We prove a reverse form of the multidimensional Brascamp-Lieb inequality. Our method also gives a new way to derive the Brascamp-Lieb inequality and is rather convenient for the study of equality cases. Introduction We will work on the space R with its usual Euclidean structure. We will denote by 〈, 〉 the canonical scalar product. In [BL], H. J. Brascamp and E. H. Lieb showed that for m ≥ n, p1...

In the present paper, we extend Garaev’s techniques to the set of fields which are not necessarily of prime order. Our goal here is just to find an explicit estimate in the supercritical setting where the set A has less cardinality than the square root of the cardinality of the field, and interacts in a less than half-dimensional way with any subfields. (We make this precise below.) Precisely, ...

We first prove a generalized Wirtinger’s inequality. Then, applying the inequality, we study estimates for lower bounds of periods of periodic solutions for a class of delay differential equations ẋ t −∑nk 1f x t − kr , and ẋ t − ∑n k 1g t, x t − ks , where x ∈ R, f ∈ C R,R , and g ∈ C R×Rp,Rp and r > 0, s > 0 are two given constants. Under some suitable conditions on f and g, lower bounds of p...

In this paper, we give a unified generalization of Aczél, Popoviciu and Bellman's inequalities. The result is then applied to deriving a refinement of Aczél's inequality and Bellman's inequality. As consequences, several interesting integral inequalities of Aczél-Popoviciu-Bellman type are obtained.

BACKGROUND The basic premise of preadjusted bracket system is accurate bracket positioning. It is widely recognized that accurate bracket placement is of critical importance in the efficient application of biomechanics and in realizing the full potential of a preadjusted edgewise appliance. AIM The purpose of this study was to design a calibrating system to accurately detect a point on a plan...

We provide necessary and sufficient conditions for the validity of the inequality of Simes (1986) in models with elliptical dependencies. Necessary conditions are presented in terms of sufficient conditions for the reverse Simes inequality. One application of our main results concerns the problem of model misspecification, in particular the case that the assumption of Gaussianity of test statis...

Motivated by quantum probability, Junge and Xu recently extended this result to the range 1 < p < 2. In this paper we study Burkholder’s inequality for p = 1, for which the techniques (as we shall explain) must be different. Quite surprisingly, we obtain two non-equivalent estimates which play the role of the weak type (1, 1) analog of Burkholder’s inequality. As application, we obtain new prop...

BACKGROUND The inequality of health human resource is a worldwide problem, and solving it also is one of the major goals of China's recent health system reform. Yet there is a huge disparity among cities in mainland China. The aim of this study is to analyze the distribution inequality of the health human resource in 322 prefecture-level cities of mainland China in 2014, and to reveal the facet...

This article evaluates the legitimacy and degree of inevitability of unequal access to medicine. The author introduces 'fractal inequality' to the access issue by using the term to describe skewed patterns in distributions of income and wealth that lead to reallocative effects of higher spending on health care by the wealthiest that can cascade down the distributive ladder. 'Fractal inequality'...

G. E. Forsythe, who edited the translation of Kantorovich's paper, included the following remark about this footnote: "It is not clear to me that Kantorovich's inequality really is a special case of that of Polya and Szego." Examining the relation between the two inequalities more closely we found that this remark is well justified and can be made even more specific in that the inequality of Po...