Related papers: Localization and anti-localization cardinals
The aim of this paper is a characterization of great antipodal sets of complex Grassmannian manifolds as certain designs with the smallest cardinalities.
We introduce and study effective versions of the localization numbers introduced by Newelski and Roslanowski (cite in paper). We show that proper hierarchies are produced, and that the corresponding highness notions are relatively weak, in…
We study several intertwined hierarchies between $\kappa$-Ramsey cardinals and measurable cardinals to illuminate the structure of the large cardinal hierarchy in this region. In particular, we study baby versions of measurability…
This paper presents a definition for local linearizations of rational matrices and studies their properties. This definition allows us to introduce matrix pencils associated to a rational matrix that preserve its structure of zeros and…
The alignments between galaxies, their underlying matter structures, and the cosmic web constitute vital ingredients for a comprehensive understanding of gravity, the nature of matter, and structure formation in the Universe. We provide an…
We construct long sequences of localization functors L_a in the category of abelian groups such that L_a > L_b for infinite cardinals a < b less than some k. For sufficiently large free abelian groups F and a < b we have proper inclusions…
Let $\mathcal{E}$ be the ideal generated by the $F_\sigma$ measure zero subsets of the reals. The purpose of this survey paper is to study the cardinal characteristics (the additivity, covering number, uniformity, and cofinality) of…
While topology given by a linear order has been extensively studied, this cannot be said about the case when the order is given only locally. The aim of this paper is to fill this gap. We consider relation between local orderability and…
This expository note explores Laplacian eigenfunction localization for compact domains. We work in the context of a particular numerically determined, localized, low frequency eigenfunction.
We introduce a local multifractal formalism adapted to functions, measures or distributions which display multifractal characteristics that can change with time, or location. We develop this formalism in a general framework and we work out…
The paper establishes several inequalities between cardinal characteristics of the continuum. In particular, it is shown that the partition splitting number is not larger than the uniformity of the meagre ideal; not all sets of reals having…
Localization properties for Schr\"odinger means are studied in dimension higher than one.
The paper has two main goals. The first is to take a new approach to rearrangements on certain classes of measurable real-valued functions on $\mathbb{R}^n$. Rearrangements are maps that are monotonic (up to sets of measure zero) and…
This paper develops a rich theory of cardinality in the paraconsistent and paracomplete set theory $\mathrm{BZFC}$, where sets can be inconsistent ($A$ such that ``$x\in A$'' is both true and false for some $x$) or incomplete ($A$ such that…
We examine what happens if we replace ZFC with a localistic/relativistic system, LZFC, whose central new axiom, denoted by $Loc({\rm ZFC})$, says that every set belongs to a transitive model of ZFC. LZFC consists of $Loc({\rm ZFC})$ plus…
The paper focuses on the problem of localization in quantum mechanics. It is well known that it is not possible to define a localization observable for the photon by means of projection valued measures. Conversely, that is possible by using…
The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…
This paper studies cardinal invariants b_kappa and t_kappa, the natural generalizations of the invariants b and t to a regular cardinal kappa.
The hierarchy associated to clusters in the HDBSCAN algorithm has layers, which are defined by cardinality. The layers define a layer subposet of the HDBSCAN hierarchy, which is a strong deformation retract and admits a stability analysis.…
A new proposal for a Lorentz-invariant spontaneous localization theory is presented. It is based on the choice of a suitable set of macroscopic quantities to be stochastically induced to have definite values. Such macroscopic quantities…