Sentence examples for the definition of a function from inspiring English sources

By the definition of a function ψ, we get ϵ = 0 which is a contraction.

By contrast, the definition of a function in set theory as a set f of ordered pairs satisfying the property that (x,y) ∈ f and (x,z) ∈ f implies y = z.

The properties (iv) in Lemma 2.2 suggest the definition of a function (Vert cdot Vert :{{mathbb{R}}}_{{mathcal{F}}}to {mathbb{R}}) by (Vert uVert =D (u,tilde{0} )), which has the properties of the usual norms.

In Hilbert spaces, Π C = P C. It is obvious from the definition of a function ϕ that ϕ ( x, y ) = ϕ ( x, z ) + ϕ ( z, y ) + 2 〈 x − z, J z − J y 〉, (2.1).

In Hilbert spaces, Π C = P C. It is obvious from the definition of a function ϕ that ϕ ( x, y ) = ϕ ( x, z ) + ϕ ( z, y ) + 2 〈 x − z, J z − J y 〉, ∀ x, y, z ∈ E, (1.1).

A probabilistic theory of confirmation can be spelled out through the definition of a function \(C_{P}(h, e\mid k): \{\bL^3 \times \bP\} \rightarrow \Re\) representing the degree of confirmation that hypothesis \(h\) receives from evidence \ e\) relative to \ k\) and probability function \(P\).

The above theorem is not generally true for the union of GSEC subsets of N. Now, we extend the definition of a GEC function on a Riemannian manifold to a GSEC function on a Riemannian manifold.

The method is based on the definition of a new function, the Geodesic Path Density Map (GPDM), within each sulcal basin (i.e. regions with a negative mean curvature).

Let us recall the definition of a comparison function.

Such goals allow the definition of a fitness function and selection of some given designs.

Besides, it would need the definition of a merit function combining properly the performance parameters.