Sentence examples for be a map defined from inspiring English sources

Let be a map defined by for.

Assume further that U is chosen according to Definition  3.3 and (varphi_{U} colon U multimap U) be a map defined in (3.4).

Let f : I → I be a map defined on the numerical segment I and X be an orbit, X = ( f ( 0 ) ( x ), f ( 1 ) ( x ), …, f ( n ) ( x ), … ), that is, we put in (1) f n = f ( n ) ( x ), where f ( n ) ( f ( 0 ) ( x ) ≡ x, f ( n + 1 ) = f ∘ f ( n ) ), n ≥ 0 denote the iterates of the map f.

Theorem 4.3 Let β ≠ 0 be a constant and let f be a map defined on [ 0, ∞ ). Define a map f β : R → R by f β ( x ) : = ⌊ x ⌋ β + f ( x − ⌊ x ⌋ ) for all x ∈ R. Then g ( x ) : = [ Φ 1 / β ] f β ( x ) is a Fibonacci function.

Let be a map defined so that each meridian, for, is carried homeomorphically onto a same distinguished meridian of the range 2-sphere containing, and each of the tracks covers once the sphere, always in the same direction, which is chosen according to the orientation of, so that is a map of degree.

Let be a mapping defined by (3.3).

Let be a mapping defined by.

Let and be a mapping defined by (2.7).

Let for all, and be a mapping defined by (2.9).

for all and all Let be a mapping defined by.

Let be a mapping defined by Then : is a firmly nonexpansive mapping and.