Related papers: Uniform stability of ranks
We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…
It is proved that for every stratifiable space $Y$ and a closed subset $X\subset Y$ there exists a regular (i.e. linear positive with unit norm) extension operator $T:C(X\times X)\to C(Y\times Y)$ preserving the class of (pseudo)metrics.…
We study ample stable vector bundles on minimal rational surfaces. We give a complete classification of those moduli spaces for which the general stable bundle is both ample and globally generated. We also prove that if $V$ is any stable…
The article is concerned with the problem of the additivity of the tensor rank. That is for two independent tensors we study when the rank of their direct sum is equal to the sum of their individual ranks. The statement saying that…
We consider T(x), a tensor of arbitrary rank that is symmetric in all of its indices and conserved in the sense that the divergence on any one index vanishes. Our conjecture is that all integral moments of this tensor will vanish if the…
A group of $n$ agents with numerical preferences for each other are to be assigned to the $n$ seats of a dining table. We study two natural topologies:~circular (cycle) tables and panel (path) tables. For a given seating arrangement, an…
We present several conditions for generic uniqueness of tensor decompositions of multilinear rank (1,L_{1}, L_{1}),..., (1, L_{R}, L_{R}) terms. In geometric language, we prove that the joins of relevant subspace varieties are not…
Forces and torques exerted by a superconducting torus on a permanent magnet have been mapped. It is demonstrated that stable orbits exist. Moreover, provided that the magnet remains in any of these orbits, the first critical field in the…
We introduce a class of recursive subhomogeneous algebras that we call diagonal subhomogeneous and we give a notion of diagonal maps between these algebras. We show that any simple limit of diagonal subhomogeneous algebras with diagonal…
We show that three notions of rank for matrices of multilinear forms are equivalent. This result generalizes a classical result of Flanders, corrects a minor hole in work of Fortin and Reutenauer, answers a question of Lampert on the…
This paper answers the question if a qualitatively heterogeneous passive networked system containing damped and undamped nodes shows consensus in the output of the nodes in the long run. While a standard Lyapunov analysis shows that the…
Replacing invertibility with quasi-invertibility in Bass' first stable range condition we discover a new class of rings, the QB-rings. These constitute a considerable enlargement of the class of rings with stable rank one (B-rings), and…
The paper is concerned with the stability of the set of trajectories of a vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in AB to study…
We consider the stability of the orthogonal Jensen additive and quadratic equations in $F$-spaces, through applying and extending the approach to the proof of a 2010 result of W.Frchner and J.Sikorska, we presenting a new method to get the…
Rank-2 and rank-3 tensors are almost all identifiable with only few exceptions. We classify them all together with the dimensions and the structures of all the sets evincing the rank.
We consider change-point tests based on rank statistics to test for structural changes in long-range dependent observations. Under the hypothesis of stationary time series and under the assumption of a change with decreasing change-point…
We analyze a criterion which guarantees that the ground states of certain many body systems are stable under perturbations. Specifically, we consider PEPS, which are believed to provide an efficient description, based on local tensors, for…
We study linear PDE with constant coefficients. The constant rank condition on a system of linear PDEs with constant coefficients is often used in the theory of compensated compactness. While this is a purely linear algebraic condition, the…
Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we…
We investigate the behavior of finitely generated projective modules over a down-up algebra. Specifically, we show that every noetherian down-up algebra $A(\alpha,\beta,\gamma)$ has a non-free, stably free right ideal. Further, we compute…