Sentence examples for exists the function from inspiring English sources

If no such set exists, the function outputs ⊥.

(1.31) Then the operator P defined by equality (1.13) continuously acts from (A_{gamma_{0}}) to the space (L_{n}(]a, b])), and there exists the function (deltain D_{n}(]a, b])) such that item (i) of Definition 1.1 holds.

Hence, if there exists the function u ∗ ∈ W ∗ ( M, m, p ) which attains the equality of (21), it holds that C ( M, m, p ) = ∥ H m ∥ L q ( − s, s ) p. On the contrary, we see that the equality holds for (21) if and only if u satisfies u ( M ) ( x ) = ( sgn H m ( x ) ) | H m ( x ) | q − 1. (22).

When no legitimate government exists, the function of stewardship may be pooled among multiple stakeholders, although effective coordination is essential [ 54].

For f′ z) to exist, the function f must be "similarity preserving in the small," or conformal, meaning that infinitesimal regions are faithfully mapped to regions of the same shape, though possibly rotated and magnified by some factor.

Moreover, assume that there exist the functions such that (2.9).

Therefore, for an arbitrary, there exist the functions,, such that (3.17).

Hence, is increasing on and therefore, there exists the inverse function mapping onto.

Arguing in Lemma 3.1.9 in [20], we see that there exists the nonnegative function (u_{0}inmathcal{N}_{alpha}) such that (J_{alpha} u_{0})=d_{alpha}).

No experimental evidence exists for the function or existence of the protein product.

To date, more knowledge exists about the function of the B2R, which is thought to mediate most of the known cardiovascular beneficial effects of kinins.