*-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.

Ringtone

A ringtone or ring tone is the sound made by a telephone to indicate an incoming call or text message. Not literally a tone nor an actual (bell-like) ring any more, the term is most often used today to refer to customizable sounds used on mobile phones.

Background

A phone “rings” when its network indicates an incoming call and the phone thus alerts the recipient. For landline telephones, the call signal can be an electric current generated by the switch or exchange to which the telephone is connected, which originally drove an electric bell. For mobile phones, the network sends the phone a message indicating an incoming call. The sound the caller hears is called the ringback tone, which is not necessarily directly related.

The electromagnetic bell system is still in widespread use. The ringing signal sent to a customer's telephone is 90 volts AC at a frequency of 20 hertz in North America. In Europe it is around 60-90 volts AC at a frequency of 25 hertz. Some non-Bell Company system party lines in the US used multiple frequencies (20/30/40 Hz, 22/33/44 Hz, etc.) to allow "selective" ringing.

Girl +

Girl + is an EP by punk blues band Boss Hog.

Track listing

All songs written by Boss Hog and produced by Cristina Martinez. The Japan version includes the Action Box EP.

Band members

Additional musicians

Girl (short story)

"Girl" is a story written by Jamaica Kincaid that was included in At the Bottom of the River (1983). It appeared in the June 26, 1978 issue of The New Yorker.

Plot summary

The story is a to-do list and a how-to-do list containing one sentence. It lists things to do and when to do them. How to do things and how not to do them. It doesn't describe how to do anything precisely; instead it simply says things like "This is how to catch a fish; this is you; this is how to bully a man." The mother repeatedly admonishes the daughter for singing benna in Sunday school and repeatedly reminds her to not become a slut by avoiding the behaviors she has been warned about. The poem ends with the exchange:

Structure

The theme for "Girl" is mother-daughter dispute. In this poem, the mother goes on and on teaching the daughter how to be the perfect woman in society. As the story goes on, the mother’s directions get more demanding. Whenever the daughter says something, which is rare, it’s a snap back at the mother.

Girl (Pharrell Williams album)

Girl (stylized as G I R L) is the second studio album by American recording artist and record producer Pharrell Williams. The album was released on March 3, 2014, through Williams' label i Am Other and Columbia Records. Girl was Williams' first studio album since his 2006 debut, In My Mind. It contains appearances by Justin Timberlake, Miley Cyrus, Daft Punk and Alicia Keys.

Upon its release, Girl received generally positive reviews from music critics. It peaked at number one in 12 countries worldwide, also peaking in the top 10 of the charts of 17 other countries. The album has sold 591,000 copies in the United States as of February 2015. The album's lead single was the Academy Award-nominated "Happy" (from the Despicable Me 2 soundtrack), which was a huge worldwide success, selling more than 13.9 million units (sales plus equivalent streams) worldwide and becoming one of the best-selling singles of all time. Follow-up singles "Marilyn Monroe", "Come Get It Bae" and "Gust of Wind" have achieved moderate success. At the 57th Grammy Awards, the album was nominated for Album of the Year and won Best Urban Contemporary Album. "Happy" also won Best Pop Solo Performance and Best Music Video.