nucleus is a function on a meet-semilattice such that (for every in ):

Every nucleus is evidently a monotone function.

Frames and locales

Usually, the term nucleus is used in frames and locales theory (when the semilattice is a frame).

Proposition: If is a nucleus on a frame , then the poset of fixed points of , with order inherited from , is also a frame.

References

Nucleus (Anekdoten album)

Nucleus is the second full-length studio album by the Swedish progressive rock band Anekdoten. The album was released in 1995.

Track list

Personnel

Additional personnel:

References

External links