Related papers: Observations on interpolation by total degree poly…
We consider large random graphs with prescribed degrees, such as those generated by the configuration model. In the regime where the empirical degree distribution approaches a limit $\mu$ with finite mean, we establish the systematic…
This paper studies algebraic residual intersections in rings with Serre's condition \( S_{s} \). It demonstrates that residual intersections admit free approaches i.e. perfect subideal with the same radical. This fact leads to determining a…
Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…
The problem of interpolation at $(n+1)^2$ points on the unit sphere $\mathbb{S}^2$ by spherical polynomials of degree at most $n$ is proved to have a unique solution for several sets of points. The points are located on a number of circles…
A zero-dimensional polynomial ideal may have a lot of complex zeros. But sometimes, only some of them are needed. In this paper, for a zero-dimensional ideal $I$, we study its complex zeros that locate in another variety $\textbf{V}(J)$…
Our starting point is a basic problem in Hermite interpolation theory, namely determining the least degree of a homogeneous polynomial that vanishes to some specified order at every point of a given finite set. We solve this problem if the…
In this article, we study multivariate polynomial interpolation and quadrature rules on non-tensor product node sets related to Lissajous curves and Chebyshev varieties. After classifying multivariate Lissajous curves and the interpolation…
In their paper on multiplicity bounds (1998), Herzog and Srinivasan study the relationship between the graded Betti numbers of a homogeneous ideal I in a polynomial ring R and the degree of I. For certain classes of ideals, they prove a…
The concepts of evaluation and interpolation are extended from univariate skew polynomials to multivariate skew polynomials, with coefficients over division rings. Iterated skew polynomial rings are in general not suitable for this purpose.…
The present paper studies the existence of valuative interpolation on the local ring of an irreducible analytic subvariety at singular points. We firstly develop the concepts and methods of Zhou weights and Tian functions near singular…
It is known that every function with a finite support over a given field can be interpolated by means of the Lagrangian polynomial. The question is if a similar interpolation is possible if one considers a unitary ring or a Boolean algebra…
The paper gives an extension of Prony's method to the multivariate case which is based on the relationship between polynomial interpolation, normal forms modulo ideals and H--bases.
This chapter presents a state-of-the-art survey of relationships, traditionally referred to as `bridges', between interpolation properties for propositional logics -- including superintuitionistic, modal, and substructural logics -- and…
We present a class of homogeneous ideals which are generated by monomials and binomials of degree two and are set-theoretic complete intersections. This class includes certain reducible varieties of minimal degree and, in particular, the…
The Hilbert polynomial of a homogeneous complete intersection is determined by the degrees of the generators of the defining ideal. The degrees of the generators are not, in general, determined by the Hilbert polynomial -- but sometimes…
Structures of multilinear maps are characterized by invariants. In this paper we introduce two invariants, named the isotropy index and the completeness index. These invariants capture the tensorial structure of the kernel of a multilinear…
We characterize monomial ideals which are intersections of monomial prime ideals and study classes of ideals with this property, among them polymatroidal ideals.
In this paper, the $mn$-dimensional space of tensor-product polynomials of two variables, of degree at most $(m-1)+(n-1)$, is considered. A theory of two-variate polynomials is developed by establishing the algebra and basic algebraic…
A lemma of Micchelli's, concerning radial polynomials and weighted sums of point evaluations, is shown to hold for arbitrary linear functionals, as is Schaback's more recent extension of this lemma and Schaback's result concerning…
The interaction between two particles with shape or interaction anisotropy can be modeled using a pairwise potential energy function that depends on their relative position and orientation; however, this function is often challenging to…