Chapter 1

1 CHAPTER 1 : Introduction

Equation Chapter 1 Section 1 Analytical Solutions for Radially Functionally Graded Annular Plates

A closed-form solution for deflections and stresses in an annular thin plate of radially functionally graded material under transverse uniform pressure loading is presented. The small displacement theory of elasticity is assumed in the present work. Young’s modulus of the material is taken in the form of a simple power law to vary in the radial direction with an arbitrary exponent showing heter...

Equation Chapter 1 Section 1

In this chapter, we perform six sets of experiments to evaluate the effectiveness of the APCDM and its submodels and their respective sensitivities to various parameters. First, we examine the performance of our stochastic approach towards generating aircraft trajectory realizations and conducting the overall conflict analysis. In addition to testing several probabilistic trajectory displacemen...

Fieldguide CHAPTER 1

A goal in statistical science is to infer properties of a population or process from a sample of incomplete observations. Our interest in this book is in using limited measurements of a curve or surface to estimate the function and to also provide measures of uncertainty for this estimate. This process involves three parts: 1) A statistical model for the unknown function and data, 2) a method o...

Chapter 1 CIRC Tutorial

CIRC is an automated circular coinductive prover that is implemented as an extension of Maude. CIRC implements the circularity principle, which generalizes circular coinductive deduction [4] and can be expressed in plain English as follows. Assume that each equation of interest (to be proved) e admits a frozen form fr(e) and a set of derived equations, its derivatives, Der(e). The circularity p...