Sentence examples for by using the aforesaid from inspiring English sources

By using the aforesaid functional property, many classical inequalities such as Chebyshev, Stefensen and Aczel inequalities have been generalized in [9].

By using the aforesaid technique to establish the necessary and sufficient conditions for the existence of iterative solutions to a system of coupled boundary conditions, one needs proper differential inequalities as comparison results.

First prepare the binary system of 0.3 wt% C n HSB and 0.15 % HPAM using the aforesaid method.

The RANS equations were solved using the aforesaid four equations transition turbulence model and the fully turbulent SST k ω model.

30, 31 There are certain prerequisites while using the aforesaid techniques, the most important being the depth achieved vis a vis the type of nevi.

For association analysis, the SNP-based haplotype genotyping information in the TF gene was further correlated with SW trait of 244 cultivated and 81 wild chickpea accessions using the aforesaid methods.

But, by using the conditions of the aforesaid theorems we note that the operator T in these theorems is in fact strongly monotone.

In this section, we introduce a new class of extended general nonconvex Wiener-Hopf equations and some new special cases from it, and by using the projection method, we establish that the aforesaid class is equivalent with the class of extended general nonlinear regularized nonconvex variational inequalities (3.1).

The coalescent age estimates using the three aforesaid mutation rates are presented in table 1.

On the illustrative example the effect of torsion at steel crane girder has been analyzed using the confrontation of the aforesaid methods.

It is the aim of this paper to give the refinements of the aforesaid inverse trigonometric inequalities using the Padé approximant method.