Related papers: Good and bad points in scales
In this note, we provide with a simple example to show a defect in the definition of the geometric mixing scale, and then introduce an improved scale, called as the strong geometric mixing scale. The main theorem in this note is the…
We introduce the notion of scale to generalize and compare different invariants of metric spaces and their measures. Several versions of scales are introduced such as Hausdorff, packing, box, local and quantization. They moreover are…
We study a classically scale-invariant model in which strong dynamics in a dark sector sets the scale of electroweak symmetry breaking. Our model is distinct from others of this type that have appeared in the recent literature. We show that…
The promising solution to the strong CP problem by a Peccei-Quinn (PQ) symmetry may introduce quality and hierarchy problems, which are both relevant to Planck physics. In this paper, we study whether both problems can be explained by…
We study good, bad and not-even-bad diquarks on the lattice in a gauge-invariant formalism in full QCD. We establish their spectral masses with short extrapolations to the physical point, observing agreement with phenomenological…
The paper presents a cursory examination of clustering, focusing on a rarely explored field of hierarchy of clusters. Based on this, a short discussion of clustering quality measures is presented and the F-score measure is examined more…
We introduce a real-parameter refinement of the classical integer hierarchies underlying Schmidt number, block-positivity, and $k$-positivity for maps between matrix algebras. Starting from a compact family of $\alpha$-admissible unit…
In this paper we exhibit the notion of (uniformly) good sections of arithmetic fundamental groups. We introduce and investigate the problem of cuspidalisation of sections of arithmetic fundamental groups, its ultimate aim is to reduce the…
We systematically study the connection between P, C and strong CP in the context of both non-supersymmetric and supersymmetric left-right theories. We find that the solution to the strong CP problem requires both supersymmetry and parity…
The notion of good integers, namely the divisors of the sequence $(a^s+b^s)_{s\ge 1}$ for nonzero coprime integers $a$ and $b$, together with their subfamilies such as oddly-good and evenly-good integers, has become an important arithmetic…
Geographical phenomena fall into two categories: scaleful phenomena and scale-free phenomena. The former bears characteristic scales, and the latter has no characteristic scale. The conventional quantitative and mathematical methods can…
We solve two long-standing open problems regarding the combinatorics of $\aleph_{\omega+1}$. We answer a question of Shelah by showing that it is consistent for any $n\geq 1$ that $\mathsf{GCH}$ holds and there is a stationary set of points…
A long standing problem in the area of error correcting codes asks whether there exist good cyclic codes. Most of the known results point in the direction of a negative answer. The uncertainty principle is a classical result of harmonic…
The development of dark energy models has stimulated interest to cosmological singularities, which differ from the traditional Big Bang and Big Crunch singularities. We review a broad class of phenomena connected with soft cosmological…
We have found that proposals addressing the old cosmological constant problem come in various categories. The aim of this paper is to identify as many different, credible mechanisms as possible and to provide them with a code for future…
Motivated by potential applications to partial differential equations, we develop a theory of fine scales of decay rates for operator semigroups. The theory contains, unifies, and extends several notable results in the literature on decay…
We fit the three finestructure constants of the Standard Model with three, in first approximation theoretically estimable parameters, 1) a "unifiedscale",turning out not equal to the Planck scale and thus only estimable by a very…
We introduce a notion of measuring scales for quantum abelian gauge systems. At each measuring scale a finite dimensional affine space stores information about the evaluation of the curvature on a discrete family of surfaces. Affine maps…
A bad point of a positive semidefinite real polynomial f is a point at which a pole appears in all expressions of f as a sum of squares of rational functions. We show that quartic polynomials in three variables never have bad points. We…
Starting from large cardinals we construct a model of $ZFC$ in which the $GCH$ fails everywhere, but such that $GCH$ holds in its $HOD$. The result answers a question of Sy Friedman. Also, relative to the existence of large cardinals, we…