inequalities

This research dashboard is designed for AQA A Level Sociology and fits the Health option section on inequalities in the provision of and access to healthcare. The AQA specification for Health explicitly includes this topic and asks students to study patterns in access and provision for different social groups, including social class, region, gender, ethnicity, […]

Post ICA Conference The impact of public relations and promotional communication on human rights, inequalities and social justice: Interdisciplinary reflections and future directions WHEN 08:30 – 18:30 Tuesday 25 June 2024 WHERE Queensland University of Technology – P Block Room 419, Gardens Point Campus This 2024 ICA... The post Post ICA Conference – The impact of public relations and promotiona…

Let with each component satisfying 0 < xi ≤ 1/2. Define the complement x′ by taking the complement of each entry. Let G and A represent the geometric and arithmetic mean respectively. Then Ky Fan’s inequality says Now let H be the harmonic mean. Since in general H ≤ G ≤ A, you might guess that […] The post Ky Fan’s inequality first appeared on John D. Cook .

Let An, Gn and Hn be the arithmetic mean, geometric mean, and harmonic mean of a set of n numbers. When n = 2, the arithmetic mean times the harmonic mean is the geometric mean squared. The proof is simple: When n > 2 we no longer have equality. However, W. Sierpiński, perhaps best known […] The post Sierpiński’s inequality first appeared on John D. Cook .

I stumbled upon a theorem today that I feel like I’ve needed in the past, though I can’t remember any particular applications. I’m writing it up here as a note to my future self should the need reappear. The theorem gives sufficient conditions to conclude f(g(x)) ≤ g(f(x)) and uses this to prove, for example, […] The post f(g(x)) versus g(f(x)) first appeared on John D. Cook .

This afternoon I wrote a brief post about Terence Tao’s new paper A Maclaurin type inequality. That paper builds on two classical inequalities: Newton’s inequality and Maclaurin’s inequality. The previous post expanded a bit on Newton’s inequality. This post will do the same for Maclaurin’s inequality. As before, let x be a list of real […] The post Maclaurin’s inequality first appeared on John D…

I have just uploaded to the arXiv my paper “A Maclaurin type inequality“. This paper concerns a variant of the Maclaurin inequality for the elementary symmetric means of real numbers . This inequality asserts that whenever and are non-negative. It can be proven as a consequence of the Newton inequality valid for all and arbitrary […]

A favourite result of many students doing olympiad inequality problems is the so-called Rearrangement Inequality. This is a mathematical formulation of the idea well-known to even the smallest of child that if you prefer cakes to carrots then if you … Continue reading →