Sentence examples for mathematical analysis given from inspiring English sources

More general situations are also amenable to mathematical analysis given the initial joint distribution (similar to Ref. [ 62] ). 4. Moment generating function M P of a probability distribution P is generally not defined for all real λ.

Thompson's 1917 book, "On Growth and Form," still attracts praise even though its mathematical analysis gives no clue about how biological forms develop.

His relentless application of mathematical analysis gave rise to an astonishing number of groundbreaking theorems, resolving debates that had raged among theorists for decades, if not centuries.

The game strategy in ticktacktoe is by no means simple; an excellent mathematical analysis is given by F. Schuh.

An approximate mathematical analysis is given, and agrees reasonably with the observations.

Mathematical analysis is given to demonstrate the stability of the closed-loop system so that a desired quality of service (QoS) can be guaranteed.

A mathematical analysis is given for a self-consistent dynamic model for rf sheaths in the frequency range between the ion and electron plasma frequencies for arbitrary collision parameters and arbitrary rf sheath voltages.

We have shown that mathematical analysis can give insights into the possible dynamical behaviour of gene expression models.

This is followed by a mathematical analysis, that gives some instructions for determining the controller parameters, so that the controller results in satisfactory tracking accuracy under all operating conditions.

However, it is generally very difficult to succeed with a thorough mathematical analysis of a given computational model, and this becomes even harder for larger models.

Our analysis gives a mathematical representation of the dynamics of this growth rate.