It is shown that a binary differential equation with typical linear part and degenerate singular point (0, 0) linearizable at the if only its monodromy group commutative. The convergence of formal linearizing series established in cases.

Using a geometric approach turns out to be extremely fruitful. There are several simplifications which one can make. First, if the polynomial f(X,Y ) factors in C[X,Y ], then C breaks up into a union of two or more curves, each of which may be studied separately, so it suffices to study curves defined by irreducible polynomials. Second, the curve C may be singular, but we can always replace C w...

Phase unwrapping for a noisy image suffers from many singular points. Singularity-spreading methods are useful for the noisy image to regularize the singularity. However, the methods have a drawback of distorting phase distribution in a regular area that contains no singular points. When the singular points are confined in some local areas, the regular region is not distorted. This paper propos...

Consider the Singular Value Decomposition (SVD) of a two-parameter function A(x), x ∈ Ω ⊂ R2, where Ω is simply connected and compact, with boundary Γ. No matter how differentiable the function A is (even analytic), in general the singular values lose all smoothness at points where they coalesce. In this work, we propose and implement algorithms which locate points in Ω where the singular value...