Sentence examples for is a linear functional of from inspiring English sources

If F : X ⟶ R is a linear functional of a unit norm defined on the normed linear space X endowed with the norm ∥ ⋅ ∥ and the vectors x 1, …, x n satisfy the condition 0 ≤ r ≤ F ( x i ), i ∈ { 1, …, n }. then r ∑ i = 1 n ∥ x i ∥ ≤ ∥ ∑ i = 1 n x i ∥, where equality holds if and only if both F ( ∑ i = 1 n x i ) = r ∑ i = 1 n ∥ x i ∥. and F ( ∑ i = 1 n x i ) = ∥ ∑ i = 1 n x i ∥.

Any Raman detector signal SRaman is a linear functional of LRaman.

A distribution is a linear functional on of infinitely differentiable functions on with compact supports such that for every compact set there exist constants and satisfying (2.1).

As a distribution, the Dirac delta is a linear functional on the space of test functions and is defined by \delta[\varphi] = \varphi(0)\, for every test function φ.

Recall that a distribution u is a linear functional on C c ∞ ( R ) of infinitely differentiable functions on ℝ with compact supports such that for every compact set K ⊂ R, there exist constants C > 0 and N ∈ N 0 satisfying | 〈 u, φ 〉 | ≤ C ∑ | α | ≤ N sup | ∂ α φ |. for all φ ∈ C c ∞ ( R ) with supports contained in K.

Recall that a distribution u is a linear functional on C c ∞ ( ℝ m ) of infinitely differentiable functions on ℝ m with compact supports such that for every compact set K ⊂ ℝ m there exist constants C > 0 and N ∈ ℕ0 satisfying ∣ 〈 u, φ 〉 ∣ ≤ C ∑ ∣ α ∣ ≤ N sup ∣ ∂ α φ ∣. for all φ ∈ C c ∞ ( ℝ m ) with supports contained in K.

When the heat transfer is purely convective, or solely radiative, then one assumes that f is a linear functional (Newton's law of cooling), or obeys a fourth-order power law (Stefan's law), respectively.

A linear functional of a Gaussian field is a Gaussian variable.

where is a linear bounded functional defined on the space of absolutely continuous functions.

where is a linear bounded functional and.

X ρ = X w is a linear subspace of X and the functional x ρ = d w ∘ ( x, 0 ), x ∈ X ρ, is an F-norm on X ρ ; if w is convex, X ρ * ≡ X w * ( 0 ) = X ρ is a linear subspace of X and the functional x ρ = d w * ( x, 0 ), x ∈ X ρ *, is an norm on X ρ *.