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 ...

The presence of germs in the bloodstream is referred to as bacteremia. Blood cultures are used to identify bacteria in blood. The identification of certain virulent germs in blood (Neisseria meningitidis, Streptococcus pneumoniae, Salmonella typhi) is of diagnostic value in application to certain diseases. The difficulty arises when the microorganism detected in blood is a usual colonizer of th...

Let F : (R,0)→(R,0) and g : (R,0)→R be analytic germs, let Br ⊂ R be a closed ball of small radius centred at the origin, and let Wz = F −1(z) ∩ Br. Let λ(g;Wz) = ∑ p(−1), where λ(p) is the Morse index at a critical point p of a Morse function which approximates g|Wz. For F and g satisfying some natural assumptions, we shall show that there is a finite family of analytic germs θi(z) such that λ...

In the area of water purification, nanotechnology offers the possibility of an efficient removal of pollutants and germs. Today nanoparticles, nanomembrane and nanopowder used for detection and removal of chemical and biological substances include metals (e.g. Cadmium, copper, lead, mercury, nickel, zinc), nutrients (e.g. Phosphate, ammonia, nitrate and nitrite), cyanide, organics, algae (e.g. ...

Full proofs of results announced here are to be found in [lO]. We consider the problem of classifying germs of neighbourhoods of locally flat topological submanifolds. Let M be a fixed topological manifold. An r-neighbourhood of M is a pair (i, N) where N is a topological manifold of dimension n+r and i:M—*N a locally flat embedding satisfying i^ÇdN) —dM. Denote the set of germs of r-neighbourh...

Assume that there exists a hypersurface singularity which cannot be resolved by iterated monoidal transformations in positive characteristic. We show that in the set of defining functions of hypersurface singularities which cannot be resolved, we can find a function satisfying very strong conditions. By these conditions we may be able to deduce a contradiction under the above assumption. Beside...

For a complex analytic map f from n-space to p-space with n < p and with an isolated instability at the origin, the disentanglement of f is a local stabilization of f that is analogous to the Milnor fibre for functions. For mono-germs it is known that the disentanglement is a wedge of spheres of possibly varying dimensions. In this paper we give a condition that allows us to deduce that the sam...

For quasi-homogeneous and finitely determined corank one map germs f : (C, 0) → (C, 0) we obtain formulae in function of the degree and weight of f for invariantes on the stable types of f , as polar multiplicities, number of Milnor, number of Lê. We minimize also the number of invariantes for 7, to resolve the problem that decides the Whitney equisingularity of families of such maps germs. To ...

Introduction. The problem that the author solved has its origin in Nomography: 1 how to reduce a nomogram of aligned points to a circular nomogram? In more mathematical terms: what are local diffeomorphisms that send germs of lines to germs of circles? This question was initially posed for 2-dimensional nomograms by G.S. Khovanskii and, solved by A.G. A discipline which was discovered by the Fr...