We reviewed the records and physical findings of twenty-three young adults who had had significant untreated limb-length inequality, present since childhood. The spine was studied radiographically and clinically before and after neutralization of the discrepancy of limb lengths with a lift. Movements of the spine also were measured. A significant asymmetry of lateral flexion of the spine remain...

In this paper, we focus on variational representations of some matrix symmetric norm functions that are related to the quantum Rényi relative entropy. Concretely, obtain function ( A , B ) ? | q / 2 K ? p s for norms by using Hölder inequality and Young inequality. These expressions enable us make proofs convexity/concavity trace Tr more clear give a new extension.

We present a simple proof, based on modi ed logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for the exponential distribution. We actually observe that every measure satisfying a Poincar e inequality shares the same concentration phenomenon. We also discuss exponential integrability under Poincar e inequalities and its consequence to sharp diameter upper bounds on spect...

We give a new proof of the sharp form of Young’s inequality for convolutions, first proved by Beckner [Be] and Brascamp-Lieb [BL]. The latter also proved a sharp reverse inequality in the case of exponents less than 1. Our proof is simpler and gives Young’s inequality and its converse altogether. The classical convolution inequality of Young asserts that for all functions f ∈ L(R) and g ∈ L(R) ...

This paper is an observational study of particular historical trends in mortality inequality within Great Britain, comparing England and Wales with Scotland for the period 1925-2005. The inequalities in mortality within Great Britain have become more apparent over time. Growing inequality in premature mortality in Britain affected young Scottish men most severely after 1995. It would appear tha...

The College Type: Personality and Educational Inequality I examine the effects of cognitive ability and personality traits on college graduation in a recent cohort of young Americans, and how the returns to these traits vary by family background, and find very substantial differences across family background groups in the personality traits that predict successful completion of college, particu...