Related papers: Another homogeneous, non-bihomogeneous Peano conti…

We present a contribution to the structure theory of locally compact groups. The emphasis is on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic…

We observe that there is an example of an automorphism group of a model of an omega-stable theory---in fact, the prime model of an uncountably-categorical theory---that is not locally (OB), answering a question of C. Rosendal.

We study $k$-uniform states in heterogeneous systems whose local dimensions are mixed. Based on the connections between mixed orthogonal arrays with certain minimum Hamming distance, irredundant mixed orthogonal arrays and $k$-uniform…

A planar compactum with connected complement can be an embedded in a cellular continuum by attaching a null sequence of arcs. Two based maps f and g from a planar Peano continuum X to a planar set Y are homotopic iff f and g induce the same…

In all forms of the local Langlands program the abelian category of smooth representations of p-adic groups G in vector spaces over a field k plays a central role. Of particular interest are its finiteness properties. If the field k has…

A 3-dimensional non-commutative oscillator with no mass term but with a certain momentum-dependent potential admits a conserved Runge-Lenz vector, derived from the dual description in momentum space. The latter corresponds to a Dirac…

Let s be at least 2. We construct Ricci flat pseudo-Riemannian manifolds of signature (2s,s) which are not locally homogeneous but whose curvature tensors never the less exhibit a number of important symmetry properties. They are curvature…

I investigate a class of dynamical systems in which finite pieces of spacetime contain finite amounts of information. Most of the guiding principles for designing these systems are drawn from general relativity: the systems are…

Local diffusion of strictly hyperbolic higher-order PDE's with constant coefficients at all simple singularities of corresponding wavefronts can be explained and recognized by only two local geometrical features of these wavefronts. We…

In the study of discontinuous groups for non-Riemannian homogeneous spaces, the idea of "continuous analogue" gives a powerful method (T. Kobayashi [Math. Ann. 1989]). For example, a semisimple symmetric space G/H admits a discontinuous…

Let H be a separable infinite dimensional complex Hilbert space. We prove that every continuous 2-local automorphism of the poset (that is, partially ordered set) of all idempotents on H is an automorphism. Similar results concerning the…

It is proved that no region of a homogeneous locally compact, locally connected metric space can be cut by an $F_\sigma$-subset of a "smaller" dimension. The result applies to different finite or infinite topological dimensions of…

Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…

In this contribution we present a general procedure that allows the construction of noncommutative spaces with quantum group invariance as the quantization of their associated coisotropic Poisson homogeneous spaces coming from a coboundary…

We survey recent work done on the values at integer points of irrational inhomogeneous quadratic forms, namely, inhomogeneous analogues of the famous Oppenheim conjecture. We also prove that the set of such forms in two variables whose set…

We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…

Let $\mathbb{A}$ and $\mathbb{S}$ denote the double arrow of Alexandroff and the Sorgenfrey line, respectively. We show that any homeomorphism $h:^m\mathbb{A}\to^m\mathbb{A} $ is locally (outside of a nowhere dense set) a product of…

The aim of this article is to derive discontinuous finite elements vector spaces which can be put in a discrete de-Rham complex for which an harmonic gap property may be proven. First, discontinuous finite element spaces inspired by…

The first result is the semicontinuity of automorphism groups for the collection of complex two-dimensional bounded pseudoconvex domains with smooth boundary of finite D'Angelo type. The method of proof is new so that it simplifies the…

In this article, we prove a $p$-adic analogue of the local invariant cycle theorem for $H^2$ in mixed characteristics. As a result, for a smooth projective variety $X$ over a $p$-adic local field $K$ with a proper flat regular model…