End

End or Ending may refer to:

End

END

Ending

See also

End (graph theory)

In the mathematics of infinite graphs, an end of a graph represents, intuitively, a direction in which the graph extends to infinity. Ends may be formalized mathematically as equivalence classes of infinite paths, as havens describing strategies for pursuit-evasion games on the graph, or (in the case of locally finite graphs) as topological ends of topological spaces associated with the graph.

Ends of graphs may be used (via Cayley graphs) to define ends of finitely generated groups. Finitely generated infinite groups have one, two, or infinitely many ends, and the Stallings theorem about ends of groups provides a decomposition for groups with more than one end.

Definition and characterization

Ends of graphs were defined by Rudolf Halin (1964) in terms of equivalence classes of infinite paths. A ray in an infinite graph is a semi-infinite simple path; that is, it is an infinite sequence of vertices v₀, v₁, v₂, ... in which each vertex appears at most once in the sequence and each two consecutive vertices in the sequence are the two endpoints of an edge in the graph. According to Halin's definition, two rays r₀ and r₁ are equivalent if there is another ray r₂ (not necessarily different from either of the first two rays) that contains infinitely many of the vertices in each of r₀ and r₁. This is an equivalence relation: each ray is equivalent to itself, the definition is symmetric with regard to the ordering of the two rays, and it can be shown to be transitive. Therefore, it partitions the set of all rays into equivalence classes, and Halin defined an end as one of these equivalence classes.

End (film)

End is a 1984 fiction film by Mahmoud Shoolizadeh; is a story about the children who live near the railways and their lives are full of ups and downs. This film displays the story of a small child who lives in south of Tehran during times of social problems. The film analyses an unjust and unfair society.

Director's View

Inflation, unemployment, divorce and social poverty are the major problems in modern Iran. If the officials, social and cultural experts and planners do not find solutions to these problems, the future society would face crisis due to the consequences.

Technical specifications and Film crew

Days (The Kinks song)

"Days" is a song by The Kinks, written by lead singer Ray Davies, released as a single in 1968. It also appeared on an early version of the album The Kinks Are the Village Green Preservation Society (released only in continental Europe and New Zealand), and now appears as a bonus track of the remastered CD. On the original Pye 7N 17573 label, the name of the song is "Day's".

Release and reception

The song was an important single for Davies and the Kinks, coming in a year of declining commercial fortunes for the band. The song had been intended as an album track but after the relative failure of the previous single "Wonderboy" (which only reached No. 36 in the UK), "Days" was rushed out as a single with an old unreleased track "She's Got Everything" (recorded in February 1966 in the same session as "Dedicated Follower of Fashion") as the B-side. It reached No. 12 on the UK chart, but failed to chart in the U.S. This did not help future releases however as the next four Kinks singles failed to reach the top 30 (two of them failing to chart altogether) in the UK.

Days (Alisa Mizuki song)

"Days" is the fourteenth single by Japanese recording artist Alisa Mizuki. It was released on November 19, 1997 as the fifth and final single from Mizuki's third compilation album Fiore II. It was also included on Mizuki's fifth studio album Innocence. The title track was written and produced by former Every Little Thing keyboardist Mitsuru Igarashi and served as theme song for the second season of the Fuji TV drama Nurse no Oshigoto, starring Mizuki herself. "Days" is Mizuki's first release under the record label Avex Tune.

Chart performance

"Days" debuted on the Oricon Weekly Singles chart at number 14 with 28,020 copies sold in its first week. It stayed in the top 30, at number 24, on its second week, with 18,660 copies sold. The single charted for nine weeks and has sold a total of 101,120 copies.

Track listing

Charts and sales

References

Days (Flow song)

DAYS is FLOW's seventh single. Its A-Side was used as the first opening theme song for Eureka Seven. It reached #3 on the Oricon charts in its first week and charted for 14 weeks. *

Track listing

References

Pine

Pines are conifer trees in the genus Pinus /ˈpiːnuːs/, in the family Pinaceae. They are the only genus in the subfamily Pinoideae. The Plant List compiled by the Royal Botanic Gardens, Kew and Missouri Botanical Garden accepts 126 species names of pines as current, together with 35 unresolved species and many more synonyms.

Etymology

The modern English name pine derives from Latin pinus which some have traced to the Indo-European base *pīt- ‘resin’ (source of English pituitary). In the past (pre-19th century) they were often known as fir, from Old Norse fura, by way of Middle English firre. The Old Norse name is still used for pines in some modern north European languages, in Danish fyr, in Norwegian fura/fure/furu, Swedish fura/furu, Dutch vuren, and Föhre in German, but in modern English, fir is now restricted to fir (Abies) and Douglas-fir (Pseudotsuga).

Taxonomy, nomenclature and codification

Pines are gymnosperms. The genus is divided into three subgenera, which can be distinguished by cone, seed, and leaf characters: