Related papers: The Caratheodory and Kobayashi metrics and applica…
We provide a sufficient condition for the continuous extension of isometries for the Kobayashi distance between bounded convex domains in complex Euclidean spaces having boundaries that are only slightly more regular than $\mathcal{C}^1$.…
We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…
For a two dimensional bounded pseudoconvex domain of finite type, we prove uniformization theorems via K$\ddot{\operatorname{a}}$hler-Kobayashi metric or K$\ddot{\operatorname{a}}$hler-Carath$\acute{\operatorname{e}}$odory metric with…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
Instrumental variable methods are often used for parameter estimation in the presence of confounding. They can also be applied in stochastic processes. Instrumental variable analysis exploits moment equations to obtain estimators for causal…
This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…
Factor modeling is an essential tool for exploring intrinsic dependence structures among high-dimensional random variables. Much progress has been made for estimating the covariance matrix from a high-dimensional factor model. However, the…
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.
The paper presents new and known results on estimates of important linear and nonlinear approximation characteristics of generalized Wiener classes of functions of several variables in different metrics.
Canonical metrics and conformal invariants are presented for closed oriented even-dimensional manifolds with non-degenerate conformal structures and in particular for compact Riemann surfaces.
Dimensional analysis provides many simple and useful tools for various situations in science. The objective of this paper is to investigate its relations to functions, i.e., the dimensions for functions that yield physical quantities and…
In complex geometry a classical and useful invariant of a complex manifold is its Kodaira dimension. Since its introduction by Iitaka in the early 70's, its behavior under deformations was object of study and it is known that Kodaira…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
Multivariate Analysis is an increasingly common tool in experimental high energy physics; however, many of the common approaches were borrowed from other fields. We clarify what the goal of a multivariate algorithm should be for the search…
In this article, we study notions of visibility with respect to the Kobayashi distance for relatively compact complex submanifolds in Euclidean spaces. We present a sufficient condition for a domain to possess the visibility property…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
We present a complex field formulation of the quantum estimation theory that works natively with complex statistics on the dependence of complex parameters. This formulation states new complex versions of the main quantities and results of…
We present the Carath\'eodory-Reiffen metric and the inner Carath\'eodory distance on generalized parabolas. It turns out that on such parabolas the Carath\'eodory distance is not inner.
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…
With a bird's-eye view, we survey the landscape of Calabi-Yau threefolds, compact and non-compact, smooth and singular. Emphasis will be placed on the algorithms and databases which have been established over the years, and how they have…