Sentence examples for defined in the case of from inspiring English sources

These cardinal virtues are differently, albeit analogously, defined in the case of each level.

The process is the most defined in the case of non-conductive pits.

The first part of the following result was given with an incorrect proof in [20] (using lim inf which may not be defined in the case of an arbitrary cone metric space).

Q.E.D. Definition 3 A single integral on the 2D plane in tensor representation ∫ f ( x, y ) = 0 [ A, B ] X μ d l μ is defined in the case of a piecewise smooth curve of the equation f ( x, y ) = 0 by the formula ∫ f ( x, y ) = 0 [ A, B ] X μ d l μ = lim n → ∞ ∑ k = 1 n ( X μ ) k ( Δ l μ ) k, (2.34).

Definition 2 A triangular double integral, integrands of which are partial differentials on the 2D plane in component representation ∬ f ( x, y ) ≤ 0 [ A, B ] [ ( ∂ X ′ ∂ x ′ d x ′ + ∂ X ′ ∂ y ′ d y ′ ) d y − ( ∂ Y ′ ∂ x ′ d x ′ + ∂ Y ′ ∂ y ′ d y ′ ) d x ], is defined in the case of a piecewise smooth curve of the equation f ( x, y ) = 0 by the formula (2.13).

Q.E.D. Definition 1 A single integral on the 2D plane in component representation ∫ f ( x, y ) = 0 [ A, B ] ( X d y − Y d x ) is defined in the case of a piecewise smooth curve of the equation f ( x, y ) = 0 by the formula ∫ f ( x, y ) = 0 [ A, B ] ( X d y − Y d x ) = lim n → ∞ ∑ k = 1 n ( X k Δ y k − Y k Δ x k ), (2.12).

More specifically, the basic parameters of the design of the heat exchangers will be defined in the cases of supercritical fluid parameters and the convective coefficients as well as resulting heat transfer surface will be calculated for various fluid parameters.

The determinant is only defined in the case where the number of features is p - 1, p being the number of desired endmembers [9].

Under American libel law as defined in the 1964 case of New York Times v Sullivan, any public figure suing for libel must prove a defamatory statement was made with actual malice, "with knowledge that it was false or with reckless disregard of whether it was false or not".

American libel law as defined in the 1964 case of New York Times v Sullivan states that any public figure suing for libel must prove a defamatory statement was made with actual malice, "with knowledge that it was false or with reckless disregard of whether it was false or not".

The ℓ 2-inner product and its induced norm is defined similarly in the case of discrete-time signals.