Dual sets of envelopes and characteristic regions of quasi-polynomials

Existence and nonexistence of roots of functions involving one or more parameters has been the subject of numerous investigations. For a wide class of functions called quasi-polynomials, the above problems can be transformed into the existence and nonexistence of tangents of the envelope curves asso...

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Bibliographic Details
Main Authors Cheng, Sui Sun, Lin, Yi-Zhong
Format eBook Book
LanguageEnglish
Published New Jersey World Scientific Publishing Co. Pte. Ltd 2009
World Scientific
World Scientific Publishing Company
WORLD SCIENTIFIC
Edition1
Subjects
Functions, Special
General Mathematics
Mathematical Logic and Foundations
Numerical & Computational Mathematics
Polynomials
Pure Mathematics
SCIENCE
Polynomial
Root
Quasi-Polynomial
Function with Parameters
Characteristic Function
Characteristic Region
Envelope
Dual Point
Dual Set
Online AccessGet full text
ISBN9814277274
9789814277273
9789814277280
9814277282
DOI10.1142/7338

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Summary:Existence and nonexistence of roots of functions involving one or more parameters has been the subject of numerous investigations. For a wide class of functions called quasi-polynomials, the above problems can be transformed into the existence and nonexistence of tangents of the envelope curves associated with the functions under investigation. In this book, we present a formal theory of the Cheng-Lin envelope method, which is completely new, yet simple and precise. This method is both simple — since only basic Calculus concepts are needed for understanding — and precise, since necessary and sufficient conditions can be obtained for functions such as polynomials containing more than four parameters.
Bibliography:Includes bibliographical references and index
ISBN:9814277274
9789814277273
9789814277280
9814277282
DOI:10.1142/7338