Related papers: Classification of Complex Polynomial Vector Fields…

It will be shown that the polynomial time computable numbers form a field, and especially an algebraically closed field.

In this paper we introduce the concept of generalized vector groupoid. Several properties of them are established.

We study monic univariate polynomials whose coefficients are analytic functions of a real variable and whose roots lie in a specified analytic curve. These include characteristic polynomials of unitary and hermitian matrices whose entries…

The p-adic valuation of a polynomial can be given by its valuation tree. This work describes the 2-adic valuation tree of the general degree 2 polynomial in 2 variables.

We find an explicit combinatorial gradient vector field on the well known complex S (Salvetti complex) which models the complement to an arrangement of complexified hyperplanes. The argument uses a total ordering on the facets of the…

The range of a trigonometric polynomial with complex coefficients can be interpreted as the image of the unit circle under a Laurent polynomial. We show that this range is contained in a real algebraic subset of the complex plane. Although…

In this paper we study the classification problem of convex lattice ploytopes with respect to given volume or given cardinality.

This note aims at obtaining a variational characterization of complex structures by means of a calculus of variations for real vector bundle valued differential forms, and outlines a perspective to study existence questions via functionals…

Each simplicial complex and integer vector yields a vector configuration whose combinatorial properties are important for the analysis of contingency tables. We study the normality of these vector configurations including a description of…

We study a specific family of uniformly isochronous polynomial systems. Our results permit to solve a problem about centers of such systems.

We classify equivariant topological complex vector bundles over real projective plane under a compact Lie group (not necessarily effective) action. It is shown that nonequivariant Chern classes and isotropy representations at (at most)…

A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of multivector and multiform fields is presented using algebraic and analytical tools developed in previous papers.

We introduce a method to estimate the size of the domain of definition of the solutions of a meromorphic vector field on a neighborhood of its pole divisor. The corresponding techniques are, in a certain sense, quantitative versions of some…

The vector field problem is an important and classical problem in differential topology. In this survey we shall consider the vector field problem focusing mainly on the class of compact homogeneous spaces.

In this paper we study the complex symmetry in the several variable Fock space by using the techniques of weighted composition operators and semigroups. We characterize unbounded weighted composition operators that are (real) complex…

A new cohomology, induced by a vector field, is defined on pairs of differential forms ($1$--differentiable forms) in a manifold. It is proved a link with the classical de Rham cohomology and an $1$-differentable cohomology of Lichnerowicz…

We consider in this work planar polynomial differential systems having a polynomial first integral. We prove that these systems can be obtained from a linear system through a polynomial change of variables.

A unit-vector field n on a convex three-dimensional polyhedron P is tangent if, on the faces of P, n is tangent to the faces. A homotopy classification of tangent unit-vector fields continuous away from the vertices of P is given. The…

We characterize characteristic polynomials of elements in a central simple algebra. We also give an account for the theory of rational canonical forms for separable linear transformations over a central division algebra, and a description…

We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for $CR$ manifolds and H\"ormander's bracket condition for real vector fields. Applications are given…