In mathematics, particularly in the fields of topology and differential geometry, the term "submersion" refers to a specific type of smooth map between differentiable manifolds. A smooth map \( f: M \to N \) is called a submersion at a point \( p \in M \) if its differential \( df_p: T_pM \to T_{f(p)}N \) is surjective.
A **Riemannian submersion** is a specific type of mathematical structure that arises in differential geometry. It involves two Riemannian manifolds and a smooth map between them that preserves certain geometric properties. More formally, let \( (M, g_M) \) and \( (N, g_N) \) be two Riemannian manifolds, where \( g_M \) and \( g_N \) are their respective Riemannian metrics.
Łukasiewicz logic, named after the Polish logician Jan Łukasiewicz, is a non-classical system of logic that extends classical propositional logic. It is particularly known for its treatment of many-valued logics, where it allows for more than just the binary true and false values. 1. **Many-Valued Logic**: One of the key contributions of Łukasiewicz is his development of many-valued logic, which allows for a spectrum of truth values.
Three-valued logic is a type of formal logic that extends classical binary logic (which uses only two truth values: true and false) by introducing a third truth value. The most common interpretation of this third value is "unknown" or "indeterminate," but the specific interpretation can vary depending on the context. In three-valued logic, the three truth values are often represented as: 1. **True (T)**: Represents objects that are true.
Infinite-valued logic is a type of many-valued logic in which propositions can take on an infinite number of truth values, rather than being limited to the classic binary values of true or false. In traditional binary logic, a statement can only be either true (1) or false (0). In contrast, infinite-valued logic allows for a spectrum of truth values that can represent varying degrees of truth or uncertainty.
Four-valued logic, also known as "many-valued logic," is a type of logical system that extends traditional two-valued logic (true and false) by introducing additional truth values. In four-valued logic, the four truth values are typically represented as: 1. **True (T)** 2. **False (F)** 3. **Unknown (U)** or **Indeterminate**, which represents a state where the truth value is not known.
Finite-valued logic is a type of logical system in which propositions can take on a finite number of truth values, rather than just the traditional two values found in classical binary logic (true and false). While classical logic operates under a binary scheme (true = 1, false = 0), finite-valued logics extend this idea by allowing multiple truth values. In finite-valued logic, truth values can be, for example, {0, 1, 2, ...
"Waxwork II: Lost in Time" is a horror-comedy film and the sequel to the 1988 film "Waxwork." Directed by Anthony Hickox and released in 1992, the movie continues the story of the original characters as they face new supernatural challenges. In "Waxwork II," the protagonist, Mark, is on a quest to clear his name after being wrongly accused of murder. He discovers a portal that allows him to travel through various film genres and historical events.
"Waxwork" is a horror-comedy film released in 1988, directed by Anthony Hickox. The film follows a group of young friends who visit a mysterious wax museum, only to discover that the exhibits come to life and are connected to various horrifying stories and characters from horror history. As they explore the museum, they find themselves trapped in a nightmarish scenario where they must confront their worst fears and the deadly wax figures that inhabit the exhibits.
"Tourist Trap" is a 1979 horror film directed by David Schmoeller. The story revolves around a group of young friends who become stranded at a remote, eerie roadside museum and tourist attraction after their car breaks down. The attraction is run by a strange and unsettling man named Mr. Slausen, played by Chuck Connors. As the friends explore the museum, they encounter a series of creepy mannequins and soon discover that they are not alone.
"Tombs of the Blind Dead" (original title: "Los olvidados") is a Spanish horror film released in 1972, directed by Amando de Ossorio. The film is known for introducing the "Blind Dead" franchise, which features a series of films centered around a group of undead Templar Knights who are blind but possess heightened other senses, allowing them to hunt their victims.
"The Stepford Wives" is a 2004 satirical science fiction comedy film directed by Frank Oz, based on the 1972 novel of the same name by Ira Levin. The film stars Nicole Kidman as Joan, Matthew Broderick as her husband Walter, Bette Midler, and Christine Baranski among others. The story revolves around Joan and Walter, a couple who move from New York City to a seemingly idyllic suburban community called Stepford.
"The Stepford Wives" is a 1975 American satirical science fiction horror film directed by Bryan Forbes. The movie is based on the 1972 novel of the same name by Ira Levin. It stars Katharine Ross as Joanna Eberhart, a woman who moves to the seemingly idyllic suburban community of Stepford, Connecticut, with her husband, Walter (played by Peter Masterson).
"The Rocky Horror Picture Show" is a musical comedy film that was released in 1975, directed by Jim Sharman and based on the stage musical "The Rocky Horror Show" created by Richard O'Brien. The film follows the story of a young couple, Brad Majors and Janet Weiss, who, after their car breaks down, seek help at a mysterious castle owned by Dr. Frank-N-Furter, a flamboyant and eccentric transvestite who is hosting a strange party.
"The Omega Man" is a 1971 science fiction film directed by Boris Sagal and starring Charlton Heston. It is based on Richard Matheson's 1954 novel "I Am Legend." The film is set in a post-apocalyptic world where a deadly biological war has decimated the population, leaving Heston's character, Robert Neville, as one of the last surviving humans.
"The Night Walker" is a 1964 American horror film directed by William Castle. The film is notable for its use of the 3-D format, which was a popular gimmick during the era. The story centers around a blind woman named Mary who is plagued by nightmares involving a mysterious figure. As the narrative unfolds, it becomes clear that her dreams may be connected to a series of murders.
"The Hourglass Sanatorium" is a 1973 Polish film directed by Wojciech Has, based on the influential novel "The Hourglass Sanatorium" ("Sanatorium pod Klepsydrą") by Bruno Schulz. The film is noted for its surreal, dream-like narrative that explores themes of time, memory, and the human condition. The story follows a young man who visits a sanatorium to find his ailing father.
"The Holy Mountain" is a surrealist film directed by Alejandro Jodorowsky, released in 1973. It is known for its visually striking and avant-garde style, as well as its challenging themes and complex symbolism. The film follows a character known as "The Thief," who embarks on a journey of spiritual enlightenment and self-discovery.
"The Hills Have Eyes" is a horror film released in 2006, directed by Alexandre Aja. It is a remake of the 1977 film of the same name, which was originally created by Wes Craven. The 2006 version retains the basic premise of the original but features updated visuals, more intense violence, and a modern storytelling approach. The plot follows a family who becomes stranded in the desert after their car breaks down.
"The Fear" is a 1995 horror film directed by Vincent Guastini. The movie follows a group of friends who take a trip to a remote house in the woods, where they become trapped and targeted by a mysterious and malevolent force. The film explores themes of psychological horror and the nature of fear itself, blending elements of thriller and supernatural horror. The storyline typically revolves around the characters facing their own fears while confronting the dangers around them.