Related papers: Vandermonde sets and hyperovals

In this article, using key tools including Zhou valuations, Tian functions and a convergence result for relative types, we establish necessary and sufficient conditions for the existence of valuative interpolations on the rings of germs of…

As set systems, hypergraphs are omnipresent and have various representations ranging from Euler and Venn diagrams to contact representations. In a geometric representation of a hypergraph $H=(V,E)$, each vertex $v\in V$ is associated with a…

Let V be a variety of not necessarily associative algebras, and A an inverse limit of nilpotent algebras A_i\in V, such that some finitely generated subalgebra S \subseteq A is dense in A under the inverse limit of the discrete topologies…

We introduce an object that has obvious similarity to the classical one - the algebra of supersymmetric polynomials. Despite the similarity, the known structure theorems on supersymmetric polynomials do not help in the study of the new…

We describe the groups that have the same holomorph as a finite perfect group. Our results are complete for centerless groups. When the center is non-trivial, some questions remain open. The peculiarities of the general case are illustrated…

Symmetric hyperbolic systems of equations are explicitly constructed for a general class of tensor fields by considering their structure as r-fold forms. The hyperbolizations depend on 2r-1 arbitrary timelike vectors. The importance of the…

A system of linear homogeneous algebraic equations for coupling constant ratios of vector-mesons to hadrons is derived by imposing an asymptotic behaviuor upon the VMD pole parametrization of an hadron electromagnetic form factor. A similar…

Let D be a divisor in a complex analytic manifold X. A natural problem is to determine when the de Rham complex of meromorphic forms on X with poles along D is quasi-isomorphic to its subcomplex of logarithmic forms. In this mostly…

Let $f_{1}, \ldots, f_{k}$ be polynomials defining an algebraic set in affine $n$-space over a finite field. Suppose $k>n$. We prove that there exists a system of polynomials $g_{1}, \ldots, g_{n}$, each being a linear combination with…

We describe the adjacency of vertices of the (unbounded version of the) set covering polyhedron, in a similar way to the description given by Chvatal for the stable set polytope. We find a sufficient condition for adjacency, and…

Let $\Omega$ be a convex open set in $\mathbb R^n$ and let $\Lambda_k$ be a finite subset of $\Omega$. We find necessary geometric conditions for $\Lambda_k$ to be interpolating for the space of multivariate polynomials of degree at most…

The idea of orthogonal polynomials has been generalized in two ways to achieve new types of polynomials: noncommutative orthogonal polynomials and biorthogonal polynomials. This paper brings these two different generalizations together to…

A structure M is pregeometric if the algebraic closure is a pregeometry in all M' elementarily equivalent to M. We define a generalisation: structures with an existential matroid. The main examples are superstable groups of U-rank a power…

Using an algebraic method for solving the wave equation in quantum mechanics, we encountered a new class of orthogonal polynomials on the real line. It consists of a four-parameter polynomial with continuous spectrum on the whole real line…

Let $(\mathrm{M}, \omega_{0})$ be a connected paracompact smooth oriented manifold. We establish a necessary and sufficient conditions on Lie subalgebra $\mathfrak{a}$ of $\mathrm{T M}$ such that its orbits becomes diffeomorphic to an open…

We study structural conditions in dense graphs that guarantee the existence of vertex-spanning substructures such as Hamilton cycles. It is easy to see that every Hamiltonian graph is connected, has a perfect fractional matching and,…

We give a criterion when a polynomial $x^n-g$ is irreducible over a pseudofinite field. As an application we give an explicit description of algebraic closure of some pseudofinite fields of zero characteristic.

We generalize the notion of semi-universality in the classical deformation problems to the context of derived deformation theories. A criterion for a formal moduli problem to be semi-prorepresentable is produced. This can be seen as an…

For large classes of systems of polynomial nonlinear PDEs necessary and sufficient conditions are given for the existence of solutions which are discontinuous across hyper-surfaces. These PDEs contain the Navier-Stokes equations, as well as…

The van der Geer-van der Vlugt curves are Artin-Schreier coverings of the affine line defined by linearized polynomials over finite fields. We give several criteria for them to be maximal or minimal, i.e. attaining the upper or lower bound…