Sentence examples for norm definition from inspiring English sources

Use Theorem 1, Combine (25), (29) and norm definition, the (20) and (21) are obtained.

Since we have constraints 2 and 3, we can induce a norm function p(x)=d(x−0) which satisfies the norm definition.

Vice versa, let u ∈ E ∞ t ( D q ) with a fixed t > 0. The norm definition in E ∞ t ( D q ) implies that ∥ D q k u ∥ L q ≤ t k ∥ u ∥ E ∞ t for all k ∈ Z +.

The proof directly follows from the norm definition and direct estimation of attractor shift when the kernel is changed.

This is the cleanest choice of norm definitions for present purposes.

We then determine the coefficients C k such that the entity of measurement data differs as little as possible from the model data of eq 7, 8resulting in a least-squares optimization (we adopt the norm definitions ∥ x∥ L 22 = ∑ i | x i | and ∥ x∥ L 1 = ∑ i | x i |).

Although they obtained a Gaussian form as a choice of the covariance function, the Matérn function is bounded by the Euclidean norm by definition, which may not be suited for discrete genomic data.

Using common social concepts, like skills, diversity, social exchange theory, and norms in definition of the algorithm, the outcomes of this research can be used in wide ranges of distributed applications.

A t-norm ∗ is said to be positive if a ∗ b > 0 for all a, b ∈ ( 0, 1 ]. Obviously, ∗1 and ∗2 are positive t-norms. Definition 2.2 [9].

The development of common norms, agreed definitions, clear boundaries and cognitive legitimacy are contested processes.

Clearly, is closed in and to prove that has a unique fixed point in, it suffices to prove that is a strict contraction, for instance for the norm defined in definition of with suitable.