Sentence examples for define by using from inspiring English sources

This motivates the introduction of essential Hochschild cohomology which we define by using the point weak star closure of coboundaries in place of the usual coboundaries.

Proof For each n ≥ 1 and u n ≤ k ≤ v n, we define, by using the method of continuous truncation, the following: Y n k = − h 1 / r ( n ) I ( X n k < − h 1 / r ( n ) ) + X n k I ( | X n k | ≤ h 1 / r ( n ) ) + h 1 / r ( n ) I ( X n k > h 1 / r ( n ) ). and Z n k = X n k − Y n k.

The "emotion of love has been perverted and misused to such an extent that it can only be defined by using another word," he answered in part.

Relationships are defined

Crashworthiness is defined by using a multi-objective function.

Surface morphology was defined by using scanning electron microscopy.

These are defined by using the usual Hukuhara difference ⊖. ([22]).

Optimal hyperpaths are defined by using mixed strategy Nash equilibrium.

where L 1/2 is defined by using the spectral theorem.

Function ({ matches}) is defined by using function ({ sats}) (Sect.

The equivalent damping ratio was defined by using DAF at natural frequency.