Dual Sets of Envelopes and Characteristic Regions of Quasi-Polynomials

Dual Sets of Envelopes and Characteristic Regions of Quasi-Polynomials

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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 ChengLin 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 suffic...