Sentence examples for by applying the generated from inspiring English sources

By applying the generated asset index, sample households were classified into five quintiles.

This work addresses this challenge by applying the generated data to relate glucan enzymatic digestibility to lignin and plant cell wall properties, to better characterize and understand the mechanism of AHP pretreatment for improved cell wall deconstruction, and to compare three analytical platforms (HSQC NMR, Py-GC/MS, and thioacidolysis) for the analysis of grass lignins.

Some new formulae of products of the Frobenius-Euler polynomials are established by applying the generating function methods and some summation transform techniques.

In this paper, by applying the generating function methods and summation transform techniques, we establish some new convolution identities for the Frobenius-Euler polynomials.

By applying the generating function technique, some important performance measures are derived, which may be useful for network and software system engineers.

Motivated and inspired by the work of the above authors, in this paper we establish some similar convolution identities for the classical Frobenius-Euler polynomials to (1.6) by applying the generating function methods and summation transform techniques developed in [18].

Motivated by the work of Carlitz [24], in the present paper we establish some new formulae of products of the Frobenius-Euler polynomials by applying the generating function methods and some summation transform techniques.

Some closed formulae of sums of products of any number of Apostol-Bernoulli and Apostol-Euler polynomials and numbers are established by applying the generating function methods and some summation transform techniques.

As further applications, we obtain some closed formulae of sums of products of any number of Apostol-Bernoulli and Apostol-Euler polynomials and numbers by applying the generating function methods and some summation transform techniques.

By applying the generating function methods and some combinatorial techniques, developed in [6, 17], we establish some new recurrence formulae for the Apostol-Bernoulli and Apostol-Euler polynomials, by virtue of which, some known results including the ones presented in [6], are obtained as special cases.

The following relationship is established between the polynomials due to Erkuş and Srivastava [35] and the Chan-Chyan-Srivastava polynomials by applying the generating functions (2.2) and (2.6) in [36].