Related papers: Hankel Weighing Matrices
We present a new direct proof of a topological representation theorem for oriented matroids in the general rank case. Our proof is based on an earlier rank 3 version. It uses hyperline sequences and the generalized Sch{\"o}nflies theorem.…
In this paper we introduce the notion of linear computability as a method of finding the Waring rank of forms. We use this notion to find infinitely many new examples which satisfy Strassen's Conjecture.
We prove an injective version of Schanuel's lemma from homological algebra in the setting of exact categories.
We give a new proof of Mikhalkin's Theorem on the topological classification of simple Harnack curves, which in particular extends Mikhalkin's result to real pseudoholomorphic curves.
Willems' fundamental lemma enables a trajectory-based characterization of linear systems through data-based Hankel matrices. However, in the presence of measurement noise, we ask: Is this noisy Hankel-based model expressive enough to…
Using homological residue fields, we define supports for big objects in tensor-triangulated categories and prove a tensor-product formula.
We prove evaluations of Hankel determinants of linear combinations of moments of orthogonal polynomials (or, equivalently, of generating functions for Motzkin paths), thus generalising known results for Catalan numbers.
A short proof of the elliptical range theorem concerning the numerical range of $2\times2$ complex matrices is given.
We give a new analytical proof of the Morse index theorem for geodesics in Riemannian manifolds.
We show how tools from computational group theory can be used to prove that a subgroup of matrices has infinite index.
We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley-Hamilton theorem for hypermatrices.
We prove an interpolation theorem for bounded free holomorphic functions.
We present a new solution to the classification problem for the category of representations of a quiver of type $\widetilde{A}_{3}$. Our approach uses linear algebra techniques which lead us to a reduction that allows to use induction. As…
We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.
We present some results concerning the $l^p$ norms of weighted mean matrices. These results can be regarded as analogues to a result of Bennett concerning weighted Carleman's inequalities.
A proof is given of Rosenthal's \(\ell_1\) theorem.
We introduce the warping matrix which is a new description of oriented knots from a viewpoint of warping degree.
In this paper we give improved, probably not sharp, upper bounds of the Hankel determinant of third order for various classes of univalent functions and conjecture the sharp one.
The Ehrhart polynomial and the reciprocity theorems by Ehrhart \& Macdonald are extended to tensor valuations on lattice polytopes. A complete classification is established of tensor valuations of rank up to eight that are equivariant with…
We prove a result that enables us to calculate the rational homotopy of a wide class of spaces by the theory of minimal models.