- 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, sexWhat i gotta do
Everything i say, everything i do
You seem to think that i can't tell the truth
What i gotta do to prove to you (i'm still in love)
Even though i try
You seem like you'll never be satisfied
All you seem to care about is who, what, when, and why
I'm doing this, and doing that i just wanna throw it back, back to the day around the way in va (va)
When everything was cool and all i had to say, was trust me babe
But now, no
[chorus]
Everything has changed, will it always
Always be this way
And i know that
That it's all my fault
One night of pleasure really cost me
I'm the one so wrong this time
The tables have turned,
I found a really good man, no i've
Gotta let it burn
Cause i'm still in love
Woah, i, baby (i'm still in love)
Still in love
And i'm so proud of you (so proud of you)
Cause not a lot of guys can do what you do (what you do)
You stay true to me, so faithfull (so faithfull)
So what i gotta do to prove to you (i'm still in love)
And i can't give up
Because i refuse to lose ya love (lose ya love)
It's only me and you i'm thinking of (thinking of)
And i can't let it end
Can we start all over again
Because
[repeat chorus]
[bridge]
Hold on, just don't let it go, cause i can't do it without you, you won't hurt no more
Hold on (hold on), just don't let it go, cause i can't do it without you, you won't hurt no more
[chorus]
Everything has changed, will it always
Always be this way
And i know that
That it's all my fault
One night of pleasure really cost me (it really cost me)
I'm the one so wrong this time (i know i was wrong)
The tables have turned(i know what i gotta do)
I've found a really good man, now i (i know i hurt you)
Gotta let it burn (i'll let burn if i have to)
Cause i'm still in love
Woah, i, baby (i'm still in love)