Advances in Mathematics Research. Volume 27

This book aims to approach the dynamical systems analysis from a new standpoint: feedback linearization — a method with a lot of applications. For both linear and non-linear dynamic systems, this method offers an interesting perspective from the qualitative approach stance. The authors examine the implementation of gas-assisted electrical discharge machining of D3 die steel. One of the fundamental disadvantages of the traditional EDM machining process is poor material removal rate. Numerical results for a wide range of Reynolds numbers are presented, including moderate and high Reynolds numbers, and two different numerical schemes to solve this kind of problem are described. For the analysis and interpretation of probabilistic engineering calculations, including those concerning the estimation of the safety of structures, symmetrical normal distribution is often used. In one study, the authors propose that such a distribution may be a linear combination of normal distribution and Gumbel distribution. This compilation goes on to present the problems that arise from the M|G|∞ queue system busy period and busy cycle, an idle period followed by a busy period. The renewal function is calculated, as well as the “peakedness” and the “modified peakedness” for the M|G|∞ busy period and busy cycle time length. Based on earlier research and using new mathematical methods, the authors present a theory using functional integrals for obtaining probability distributions of phase invariants in which N (the number of atoms in the asymmetric unit) doesn''t appear anymore. Also proposed is a numerically realizable explicit formula for the solution to the Cauchy problem for a linear elliptic equation. In closing, a mathematical model assessing the effect of tobacco smoking on the dynamics of tuberculosis transmission is formulated and analyzed. In the absence and presence of smokers, theoretical results indicate the possibility of the phenomenon of backward bifurcation where a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction threshold is less than unity. However, the analysis of the associated reproduction thresholds of the model with smokers shows that tobacco smoking has a detrimental effect on tuberculosis dynamics.