Related papers: A combinatorial characterisation of embedded polar…
In this paper, plane polynomial systems having a singular point attracting all orbits in positive time are classified up to topological equivalence. This is done by assigning a combinatorial invariant to the system (a so-called "feasible…
We study polar orbitopes, i.e. convex hulls of orbits of a polar representation of a compact Lie group. The face structure is studied by means of the gradient momentum map and it is shown that every face is exposed and is again a polar…
We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…
A common point of view is that stable polar structures are mainly present in the E/S0 early-type galaxies lacking dense gas in their host disks. However, nuclear, as well as external polar rings and disks also exist in the late-type hosts,…
Polar magnetism is present when ions occupy sites that are not centres of inversion symmetry. Fortunately, such magnetization contributes to neutron scattering that is the bedrock of magnetic structure determinations. Experiments in which…
We consider the vanishing ideal of an arrangement of linear subspaces in a vector space and investigate when this ideal can be generated by products of linear forms. We introduce a combinatorial construction (blocker duality) which yields…
Multiplicatively invariant (MI) spaces are closed subspaces of $L^2(\Omega,\mathcal{H})$ that are invariant under multiplications of (some) functions in $L^{\infty}(\Omega)$. In this paper we work with MI spaces that are finitely generated.…
Let D be a division ring with centre F. Let T(D) be the vector space over F generated by all multiplicative commutators in D. In [1], authors have conjectured that every division ring is generated as a vector space over its centre by all of…
The stochastic generators of Markov-regular operator cocycles on symmetric Fock space are studied in a variety of cases: positive cocycles, projection cocycles, and partially isometric cocycles. Moreover a class of transformations of…
The interrelations between various classes of convergence spaces defined by countability conditions are studied. Remarkably, they all find characterizations in the usual space of ultrafilters in terms of classical topological properties.…
We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and…
Using a scheme based on a Mach-Zehnder interferometer, we propose an analysis of the superposition of polarized laser beams at a given angle. The focus of our study is the spatially varying polarization state of the resulting field, also…
Polar ring galaxies are flattened stellar systems with an extended ring of gas and stars rotating in a plane almost perpendicular to the central galaxy. We show that their formation can occur naturally in a hierarchical universe where most…
A combinatorial tiling of the sphere is naturally given by an embedded graph. We study the case that each tile has exactly five edges, with the ultimate goal of classifying combinatorial tilings of the sphere by geometrically congruent…
There are 6 families of finite polar spaces of rank $3$. The set of lines in a rank $3$ polar space form a rank $5$ association scheme. We determine the regular sets of minimal size in several of these polar spaces, and describe some…
We define the polar curves and the polar family associated to a projective web and obtain some results about the geometry of the generic element of this family. We also deal with the particular case of foliations and prove the constancy of…
The analogue of polar coordinates in the Euclidean space, a polar decomposition in a metric space, if well-defined, can be very useful in dealing with integrals with respect to a sufficiently regular measure. In this note we handle the…
Parapolar spaces are point-line geometries introduced as a geometric approach to (exceptional) algebraic groups. We characterize a wide class of Lie geometries as parapolar spaces satisfying a simple intersection property. In particular…
Epsilon-near-zero and epsilon near-pole materials enable reflective systems supporting a class of symmetry-protected and accidental embedded eigenstates (EE) characterized by a diverging phase-resonance. Here we show that pairs of…
Traditional neural embeddings represent concepts as points, excelling at similarity but struggling with higher-level reasoning and asymmetric relationships. We introduce a novel paradigm: embedding concepts as linear subspaces. This…