Related papers: A Generalization of Desargues' Involution Theorem

In this paper, we define a new structure analogous to group, called partial group. This structure concerns the partial stability by the composition inner law. We generalize the three isomorphism theorems for groups to partial groups.

Recently Krichever proposed a generalization of the amoeba and the Ronkin function of a plane algebraic curve. In our paper higher-dimensional version of this generalization is studied. We translate to the generalized case different…

In the spirit of the many recent simple models of evolution inspired by statistical physics, we put forward a simple model of the evolution of such models. Like its objects of study, it is (one supposes) in principle testable and capable of…

We give a new simpler proof of a theorem of Jayne and Rogers.

The usual concept of shape invariance is discussed and one extension of this concept is suggested.

Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.

We state and prove a generalization of the Poincar\'e-Hopf index theorem for manifolds with boundary. We then apply this result to non-vanishing complex vector fields.

A generalized translational invariant noncommutative field theory is analyzed in detail, and a complete description of translational invariant noncommutative structures is worked out. The relevant gauge theory is described, and the planar…

In this article we focus on evolving information systems. First a delimitation of the concept of evolution is provided, resulting in a first attempt to a general theory for such evolutions. The theory makes a distinction between the…

We provide an algorithm for detecting the involutions leaving a surface defined by a polynomial parametrization invariant. As a consequence, the symmetry axes, symmetry planes and symmetry center of the surface, if any, can be determined…

In this paper, we apply the moving plane method to some degenerate elliptic equations to get a Liouville type theorem. As an application, we derive the a priori bounds for positive solutions of some semi-linear degenerate elliptic…

A special formula for the total mean curvature of an ovaloid is derived. This formula allows us to extend the notion of the mean curvature to the class of boundaries of strictly convex sets. Moreover, some integral formula for ovaloids is…

In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…

We give an inductive proof that the generalized Severi varieties -- the varieties which parametrize (irreducible) plane curves of given degree and genus, with a fixed tangency profile to a given line at several general fixed points and…

In this paper, we establish a demi-distributions theory which develops the usual distribution theory, in particular, we show that many conclusions as differentiations, Fourier transforms and convolutions can be generalized to the…

In this paper we generalize notions of iterated integral with regard to an unpredictable process. We establish a formula of integration by parts, the existence of a continuous modification and give an expression of the increasing process.

In this paper, we prove a general second main theorem for meromorphic mappings into a subvariety $V$ of $\mathbb P^N(\mathbb C)$ with an arbitrary family of moving hypersurfaces. Our second main theorem generalizes and improves all previous…

In his \textit{Brouillon Project} on conic sections, Girard Desargues studies the notion of \textit{traversale}, which generalizes that of diameter introduced by Apollonius. One often reads that it is equivalent to the notion of…

We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be…

We generalize Pappus chain theorem and give an analogue to this theorem.