Related papers: A Generalization of Desargues' Involution Theorem
It is known that Plotkin's reduction theorem is very important for his theory of universal algebraic geometry [arXiv:math. GM/0210187], [arXiv:math. GM/0210194]. It turns out that this theorem can be generalized to arbitrary categories…
In this paper, we prove a generalization of Geraghty's fixed point theorem for multi--valued mappings.
This paper introduces a notion of generalised geometric logic. Connections of generalised geometric logic with L-topological system and L-topological space are established.
In this paper, we develop the theory of flashes of an algebraic curve. We show that the theory is birationally invariant in a sense which we will make more precise below. We also show how the theory provides a foundation for the method of…
We investigate the problem of existence of degenerations of surfaces in $\mathbb P^3$ with ordinary singularities into plane arrangements in general position.
In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem are considered.
In this paper we prove using quite elementary methods, with a combinatorial nature, two general results related to Marstrand's projection theorem in a quite general formulation over metric spaces under a suitable transversality condition…
We will use toric degenerations of the projective plane ${{\mathbb{P}}^ 2}$ to give a new proof of the triple points interpolation problems in the projective plane. We also give a complete list of toric surfaces that are useful as…
We present a general formalism which allows us to derive the evolution equations describing one-dimensional (1D) and isotropic 2D interfacelike systems, that is based on symmetries, conservation laws, multiple scale arguments, and exploits…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
We introduce a bulging triangle like the generalization of the Reuleaux triangle. We may be able to propose various ways to bulge a triangle, but this paper presents the way so that its vertices are the same as them of the original…
This paper introduces invariant transforms that preserve the ratio of either two or three co-linear points in the Desargues affine plane skew field. The results given here have a clean, geometric presentation based based Desargues affine…
In this paper, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem.
This article describes the mean curvature flow, some of the discoveries that have been made about it, and some unresolved questions.
We revise a proof of a Mazur-Ulam theorem for generalized gyrovector spaces.
The weighted triangulation algebras associated to triangulation quivers and their socle deformations were recently introduced and studied in [15]-[20] and [2]. These algebras, based on surface triangulations and originated from the theory…
A general expression for the optical theorem for probe sources given in terms of propagation invariant beams is derived. This expression is obtained using the far field approximation for Rayleigh regime. In order to illustrate this results…
We give a simple and self-contained proof of an extension of a projection theorem of Bourgain over the reals to division algebras over local fields of zero characteristic.
We prove a truncated second main theorem in the projective plane for entire curves which cluster on an algebraic curve.
We give a systematic, abstract formulation of the image normalization method as applied to a general group of image transformations, and then illustrate the abstract analysis by applying it to the hierarchy of viewing transformations of a…