- published: 08 Jul 2010
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In mathematics, a linear map or linear function f(x) is a function which satisfies the following two properties:
It can be shown that additivity implies the homogeneity in all cases where α is rational; this is done by proving the case where α is a natural number by mathematical induction and then extending the result to arbitrary rational numbers. If f is assumed to be continuous as well then this can be extended to show that homogeneity for α any real number, using the fact that rationals form a dense subset of the reals.
In this definition, x is not necessarily a real number, but can in general be a member of any vector space. A less restrictive definition of linear function, not coinciding with the definition of linear map, is used in elementary mathematics.
The concept of linearity can be extended to linear operators. Important examples of linear operators include the derivative considered as a differential operator, and many constructed from it, such as del and the Laplacian. When a differential equation can be expressed in linear form, it is particularly easy to solve by breaking the equation up into smaller pieces, solving each of those pieces, and adding the solutions up.
Actors: Rodney Luis Aquino (miscellaneous crew), Rodney Luis Aquino (producer), Rodney Luis Aquino (director), Rodney Luis Aquino (writer), Cody Foltz (producer), Jolene Perez (actress), Cody Foltz (editor), Mark Niznik (producer), Laurie Miller (actress), Rockell Mercaldo (actress), Joey Restivo (actor), Laurie Miller (actor),
Plot: A journey to re-discover the original founding members of the east coasts freestyle music scene who paved the way for a new genre of music in the 80's - 90's. We interview them and describe the hardship's of the music entertainment industry and where they are today.
Genres: Biography, Documentary, Drama, History, Music,Actors: Yûko Kobayashi (actress), Kumiko Nishihara (actress), Rie Iwatsubo (actress), Yûtarô Mochizuki (producer), Toshiaki Okuno (producer), Donna Coney Island (actress), Shigeyuki Yamamori (editor), Naohito Takahashi (director), T. Bone Wang (actor), Georgia Lee (actress), Chrissie Squirt (actor), Slam Dunk (actor), Keisaku Iriki (composer), Bunni Fuxx (actress), Kaoru Fujino (actress),
Plot: After ten years of dormancy, Linea awakes from a capsule in the countryside of Japan. Without any memories, she wanders into a small research center staffed by three beautiful women. One of the researchers, Sayako, is entranced by the strange woman and leaves her present lover. Sayako takes Linea to bed, and finds that her abilities are beyond that of any ordinary woman!
Keywords: android, anime, hardcore, hentai, lesbian, lesbian-sex, rape, schoolgirl, sexActors: Yûko Kobayashi (actress), Kumiko Nishihara (actress), Rie Iwatsubo (actress), Yûtarô Mochizuki (producer), Toshiaki Okuno (producer), Donna Coney Island (actress), Shigeyuki Yamamori (editor), Naohito Takahashi (director), T. Bone Wang (actor), Georgia Lee (actress), Chrissie Squirt (actor), Slam Dunk (actor), Keisaku Iriki (composer), Bunni Fuxx (actress), Kaoru Fujino (actress),
Plot: After ten years of dormancy, Linea awakes from a capsule in the countryside of Japan. Without any memories, she wanders into a small research center staffed by three beautiful women. One of the researchers, Sayako, is entranced by the strange woman and leaves her present lover. Sayako takes Linea to bed, and finds that her abilities are beyond that of any ordinary woman!
Keywords: android, anime, hardcore, hentai, lesbian, lesbian-sex, rape, schoolgirl, sex