The phrase "a function that belongs" is correct and usable in written English.
It can be used when describing a function that is associated with or part of a particular system, category, or context.
Example: "In mathematics, a function that belongs to a specific class can exhibit certain properties that are useful for analysis."
Alternatives: "a function that is part of" or "a function that is associated with".
Note that a typical Young function that belongs to the class φ p is φ(t) = t s with 1 ≤ s < p. We can easily increase s → ∞ as p → ∞, then for p ≥ 1, our results can be held with L p -norms.
The principle of matching pursuit is to decompose a signal into the linear superposition of the basis function that belongs to a redundant dictionary.
A hierarchy of flatter functions that belong to E ˜ ( 1 ) was constructed by Bak et al. [14].
We denote by Λ the set of all functions α : [ 0, + ∞ ) → [ 0, + ∞ ) verifying the following conditions: (i) α is a positive Lebesgue integrable mapping on each compact subset of [ 0, + ∞ ) (ii) for all ε > 0, we have ∫ 0 ε α ( t ) d t > 0. Let N ∈ N be a fixed positive integer. Let { α i } 1 ≤ i ≤ N be a family of N functions that belong to Λ.
Here the nonlinearity is superlinear at zero, and it is located near infinity between two functions that belong to a class of functions where the Ambrosetti-Rabinowitz condition is satisfied.
Nevertheless, there are functions that belong to E p ( A ) but do not belong to E ˜ ( A ′ ) for any A ′ > 0. Two examples of curves that our result covers that are not covered in [11] can be constructed with the aid of the examples given below. .
Nevertheless, there are functions that belong to E p ( A ) but do not belong to E ˜ ( A ′ ) for any A ′ > 0. Two examples of curves that our result covers that are not covered in [11] can be constructed with the aid of the examples given below.
This paper presents stability analysis and robust H∞ control for a particular class of switched systems characterized by nonlinear functions that belong to sector sets with arbitrary boundaries.
The following two examples are simple applications to a generalized Lebesgue point and μ-generalized Lebesgue point of some functions that belong to (L_{1}(mathbb{R} ^{2})).
