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Anglický jazyk
Stability Theorems in Geometry and Analysis
Autor: Yu. G. Reshetnyak
1. Preliminaries, Notation, and Terminology n n 1.1. Sets and functions in lR. . Throughout the book, lR. stands for the n-dimensional arithmetic space of points x = (X},X2,'" ,xn)j Ixl is the length of n n a vector x E lR. and (x, y) is the scalar product... Viac o knihe
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O knihe
1. Preliminaries, Notation, and Terminology n n 1.1. Sets and functions in lR. . Throughout the book, lR. stands for the n-dimensional arithmetic space of points x = (X},X2,'" ,xn)j Ixl is the length of n n a vector x E lR. and (x, y) is the scalar product of vectors x and y in lR. , i.e., for x = (Xl, X2, ... , xn) and y = (y}, Y2,··., Yn), Ixl = Jx~ + x~ + ... + x~, (x, y) = XIYl + X2Y2 + ... + XnYn. n Given arbitrary points a and b in lR. , we denote by [a, b] the segment that joins n them, i.e. the collection of points x E lR. of the form x = >.a + I'b, where>. + I' = 1 and >. ~ 0, I' ~ O. n We denote by ei, i = 1,2, ... ,n, the vector in lR. whose ith coordinate is equal to 1 and the others vanish. The vectors el, e2, ... ,en form a basis for the space n lR. , which is called canonical. If P( x) is some proposition in a variable x and A is a set, then {x E A I P(x)} denotes the collection of all the elements of A for which the proposition P( x) is true.
- Vydavateľstvo: Springer Netherlands
- Rok vydania: 2010
- Formát: Paperback
- Rozmer: 235 x 155 mm
- Jazyk: Anglický jazyk
- ISBN: 9789048144679
