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.
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 (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).
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.
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.
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.
In telecommunications, a slip is a positional displacement in a sequence of transmitted symbols that causes the loss or insertion of one or more symbols. Slips are usually caused by inadequate synchronization of the two clocks controlling the transmission or by poor reception of the signal.
In materials science, a slip system describes the set of symmetrically identical slip planes and associated family of slip directions for which dislocation motion can easily occur and lead to plastic deformation. An external force makes parts of the crystal lattice glide along each other, changing the material's geometry. Depending on the type of lattice, different slip systems are present in the material. More specifically, slip occurs on close-packed planes (those containing the greatest number of atoms per area), and in close-packed directions (most atoms per length). The magnitude and direction of slip are represented by the Burgers vector. The picture on the right shows a schematic view of the slip mechanism. The slip planes and slip directions in a crystal have specific crystallographic forms. The slip planes are normally the planes with the highest density of atoms, i.e., those most widely spaced, and the direction of the slip is the direction in the slip plane that corresponds to one of the shortest lattice translation vectors. Often, this is the direction in which atoms are most closely spaced. A slip plane and a slip direction constitute a slip system. A critical resolved shear stress is required to initiate a slip. Slip is an important mode of deformation mechanism in crystals. For metals and technically used metallic alloys it is by far the most important deformation mechanism and subject to current research in materials science.
In medicine, relapse or recidivism is a recurrence of a past (typically medical) condition. For example, MS or malaria often exhibit peaks of activity and sometimes long periods of dormancy.
In the context of drug use, relapse or reinstatement of drug-seeking behavior, is a form of spontaneous recovery that involves the recurrence of pathological drug use after a period of abstinence. Relapse is often observed in individuals who have developed a drug addiction or either form of drug dependence.
Substances that may cause addiction or dependence include: