Related papers: Coincidence of extendible vector-valued ideals wit…

An equigenerated monomial ideal $I$ in the polynomial ring $R=k[z_1,\ldots, z_n]$ is a Freiman ideal if $\mu(I^2)=\ell(I)\mu(I)-{\ell(I)\choose 2}$ where $\ell(I)$ is the analytic spread of $I$ and $\mu(I)$ is the number of minimal…

Let A, B, S be categories, let F:A-->S and G:B-->S be functors. We assume that for "many" objects a in A, there exists an object b in B such that F(a) is isomorphic to G(b). We establish a general framework under which it is possible to…

In this paper we consider several problems of joint similarity to tuples of bounded linear operators in noncommutative polydomains and varieties associated with sets of noncommutative polynomials. We obtain analogues of classical results…

We show how multiplier ideals can be used to obtain uniform multiplicative bounds for certain families of ideals on a smooth complex algebraic variety. In particular we prove a quick but rather surprising result about symbolic powers of…

Let $R=\mathbb{K}[x_1,\dots,x_n]$ and let $\mathfrak{a}_1,\dots,\mathfrak{a}_m$ be homogeneous ideals satisfying certain properties, which include a description of the Noetherian symbolic Rees algebra. We give a solution to a question of…

We introduce a concept of bilinear ideal of jointly completely bounded mappings between operator spaces. In particular, we study the bilinear ideals $\mathcal{N}$ of completely nuclear, $\mathcal{I }$ of completely integral, $\mathcal{E}$…

We derive a sufficient condition for a Hermitian $N \times N$ matrix $A$ to have at least $m$ eigenvalues (counting multiplicities) in the interval $(-\epsilon, \epsilon)$. This condition is expressed in terms of the existence of a…

In the first part of this paper we study scrollers and linearly joined varieties. A particular class of varieties, of important interest in classical Geometry are Cohen--Macaulay varieties of minimal degree. They appear naturally studying…

A basic problem in the theory of partially ordered vector spaces is to characterise those cones on which every order-isomorphism is linear. We show that this is the case for every Archimedean cone that equals the inf-sup hull of the sum of…

Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the…

We study random exponential sums of the form $\sum_{k=1}^nX_k\times\ex p\{i(\lambda_k^{(1)}t_1+...+\lambda_k^{(s)}t_s)\}$, where $\{X_n\}$ is a sequence of random variables and $\{\lambda_n^{(i)}:1\leq i\leq s\}$ are sequences of real…

For each ideal of multilinear mappings $\cal M$ we explicitly construct a corresponding ideal $^{a}{\cal M}$ such that multilinear forms in $^{a}{\cal M}$ are exactly those which can be approximated, in the uniform norm, by multilinear…

When a monomial ideal has linear quotients with respect to an admissible order of increasing support-degree, we provide two proofs of different flavors to show that it is componentwise support-linear. We also introduce the variable…

An ideal of polynomials is symmetric if it is closed under permutations of variables. We relate general symmetric ideals to the so called Specht ideals generated by all Specht polynomials of a given shape. We show a connection between the…

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…

Let $S_d$ be the vector space of monomials of degree $d$ in the variables $x_1, ..., x_s$. For a subspace $V \sus S_d$ which is in general coordinates, consider the subspace $\gin V \sus S_d$ generated by initial monomials of polynomials in…

We characterize the variety of compatible fundamental matrix triples by computing its multidegree and multihomogeneous vanishing ideal. This answers the first interesting case of a question recently posed by Br{\aa}telund and Rydell. Our…

Let $\mathbb{K}$ be a field and $S=\mathbb{K}[x_1,\dots,x_n]$ be the polynomial ring in $n$ variables over the field $\mathbb{K}$. Suppose that $\mathcal{C}$ is a chordal clutter with $n$ vertices and assume that the minimum edge…

In this paper we prove global regularity results and Schauder estimates for non-divergence stationary operators of the form L=\sum_{i,j=1}^m a_{ij}(x) X_i X_j, where X_1, ..., X_m are homogeneous (but not necessarily left-invariant)…

We prove that the algebra $\mI_n:=K\langle x_1, ..., x_n, \frac{\der}{\der x_1},...,\frac{\der}{\der x_n}, \int_1, ..., \int_n\rangle $ of integro-differential operators on a polynomial algebra is a prime, central, catenary, self-dual,…