*-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.

Ring (film)

Ring (リング, Ringu) is a 1998 Japanese psychological horror film directed by Hideo Nakata, adapted from the novel Ring by Kôji Suzuki, which in turn draws on the Japanese folk tale Banchō Sarayashiki. The film stars Nanako Matsushima, Hiroyuki Sanada, and Rikiya Ōtaka. The film follows TV reporter and single mother Reiko who is caught up in a series of deaths surrounding a cursed video tape.

Production took approximately 9 months.Ring and its sequel Rasen were released in Japan at the same time.

After release, Ring inspired numerous follow-ups within the Ring franchise and triggered a trend of Western remakes.

Plot

Two teenagers, Masami (Hitomi Satō) and Tomoko (Yūko Takeuchi), talk about a videotape recorded by a boy in Izu which is fabled to bear a curse that kills the viewer seven days after watching. Tomoko reveals that a week ago, she and three of her friends watched a weird tape and received a call after watching. Tomoko is killed by an unseen force as Masami watches, horrified.

Alexia (Italian singer)

Alexia (born Alessia Aquilani, 19 May 1967) is an Italian singer. Before recording in Italian in the 2000s, she made records in English in the 1990s. Many of those were international hits. Before her solo career she was the vocalist of Ice Mc.

In her career she has sold over 6 million records with 10 top-ten single, of which 4 number-one hits and numerous international sales certifications. She has performed at the Festivalbar for nine times, and four times at the Sanremo Music Festival in which she has earned, besides several music critic awards, three second-places, and has won one in the 2003.

Career

Early work

Alexia was born in La Spezia, Liguria, and from a young age regularly entered singing talent competitions.

She started working for Italian label Euroenergy (by Disco Magic) in 1989 with the singles (Eurobeat/Hi NRG style) Alexia Cooper - Boy and Lita Beck – It's All Right. One year later she gave "Backing Vocals" in the singles Cinema and Scream by Ice Mc. Later she worked with producer Roberto Zanetti (better known as Robyx) in 1990, as a back-up singer to several of Zanetti's eurodance acts on his DWA label, including Double You and Ice MC and notably featured on many of the latter's biggest hits such as "Think About The Way" (on the Trainspotting soundtrack), "It's A Rainy Day" and "Russian Roulette". When Ice MC left DWA, Robyx turned his attention to Alexia, and the pair wrote the song "Me And You", which included the vocals of "Double You". The song was a big international hit and was followed the next year by "Summer Is Crazy" and "Number One", which again were international hits.

Alexia (given name)

Alexia is a feminine form of the name Alexius.

People with the name

See also

Dyslexia

Dyslexia, also known as reading disorder, is characterized by trouble with reading despite normal intelligence. Different people are affected to varying degrees. Problems may include difficulties in spelling words, reading quickly, writing words, "sounding out" words in the head, pronouncing words when reading aloud and understanding what one reads. Often these difficulties are first noticed at school. When someone who previously could read loses their ability, it is known as alexia. The difficulties are involuntary and people with this disorder have a normal desire to learn.

The cause of dyslexia is believed to involve both genetic and environmental factors. Some cases run in families. It often occurs in people with attention deficit hyperactivity disorder (ADHD) and is associated with similar difficulties with numbers. It may begin in adulthood as the result of a traumatic brain injury, stroke, or dementia. The underlying mechanisms are problems within the brain's language processing. Dyslexia is diagnosed through a series of tests of memory, spelling, vision, and reading skills. Dyslexia is separate from reading difficulties caused by insufficient teaching; or either hearing or vision problems.