By Axiom of Choice, there exists a mapping on such that (3.12).
But by definition of union, F ⊆ U; hence there would exist a map of U onto F and a contradiction could be derived by diagonalization.
Its element a i,j) is 1, if there exists an mapping between protein i of one species and protein j of the other one, 0 otherwise.
[There exists] a map of the island of California.
A mapping is said to be relaxed - monotone if there exist a mapping and a function positively homogeneous of degree, that is, for all and such that (1.9).
Then there exists a proper map (y=y(x)) of ({overline{D}}_0times mathbb {R}) onto (overline{{hat{D}}_0}times mathbb {R}, y=x) on (Gamma _0times mathbb {R}), and there exists a gauge transformation with the gauge (c' y)in G_0 overline{{hat{D}}_0}times mathbb {R}), c' y)=1) on ({overline{Gamma }}_0times mathbb {R}) such that (L'= c'circ y^* L).
Then there exists a sequence of maps convergent pointwise on I to a map f : I → K of bounded variation such that.
If we consider M to be a Cartan-Hadamard manifold (either infinite or finite dimensional), then on M there exists a natural map η playing the role of x − y in the R n.
It is well-known (cf. [[23], Theorem 3.1]) that there exists a pair of maps (f', g') such that (f, g) is homotopic to (f', g') and Coin(f', g') is finite.
will be said to be an asymptotic pointwise nonexpansive mapping if there exists a sequence of mappings such that (2.1).
T : M → M will be said to be an asymptotic pointwise nonexpansive mapping if there exists a sequence of mappings α n : M → [0, ∞) such that d ( T n ( x ), T n ( y ) ) ≤ α n ( x ) d ( x, y ). and lim sup n → ∞ α n ( x ) ≤ 1. for any x, y ∈ M. For more details on it we refer [15].
