Sentence examples for any normalized from inspiring English sources

Then for any normalized linear isotonic functional A : L → R one has the inequality A ( f g ) − A ( f ) A ( g ) ≤ ( Γ 1 − A ( f ) ) ( A ( f ) − γ 1 ) ( Γ 2 − A ( g ) ) ( A ( g ) − γ 2 ).

A new basis function is defined as where represents any normalized pulse shape satisfying the nonnegativity constraint, with in the bit period and otherwise, and is the electrical energy.

Note that for any normalized state ket |ψ〉, 〈ψ |U| ψ〉 and 〈ψ |V| ψ〉 are located in the convex hull formed by the vertices and on the complex plane ℂ, respectively.

The magnitude of any normalized modal shape of the simply supported beam is irrespective of the modal frequency or the wavelength, whereas the maximum generalized force in every mode may be different owing to the difference of the wavelength.

Now, any normalized ECG segment X i can be represented as a weighted sum of the orthonormal vectors v ik as follows: X i = ∑ k = 1 L F c i k v i k, c i k = X i T v i k (6).

Theorem 11 Let f ∈ L be such that f 2 ∈ L and assume that there exist real numbers γ 1 and Γ 1 so that γ 1 ≤ f ≤ Γ 1. Then for any normalized isotonic linear functional A : L → R one has the inequality A ( f 2 ) − [ A ( f ) ] 2 ≤ ( Γ 1 − A ( f ) ) ( A ( f ) − γ 1 ).

Since, the proposed biofilm model does not consider any nomographs, normalized loading curves, etc., there is no chance of any manual error.

In the Humpolec, Lukavec, and Vörden soils, BE inoculation did not result in any increased normalized shoot biomass (Fig. 2 c e).

As well as the production frequency, researchers have access to the linguistic variations that have been collapsed to create any given normalized feature.

In any case, normalized deviation in ages of death is of the same order of magnitude as that of ages of menarche and menopause [ 31].

After normalization, any spot whose normalized intensity remained below the threshold value of 150 was considered to be undetectable, and its value was replaced by the threshold value.