相关论文: Mean dimension of Bernstein spaces and universal r…

In this paper, we study the shift on the space of uniformly bounded continuous functions band-limited in a given compact interval with the standard topology of tempered distributions. We give a constructive proof of the existence of minimal…

We develop mean dimension theory for $\mathbb{R}$-flows. We obtain fundamental properties and examples and prove an embedding theorem: Any real flow $(X,\mathbb{R})$ of mean dimension strictly less than $r$ admits an extension…

We provide a new universal real flow of the Hilbert-cubical type. We prove that any real flow can be equivariantly embedded in the translation on $L(\mathbb{R})^\mathbb{N}$, where $L(\mathbb{R})$ denotes the space of $1$-Lipschitz functions…

The existence of a Banach limit as a translation invariant positive continuous linear functional on the space of bounded scalar sequences which is equal to 1 at the constant sequence (1,1,...,1,...) is proved in a first course on functional…

We consider the 1-harmonic flow of maps from a bounded domain into a submanifold of a Euclidean space, i.e. the gradient flow of the total variation functional restricted to maps taking values in the manifold. We restrict ourselves to…

Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…

We study the mean curvature flow of smooth $m$-dimensional compact submanifolds with quadratic pinching in the Riemannian manifold $\mathbb{C}P^n$. Our main focus is on the case of high codimension, $k\geq 2$. We establish a codimension…

The present paper aims to investigate the metric mean dimension theory of continuous flows. We introduce the notion of metric mean dimension for continuous flows to characterize the complexity of flows with infinite topological entropy. For…

We study the mean curvature flow of complete space-like submanifolds in pseudo-Euclidean space with bounded Gauss image, as well as that of complete submanifolds in Euclidean space with convex Gauss image. By using the confinable property…

We study the a.s. convergence of a sequence of random embeddings of a fixed manifold into Euclidean spaces of increasing dimensions. We show that the limit is deterministic. As a consequence, we show that many intrinsic functionals of the…

First we investigate the evolutions of the radius function and its gradient along the volume-preserving mean curvature flow starting from a tube (of nonconstant radius) over a compact closed domain of a reflective submanifold in a symmetric…

We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. The approximation of continuous bounded functions by entire functions of exponential type…

The Kakutani-Bebutov Theorem (1968) states that any compact metric real flow whose fixed point set is homeomorphic to a subset of $\mathbb{R}$ embeds into the Bebutov flow, the $\mathbb{R}$-shift on $C(\mathbb{R},[0,1])$. An interesting…

It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm which is itself locally uniformly convex. It follows that on any such space all continuous real-valued functions may be uniformly approximated by…

Michor and Mumford showed that the mean curvature flow is a gradient flow on a Riemannian structure with a degenerate geodesic distance. It is also known to destroy the uniform density of gridpoints on the evolving surfaces. We introduce a…

The problem of estimating, from a random sample of points, the dimension of a compact subset $S$ of the Euclidean space is considered. The emphasis is put on consistency results in the statistical sense. That is, statements of convergence…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

We prove long-time existence and convergence results for spacelike solutions to mean curvature flow in the pseudo-Euclidean space $\mathbb{R}^{n,m}$, which are entire or defined on bounded domains and satisfying Neumann or Dirichlet…

We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…