Related papers: Localisation principle for one-scale H-measures
Davydov, Moldavskaya, and Zitikis introduced local indices for quantifying the lack of convexity of a \(C^2\) function by measuring the nuclear-norm distance of its Hessian from the cone of positive semidefinite matrices. This paper…
We establish new bounds of the Sobolev norms of solutions of semilinear wave equations for data lying in the Hs, s<1, closure of compactly supported data inside a ball of radius R, with R a fixed and positive number. In order to do that we…
We generalize ultraproducts and local-global limits of graphs to hypergraphs and other structures. We show that the local statistics of an ultraproduct of a sequence of hypergraphs are the ultralimits of the local statistics of the…
H-holomorphic maps are a parameter version of J-holomorphic maps into contact manifolds. They have arisen in efforts to prove the existence of higher--genus holomorphic open book decompositions and efforts to prove the existence of finite…
The aim of the paper is to characterize (pre)compactness in the spaces of Lipschitz/H\"older continuous mappings acting from a compact metric space to a normed space. To this end some extensions and generalizations of already existing…
In this paper, we develop an analytical framework for the partial differential equation underlying the consensus-based optimization model. The main challenge arises from the nonlinear, nonlocal nature of the consensus point, coupled with a…
It is often said that measuring a system's position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a "weak-measurement", this disturbance can be reduced. One…
Dimensions of level sets of generic continuous functions and generic H\"older functions defined on a fractal $F$ encode information about the geometry, ``the thickness" of $F$. While in the continuous case this quantity is related to a…
Fine shape, as defined by Melikhov, is an extension of the strong shape category of compacta (compact metrizable topological spaces) to all metrizable spaces, notable for being compatible with both \v{C}ech cohomology and Steenrod-Sitnikov…
We define a class of random measures, spatially independent martingales, which we view as a natural generalisation of the canonical random discrete set, and which includes as special cases many variants of fractal percolation and Poissonian…
Hierarchical Multi-Label Classification (HMC) faces critical challenges in maintaining structural consistency and balancing loss weighting in Multi-Task Learning (MTL). In order to address these issues, we propose a classifier called HCAL…
One considers Hilbert space valued measures on the Borel sets of a compact metric space. A natural numerical valued integral of vector valued continuous functions with respect to vector valued functions is defined. Using this integral,…
There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…
We characterize measure spaces such that the canonical map $L_\infty \to L_1^*$ is surjective. In case of $d$ dimensional Hausdorff measure of a complete separable metric space $X$ we give two equivalent conditions. One is in terms of the…
In this paper we estimate the Kuratowski and the Hausdorff measures of noncompactness of bounded subsets of spaces of vector-valued bounded functions and of vector-valued bounded differentiable functions. To this end, we use a quantitative…
Co-localization is the problem of localizing objects of the same class using only the set of images that contain them. This is a challenging task because the object detector must be built without negative examples that can lead to more…
We develop a complete theory of non-formal deformation quantization exhibiting a nonzero minimal uncertainty in position. An appropriate integral formula for the star-product is introduced together with a suitable space of functions on…
We study the local H\"{o}lder regularity of weak solutions to the fully fractional parabolic equations involving spatial fractional diffusion and fractional time derivatives of the Marchaud type. It is worth noting that we do not impose…
We introduce a technique that uses projection properties of fractal percolation to establish dimension conservation results for sections of deterministic self-similar sets. For example, let $K$ be a self-similar subset of $\mathbb{R}^2$…
The analysis of nonlocal discrete equations driven by fractional powers of the discrete Laplacian on a mesh of size $h>0$ \[ (-\Delta_h)^su=f, \] for $u,f:\mathbb{Z}_h\to\mathbb{R}$, $0<s<1$, is performed. The pointwise nonlocal formula for…