In this note we prove the following law of the iterated logarithm for the Grenander estimator of a monotone decreasing density: If f(t0) > 0, f'(t0) < 0, and f' is continuous in a neighborhood of t0, then [Formula: see text]almost surely where [Formula: see text]here [Formula: see text] is the two-sided Strassen limit set on [Formula: see text]. The proof relies on laws of the iterated logarith...

background: hundreds of patient education materials i.e. pamphlets are annually published in healthcare systems following their design, correction, and revision. aim: to design and evaluate patient education pamphlets based on readability indexes and their comparison with literacy level in society. method: the average literacy level among 500 patients admitted to two training hospitals in bojnu...

obesity usually results from a combination of several modifiable and non-modifiable contributing factors, such as genetics, race, and socioeconomic status. other factors, including birth by cesarean section, perinatal antibiotics usage, and promotion of exclusive breastfeeding for six months, could be potentially prevented or modulated. however, one of the factors can be easily implemented thro...

Under some assumptions on the nonlinearity f, we will study the nonexistence of nontrivial stable solutions or solutions which are stable outside a compact set of [Formula: see text] for the following semilinear higher-order problem: [Formula: see text] with [Formula: see text]. The main methods used are the integral estimates and the Pohozaev identity. Many classes of nonlinearity will be cons...

This research attempts to investigate the effect of financial constraints and different levels of agency costs on the investment efficiency of companies in Iran. Following the design of the financial risk assessment indexes, the transaction information was collected from the Stock Exchange in the five-year period of 2011-2015. The statistical sample consists of 128 companies selected by samplin...

Erratum Following publication of the original version [1] of the article in BMC Gastroenterology, it was brought to our attention that there was a mistake in the references list. Please see updated references below: 32. Gomez-Gallego C, Collado MC, Perez G, Ilo T, Jaakkola UM, Bernal MJ et al. Resembling breast milk: influence of polyamine-supplemented formula on neonatal BALB/cOlaHsd mouse mic...

Following-up Fukasawa and Gatheral (Frontiers of Mathematical Finance, 2022), we prove that the BBF formula, SABR rough formula provide asymptotically arbitrage-free approximations implied volatility under, respectively, local model, model.

In this article, we deal with the following problem which we call Boolean unification with predicates: For a given formula F[X ] in first-order logic with equality containing an n-ary predicate variable X , is there a quantifier-free formula G[x1,...,xn] such that the formula F[G] is valid in first-order logic with equality? We obtain the following results. Boolean unification with predicates f...