Related papers: Atomic Pseudo-Valuation Domains
We develop Boolean-valued domain theory and show how the lambda-calculus can be interpreted in using domain-valued random variables. We focus on the reflexive domain construction rather than the language and its semantics. The notion of…
This is an extended introduction to discrete valuation rings and Dedekind domains. Some natural generalizations of Dedekind domains are also (briefly) discussed including "almost Dedekind domains", Pr\"ufer domains, Krull domains, and…
We show how to construct a class of smooth bounded pseudoconvex domains whose boundary contains a given Stein manifold with strongly pseudoconvex boundary, having a prescribed codimension and D'Angelo class (a cohomological invariant…
Pseudo-labelling is a popular technique in unsuper-vised domain adaptation for semantic segmentation. However, pseudo labels are noisy and inevitably have confirmation bias due to the discrepancy between source and target domains and…
In quantum theory, a weak value is a complex number with a somewhat technical definition: it is a ratio whose numerator is the matrix element of a self-adjoint operator and whose denominator is the inner product of a corresponding pair of…
The notion of key polynomials was first introduced in 1936 by S. Maclane in the case of discrete rank 1 valuations. . Let K -> L be a field extension and {\nu} a valuation of K. The original motivation for introducing key polynomials was…
In the second section, we introduce hemiring-valued pseudonormed rings and generalize Albert's result which states that every finite-dimensional algebra can be normed. Next, we introduce shrinkable hemirings and prove that dense division…
This paper deals with four types of point estimators based on minimization of information-theoretic divergences between hypothetical and empirical distributions. These were introduced (i) by Liese & Vajda (2006) and independently…
The aim of this paper is to establish a theory of random variables on domains. Domain theory is a fundamental component of theoretical computer science, providing mathematical models of computational processes. Random variables are the…
Recently, N. Epstein and J. Shapiro introduced and studied the perinormal domains: those domains A whose going down overrings are flat A-modules. We show that every Pr\"ufer v-multiplication domain is perinormal and has no proper lying over…
In 1983, Hartle and Hawking proposed the no-boundary proposal, suggesting that the universe has no beginning in the sense of a spacetime singularity or boundary. Nevertheless, there is an origin of time. Mathematically, this involves…
In the last paper \cite{R7}, it was studied Hilbert, Poincare and Neumann boundary-value problems with arbitrary measurable data for generalized analytic functions and generalized harmonic functions with applications to the relevant…
A recent Letter in Physical Review Letters, "Contextual Values of Observables in Quantum Measurements", by J. Dressel, S. Agarwal, and A. N. Jordan (abbreviated DAJ below), introduces the concept of "contextual values" and claims that they…
The ordinary Poisson brackets in field theory do not fulfil the Jacobi identity if boundary values are not reasonably fixed by special boundary conditions. We show that these brackets can be modified by adding some surface terms to lift…
Deep neural models have achieved state of the art performance on a wide range of problems in computer science, especially in computer vision. However, deep neural networks often require large datasets of labeled samples to generalize…
We show how the notion of {\em pseudo-bosons}, originally introduced as operators acting on some Hilbert space, can be extended to a distributional settings. In doing so, we are able to construct a rather general framework to deal with…
We generalize proper scoring rules to the quantum domain, replacing probability distributions with density operators. We define Quantum Value Functionals via operator convex generators and establish a complete duality theory yielding proper…
The so-called topos approach provides a radical reformulation of quantum theory. Structurally, quantum theory in the topos formulation is very similar to classical physics. There is a state object, analogous to the state space of a…
We prove well-posedness and regularity results for elliptic boundary value problems on certain domains with a smooth set of singular points. Our class of domains contains the class of domains with isolated oscillating conical singularities,…
In this study we consider domains that are composed of an infinite sequence of self-similar rings and corresponding finite element spaces over those domains. The rings are parameterized using piecewise polynomial or tensor-product B-spline…