Related papers: Localization and anti-localization cardinals
We introduce a new covering property, defined in terms of order types of sequences of open sets, rather than in terms of cardinalities of families. The most general form of this compactness notion depends on two ordinal parameters. In the…
Anderson localization provides a challenge to numerical approaches due to the inherent randomness, and hence absence of simple symmetries, in its discrete Hamiltonian representation. Numerous algorithmic approaches have been developed or…
We review a few useful concepts about polarization measurements in the quantum domain. Using a perfectly general formalism, we show how to build the quantum counterpart of some classical quantities like Stokes parameters and Mueller…
Combining creature forcing approaches from arXiv:1003.3425 and arXiv:1402.0367, we show that, under CH, there is a proper $\omega^\omega$-bounding poset with $\aleph_2$-cc that forces continuum many pairwise different cardinal…
We prove that, under suitable assumptions on a category C, the existence of supercompact cardinals implies that every absolute epireflective class of objects of C is a small-orthogonality class. More precisely, if L is a localization…
This paper is a contribution to the problem of particle localization in non-relativistic Quantum Mechanics. Our main results will be (1) to formulate the problem of localization in terms of invariant subspaces of the Hilbert space, and (2)…
Locality is a fundamental principle used extensively in program and system optimization. It can be measured in many ways. This paper formalizes the metrics of locality into a measurement theory. The new theory includes the precise…
In characteristic zero, we construct relative principalization of ideals for logarithmically regular morphisms of logarithmic schemes, and use it to construct logarithmically regular desingularization of morphisms. These constructions are…
We investigate a variety of cut and choose games, their relationship with (generic) large cardinals, and show that they can be used to characterize a number of properties of ideals and of partial orders: certain notions of distributivity,…
It is pointed out that there exists an unambiguous definition of locality that enables one to distinguish local and nonlocal quantities. Observables of both types coexist in quantum optics but one must be very careful when attempting to…
There has been much discussion in the literature about rival measures of classical polarization in three dimensions. We gather and compare the various proposed measures of polarization, creating a geometric representation of the…
Using a countable support product of creature forcing posets, we show that consistently, for uncountably many different functions the associated Yorioka ideals' uniformity numbers can be pairwise different. In addition we show that, in the…
In this paper we continue to study of properties of $S(n)$-spaces. We establish bounded on the cardinality of $S(n)$-spaces.
Earlier, Lunts and Rosenberg studied a notion of compatibility of endofunctors with localization functors, with an application to the study of differential operators on noncommutative rings and schemes. Another compatibility -- of Ore…
The aim of this paper is to introduce the concept of Delta-Compact spaces along with some basic properties of it. Here, we try to establish the behavior of Delta-Compact spaces under the continuous mapping. Finally, we define another…
In this paper, local monomialization theorems are proven for analytic morphisms of complex and real analytic spaces. This gives the generalization of the local monomialization theorem for morphisms of algebraic varieties over a field of…
Localization properties of scalar single particle states are analyzed by explicit calculational examples with a focus on the massless case. Problems arising from the non-existence of relativistic particle position operators respecting the…
We introduce a two-parameter modification of the cofinality invariant of ideals. This allows us to include the interaction of a pair of ideals in the study of base-like structures. We find the values (cardinal numbers or well-known cardinal…
We claim that both multipartiteness and localization of subsystems of compound quantum systems are of an essentially relative nature crucially depending on the set of operationalistically available states. In a more general setting, to…
Relativistic positioning systems are interesting {\em technical objects} for applications around the Earth and in the Solar system. But above all else, they are basic {\em scientific objects} allowing developing relativity from its own…