Related papers: Problems and memories
We establish some new generalizations of Erd\H{o}s-Mordell inequality by adding weights to its terms. Using these generalizations, we derived strengthened versions of the original Erd\H{o}s-Mordell inequality. We also found two other…
I review what we have learned about the BLR from reverberation mapping, point to some problems and complications that have emerged, and outline some future directions.
Creative processes are widely believed to involve the generation of multiple, discrete, well-defined possibilities followed by exploration and selection. An alternative, inspired by parallel distributed processing models of associative…
The Paulsen Problem in Hilbert space frame theory has proved to be one of the most intractable problems in the field. We will help explain why by showing that this problem is equivalent to a fundamental, deep problem in operator theory.…
We consider the problem of perfectly recovering the vertex correspondence between two correlated Erd\H{o}s-R\'enyi (ER) graphs. For a pair of correlated graphs on the same vertex set, the correspondence between the vertices can be obscured…
This paper is an extension program of the notion of circle of partition developed in our first paper \cite{CoP}. As an application we prove the Erd\H{o}s-Tur\'{a}n additive base conjecture.
We present some recent results on the existence of solutions of the Schr\"odinger flows, and pose some problems for further research.
At the heart of both black hole physics and Wigner's friend scenarios lies the question of unitarity. In Wigner's friend setups, sealed-lab measurements are modeled unitarily, probing the measurement problem. In black hole physics, the…
In this paper, we will continue the investigation of Waring's problem, and give further improvements.
I would like to thank Junk and Lyons (arXiv:2009.06864) for beginning a discussion about replication in high-energy physics (HEP). Junk and Lyons ultimately argue that HEP learned its lessons the hard way through past failures and that…
Erd\H{o}s and Graham (Erd\H{o}s and Graham, 1980) asked if there exists an $n$ such that the divisors of $n$ greater than 1 are the moduli of a distinct covering system with the following property: If there exists an integer which satisfies…
I begin with an anecdote, and then discuss my recent work on anomalies in spin-$\frac{3}{2}$ theories.
These informal notes deal with a number of questions related to sums and integrals in analysis.
The physics of matter in the condensed state is concerned with problems in which the number of constituent particles is vastly greater than can be easily comprehended. The inherent physical limitations of the human mind are fundamental and…
Personal recollections about Alexandre Grothendieck and early days of his theory of motives
We make a few remarks on possible sources of uncertainties of the $\bar d - \bar u$ asymmetry obtained by different methods and comment on its possible verification in the future. In addition we comment on its present understanding.
The past year has seen an explosion of new and old ideas about black hole physics. Prior to the firewall paper, the dominant picture was the thermofield model apparently implied by ADS/CFT duality\cite{mal2}. While some seek a narrow…
Errors in Eberly's derivation of several Bell inequalities are pointed out: (1) it is based on an equation that is incorrect; (2) it uses neither two-particle states nor locality to derive Bell's inequalities and; (3) it does not use…
In this article, we tackle the math word problem, namely, automatically answering a mathematical problem according to its textual description. Although recent methods have demonstrated their promising results, most of these methods are…
The majority of extensions to General Relativity display mathematical pathologies (higher derivatives, character change in equations that can be classified within PDE theory, and even unclassifiable ones) that cause severe difficulties to…