In this paper we recall with short proofs of some classical triangle inequalities, and prove corresponding non-Euclidean, i.e., spherical and hyperbolic versions of these inequalities. Among them are the well known Euler’s inequality, Rouché’s inequality (also called “the fundamental triangle inequality”), Finsler–Hadwiger’s inequality, isoperimetric inequality and others.

Inequalities and Their Measurement This paper is a review of the recent advances in the measurement of inequality. Inequality can have several dimensions. Economists are mostly concerned with the income and consumption dimensions of inequality. Several inequality indices including the most widely used index of inequality namely the Gini coefficient is discussed. Non-income inequality includes i...

Growth, Inequality and Poverty Relationships This paper examines the causal relationship between inequality and a number of macroeconomic variables frequently found in the inequality and growth literature. These include growth, openness, wages, and liberalisation. We review the existing cross-country empirical evidence on the effects of inequality on growth and the extent to which the poorest i...

Einstein’s locality is invoked to derive a correlation inequality. In the case of ideal experiments, this inequality is equivalent to Bell’s original inequality of 1965 which, as is well known, is violated by a maximum factor of 1.5. The crucial point is that even in the case of real experiments where polarizers and detectors are non-ideal, the present inequality is violated by a factor of 1.5,...

An inequality is deduced from Einstein’s locality and a supplementary assumption. This inequality defines an experiment which can actually be performed with present technology to test local realism. Quantum mechanics violate this inequality a factor of 1.5. In contrast, quantum mechanics violates previous inequalities (for example, Clauser-Horne-Shimony-Holt inequality of 1969, Freedman-Clauser...

background: inequality in households’ and individuals' consumption expenditures is one of the most important aspects of health status difference among households and individuals. objectives: we investigated the impact of some macro-economic factors specially inequality factors on the iranian rural health status since 1986 through 2012. patients and methods: we conducted a longitudinal ecologica...

In this paper, we study some functional inequalities (such as Poincaré inequality, logarithmic Sobolev inequality, generalized Cheeger isoperimetric inequality, transportation-information inequality and transportation-entropy inequality) for reversible nearest-neighbor Markov processes on connected finite graphs by means of (random) path method. We provide estimates of the involved constants.

Maclaurin’s inequality is a natural, but nontrivial, generalization of the arithmetic-geometric mean inequality. We present a new proof that is based on an analogous generalization of Bernoulli’s inequality. Applications of Maclaurin’s inequality to iterative sequences and probability are discussed, along with a graph-theoretic version of the inequality.

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