Pre

Pre or PRE may refer to:

See also

Pre (band)

Pre, often written as PRE, is a British noise rock band releasing music on the labels Skin Graft Records and Lovepump United. It is based in London and was formed around 2005 with singer Akiko Matsuura, known for taking the stage in only her underwear and extensive stage diving. Pre includes former members of Todd and Seafood. Guitar player John Webb is also a member of the noise rock band Male Bonding along with Kevin Hendrick.

Discography

Brazilian guinea pig

The Brazilian guinea pig (Cavia aperea) (preá in Portuguese) is a guinea pig species found in Argentina, Brazil, Bolivia, Colombia, Ecuador, Guyana, Paraguay, Uruguay and Venezuela.

C. aperea has been successfully mated to the domestic guinea pig, Cavia porcellus, though many females become infertile in successive generations. Brazilian guinea pigs are mainly diurnal animals and are narrower and longer than domesticated guinea pigs.

Description

This is a medium-sized guinea pig with an adult length of about 272 mm (11 in) and a weight of 637 grams (22.5 oz). The tail, at around 2.4 mm, is almost non-existent. The dorsal fur is dark olive-brown mixed with brown and black, and the underparts are a pale grey or yellowish-grey.

Its karyotype has 2n = 64 and a reportedly variable FN of 116 or 128 for C. a. aperea and 128 for C. a. pamparum.

Distribution

The Brazilian guinea pig has a wide distribution in South America at altitudes between 400 and 3,000 metres (1,300 and 9,800 ft) above sea level. Its range extends from Colombia, Ecuador and Venezuela to northern Argentina. Its typical habitat is open grassland and savannah.

*-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.

References