By James Morris Page
Writer: London, long island, Macmillan e-book date: 1897 matters: Differential equations Lie teams Notes: this can be an OCR reprint. there's typos or lacking textual content. There aren't any illustrations or indexes. if you purchase the final Books variation of this e-book you get loose trial entry to Million-Books.com the place you could make a choice from greater than 1000000 books at no cost. you can even preview the ebook there.
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Japan, 26 (1974) 454463. [22] A. G. , 32 (1976), l-31. [23] H. Laufer, On minimally elliptic singularities, Amer. J. , 99 (1977) 125771295. [24] S. Lefschetz, L’analysis situs et la geomttrie algtbrique, Gauthiers-Villars, 1924. [25] B. Malgrange, Le polynome de Bernstein d’une singularite isolee, Lecture notes in math. 459, Springer, 1976,98&l 19. [26] J. N. Mather, Stability of C”‘-mappings. 1, Ann. ; II, (2) 89 (1969), 2544291; III, Publ. Math. Inst. HES, 35 (1970) 301-336; IV, Lecture notes in math.
Adjacency relations are important for the 418 F Theory of Singularities 1580 understanding of the degeneration phenomena of functions. The unfolding theory can be considered in exactly the same way as that for the germ of a real-valued smooth function that is finitely determined [36,26]. The germs of analytic functions with modulus number 0, 1, and 2 are called simple, unimodular, and bimodular, respectively. They were classified by V. I. V). Simple germs correspond to the equations for the rational double points, and unimodular germs define simply elliptic singularities or cusp singularities.
Let (t,} be as above. If X, is expressed as X, = Cf=, bitl-r, where the hr are constants, h, = 1 and bL # 0, X, is called a moving average process of order L (MA(L) process). -, with a, = 1, h, = 1, and aK b, # 0, then X, is called an autoregressive moving average process of order (K, L) (ARMA(K, L) process). Let A(Z) and B(Z) be two polynomials of Z such that A(Z) = C,“=, a,ZKek and B(Z) = ck, b,ZLm’, and let {mkl 1