Related papers: Distance Domains: Completeness
In transferring some results from universal Taylor series to the case of Pad\'e approximants we obtain stronger results, such as, universal approximation on compact sets of arbitrary connectivity and generic results on planar domains of any…
The concept of distance rationalizability of social choice rules has been explored in recent years by several authors. We deal here with several foundational questions, and unify, correct, and generalize previous work. For example, we study…
We revisit the standard axioms of domain theory with emphasis on their relation to the concept of partiality, explain how this idea arises naturally in probability theory and quantum mechanics, and then search for a mathematical setting…
Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…
Non-homogeneous self-similar measures are generically absolute continuous in the domain of parameters for which the similarity dimension is larger than one, see \cite{[SSS]}. Using certain algebraic curves we construct here exceptional…
We write down the general conditions for N=1 supersymmetric four-dimensional domain walls, deriving them from a ten-dimensional point of view using generalized complex geometry. In cases where the compactification allows for a truncation to…
We define symmetric spaces in arbitrary dimension and over arbitrary non-discrete topological fields $\K$, and we construct manifolds and symmetric spaces associated to topological continuous quasi-inverse Jordan pairs and -triple systems.…
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
Convergence theory is an extension of general topology. In contrast with topology, it is closed under some important operations, like exponentiation. With all its advantages, convergence theory remains rather unknown. It is an aim of this…
We review in detail the Hamiltonian dynamics for constrained systems. Emphasis is put on the total Hamiltonian system rather than on the extended Hamiltonian system. We provide a systematic analysis of (global and local) symmetries in total…
In this thesis we study different aspects of noncommutativity in quantum mechanics, field theory and gravity. We give particular emphasis on the underlying symmetries of these theories. Deformations of usual symmetries like the external…
We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…
In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion. In particular, spaces of generalized functions are constructed that contain generalized solutions to all systems of continuous,…
We investigate a large class of infinitesimal, but fully nonlinear in the field, transformations of the Galileon and search for extended symmetries. The transformations involve powers of the coordinates $x$ and the field $\pi$ up to any…
In this work we investigate the transfer of fundamental order and completeness properties between truncated Riesz spaces and their unitizations. Specifically, we provide characterizations and equivalences for several notions of…
We provide a brief overview into recent tests of gravity, focusing on its foundational spacetime symmetries. In particular, we work with an agnostic, effective field-theory framework, named the Standard-Model Extension, that allows for…
The present paper is devoted to study some completeness properties of transitive binary relational set, i.e., a set together with a transitive binary relation (so called t-set).
This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the…
In this paper we extend the Tanaka finiteness theorem and inequality for the number of symmetries to arbitrary distributions (differential systems) and provide several applications.
We study the completions of the space of Hamiltonian diffeomorphisms of the standard linear symplectic space, for Viterbo's distance and some others derived from it, we study their different inclusions and give some of their properties. In…