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Dual Numbers

By Smarandache, Florentin

Book Id: WPLBN0002828236
Format Type: PDF (eBook)
File Size: 3.55 mb
Reproduction Date: 7/17/2013

Title:	Dual Numbers
Author:	Smarandache, Florentin
Volume:
Language:	English
Subject:	Non Fiction, Education, Dual Numbers
Collections:	Mathematics, Authors Community, Math, Literature, Education
Historic Publication Date:	2013
Publisher:	World Public Library

Member Page:	Florentin Smarandache
Citation APA MLA Chicago Smarandache, F., & Vasantha Kandasamy, W. B. (2013). Dual Numbers. Retrieved from http://self.gutenberg.org/

Description
In this book the authors study dual numbers in a special way. The main aim of this book is to find rich sources of new elements g such that g2 = 0. The main sources of such new elements are from Zn, n a composite number. We give algebraic structures on them. This book is organized into six chapters. The final chapter suggests several research level problems. Fifth chapter indicates the applications of dual numbers. The forth chapter introduces the concept of interval dual numbers, we also extend it to the concept of neutrosophic and 8 fuzzy dual numbers. Higher dimensional dual numbers are defined, described and developed in chapter three. Chapter two gives means and methods to construct the new element g such that g2 = 0. The authors feel Zn (n a composite positive integer) is a rich source for getting new element, the main component of the dual number x = a + bg.

Summary
Dual numbers was first introduced by W.K. Clifford in 1873. This nice concept has lots of applications; to screw systems, modeling plane joint, iterative methods for displacement analysis of spatial mechanisms, inertial force analysis of spatial mechanisms etc.

Table of Contents
Dedication 5 Preface 7 Chapter One INTRODUCTION 9 Chapter Two DUAL NUMBERS 11 Chapter Three HIGHER DIMENSIONAL DUAL NUMBERS 55 Chapter Four DUAL INTERVAL NUMBERS AND INTERVAL DUAL NUMBERS 89 Chapter Five APPLICATION OF THESE NEW TYPES OF DUAL NUMBERS 129 Chapter Six SUGGESTED PROBLEMS 131 FURTHER READING 153 INDEX 156 ABOUT THE AUTHORS 159