Related papers: Characterization of the alldifferent kernel by Hal…

We present new classes of positive definite kernels on non-standard spaces that are integrally strictly positive definite or characteristic. In particular, we discuss radial kernels on separable Hilbert spaces, and introduce broad classes…

Consider a finite collection of affine hyperplanes in $\mathbb R^d$. The hyperplanes dissect $\mathbb R^d$ into finitely many polyhedral chambers. For a point $x\in \mathbb R^d$ and a chamber $P$ the metric projection of $x$ onto $P$ is the…

We introduce algebraic sets in the products of complex projective spaces for the mixed states in multipartite quantum systems as their invariants under local unitary operations. The algebraic sets have to be the union of the linear…

This paper is concerned with the problem of determining the number of division algebras which share the same collection of finite splitting fields. As a corollary we are able to determine when two central division algebras may be…

In this paper we study the problem of computing a Kolchin characteristic set of a radical differential ideal. The central part of the article is the presentation of algorithms solving this problem in two principal cases: for ordinary…

We prove the existence of Hall polynomials for prinjective representations of finite partially ordered sets of finite prinjective type. In Section 4 we shortly discuss consequences of the existence of Hall polynomials, in particular, we are…

For any positive integers $a$ and $b$, we enumerate all colored partitions made by noncrossing diagonals of a convex polygon into polygons whose number of sides is congruent to $b$ modulo $a$. For the number of such partitions made by a…

Using the smallest eigenvalues of Hankel forms associated with a multidimensional moment problem, we establish a condition equivalent to the existence of a reproducing kernel. This result is a multivariate analogue of Berg, Chen,and…

We investigate the question of studying spectral clustering in a Hilbert space where the set of points to cluster are drawn i.i.d. according to an unknown probability distribution whose support is a union of compact connected components. We…

We show the existence of Hall polynomials for representation-finite cluster-tilted algebras.

Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material, greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and…

We start with a brief survey on H\"offding's kernels, its properties, related spectral decompositions, and discuss marginal distributions of H\"offding measures. In the second part of this note, one-dimensional covariance representations…

The notion of a flag kernel on a homogeneous group is exteded to distributions of arbitrary multidimensional order. It is shown that under natural restrictions on order the operation of convolution admits an extension to thus generalised…

A packing of partial difference sets is a collection of disjoint partial difference sets in a finite group $G$. This configuration has received considerable attention in design theory, finite geometry, coding theory, and graph theory over…

The problem of classification in machine learning has often been approached in terms of function approximation. In this paper, we propose an alternative approach for classification in arbitrary compact metric spaces which, in theory, yields…

The matrix Whittaker kernel has been introduced by A. Borodin in Part IV of the present series of papers. This kernel describes a point process -- a probability measure on a space of countable point configurations. The kernel is expressed…

For each integer $k\ge 1$, we define an algorithm which associates to a partition whose maximal value is at most $k$ a certain subset of all partitions. In the case when we begin with a partition $\lambda$ which is square, i.e…

Permutation-valued features arise in a variety of applications, either in a direct way when preferences are elicited over a collection of items, or an indirect way in which numerical ratings are converted to a ranking. To date, there has…

We provide some applications of a polynomial criterion for difference sets. These include counting the difference sets with specified parameters in terms of Hilbert functions, in particular a count of bent functions. We also consider the…

A matrix A is image partition regular over Q provided that whenever Q - {0} is finitely coloured, there is a vector x with entries in Q - {0} such that the entries of Ax are monochromatic. It is kernel partition regular over Q provided that…