Related papers: Michael selections and Castaing representations wi…
We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict $\omega$-categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the…
If $u : \Omega\subset \mathbb{R}^d \to {\rm X}$ is a harmonic map valued in a metric space ${\rm X}$ and ${\sf E} : {\rm X} \to \mathbb{R}$ is a convex function, in the sense that it generates an ${\rm EVI}_0$-gradient flow, we prove that…
Considering evolutionary equations in the sense of Picard, we identify a certain topology for material laws rendering the solution operator continuous if considered as a mapping from the material laws into the set of bounded linear…
For an infinite Toeplitz matrix $T$ with nonnegative real entries we find the conditions, under which the equation $\boldsymbol{x}=T\boldsymbol{x}$, where $\boldsymbol{x}$ is an infinite vector-column, has a nontrivial bounded positive…
We provide a compactness criterion for the set of laws $\mathfrak{P}^{ac}_{sem}(\Theta)$ on the Skorokhod space for which the canonical process $X$ is a semimartingale having absolutely continuous characteristics with differential…
A popular approach to semi-supervised learning proceeds by endowing the input data with a graph structure in order to extract geometric information and incorporate it into a Bayesian framework. We introduce new theory that gives appropriate…
We prove an equivariant version of the classical Menger-Nobeling theorem regarding topological embeddings: Whenever a group $G$ acts on a finite-dimensional compact metric space $X$, a generic continuous equivariant function from $X$ into…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…
The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…
Several topological and analytical notions of continuity and fading memory for causal and time-invariant filters are introduced, and the relations between them are analyzed. A significant generalization of the convolution theorem that…
We consider positive semidefinite kernels valued in the $*$-algebra of adjointable operators on a VE-space (Vector Euclidean space) and that are invariant under actions of $*$-semigroups. A rather general dilation theorem is stated and…
Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent…
In this paper we consider an abstract Cauchy problem for a Maxwell system modelling electromagnetic fields in the presence of an interface between optical media. The electric polarization is in general time-delayed and nonlinear, turning…
For a class of integral operators with kernels metric functions on manifold we find some necessary and sufficient conditions to have finite rank. The problem we pose has a stochastic nature and boils down to the following alternative…
Let $k$ be a perfect complete valued field with a nontrivial non-archimedean norm $|\cdot|$ and $\omega\in k$ with $0<|\omega|<1.$ Let $X$ be a reduced and normal $k$-analytic space. Then $O^{\circ}\simeq…
The dynamics of an ideal fluid or plasma is constrained by topological invariants such as the circulation of (canonical) momentum or, equivalently, the flux of the vorticity or magnetic fields. In the Hamiltonian formalism, topological…
A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally…
We obtain necessary and sufficient conditions for the admissible vectors of a new unitary non irreducible representation $U$. The group $G$ is an arbitrary semidirect product whose normal factor $A$ is abelian and whose homogeneous factor…
A basic idea in optimal transport is that optimizers can be characterized through a geometric property of their support sets called cyclical monotonicity. In recent years, similar "monotonicity principles" have found applications in other…
For systems which contain both superselection structure and constraints, we study compatibility between constraining and superselection. Specifically, we start with a generalisation of Doplicher-Roberts superselection theory to the case of…