Related papers: Metric Regularity. Theory and Applications - a sur…
We introduce and study strongly and weakly harmonic functions on metric measure spaces defined via the mean value property holding for all and, respectively, for some radii of balls at every point of the underlying domain. Among properties…
The distortion of six different intrinsic metrics and quasi-metrics under conformal and quasiregular mappings is studied in a few simple domains $G\subsetneq\mathbb{R}^n$. The already known inequalities between the hyperbolic metric and…
In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with…
A central question in General Relativity (GR) is how to determine whether singularities are geometrical properties of spacetime, or simply anomalies of a coordinate system used to parameterize the spacetime. In particular, it is an open…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
The widespread adoption of the \emph{maximum mean discrepancy} (MMD) in goodness-of-fit testing has spurred extensive research on its statistical performance. However, recent studies indicate that the inherent structure of MMD may constrain…
Estimating Wasserstein distances between two high-dimensional densities suffers from the curse of dimensionality: one needs an exponential (wrt dimension) number of samples to ensure that the distance between two empirical measures is…
Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories…
Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…
Metric projection operators can be defined in similar wayin Hilbert and Banach spaces. At the same time, they differ signifitiantly in their properties. Metric projection operator in Hilbert space is a monotone and nonexpansive operator. It…
Generalized equations are problems emerging in contexts of modern variational analysis as an adequate formalism to treat such issues as constraint systems, optimality and equilibrium conditions, variational inequalities, differential…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
General characterization of physical measurements is discussed within the framework of a classical information theory. Uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…
A plethora of spaces in Functional Analysis (Braun-Meise-Taylor and Carleman ultradifferentiable and ultraholomorphic classes; Orlicz, Besov, Lipschitz, Lebesque spaces, to cite the main ones) are defined by means of a weighted structure,…
This report introduces and investigates a family of metrics on sets of pointed Kripke models. The metrics are generalizations of the Hamming distance applicable to countably infinite binary strings and, by extension, logical theories or…
This paper explores and ties together three themes. The first is to establish regularity of a metric tensor, on a manifold with boundary, on which there are given Ricci curvature bounds, on the manifold and its boundary, and a Lipschitz…
In this paper, we study the connections between the normality, regularity, full regularity, and chain-complete property in partially ordered Banach spaces. Then, by applying these properties, we prove some fixed point theorems on partially…
Our aim is to study the Total Variation Flow in Metric Graphs. First, we define the functions of bounded variation in Metric Graphs and their total variation, we also give an integration by parts formula. We prove existence and uniqueness…
In this article, we generalize some frequently used metrical notions such as: completeness, closedness, continuity, g-continuity and compatibility to relation-theoretic setting and utilize these relatively weaker notions to prove results on…