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The theory of majorization has seen substantial application in quantum information. Its framework predicates on the comparability between real vectors. We explore the antithesis of this premise, namely, incomparability. Specifically, we…

Quantum Physics · Physics 2018-05-01 Liwen Hu

We propose a generalization of the concept of symmetry as a continuous function of the reference center or line location. We suggest that this concept can be applied to many closed systems and exploring its time evolution. When the function…

General Physics · Physics 2015-01-16 Hector Rabal , Nelly Cap

This paper aims to generalize and unify classical criteria for comparisons of balanced lattice designs, including fractional factorial designs, supersaturated designs and uniform designs. We present a general majorization framework for…

Statistics Theory · Mathematics 2007-06-13 Aijun Zhang , Kai-Tai Fang , Runze Li , Agus Sudjianto

We consider the sum of squared logarithms inequality and investigate possible connections with the theory of majorization. We also discuss alternative sufficient conditions on two sets of vectors $a,b\in\mathbb{R}_+^n$ so that…

Classical Analysis and ODEs · Mathematics 2015-07-31 Fozi M. Dannan , Patrizio Neff , Christian Thiel

The concept of an $i$-symmetrization is introduced, which provides a convenient framework for most of the familiar symmetrization processes on convex sets. Various properties of $i$-symmetrizations are introduced and the relations between…

Metric Geometry · Mathematics 2019-09-11 G. Bianchi , R. J. Gardner , P. Gronchi

Recently, extensions of gamma and beta functions have been studied by many researchers due to their nice properties and variety of applications in different fields of science. The aim of this note is to investigate generalized inequalities…

General Mathematics · Mathematics 2024-07-18 S. Mubeen , I. Aslam , Ghazi S. Khammash , Saralees Nadarajah , Ayman Shehata

An inequality is derived for the correlation of two univariate functions operating on symmetric bivariate normal random variables. The inequality is a simple consequence of the Cauchy-Schwarz inequality.

Information Theory · Computer Science 2017-02-22 Ran Hadad , Uri Erez , Yaming Yu

The digitization of healthcare data coupled with advances in computational capabilities has propelled the adoption of machine learning (ML) in healthcare. However, these methods can perpetuate or even exacerbate existing disparities,…

Machine Learning · Computer Science 2024-02-02 Qizhang Feng , Mengnan Du , Na Zou , Xia Hu

Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain limits. As a consequence, we deduce a tight double…

Classical Analysis and ODEs · Mathematics 2019-04-23 Robert E. Gaunt

In this paper we explore inequalities between symmetric homogeneous polynomials of degree four of three real variables and three nonnegative real variables. The main theorems describe the cases in which the smallest possible coefficient is…

Classical Analysis and ODEs · Mathematics 2016-04-05 Mariyan Milev , Nedecho Milev

We show that recent multivariate generalizations of the Araki-Lieb-Thirring inequality and the Golden-Thompson inequality [Sutter, Berta, and Tomamichel, Comm. Math. Phys. (2016)] for Schatten norms hold more generally for all unitarily…

Mathematical Physics · Physics 2017-12-12 Fumio Hiai , Robert Koenig , Marco Tomamichel

This paper studies the bidiagonal factorization of the collocation matrices of analytic bases using symmetric functions. Explicit formulas for their initial minors are derived in terms of Schur functions. The structure of these formulas…

Combinatorics · Mathematics 2026-01-29 Pablo Díaz , Esmeralda Mainar

We introduce a symmetrization technique that allows us to translate a problem of controlling the deviation of some functionals on a product space from their mean into a problem of controlling the deviation between two independent copies of…

Probability · Mathematics 2007-05-23 Dmitry Panchenko

In this article, we prove some normality criteria for a family of meromorphic functions having zeros with some multiplicity. Our main result involves sharing of a holomorphic function by certain differential polynomials. Our results…

Complex Variables · Mathematics 2024-02-20 Gopal Datt , Yuntong Li , Poonam Rani

Algorithmic fairness is receiving significant attention in the academic and broader literature due to the increasing use of predictive algorithms, including those based on artificial intelligence. One benefit of this trend is that algorithm…

Computers and Society · Computer Science 2020-01-28 Pratyush Garg , John Villasenor , Virginia Foggo

Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.

Functional Analysis · Mathematics 2023-07-21 Daniel Alpay , Liora Mayats-Alpay

While shorter characteristic path length has in general been believed to enhance synchronizability of a coupled oscillator system on a complex network,the suppressing tendency of the heterogeneity of the degree distribution, even for…

Statistical Mechanics · Physics 2009-11-10 H. Hong , Beom Jun Kim , M. Y. Choi , Hyunggyu Park

In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…

Classical Analysis and ODEs · Mathematics 2015-06-25 Kwara Nantomah

We give the definition of uniform symmetric continuity for functions defined on a nonempty subset of the real line. Then we investigate the properties of uniformly symmetrically continuous functions and compare them with those of…

Classical Analysis and ODEs · Mathematics 2016-02-10 Tammatada Khemaratchatakumthorn , Prapanpong Pongsriiam

In clustering problems, a central decision-maker is given a complete metric graph over vertices and must provide a clustering of vertices that minimizes some objective function. In fair clustering problems, vertices are endowed with a color…

Machine Learning · Computer Science 2023-06-06 Seyed A. Esmaeili , Brian Brubach , Leonidas Tsepenekas , John P. Dickerson