Cage (graph theory)

In the mathematical area of graph theory, a cage is a regular graph that has as few vertices as possible for its girth.

Formally, an (r,g)-graph is defined to be a graph in which each vertex has exactly r neighbors, and in which the shortest cycle has length exactly g. It is known that an (r,g)-graph exists for any combination of r ≥ 2 and g ≥ 3. An (r,g)-cage is an (r,g)-graph with the fewest possible number of vertices, among all (r,g)-graphs.

If a Moore graph exists with degree r and girth g, it must be a cage. Moreover, the bounds on the sizes of Moore graphs generalize to cages: any cage with odd girth g must have at least

vertices, and any cage with even girth g must have at least

vertices. Any (r,g)-graph with exactly this many vertices is by definition a Moore graph and therefore automatically a cage.

There may exist multiple cages for a given combination of r and g. For instance there are three nonisomorphic (3,10)-cages, each with 70 vertices : the Balaban 10-cage, the Harries graph and the Harries–Wong graph. But there is only one (3,11)-cage : the Balaban 11-cage (with 112 vertices).

Cage (enclosure)

A cage is an enclosure made of mesh, bars or wires, used to confine, contain or protect something or someone. A cage can serve many purposes, including keeping an animal in captivity, capturing, and being used for display of an animal at a zoo.

Humans

In history, prisoners were sometimes kept in a cage. They would sometimes be chained up inside into uncomfortable positions to intensify suffering.

History

Cages have been usually been used to capture or trapping a certain life form. For this reason, they've been known as a hunting accessory, often used for poaching animals or simply seizing them.

In captivity

Cages are often used now as a source to confine animals. These provide as a habitat to the animal, and since they've advanced so greatly, they are now specially designed to fit that species of animal. Captive breeds of birds, rodents, reptiles, and even larger animals have also been known to be confined in a cage as a domesticated animal (also known as a pet). Captivity is a common purpose of the cage.

Luke Cage

Luke Cage (born Carl Lucas and also called Power Man) is a fictional superhero appearing in American comic books published by Marvel Comics. Created by Archie Goodwin and John Romita, Sr., he first appeared in Luke Cage, Hero for Hire #1 (June 1972). Imprisoned for a crime he did not commit, he gains superpowers in the form of unbreakable skin and superhuman strength. The character frequently teams up with fellow superhero Iron Fist, and is married to Jessica Jones, with whom he has a daughter. In 2005, writer Brian Michael Bendis added Luke Cage to the lineup of the New Avengers, and he has appeared in various Avengers titles since.

Actor Mike Colter plays the character in Jessica Jones, a live-action television series set in the Marvel Cinematic Universe, and will headline in his own series, which will premiere in 2016.

Publication history

Luke Cage was created by Archie Goodwin and John Romita, Sr. shortly after Blaxploitation films emerged as a popular new genre. He debuted in his own series, Luke Cage, Hero for Hire, which was initially written by Goodwin and pencilled by George Tuska. Cage's adventures were set in a grungier, more crime-dominated New York City than that inhabited by other Marvel superheroes of the time. The series was retitled Luke Cage, Power Man with issue #17.

Seoul Museum of Art

The Seoul Museum of Art is an art museum operated by Seoul City Council and located in central of Seoul, South Korea.

History

It was opened in the Gyeonghuigung Palace area, a royal palace of Joseon dynasty, with six exhibition rooms and an outdoor sculpture park. However, in 2002 a larger main branch was opened behind Deoksugung Palace, replacing the Gyeonguigung Branch as the main branch. Occupying the old Korean Supreme Court building this remodeled and renovated version houses three floors of exhibition halls, a connected administration annex, and a basement with lecture halls, classrooms and offices. The museum has two more branches in Seoul: one is located in Gyeonghuigung (SeMa GyeongHuiGung) and the other is located in Namhyeon-dong, Gwanak-gu (SeMa NamSeoul).

The Seoul Museum of Art's main branch offers a wide variety of services to the general public. Offered by the museum are low, or no-cost, public art classes in Korean traditional arts, docent programs in English and Korean and lectures open to the public in order to further its mission.

Airó

Airó is a Portuguese parish, located in the municipality of Barcelos. The population in 2011 was 913, in an area of 3.02 km².

References

Air (classical element)

Air (also sometimes called Wind) is often seen as a universal power or pure substance. Its fundamental importance to life can be seen in words such as aspire, inspire, perspire and spirit, all derived from the Latin spirare.

Greek and Roman tradition

Air is one of the four classical elements in ancient Greek philosophy and science. According to Plato, it is associated with the octahedron; air is considered to be both hot and wet. The ancient Greeks used two words for air: aer meant the dim lower atmosphere, and aether meant the bright upper atmosphere above the clouds.Plato, for instance writes that "So it is with air: there is the brightest variety which we call aether, the muddiest which we call mist and darkness, and other kinds for which we have no name...." Among the early Greek Pre-Socratic philosophers, Anaximenes (mid-6th century BCE) named air as the arche. A similar belief was attributed by some ancient sources to Diogenes Apolloniates (late 5th century BCE), who also linked air with intelligence and soul (psyche), but other sources claim that his arche was a substance between air and fire.Aristophanes parodied such teachings in his play The Clouds by putting a prayer to air in the mouth of Socrates.

Air (Agua de Annique album)

Air is the debut album of the band Agua de Annique formed by the former The Gathering vocalist Anneke van Giersbergen. The album is a pop/rock oriented album and was released in 2007. Anneke van Giersbergen also plays piano on the album.

Track listing

All tracks by Anneke van Giersbergen except where noted

There is an animated video of the song "Day After Yesterday" which can be viewed on their official site. There is also a video for the cover song "Come Wander With Me," which was released as a download-single in 2008.

Personnel

External links