Sentence examples for mathematical derivation presented from inspiring English sources

(4) I found the mathematical derivation presented in the appendix a little hard to read.

Simulations were in perfect agreement with the mathematical derivations presented in the Models section for both type of layouts (as in Figure 1).

Starting with an interatomic potential description, a mathematical derivation is presented to show that the local environment dependence of the activation barrier can be captured using cluster interaction models.

Full mathematical derivations are presented for the mechanisms before they are evaluated according to contemporary needs.

The experimental procedures and mathematical derivations are presented here in details.

The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as small scale effects, different material compositions, mode number and thickness ratio on the normalized natural frequencies of the FG nanobeams in detail.

The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as thermal effect, material distribution profile, small scale effects, mode number and boundary conditions on the normalized natural frequencies of the temperature-dependent FG nanobeams in detail.

In the present paper, the mathematical derivation of the method is presented, with stress placed on peculiarities of the method when applied to transient half-space dynamics.

The mathematical derivation of the model is presented with and without neglect of the actuator mass components as well as friction effects.

A mathematical derivation of the method is presented and the theory is applied to smaller theoretical samples and to a simplified real example.

We present a mathematical derivation of a closure relating the Reynolds stress to the mean strain rate for incompressible flows.