and Applied Analysis 3 If there does not exist such y for some X as above, we set γ s (A, β) = +∞ and to be compatible with the special case given by [24] we write γ s (A), γ s (A) instead of γ s (A, +∞), γ s (A, +∞), respectively. From the above definition, we easily see that the set of values that γ takes is closed. Thus, when γ s (A, β) < +∞, for every matrix X ∈ Rm×n with s nonzero singular...

A simple proof is given of the best known upper bound on the cardinality of a set of vectors of length t over an alphabet of size b, with the property that, for every subset of k vectors there is a coordinate in which they all differ. This question is motivated by the study of perfect hash functions. A set of vectors of length t over an alphabet of size b is called k-separated if for every k di...

where m(f(X)) is a median of f(X) and where Φ is the (one–dimensional) standard normal distribution function. The inequality (1) has seen many extensions and to date, most of the conditions under which these developments hold require the existence of finite exponential moments for the underlying vector X . It is thus natural to explore the robustness of this “concentration phenomenon” and to st...

Background Exploring changes in health inequality and its determinants over time is of policy interest. Accordingly, this study aimed to decompose inequality in neonatal mortality into its contributing factors and then explore changes from 1995-2000 to 2005-2010 in Iran.   Methods Required data were drawn from two Iran’s demographic and health survey (DHS) conducted in 2000 and 2010. Normalized...

Let L be a finite distributive lattice and μ : L → R a logsupermodular function. For functions k : L → R let Eμ(k; q) def = ∑ x∈L k(x)μ(x)q ∈ R[q]. We prove for any pair g, h : L → R of monotonely increasing functions, that Eμ(g; q) ·Eμ(h; q) ≪ Eμ(1; q) · Eμ(gh; q), where “≪ ” denotes coefficientwise inequality of real polynomials. The FKG inequality of Fortuin, Kasteleyn and Ginibre (1971) is ...

According to the Ahlowalia hypothesis (1995), the growth of total factor productivity (TFP) beside infrastructure investments of government lead to income inequality decrease in rural areas of countries. The main objective of this study is to investigate the effects of public investments such as agricultural R&E, road, education and irrigation on income inequality in rural areas of Iran. In ord...