Sentence examples for integral presented from inspiring English sources

In the study of (4.1), the regulated primitive integral is replaced by the continuous primitive integral presented in [6].

Recently, Anber and Dahmani [2], by using the Riemann-Liouville fractional integral, presented some interesting integral inequalities of Pólya and Szegö type.

The integral presented in the book is justified as follows: 'to dispense with any considerations drawn from measure theory; this is what we have done by defining only the integral of regulated mappings (sometimes called the 'Cauchy integral').

The integral presented above does not have a closed formula.

The integrals presented in Equations 55 and 63 are computed using MATLAB in order to determine the average BER, because the calculation of these integrals is intractable.

In this work, we find an identity and several Hermite-Hadamard type inequalities for conformable fractional integrals, present some new inequalities for the arithmetic, logarithmic and generalized logarithmic means of two positive real numbers and provide the error estimations for the trapezoidal formula.

Although a preliminary validation of MRDI on PCa has shown promising results, parameter estimation can become burdensome due the convolution integral present in the dispersion model.

In contrast to other numerical methods, the advantage of our method is that it does not involve any intermediate numerical technique for evaluation of the integral present in integral equations.

In this paper, we prove an identity associated with the Ostrowski inequality for conformable fractional integral, present several Ostrowski type inequalities involving the conformable fractional integrals, and provide the applications in bivariate means theory.

Owing to the convolution integral present in (13) and (21), the time-series introduced in this work exhibit, in general, multiple peaks about the 120 Hz center frequency of γ.

A modified approach to the Livengood Wu integral is presented to capture the integrated effects of the compression stroke on the potential for using the first stage of ignition to distribute heat release.