*-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.

Leo (comics)

Leo is the name of different fictional characters in Marvel Comics.

Publication history

The original Leo first appeared in Avengers #72 (January 1970), and was created by Roy Thomas and Sal Buscema.

The character subsequently appears in Avengers #120-123 (February–May 1974), Ghost Rider #7 (August 1974), Iron Man #184 (July 1984), and West Coast Avengers #26 (November 1987), in which he is killed.

Leo appeared as part of the "Zodiac" entry in the Official Handbook of the Marvel Universe Deluxe Edition #20.

Fictional character biography

Daniel Radford

Daniel Radford is a founding member of the Zodiac, and his base of operations was Los Angeles, California. The Zodiac Cartel was founded by Cornelius van Lunt (Taurus), handpicking the eleven other members; van Lunt concealed his own identity, while he was the only one who knew the identities of the others. Each member was based in a different American city as part of his nationwide criminal network, with the ultimate goal of world economic and political domination.

Léo (footballer, born 1990)

Leonardo da Silva Vieira (born 22 September 1990), known simply as Léo, is a Brazilian professional footballer who plays for São Paulo FC as a goalkeeper.

References

External links

Leo (Tserpitsky)

Metropolitan Leo (or Lev, Russian: Лев, secular name Nikolay Lvovich Tserpitsky, Николай Львович Церпицкий; born April 13, 1946) is the current Metropolitan of Novgorod and Staraya Russa. He was named Bishop of Novgorod the Great and Staraya Russa on July 20, 1990 and elevated to the archiepiscopal dignity on February 25, 1995, and to the metropolitan dignity in January 2012.

Biography

He was born in the village of Zaluzhye in the Stowbtsy Raion of Minsk Oblast in Belarus on April 13, 1946. He is the grandson of a priest.

After his service in the Soviet Army in 1966-1969, Lev entered the Leningrad Spiritual Academy, graduating in 1975 and successfully defending a candidate's dissertation entitled "Decrees of the Second Vatican Council's 'Constitution on the Divine Liturgy'" («Постановление II Ватиканского Собора „Конституция о богослужении“»). He studied at the Papal Gregorian University from 1975-1978.

On 28 March 1971, he was shorn a monk by Metropolitan Nikodim (Rotov) of Leningrad and Novgorod; he was consecrated a hierodeacon in April of that same year and was consecrated a hieromonk in April 1975. From 1972 to 1975, he was personal secretary to Metropolitan Nikodim. In 1978, he was elevated to the rank of archimandrite and was part of the Russian Orthodox Church's delegation at the funeral of Pope Paul VI and the inauguration of John Paul I; he was with the Metropolitan when Nikodim collapsed and died during an audience with the Pope.