Related papers: The Caratheodory and Kobayashi metrics and applica…
Working with letters that represent unknown constants, i.e., parameters, has been historically challenging for students. This is an important skill for their success in many future quantitative settings, and yet it appears this topic is…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…
This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…
This note is an invitation to the theory of geometric functions. The foundation techniques and some of the developments in the field are explained with the mindset that the audience is principally young researchers wishing to understand…
The authors study the method of scaling in the context of the study of automorphism groups of complex domains in multiple dimensions. Various types of scaling techniques are compared and contrasted. Applications are given in a number of…
We extend the upper estimates obtained by M. Carlehed and B.-Y. Chen about the ratio of the classical and pluricomplex Green functions to the case of $\mathcal C^2$-smooth locally $\mathbb C$-convexifiable domains of finite type. We also…
The Carath\'eodory theorem on the construction of a measure is generalized by replacing the outer measure with an approximation of it and generalizing the Carath\'eodory measurability. The new theorem is applied to obtain dynamically…
This article addresses the overlooked but crucial role of the Haar measure in solid mechanics, a concept well-established in mathematical literature but frequently misunderstood by mechanicians. The aim is to provide practical insights and…
We will cover the basics of several complex variables in 4 lectures: Basic properties of holomorphic functions in several variables, the notion of pseudoconvexity, CR functions and CR geometry, and the $\bar\partial$-problem. The main…
In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class. Here we apply this viewpoint to geometry and initiate a program…
The paper studies the complex differentiable functions of double argument and their properties, which are similar to the properties of the holomorphic functions of complex variable: the Cauchy formula, the hyperbolic harmonicity, the…
The new results concerning the continuity of holomorphically contractible systems treated as set functions with respect to non-monotonic sequences of sets are given. In particular, continuity properties of Kobayashi and Carath\'eodory…
Irreversible thermodynamics of simple fluids have been connected recently to the theory of dynamical systems and some interesting assumptions have been made about the nature of the associated invariant measures. We show that the tests of…
Very recently J. Kotrbaty has proven general inequalities for translation invariant smooth valuations formally analogous to the Hodge- Riemann bilinear relations in the Kahler geometry. The goal of this note is to apply Kotrbaty's theorem…
A survey of recent results concerning cardinal invariants of measure and category. Submitted as a chapter of the upcoming Handbook of Set Theory.
In this paper we define Kobayashi-Royden pseudonorm for almost complex manifolds. Its basic properties known from the complex analysis are preserved in the nonintegrable case as well. We prove that the pseudodistance induced by this…
We show a surgery formula for the relative Yamabe invariant and give applications to the study of concordance classes of metrics.
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…