Sentence examples for define by using the 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 manifold boundary is first defined by using the unilateral constraint representing the contact event.

Displacement fields are defined by using the four variable plate theory.

Business objects can be easily defined by using the proposed mtCMF, and database tables are created from these objects automatically.

An initial defect tensor for a single grain of sea ice is defined by using the geometric pattern.

The multicomponent coupled ionic diffusive fluxes of reactants and products were defined by using the gradient of the electrochemical potentials as driving forces for the diffusion.

Low and very high-human-development countries are defined by using the fixed cutoff points based on quartiles of HDI values introduced by the 2014 Human Development Report (HDI < 0.55 and HDI > 0.8, respectively (see HDR_technical_notes.pdf and Methods).

The amount of copper in the superconducting cable has been defined by using the classical hotspot temperature design criterion that is based on the adiabatic condition.

Some order relations on the fuzzy number space are defined by using the method of fuzzy structured element, and some properties of the order relations are discussed.

The objective function is defined by using the network calculus, which is a deterministic theory and enables to bound these delays.