Let k be an algebraically closed field of any characteristic. We apply the Hamburger-Noether process of successive quadratic transformations to show the equivalence of two definitions of the Łojasiewicz exponent £ (a) of ...

We prove that if two plane curve singularities are equisingular, then they are topologically equivalent. The method we will use is P. Fortuny Ayuso’s who proved this result for irreducible plane curve singularities.

We give a recursive description of polynomials with non-negative rational coefficients, which are coefficients of expansion in a power series solutions of partial differential equations in Cauchy-Kowalevski theorem.