*-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.

Frances (ship)

A number of sailing ships have been named Frances:

See also

Frances, Washington

Frances is an unincorporated community in Pacific County, Washington, United States. Frances is located along State Route 6 east of the community of Lebam. Frances and surrounding areas are part of an area heavily affected by the logging industry.

References

Frances (1839)

Frances was a cutter built in 1839 at Encounter Bay, South Australia. It was wrecked on South Neptune Island on 29 August 1840. It was reported that the crew survived the wrecking event, came ashore and survived on a diet of penguin for 50 days before sending 2 people in a dinghy to Port Lincoln to seek help. Those remaining at South Neptune Island were subsequently rescued. While the wreck site is protected by the Commonwealth Historic Shipwrecks Act 1976 and its location is recorded as being at 35°33′00″S 136°12′00″E / 35.55000°S 136.20000°E / -35.55000; 136.20000Coordinates: 35°33′00″S 136°12′00″E / 35.55000°S 136.20000°E / -35.55000; 136.20000, as of 2004 it had not been found.

See also

References