Sentence examples for the derivations for from inspiring English sources

Some of the equations are found to be fully correct, indeed superior to those derived here, while others are found to be deficient, because of assumptions made or inconsistencies in the derivations; for pipes with both ends fixed, the equations given in this paper are considered to be the most complete and correct.

The derivations for CRLB can be referred to [17].

The derivations for CRB are presented in the Appendix for clarity.

We assume flat fading channels and present the derivations for the single carrier case.

This section represents the derivations for phase estimation from the TFR generated by the XWVD.

Section 6 demonstrates the derivations for average channel capacity and an upper bound on channel capacity.

In the derivation for gases, the gas law is initially assumed, whence the independence of pressure is easily obtained.

Being a new extended architecture, we also established the derivation for the hybrid system speedup.

This is based on the derivation for surface path tracing found on page 746 of the PBRT book.

First, we presented the derivation for a Helmholtz free energy suitable for finite temperature changes using basic thermodynamics concepts.

The emitter lead can then be handled perturbatively in the tunnel coupling following closely the derivation for dissipative double quantum dot from Ref. 31 by first separating equation (4) into four equations for the elements of σ.