*-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.

Mood

Mood may refer to:

Music

Places

Stimmung

Stimmung, for six vocalists and six microphones, is a piece by Karlheinz Stockhausen, written in 1968 and commissioned by the City of Cologne for the Collegium Vocale Köln. Its average length is seventy-four minutes, and it bears the work number 24 in the composer's catalog. It is a tonal, and yet also a serial composition (Toop 2005, 39; Stuppner 1974).

Title

The German word Stimmung [ˈʃtɪmʊŋ] has several meanings, including "tuning" and "mood". The word is the noun formed from the verb stimmen, which means "to harmonize, to be correct", and related to Stimme (voice). The primary sense of the title "implies not only the outward tuning of voices or instruments, but also the inward tuning of one's soul" (Hillier 2007, 4). According to the composer, the word

Overview

Stimmung is in just intonation. Six singers amplified by six microphones tune to a low B♭₁drone, inaudible to the audience, and expand upwards through overtone singing, with that low B♭'s harmonics 2, 3, 4, 5, 7, and 9 (B♭₂, F+₂, B♭₃, D₄, A♭+₄, and C+₅) becoming in turn fundamentals for overtone singing. It is composed using what the composer calls moment form, and consists of 51 sections (called "moments"). It is "the first major Western composition to be based entirely on the production of vocal harmonics" (Rose and Ireland 1986) or, alternatively, the first "to use overtones as a primary element" (Rose and Emmerson 1979, 20). An additional innovation is "the unique kind of rhythmic polyphony which arises from the gradual transformation/assimilation of rhythmic models" (Toop 2005, 48).

Mood (psychology)

A mood is an emotional state. Moods differ from emotions, feelings or affects in that they are less specific, less intense, and less likely to be triggered by a particular stimulus or event. Moods are typically described as having either a positive or negative valence. In other words, people usually speak of being in a good mood or a bad mood.

Mood also differs from temperament or personality traits which are even longer lasting. Nevertheless, personality traits such as optimism and neuroticism predispose certain types of moods. Long term disturbances of mood such as clinical depression and bipolar disorder are considered mood disorders. Mood is an internal, subjective state but it often can be inferred from posture and other behaviors. "We can be sent into a mood by an unexpected event, from the happiness of seeing an old friend to the anger of discovering betrayal by a partner. We may also just fall into a mood."

Research also shows that a person's mood can influence how they process advertising. Mood has been found to interact with gender to affect consumer processing of information.