Polynomial Reformulation of the Kuo Criteria for V-sufficiency of Map-germs
نویسندگان
چکیده
In the paper a set of necessary and sufficient conditions for vsufficiency (equiv. sv-sufficiency) of jets of map-germs f : (Rn, 0) → (Rm, 0) is proved which generalize both the Kuiper-Kuo and the Thom conditions in the function case (m = 1) so as the Kuo conditions in the general map case (m > 1). Contrary to the Kuo conditions the conditions proved in the paper do not require to verify any inequalities in a so-called horn-neighborhood of the (a’priori unknown) set f(0). Instead, the proposed conditions reduce the problem on v-sufficiency of jets to evaluating the local Lojasiewicz exponents for some constructively built polynomial functions.
منابع مشابه
Omega Polynomial in Polybenzene Multi Tori
The polybenzene units BTX 48, X=A (armchair) and X=Z (zig-zag) dimerize forming “eclipsed” isomers, the oligomers of which form structures of five-fold symmetry, called multi-tori. Multi-tori can be designed by appropriate map operations. The genus of multi-tori was calculated from the number of tetrapodal units they consist. A description, in terms of Omega polynomial, of the two linearly peri...
متن کاملCircles and Quadratic Maps Between Spheres
Consider an analytic map from a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs of vector lines to germs of circles. Such map is called rounding. Two roundings are equivalent if they take the same lines to the same circles. We prove that any rounding whose differential at 0 has rank at least 2 is equivalent to a fractional quadratic rounding. The ...
متن کاملEquivalence Relations for Two Variable Real Analytic Function Germs
For two variable real analytic function germs we compare the blowanalytic equivalence in the sense of Kuo to the other natural equivalence relations. Our main theorem states that C equivalent germs are blow-analytically equivalent. This gives a negative answer to a conjecture of Kuo. In the proof we show that the Puiseux pairs of real Newton-Puiseux roots are preserved by the C equivalence of f...
متن کاملNon-polynomial Spline Method for Solving Coupled Burgers Equations
In this paper, non-polynomial spline method for solving Coupled Burgers Equations are presented. We take a new spline function. The stability analysis using Von-Neumann technique shows the scheme is unconditionally stable. To test accuracy the error norms 2L, L are computed and give two examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equation...
متن کاملGray Images of Constacyclic Codes over some Polynomial Residue Rings
Let be the quotient ring where is the finite field of size and is a positive integer. A Gray map of length over is a special map from to ( . The Gray map is said to be a ( )-Gray map if the image of any -constacyclic code over is a -constacyclic code over the field . In this paper we investigate the existence of ( )-Gray maps over . In this direction, we find an equivalent ...
متن کامل