Abstract: An affine Moser-Trudinger inequality, which is stronger than the Euclidean MoserTrudinger inequality, is established. In this new affine analytic inequality an affine energy of the gradient replaces the standard L energy of gradient. The geometric inequality at the core of the affine Moser-Trudinger inequality is a recently established affine isoperimetric inequality for convex bodies...

This study performs a long-run, inter-temporal analysis of income inequality in the U.S. spanning the period 1916-2012. We employ both descriptive analysis and the ThresholdMinimum Dominating Set methodology from Graph Theory, to examine the evolution of inequality through time. In doing so, we use two alternative measures of inequality: the Top 1% share of income and the Gini coefficient. This...

As an indicator of social development and human capital, health has aroused ever-increasing concerns. Using CHNS2000 data, we attempt to address the following two issues: how could income inequality influence health; does the rising income inequality result in health inequality, especially will the health of the lower-income group get worse. We find that there is an “inverted-U” association bet...

in this paper, we extend some famous maximal inequalities and obtain strong laws of largenumbers for arbitrary random variables by use of these inequalities and martingale techniques.

In this note, we present an information diffusion inequality derived from an elementary argument, which gives rise to a very general Fano-type inequality. The latter unifies and generalizes the distance-based Fano inequality and the continuous Fano inequality established in [DW13, Corollary 1, Propositions 1 and 2], as well as the generalized Fano inequality in [HV94, Equation following (10)].

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,...