Related papers: Dickson's lemma and weak Ramsey theory
We investigate possible quantifications of the Banach-Saks property and the weak Banach-Saks property. We prove quantitative versions of relationships of the Banach-Saks property of a set with norm compactness and weak compactness. We…
In this article, the weak-strong uniqueness principle is proved for an Euler-Poisson system in the whole space, with initial data so that the strong solution exists. Some results on Riesz potentials are used to justify the considered weak…
The problem of weak radiative hyperon decays (WRHD) is reviewed. With the recent measurement of the $\Xi ^0 \to \Lambda \gamma$ asymmetry confirming Hara's theorem, implications from its violation in low-energy theoretical approaches are…
We calibrate the reverse mathematical strength of a family of extensions of Ramsey's theorem to finite colorings of certain subsets of the natural numbers of unbounded finite dimension. Specifically, we analyze the principles…
In this note we study and obtain factorization theorems for colorings of matrices and Grassmannians over $\mathbb{R}$ and ${\mathbb{C}}$, which can be considered metric versions of the Dual Ramsey Theorem for Boolean matrices and of the…
We deal with the combinatorial principle Weak Diamond, showing that we always either a local version is not saturated or we can increase the number of colours. Then we point out a model theoretic consequence of Weak Diamond.
We study properties of Diophantine exponents of lattices and so-called related "weak" uniform approximations introduced in recent papers by Oleg German, in the simplest two-dimensional case. In contrast to the multidimensional case, in the…
In the paper we prove, in particular, that for any measurable coloring of the euclidian plane into two colours there is a monochromatic triangle with some restrictions on the sides. Also we consider similar problems in finite fields…
Main theoretical approaches to weak radiative hyperon decays are briefly reviewed. It is emphasized that only approaches with great predictive power should be seriously considered when seeking a resolution of the puzzle presented by…
Inspired by the recent measurements on the $J/{\psi}(1S)$ ${\to}$ $D_{s}{\rho}$, $D_{u}K^{\ast}$ weak decays at BESIII and the potential prospects of the charmonium at the high-luminosity heavy-flavor experiments, we study ${\psi}(1S,2S)$…
In this note, we state various generalisations of the Nakano vanishing theorem under weak positivity assumptions, and compare them with the known results.
We discuss prospects for detecting the two charm-related phenomena of $D^0$-${\bar D}^0$ mixing and weak radiative decays of $D$ mesons ({\it e.g.} $D\to K^* + \gamma$). A general update of particle-antiparticle mixing for the pseudoscalar…
We study the reverse mathematics of pigeonhole principles for finite powers of the ordinal $\omega$. Four natural formulations are presented and their relative strengths are compared. In the analysis of the pigeonhole principle for…
We reconsider Hara's theorem in its relation to the well-known properties of beta-decay. All assumptions necessary for the theorem to be true are explicitly formulated. Further, we study the W-exchange contribution to weak radiative decays…
In this series of papers we advance Ramsey theory of colorings over partitions. In this part, we concentrate on anti-Ramsey relations, or, as they are better known, strong colorings, and in particular solve two problems from [CKS21]. It is…
Weak KAM theory for discount Hamilton-Jacobi equations and corresponding discount Lagrangian/Hamiltonian dynamics is developed. Then it is applied to error estimates for viscosity solutions in the vanishing discount process. The main…
In this paper the lightface $\Pi^{1}_{1}$-Comprehension axiom is shown to be proof-theoretically strong even over $\mbox{RCA}_{0}^{*}$, and we calibrate the proof-theoretic ordinals of weak fragments of the theory $\mbox{ID}_{1}$ of…
In this paper we study Hardy and Poincar\'e inequalities and their weak versions for quadratic forms satisfying the first Beurling-Deny criterion. We employ these inequalities to establish a criticality theory for such forms.
In this article, based on a recent formularization of the holographic principle proposed and investigated by the present author, we show that the weak equivalence principle in general relativity is equivalent to the equivalence between two…
We define a collection of topological Ramsey spaces consisting of equivalence relations on $\omega$ with the property that the minimal representatives of the equivalence classes alternate according to a fixed partition of $\omega$. To prove…