The BKR inequality conjectured by van den Berg and Kesten in [11], and proved by Reimer in [8], states that for A and B events on S, a finite product of finite sets Si, i = 1, . . . , n, and P any product measure on S, P (A B) ≤ P (A)P (B), where the set A B consists of the elementary events which lie in both A and B for ‘disjoint reasons.’ Precisely, with n := {1, . . . , n} and K ⊂ n, for x ∈...

We prove the Harnack inequality for antisymmetric s-harmonic functions, and more generally solutions of fractional equations with zero-th order terms, in a general domain. This may be used conjunction method moving planes to obtain quantitative stability results symmetry overdetermined problems semilinear driven by Laplacian. The proof is split into two parts: an interior away from plane symmet...

background: health inequalitymonitoring especially in health care financing field is very important. hence, this study tends to assess the inequality in household's capacity to pay and out-of-pocket health carepaymentsin tehran metropolis. methods: this cross-sectional study was performed in 2013.thestudy population was selected by stratified cluster sampling, and they constitute the typic...

Subgroup Decomposability is a very useful property in an inequality measure, and level-sensitivity, which requires a given level of inequality to acquire a greater significance the poorer a population is, is a distributionally appealing axiom for an inequality index to satisfy. In this paper, which is largely in the nature of a recollection of important results on the characterization of subgro...

We consider the sum of squared logarithms inequality and investigate possible connections with the theory of majorization. We also discuss alternative sufficient conditions on two sets of vectors a,b ∈ R+ so that n ∑ i=1 (logai) n ∑ i=1 (logbi) . Generalizations of some inequalities from information theory are obtained, including a generalized information inequality and a generalized log sum in...

We prove a dual version of the celebrated inequality of D. Reimer (a.k.a. the van den Berg-Kesten conjecture). We use the dual inequality to prove a combinatorial conjecture of S. Rudich motivated by questions in cryptographic complexity. One consequence of Rudich’s Conjecture is that there is an oracle relative to which one-way functions exist but one-way permutations do not. The dual inequali...