Related papers: The Damascus Inequality
We revisit Smullyan's paper ``Truth and Provability'' (2013) for three purposes. First, we introduce the notion of Smullyan models to give a precise definition for Smullyan's framework discussed in that paper. Second, we clarify the…
We consider the age-old problem of allocating items among different agents in a way that is efficient and fair. Two papers, by Dolev et al. and Ghodsi et al., have recently studied this problem in the context of computer systems. Both…
Tight bounds for several symmetric divergence measures are introduced, given in terms of the total variation distance. Each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these bounds…
We give an explicit counterexample to an entanglement inequality suggested in a recent paper [quant-ph/0005126] by Benatti and Narnhofer. The inequality would have had far-reaching consequences, including the additivity of the entanglement…
We present a complete system of inequalities for the inradius, circumradius, and diameter in the $3$-dimensional Euclidean space. To do so, we prove quasiconcavity of the inradius evaluated over $n$-simplices with a common facet…
The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].
Machine learning has seen an increase in negative publicity in recent years, due to biased, unfair, and uninterpretable models. There is a rising interest in making machine learning models more fair for unprivileged communities, such as…
Fairness in machine learning is of considerable interest in recent years owing to the propensity of algorithms trained on historical data to amplify and perpetuate historical biases. In this paper, we argue for a formal reconstruction of…
In this note we revisit the classical geometric-arithmetic mean inequality and find a formula for the difference of the arithmetic and the geometric means of given $n\in\mathbb N$ nonnegative numbers $x_1,x_2,\dots,x_n$. The formula yields…
Efforts to combat continuing gender inequalities in academia need to be informed by evidence about where differences occur. Citations are relevant as potential evidence in appointment and promotion decisions, but it is unclear whether there…
This preprint is a text for students and teachers on inequalities. Some standard topics are covered on application of calculus to inequality proving. Many examples are considered, stated, solved or partially solved. Some problems are…
Fairness in multiwinner elections is studied in varying contexts. For instance, diversity of candidates and representation of voters are both separately termed as being fair. A common denominator to ensure fairness across all such contexts…
Inspired by a recent pointwise differential inequality for positive bounded solutions of the fourth-order H\'enon equation $\Delta^2 u = |x|^a u^p$ in ${\mathbb R}^n$ with $a \geqslant 0$, $p > 1$, $n \geqslant 5$ due to Fazly, Wei, and Xu…
The quantities of dimension one - known as the dimensionless quantities - are widely used in physics. However, the debate about some dimensionless units is still open. The paper brings new interrelated arguments that lead to the conclusion…
We improve the classical discrete Hardy inequality \begin{equation*}\label{1} \sum _{{n=1}}^{\infty }a_{n}^{2}\geq \left({\frac {1}{2}}\right)^{2} \sum _{{n=1}}^{\infty }\left({\frac {a_{1}+a_{2}+\cdots +a_{n}}{n}}\right)^{2},…
We consider a new and simpler proof of an inequality of A.S. Gasparyan, which was originally derived in terms of complex algebraical objects --- multidimensional hyperdeterminants. Our proof is much simpler and use only standard technics…
The Rashomon effect -- the existence of multiple, distinct models that achieve nearly equivalent predictive performance -- has emerged as a fundamental phenomenon in modern machine learning and statistics. In this paper, we explore the…
This note revisits the analysis of third-degree price discrimination developed by Bergemann et al. (2015), which characterizes the set of consumer-producer surplus pairs that can be achieved through market segmentation. This was proved by…
Across machine learning (ML) sub-disciplines, researchers make explicit mathematical assumptions in order to facilitate proof-writing. We note that, specifically in the area of fairness-accuracy trade-off optimization scholarship, similar…
We establish a sharp quantum advantage in determining the parity (even/odd) of an unknown permutation applied to any number $n \ge 3$ of particles. Classically, this is impossible with fewer than $n$ labels, being that the success is…