City

A city is a large and permanent human settlement. Although there is no agreement on how a city is distinguished from a town in general English language meanings, many cities have a particular administrative, legal, or historical status based on local law.

Cities generally have complex systems for sanitation, utilities, land usage, housing, and transportation. The concentration of development greatly facilitates interaction between people and businesses, benefiting both parties in the process, but it also presents challenges to managing urban growth.

A big city or metropolis usually has associated suburbs and exurbs. Such cities are usually associated with metropolitan areas and urban areas, creating numerous business commuters traveling to urban centers for employment. Once a city expands far enough to reach another city, this region can be deemed a conurbation or megalopolis. In terms of population, the largest city proper is Shanghai, while the fastest-growing is Dubai.

Origins

There is not enough evidence to assert what conditions gave rise to the first cities. Some theorists have speculated on what they consider suitable pre-conditions and basic mechanisms that might have been important driving forces.

City (disambiguation)

A city is generally an urban settlement with a large population.

City or Cities may also refer to:

Places

Literature

Music

Cities (TV series)

Cities is a Canadian documentary television series broadcast on CBC Television from 1979 to 1980, followed by repeats for two years. Produced and directed by John McGreevy.

The series featured a celebrity who would appear in an episode on location in a personal favourite city or more specific location. Appearances included Glenn Gould (Toronto, Canada), Peter Ustinov (Leningrad, Russia), Elie Wiesel (Jerusalem, Israel), George Plimpton (New York City, United States) and Mai Zetterling (Stockholm, Sweden). Also appearing were Anthony Burgess, John Huston, Melina Mercouri and Hildegard Knef.

References

*-algebra

In mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra) is a mathematical structure consisting of two involutive rings R and A, where R is commutative and A has the structure of an associative algebra over R. Involutive algebras generalize the idea of a number system equipped with conjugation, for example the complex numbers and complex conjugation, matrices over the complex numbers and conjugate transpose, and linear operators over a Hilbert space and Hermitian adjoints.

Terminology

*-ring

In mathematics, a *-ring is a ring with a map * : A → A that is an antiautomorphism and an involution.

More precisely, * is required to satisfy the following properties:

for all x, y in A.

This is also called an involutive ring, involutory ring, and ring with involution. Note that the third axiom is actually redundant, because the second and fourth axioms imply 1* is also a multiplicative identity, and identities are unique.

Algebra

Algebra (from Arabic "al-jabr" meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. Much early work in algebra, as the Arabic origin of its name suggests, was done in the Middle East, by mathematicians such as al-Khwārizmī (780 – 850) and Omar Khayyam (1048–1131).

†-algebra

A †-algebra (or, more explicitly, a †-closed algebra) is the name occasionally used in physics for a finite-dimensional C*-algebra. The dagger, †, is used in the name because physicists typically use the symbol to denote a hermitian adjoint, and are often not worried about the subtleties associated with an infinite number of dimensions. (Mathematicians usually use the asterisk, *, to denote the hermitian adjoint.) †-algebras feature prominently in quantum mechanics, and especially quantum information science.

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