Sentence examples for applications of the operators from inspiring English sources

It should be noted that properties and applications of the operators B α, B ∗ α and B − α in the class of harmonic functions in the ball Ω are studied in [10].

In [18], in the class of harmonic functions in a ball, the properties and applications of the operators in the form of δ μ = r ∂ ∂ r + μ, δ μ m = ( r ∂ ∂ r + μ ) m (6).

Some applications of the operator J s, b ( f ) to certain classes in Geometric Function Theory can be found in [14 16] and [17].

Inspired by their work, in this paper, we construct two generalized q-exponential operator with three parameters and give some operator identities to further investigate the applications of the operator technique.

Further, a proper set of conditions has been discussed to rectify the errors and applications pointed out in Remarks 1 and 2. Some interesting applications of the operator used in this paper were pointed out in Note 1.

In the framework discussed in Section  1 this means that we have to bound at least three applications of the operator b (u ⋆ ) to the exact solution.

Note that in the linear case this assumption is equivalent to the fact that b 3 u (t ) can be bounded; i.e., we have to bound three applications of the operator b to the exact solution.

Then, complex defect configurations can be constructed through reiterative application of the operators.

After producing designs, the system shows some models to the user, and then according to evaluation and application of the operators of the genetic algorithm (selection, crossover and mutation), produces better designs.

Some basic LVFs can be presented in terms of "inference rules" that regulate the application of the operators and the transition from one formula to the next when describing a biological process, as discussed in the next section.

The whole analysis may be performed by a repeated application of the operator.