Sentence examples for simpler expressions for from inspiring English sources

If an equation allows a Lie symmetry, the proposed decompositions are usually more efficient and often lead to simpler expressions for the solution.

end{aligned} (A.23) To obtain simpler expressions for the tunneling current density, we assume that (V_{i}/d_{B}) and (V_{ipm 1}/d_{B}) are approximately equal to an average field (F_{i}).

The matrix takes the form (28) Note that we have approximated (29) This is justified since these two parameters are much smaller than the others, and is done because it gives much simpler expressions for the fraction parameters derived below.

In order to obtain a simpler expression for I adm, we will assume high SNR in the data transmission phase.

Single infinite series representation: The second result provides a simpler expression for (18) involving only a single infinite sum [23], which was proposed by Moschopoulos [24].

After that, a simpler expression for the eigenvalue distribution was presented by Sun et al. [41], where only conventional ( -dimensional) determinants were involved.

2) Single infinite series representation: The second result provides a simpler expression for (18) involving only a single infinite sum [23], which was proposed by Moschopoulos [24].

The main problem in order to obtain a simpler expression for the bit error probability is to simplify the PDFs of U1 and U2 given, respectively, in (14) and (15).

This assumption simplifies the modeling approach and results in a much simpler expression for the fluid temperature as a function of radial distance and time; "Appendix B" presents this development.

In this paper we extend this equation of state and show that a simpler expression for the Gibbs energy can be derived than that given by Jacobs and Oonk.

The main scope of this section is to derive a simpler expression for eq. (6), at least for special cases.