Related papers: Dimension functions in weakly o-minimal structures…
We prove a sharp decay of capacity of sublevel sets of a $(\omega,m)$-subharmonic functions on a $n$-dimensional compact Hermitian manifold $(X,\omega)$ which generalizes the case $m=n$ as well as the case $1\leq m\leq n$ on a compact…
We study a reduct L\ast of the ring language where multiplication is restricted to a neighbourhood of zero. The language is chosen such that for p-adically closed fields K, the L\ast-definable subsets of K coincide with the semi-algebraic…
In the literature on slice analysis in the hypercomplex setting, there are two main approaches to define slice regular functions in one variable: one consists in requiring that the restriction to any complex plane is holomorphic (with the…
We study domain formation in the two-dimensional O(3) model near criticality. The fractal dimension of these domains is determined with good statistical accuracy.
In this work we investigate unions of lifted MRD codes of a fixed dimension and minimum distance and derive an explicit formula for the cardinality of such codes. This will then imply a lower bound on the cardinality of constant dimension…
Most past work on weak nonleptonic decays has mixed dimensional regularization in the weak operator product expansion with some form of a cutoff regularization in the evaluation of the matrix elements. Even with the usual technique of…
We investigate tameness in the Fr\'echet spaces O(M) of analytic functions on Stein manifolds M equipped with the compact open topology. Actually we will look into tameness in the more general class of nuclear Fr\'echet spaces with the…
For $\mathbb B^n$ the unit ball of $\mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^\Phi_\alpha(\mathbb B^n)$, which are generalizations of classical Bergman spaces. We obtain atomic decomposition for…
We study the concept of coarse disjointness and large scale $n$-to-$1$ functions. As a byproduct, we obtain an Ostrand-type characterization of asymptotic dimension for coarse structures. It is shown that properties like finite asymptotic…
We study the general problem of the behaviour of the continuum function in the presence of non-supercompact strongly compact cardinals.
To appear in J. Funct. Spaces and Appl.
We study d-minimal expansions of ordered fields, and dense pairs thereof. We also consider other generalizations of o-minimality.
Given a weakly o-minimal structure $\mathcal M$ and its o-minimal completion $\bar {\mathcal M}$, we first associate to $\bar {\mathcal M}$ a canonical language and then prove that $Th(\mathcal M)$ determines $Th(\bar {\mathcal M})$. We…
We provide sharp cylindrical parametrizations of cylindrical cell decompositions by maps with bounded $C^{r}$ norm in the sharply o-minimal setting, thus generalizing and strengthening the Yomdin-Gromov Algebraic Lemma. We introduce forts,…
We propose a multifidelity dimension reduction method to identify a low-dimensional structure present in many engineering models. The structure of interest arises when functions vary primarily on a low-dimensional subspace of the…
Let $m,n\geq 1$ are integers and $D$ be a domain in the $$ $\mathbb C^n$ or in the $m$-dimensional real space $\mathbb R^m$. We build positive subharmonic functions on $D$ vanishing on the boundary $\partial D$ of $D$. We use such (test)…
We study Leinster's notion of magnitude for a compact metric space. For a smooth, compact domain $X\subset \mathbb{R}^{2m-1}$, we find geometric significance in the function $\mathcal{M}_X(R) = \mathrm{mag}(R\cdot X)$. The function…
Cardinal functions provide valuable insight into the topological properties of spaces, helping to analyze and compare spaces in terms of their covering, convergence and separation properties. This paper focuses on investigating cardinal…
A systematic study is performed of the impact of the various resummed small-$x$ contributions to the anomalous dimensions and coefficient functions on the evolution of unpolarized structure functions in deep-inelastic scattering. The proton…
We prove that all known examples of weakly o-minimal non-valuational structures have no definable Skolem functions. We show, however, that such structures eliminate imaginaries up to (definable families of) definable cuts. Along the way we…