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Describes how to design CNC programs, and what cutting parameters are required to make a good manufacturing program. The authors explain cutting feed, depth of cut, rpm, cutting speed etc, and the G codes and M codes which are common to CNC. The skill-set of CNC program writing is covered, as well as how to cut material during different operations.

Almost all the systems in our world, including technical, social, economic, and environmental systems, are becoming interconnected and increasingly complex, and as such they are vulnerable to various risks. Due to this trend, resilience creation is becoming more important to system managers and decision makers, this to ensure sustained performance. In order to be able to ensure an acceptable sustained performance under such interconnectedness and complexity, resilience creation with a system approach is a requirement. Mathematical modeling based approaches are the most common approach for system resilience creation.Mathematical Modelling of System Resilience covers resilience creation for various system aspects including a functional system of the supply chain, overall supply chain systems; various methodologies for modeling system resilience; satellite-based approach for addressing climate related risks, repair-based approach for sustainable performance of an engineering system, and modeling measures of the reliability for a vertical take-off and landing system. Each of the chapters contributes state of the art research for the relevant resilience related topic covered in the chapter. Technical topics covered in the book include:1. Supply chain risk, vulnerability and disruptions 2. System resilience for containing failures and disruptions3. Resiliency considering frequency and intensities of disasters4. Resilience performance index5. Resiliency of electric Traction system6. Degree of resilience7. Satellite observation and hydrological risk8. Latitude of Resilience9. On-line repair for resilience10. Reliability design for Vertical Takeoff and landing Prototype

Special functions are mathematical functions that have established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. This short text gives clear descriptions and explanations of the Gamma function, the Probability Integral and its related functions, Spherical Harmonics Theory, The Bessel function, Hermite polynomials and Laguerre polynomials. Each chapter finishes with a description of how the function is most commonly applied and a set of examples for the student to work through.

This monograph is devoted to the construction of optimal estimates of values of linear functionals on solutions to Cauchy and two-point boundary value problems for systems of linear first-order ordinary differential equations, from indirect observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing the minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax or guaranteed estimates. It is established that these estimates are expressed explicitly via solutions to some uniquely solvable linear systems of ordinary differential equations of the special type. The authors apply these results for obtaining the optimal estimates of solutions from indirect noisy observations.Similar estimation problems for solutions of boundary value problems for linear differential equations of order n with general boundary conditions are considered. The authors also elaborate guaranteed estimation methods under incomplete data of unknown right-hand sides of equations and boundary data and obtain representations for the corresponding guaranteed estimates. In all the cases estimation errors are determined.

This book is designed especially for students of all levels, and can serve as a fundamental resource for advanced level studies not only in mathematics but also in various fields like engineering, interior design, architecture, etc. It includes numerical problems and problems of construction as well as practical problems.

This book "Advanced Applications of Computational Mathematics" covers multidisciplinary studies containing advanced research in the field of computational and applied mathematics. The book includes research methodology, techniques, applications, and algorithms.

A tensor is an entity which is represented in any coordinate system by an array of numbers called its components. The components change from coordinate system to coordinate in a systematic way described by rules. The arrays of numbers are not the tensor; they are only the representation of the tensor in a particular coordinate system.

Summarises interdisciplinary work within the field of applied mathematics. Topics discussed include Similarity Solutions of Spherical Shock Waves in a Self-Gravitating Ideal Gas; and Dual Solutions for Finite Element Analysis of Unsteady Hydromagnetic Stagnation Point Flow of Water Nanofluid Generated by Stretching Sheet.