Sentence examples for functions are omitted from inspiring English sources

To give an overview of the technique, a simplified data-hiding scenario is considered, and thus, any formal definition of the inputs, outputs, and component functions are omitted.

In order to determine how much additional computational overhead was imposed by the calculation of exp and log1p we performed a comparison with an artificial reference calculation, which was identical except that calls to these functions were omitted.

Edges connecting a sample to a function were omitted if the function was observed fewer than 20 times in that sample.

We only sketch the main proofs and some function definitions are omitted for brevity, when they are trivial.

Both (1) and (2) can be time-varying but the time indices for functions and matrices are omitted for convenience.

Since these lemmas are simple consequences of these function definitions, they are omitted here.

where ξ = c t + k x + ξ 0. From Case 2 we can also get some exact solutions expressed in the forms of the Jacobi elliptic functions for (14), which are omitted here.

The words "for operational continuity of the functions transferred" after "the needs" are omitted as executed.

where ξ = c t + k x + ξ 0. From Case 2 we can also get some Jacobi elliptic function solutions for (26), which are omitted here.

The resultant equation is the multimodal vMF SCF function, the mathematical details of which are omitted in here.

Proceeding in a similar manner we can derive bounds for classical Laguerre function of one variable, but details are omitted.