Page 1 Next

Displaying 1 – 20 of 28

Showing per page

Schur and Schubert polynomials as Thom polynomials-cohomology of moduli spaces

László Fehér, Richárd Rimányi (2003)

Open Mathematics

The theory of Schur and Schubert polynomials is revisited in this paper from the point of view of generalized Thom polynomials. When we apply a general method to compute Thom polynomials for this case we obtain a new definition for (double versions of) Schur and Schubert polynomials: they will be solutions of interpolation problems.

Simple framed curve singularities

Victor Goryunov, Gabor Lippner (2008)

Banach Center Publications

We obtain a complete list of simple framed curve singularities in ℂ² and ℂ³ up to the framed equivalence. We also find all the adjacencies between simple framed curves.

Singular open book structures from real mappings

Raimundo Araújo dos Santos, Ying Chen, Mihai Tibăr (2013)

Open Mathematics

We define open book structures with singular bindings. Starting with an extension of Milnor’s results on local fibrations for germs with nonisolated singularity, we find classes of genuine real analytic mappings which yield such open book structures.

Singularité générique des applications différentiables de la 2-sphère dans une 3-variété différentiable

Jean-Loïc Batude (1971)

Annales de l'institut Fourier

Dans cet article nous étudions les singularités des applications différentiables de la deux sphère dans une trois variété avec les méthodes de transversalité et nous utilisons les résultats obtenus pour reprendre dans le cas différentiable, les démonstrations de Papakyriakopoulos et de Whitehead du théorème de la sphère.

Singularities in contact geometry

Marc Chaperon (2003)

Banach Center Publications

In the first half of the paper, we consider singularities of infinitesimal contact transformations and first order partial differential equations, the main results being related to the classical Sternberg-Chen theorem for hyperbolic germs of vector fields. The second half explains how to construct global generating phase functions for solutions of Hamilton-Jacobi equations and see what their singularities look like.

Singularities in drawings of singular surfaces

Alain Joets (2008)

Banach Center Publications

When drawing regular surfaces, one creates a concrete and visual example of a projection between two spaces of dimension 2. The singularities of the projection define the apparent contour of the surface. As a result there are two types of generic singularities: fold and cusp (Whitney singularities). The case of singular surfaces is much more complex. A priori, it is expected that new singularities may appear, resulting from the "interaction" between the singularities of the surface and the singularities...

Singularities of implicit differential systems and maximum principle

Stanisław Janeczko, Fernand Pelletier (2003)

Banach Center Publications

The integrability condition for the Lagrangian implicit differential systems of (TP,ω̇), introduced in [7], is applied for the specialized control theory systems. The Pontryagin maximum principle was reformulated in the framework of implicit differential systems and the corresponding necessary and sufficient conditions were proved. The beginning of the classification list of normal forms for Lagrangian implicit differential systems according to the symplectic equivalence is provided and the corresponding...

Singularities of non-degenerate n-ruled (n + 1)-manifolds in Euclidean space

Kentaro Saji (2004)

Banach Center Publications

The objective of this paper is to study singularities of n-ruled (n + 1)-manifolds in Euclidean space. They are one-parameter families of n-dimensional affine subspaces in Euclidean space. After defining a non-degenerate n-ruled (n + 1)-manifold we will give a necessary and sufficient condition for such a map germ to be right-left equivalent to the cross cap × interval. The behavior of a generic n-ruled (n + 1)-manifold is also discussed.

Spaces of polynomials with roots of bounded multiplicity

M. Guest, A. Kozlowski, K. Yamaguchi (1999)

Fundamenta Mathematicae

We describe an alternative approach to some results of Vassiliev ([Va1]) on spaces of polynomials, by applying the "scanning method" used by Segal ([Se2]) in his investigation of spaces of rational functions. We explain how these two approaches are related by the Smale-Hirsch Principle or the h-Principle of Gromov. We obtain several generalizations, which may be of interest in their own right.

Currently displaying 1 – 20 of 28

Page 1 Next