*-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.

Angels (Within Temptation song)

"Angels" is a song by Dutch band Within Temptation from their third studio album, The Silent Force. It was released as the third single from the album on 13 June 2005, also accompanying a music video. The video earned the band a Golden God Award on the following year.

Track listing

Music video

The video is shot in a desert in Spain. It tells the story of a group of vigilante angels who make it their mission to wipe out evil. Sharon den Adel is a woman who has been seemingly abandoned on the side of the road in the middle of nowhere. She accepts a lift from a priest, who takes her back to his home. The priest is in fact a demonic serial killer, who adopts different disguises to get to his victims. All of these disguises are trustworthy people, like a doctor, a police officer, a clown, judge, or a priest. As Sharon stumbles upon a board full of newspaper clippings in the killers home, which are about his previous victims, he seemingly overpowers her with chloroform. He takes a tied up Sharon to the middle of the desert to bury her alive. However, Sharon immediately awakens as the other angels approach (the other band members) and is revealed to also be one of the angels, who was left at the side of the road as bait for the serial killer, during which time the rest of the vigilantes appear and the killer is confronted with the spirits of his victims, who destroy him. The vigilantes then move onto their next target.

Angels (P-Money song)

"Angels" is a 2009 single released by New Zealand music producer P-Money.

Release and chart performance

The single was released digitally February 8, 2009. After two days release it has currently peaked at #54 on the New Zealand iTunes Music Store and at #4 on the Dance/Electronic Singles Chart. This single was released after the highly successful single Everything.

Track listing

References

Angels (Marvel Comics)

An angel is a fictional entity within the Marvel Comics universe, based on the angels of the Abrahamic faiths. Their first Marvel Comics appearance was Marvel Tales #133. In the religious text of Christianity, Judaism, Islam and Zoroastriansim, angels are believed to be guardians of mankind and messengers of God; indeed, "angels" originates from the Greek word for messenger. In Hebrew they are mal'ach, (again messenger), Abbir (mighty) or Elohim (Godly beings).

Powers and abilities

The abilities and physical features of angels are widely varied and many seem able to alter their appearance at will, but most favor beautiful humanoid forms with large, birdlike wings growing from their backs. They are immortal and do not age. Most angels seem to have varying degrees of superhuman strength, and they often can fire bolts of heavenly fire from their hands or summon burning swords at will. They can make themselves invisible to humans, although rare sensitives may still see them. Many angels can generate illusions and compel humans to obey their will, and some can resurrect the dead by sharing their own divine essence with the deceased. When slain, the Grigori angels spontaneously combusted; whether other angels would likewise is uncertain.