End
End or Ending may refer to:
End
END
Ending
See also
Conclusion (music)
In music, the conclusion is the ending of a composition and may take the form of a coda or outro.
Pieces using sonata form typically use the recapitulation to conclude a piece, providing closure through the repetition of thematic material from the exposition in the tonic key. In all musical forms other techniques include "altogether unexpected digressions just as a work is drawing to its close, followed by a return...to a consequently more emphatic confirmation of the structural relations implied in the body of the work."
For example:
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.
Surname
A surname or family name is a name added to a given name. In many cases, a surname is a family name and many dictionaries define "surname" as a synonym of "family name". In the western hemisphere, it is commonly synonymous with last name because it is usually placed at the end of a person's given name.
In most Spanish-speaking and Portuguese-speaking countries, two or more last names (or surnames) may be used. In China, Hungary, Japan, Korea, Madagascar, Taiwan, Vietnam, and parts of India, the family name is placed before a person's given name.
The style of having both a family name (surname) and a given name (forename) is far from universal. In many countries, it is common for ordinary people to have only one name or mononym.
The concept of a "surname" is a relatively recent historical development, evolving from a medieval naming practice called a "byname". Based on an individual's occupation or area of residence, a byname would be used in situations where more than one person had the same name.
Kasparov (disambiguation)
Kasparov is a Russian surname.
People with this surname include:
Branded products include:
Kasparov is often confused with another Russian surname:
Podcasts:
