Related papers: Direction problems in affine spaces
This paper presents an overview of the current state of knowledge in the field of equivariant map algebras and discusses some open problems in this area.
We study the affine quasi-Einstein equation, a second order linear homogeneous equation, which is invariantly defined on any affine manifold. We prove that the space of solutions is finite-dimensional, and its dimension is a strongly…
We prove a general result on irregularities of distribution for Borel sets intersected with bounded measurable sets or affine half-spaces.
The proximinality of certain subspaces of spaces of bounded affine functions is proved. The results presented here are some linear versions of an old result due to Mazur. For the proofs we use some sandwich theorems of Fenchel's duality…
In this paper we give several methods to construct curves over finite fields with many points and illustrate this with examples of the results.
First, we study the linear equations in general. Second, we focus our attention in periodic sequences over finite fields and de Bruijn directed graph.
This white paper highlights current limitations in the algebraic closure Unified Form Language (UFL). UFL currently represents forms over finite element spaces, however finite element problems naturally result in objects in the dual to a…
We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.
The geometry of algebraic curves over finite fields is a rich area of research. In previous work, the authors investigated a particular aspect of the geometry over finite fields of the classical unit circle, namely how the number of…
In this paper we show that an affine space is determined by the abstract group structure of its group of regular automorphisms in the category of connected affine varieties. To prove this we study commutative subgroups of the group of…
In the last years many results in the area of semidefinite programming were obtained for invariant (finite dimensional, or infinite dimensional) semidefinite programs - SDPs which have symmetry. This was done for a variety of problems and…
In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…
Let $W$ denote the $n$-dimensional affine space over the finite field $\mathbb F_q$. We prove here a Bollob\'as-type upper bound in the case of the set of affine subspaces. We give a construction of a pair of families of affine subspaces,…
The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the…
This paper deals with continuous and compact mappings of the Fourier transform in function spaces with dominating mixed smoothness.
The paper studies the harmonic maps on a direction between a Riemannian space and a generalized Lagrange space. Also, it is proved there that the solutions of C^2 class of certain ODEs or PDEs are harmonic maps, in the sense of this paper.
The fundamental theorem of affine geometry is a classical and useful result. For finite-dimensional real vector spaces, the theorem roughly states that a bijective self-mapping which maps lines to lines is affine. In this note we prove…
Using exhaustion method and finite differences a new method to solve system of partial differential equations and is presented. This method allows design algorithm to solve linear and nonlinear systems in irregular domains. Applying this…
This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized Drinfeld-Sokolov hierarchies.
I survey problems concerning Lindelof spaces which have partial set- theoretic solutions.