Sentence examples for by using four auxiliary from inspiring English sources

By using four auxiliary functions, these equations convert into two independent partial differential equations.

Very recently, Isik and Turkoglu (Fixed Point Theory Appl. 2013:131, 2013) proved a common fixed point theorem in a rectangular metric space by using three auxiliary distance functions.

Very recently, as a generalization of the main result of [1], Isik and Turkoglu [2] reported a common fixed point result of two self-mappings in the setting of a rectangular metric space by using three auxiliary functions.

In the calculation procedure described in Fig. 1 the required iterative solution is executed by successive approximations using two auxiliary angles γ 1 and γ 2 being apart from each other by the assumed crank-angle increment, Δγ.

Aux-fed subs can even be stereo, if desired, using two auxiliary mix buses.

The successful growth of Ni-Co LDH with different morphologies on CNF membrane by using two kinds of auxiliary agents reveals the simplicity and universality of this method.

This work presents a comparative study on the tuning of structural topologies by using two N-donor ligands with different lengths as auxiliary ligands.

We use two nonoverlapping auxiliary problems over (( Omega _{1},Omega _{3} ) ) and over (( Omega_{2},Omega_{4} ) ), respectively.

Among them, using three active thrusters was chosen as the auxiliary towing system.

The risk groups are defined using two risk scores derived from two working proportional hazards models with the auxiliary variables as the covariates.

Trends were assessed by using an auxiliary uncorrected voxel threshold of P <0.001 [ Friston et al., 1994].