*-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.

Ring (Suzuki novel)

Ring (リング, Ringu) is a Japanese mystery horror novel by Koji Suzuki, first published in 1991, and set in modern-day Japan. It was the basis for a 1995 television film (Ring: Kanzenban),a television series (Ring: The Final Chapter), a film of the same name (1998's Ring), and two remakes of the 1998 film: a South Korean version (The Ring Virus) and an American version (The Ring).

Plot synopsis

After four teenagers mysteriously die simultaneously in Tokyo, Kazuyuki Asakawa, a reporter and uncle to one of the deceased, decides to launch his own personal investigation. His search leads him to "Hakone Pacific Land", a holiday resort where the youths were last seen together exactly one week before their deaths. Once there he happens upon a mysterious unmarked videotape. Watching the tape, he witnesses a strange sequence of both abstract and realistic footage, including an image of an injured man, that ends with a warning revealing the viewer has a week to live. Giving a single means of avoiding death, the tape's explanation ends suddenly having been overwritten by an advertisement. The tape has a horrible mental effect on Asakawa, and he doesn't doubt for a second that its warning is true.

Ring (film)

Ring (リング, Ringu) is a 1998 Japanese psychological horror film directed by Hideo Nakata, adapted from the novel Ring by Kôji Suzuki, which in turn draws on the Japanese folk tale Banchō Sarayashiki. The film stars Nanako Matsushima, Hiroyuki Sanada, and Rikiya Ōtaka. The film follows TV reporter and single mother Reiko who is caught up in a series of deaths surrounding a cursed video tape.

Production took approximately 9 months.Ring and its sequel Rasen were released in Japan at the same time.

After release, Ring inspired numerous follow-ups within the Ring franchise and triggered a trend of Western remakes.

Plot

Two teenagers, Masami (Hitomi Satō) and Tomoko (Yūko Takeuchi), talk about a videotape recorded by a boy in Izu which is fabled to bear a curse that kills the viewer seven days after watching. Tomoko reveals that a week ago, she and three of her friends watched a weird tape and received a call after watching. Tomoko is killed by an unseen force as Masami watches, horrified.

Identifier

An identifier is a name that identifies (that is, labels the identity of) either a unique object or a unique class of objects, where the "object" or class may be an idea, physical [countable] object (or class thereof), or physical [noncountable] substance (or class thereof). The abbreviation ID often refers to identity, identification (the process of identifying), or an identifier (that is, an instance of identification). An identifier may be a word, number, letter, symbol, or any combination of those.

The words, numbers, letters, or symbols may follow an encoding system (wherein letters, digits, words, or symbols stand for (represent) ideas or longer names) or they may simply be arbitrary. When an identifier follows an encoding system, it is often referred to as a code or ID code. Identifiers that do not follow any encoding scheme are often said to be arbitrary IDs; they are arbitrarily assigned and have no greater meaning. (Sometimes identifiers are called "codes" even when they are actually arbitrary, whether because the speaker believes that they have deeper meaning or simply because he is speaking casually and imprecisely.)

Name (song)

"Name" is an alternative rock song by the American rock band Goo Goo Dolls. It was released in September 1995 as the third single from the album A Boy Named Goo. As the band's first hit, the song topped both the US Modern Rock chart and the US Album Rock chart, and reached number 5 on the Billboard Hot 100.

Although the Goo Goo Dolls were considered an alternative group prior to the single's release, "Name" crossed over to pop and adult contemporary radio, greatly increasing the band's fan base.

Prior to the release of the Dizzy Up the Girl album three years later, "Name" was the band's most successful single. It is currently their 3rd most successful single, after "Iris" and "Slide".

The band re-recorded this song for their compilation album, Greatest Hits Volume One: The Singles; this version featured minimal arrangements and production.

Track listing

Song composition

NAME (dispersion model)

The NAME atmospheric pollution dispersion model was first developed by the UK's Met Office in 1986 after the nuclear accident at Chernobyl, which demonstrated the need for a method that could predict the spread and deposition of radioactive gases or material released into the atmosphere.

The acronym, NAME, originally stood for the Nuclear Accident ModEl. The Met Office has revised and upgraded the model over the years and it is now used as a general purpose dispersion model. The current version is known as the NAME III (Numerical Atmospheric dispersion Modeling Environment) model. NAME III is currently operational and it will probably completely replace the original NAME model sometimes in 2006.

Features and capabilities of NAME

NAME (in its current NAME III version) is a Lagrangian air pollution dispersion model for short range to global range scales. It employs 3-dimensional meteorological data provided by the Met Office's Unified National Weather Prediction Model. Random walk techniques using empirical turbulence profiles are utilized to represent turbulent mixing. In essence, NAME follows the 3-dimensional trajectories of parcels of the pollution plume and computes pollutant concentrations by Monte Carlo methods — that is, by direct simulation rather than solving equations.