There exist multilinear Bohnenblust-Hille constants (Cn)n=1(infinity) with limn ->infinity(Cn+1-Cn)=0

The n-linear Bohnenblust-Hille inequality asserts that there is a constant C-n is an element of [1, infinity) such that the l(2n/n+1)-norm of (U(e(i1), ..., e(in)))(i1, ...,in=1)(N) is bounded above by C-n times the supremum norm of U, for any n-linear form U :C-N x ... x C-N -> C and N is an element of N (the same holds for real scalars). We prove what we call Fundamental Lemma, which brings new information on the optimal constants, (K-n)(n=1)(infinity) for both real and complex scalars. For instance, Kn+1 - K-n = 2. We study the interplay between the Kahane-Salem-Zygmund and the Bohnenblust-Hille (polynomial and multilinear) inequalities and provide estimates for Bohnenblust-Hille-type inequality constants for any exponent q is an element of [2n/n+1, infinity). (C) 2012 Elsevier Inc. All rights reserved

International Nosocomial Infection Control Consortium report, data summary of 50 countries for 2010-2015: Device-associated module

•We report INICC device-associated module data of 50 countries from 2010-2015.•We collected prospective data from 861,284 patients in 703 ICUs for 3,506,562 days.•DA-HAI rates and bacterial resistance were higher in the INICC ICUs than in CDC-NHSN's.•Device utilization ratio in the INICC ICUs was similar to CDC-NHSN's. Background: We report the results of International Nosocomial Infection Control Consortium (INICC) surveillance study from January 2010-December 2015 in 703 intensive care units (ICUs) in Latin America, Europe, Eastern Mediterranean, Southeast Asia, and Western Pacific. Methods: During the 6-year study period, using Centers for Disease Control and Prevention National Healthcare Safety Network (CDC-NHSN) definitions for device-associated health care-associated infection (DA-HAI), we collected prospective data from 861,284 patients hospitalized in INICC hospital ICUs for an aggregate of 3,506,562 days. Results: Although device use in INICC ICUs was similar to that reported from CDC-NHSN ICUs, DA-HAI rates were higher in the INICC ICUs: in the INICC medical-surgical ICUs, the pooled rate of central line-associated bloodstream infection, 4.1 per 1,000 central line-days, was nearly 5-fold higher than the 0.8 per 1,000 central line-days reported from comparable US ICUs, the overall rate of ventilator-associated pneumonia was also higher, 13.1 versus 0.9 per 1,000 ventilator-days, as was the rate of catheter-associated urinary tract infection, 5.07 versus 1.7 per 1,000 catheter-days. From blood cultures samples, frequencies of resistance of Pseudomonas isolates to amikacin (29.87% vs 10%) and to imipenem (44.3% vs 26.1%), and of Klebsiella pneumoniae isolates to ceftazidime (73.2% vs 28.8%) and to imipenem (43.27% vs 12.8%) were also higher in the INICC ICUs compared with CDC-NHSN ICUs. Conclusions: Although DA-HAIs in INICC ICU patients continue to be higher than the rates reported in CDC-NSHN ICUs representing the developed world, we have observed a significant trend toward the reduction of DA-HAI rates in INICC ICUs as shown in each international report. It is INICC's main goal to continue facilitating education, training, and basic and cost-effective tools and resources, such as standardized forms and an online platform, to tackle this problem effectively and systematically