000			01640nam a2200205 4500
001			15966906
010			_a 2009279505
020			_a9789814277273 (hbk.)
020			_a9814277274 (hbk.)
082	0	0	_a515.5 _bCHE/D
100	1		_aCheng, Sui Sun
245	1	0	_aDual sets of envelopes and characteristic regions of quasi-polynomials
260			_aHackensack, NJ _bWorld Scientific _cc2009.
300			_aviii, 227 p. _bill.
520			_aExistence 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. Since the underlying principles are relatively simple, this book is useful to college students who want to see immediate applications of what they learn in Calculus; to graduate students who want to do research in functional equations; and to researchers who want references on roots of quasi-polynomials encountered in the theory of difference and differential equations.
650		0	_aFunctions, Special
650		0	_aPolynomials.
700	1		_aLin, Yi-Zhong
942			_cBK
999			_c66839 _d66839