Advances in Mathematics Research. Volume 27


Albert R. Baswell (Editor)

Series: Advances in Mathematics Research
BISAC: MAT027000

Advances in Mathematics Research. Volume 27 first 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.
(Imprint: Nova)

Table of Contents

Table of Contents


Chapter 1. Initial versus Feedback Linearized Form for Dynamic Systems: Qualitative Approach for Models Arising from Excitable Media
(Adela Ionescu, Department of Applied Mathematics, University of Craiova, Romania)

Chapter 2. A Mathematical Model to Assess the Material Removal Rate during Gas-Assisted EDM using Buckingham’s Π-Theorem
(Nishant K. Singh, Yashvir Singh and Abhishek Sharma, Department of Mechanical Engineering, HCST, Mathura, India)

Chapter 3. The Numerical Solution of the Navier-Stokes Equations for a Wide Range of Reynolds Numbers
(B. Bermúdez, S. Hidalgo-Caballero, D. Alanís and W. Fermín González, Benemérita Universidad Autónoma de Puebla, Facultad de Ciencias de la Computación, Puebla, México, and others)

Chapter 4. Three-Parameter Probability Density Function for Engineering Applications
(Roman Jaskulski, PhD and Piotr Wiliński, PhD, Faculty of Civil Engineering, Mechanics and Petrochemistry, Warsaw University of Technology, Płock, Poland)

Chapter 5. A Collection of Service Time Probability Distributions Parameters Study and Impact in M|G|∞ System Busy Period and Busy Cycle Time Length Probability Distributions
(Manuel Alberto M. Ferreira, Instituto Universitário de Lisboa, Information Sciences, Technologies and Architecture Research Center, Business Research Unit, Lisboa, Portugal)

Chapter 6. Probability Distributions of Phases Without N
(Jan Brosius, Relleu, Spain)

Chapter 7. Explicit Representation of the Solution to the Cauchy Problem for the 2nd Order 2D-Elliptic Equations
(A. S. Demidov, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia, and others)

Chapter 8. Tuberculosis and Smoking: A Deadly Duo
(Jacob I. Irunde, Jean M. Tchuenche and Senelani D. Hove-Musekwa, Mathematics Department, Mkwawa University College of Education, Tanzania, and others)


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