Sentence examples for three times continuously from inspiring English sources

Let D denote the set of all real-valued functions which are three times continuously differentiable on I.

where f : R n → R 1, u i : R n → R 1, i = 1, …, m and v j : R n → R 1, j = 1, …, l are three times continuously differentiable.

To study the reproducibility of the ZnO thin film-based acetone sensor, the response of the sample was tested to 100 ppm of acetone at an operating temperature of 280 °C three times continuously.

Theorem 2.1 Let H be defined as in (3), let f ( x ), u i ( x ), i = 1, …, m and v j ( x ), j = 1, …, l be three times continuously differentiable functions, let assumptions (A1 - A5) hold, and let ξ i ( x ), i = 1, …, m and η j ( x ), j = 1, …, l be twice times continuously differentiable functions.

We assume that either Γ = ∂ Ω is parametrized by a closed continuous and piecewise two times continuously differentiable path γ : [ a, b ] → Γ such that the restriction γ | [ a, b ) is even bijective, or that Γ ⫋ ∂ Ω is parametrized by a bijective continuous and piecewise two times continuously differentiable path γ : [ a, b ] → Γ.

space of continuous functions over I. space of six times continuously differentiable functions on I. is the non-negative weight function which satisfies the following axiom: left.

(C(I)) :  space of continuous functions over I. (C^{6}(I)) :  space of six times continuously differentiable functions on I. (w(x)) :  is the non-negative weight function which satisfies the following axiom: left.

Theorem 2.4 Let the function φ : be four times continuously differentiable.

Theorem 1.3 Let f : [ a, b ] → R be a four times continuously differentiable mapping on ( a, b ) and ∥ f ( 4 ) ∥ ∞ = sup x ∈ ( a, b ) | f ( 4 ) ( x ) | < ∞.

We seek the unknown function u ∈ C 2 ( D ) ∩ C ( 1, α ) ( D ∪ Γ ) in the class of two times continuously differentiable in D functions which satisfy Hölder condition in D ∪ Γ with their first degree derivatives.

This inequality is stated as: If f : [ a, b ] → R be four times continuously differentiable mapping on ( a, b ) and ∥ f 4 ∥ ∞ = Sup x ∈ ( a, b ) | f 4 ( x ) | < ∞.