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We prove that a class of convexity-type results for sequential fractional delta differences is sharp. More precisely, we consider the sequential fractional delta difference map t↦Δ1-μ+aνΔaμf(t), for t∈N3+a-μ-ν, where 0

Consider the following ν-th order Caputo delta fractional equation (0.1) The following asymptotic results are obtained. Theorem A. Assume0 0. Then the solutions of the equation (0.1) withx(a) > 0satisfy Theorem B. Assume0 0satisfy This shows that the solutions of the Caputo delta fractional equation , with x(a) > 0 have similar asymptotic behavior with the solutions of the first-order delta difference equation Δx(t) = cx(t),c >− 1. Copyright © 2016 John Wiley & Sons, Ltd.

We demonstrate that some recent results regarding the connection between the convexity of the map t → f (t) and the sign of Δa f (t) , with 2 < ν < 3 , can be improved. In particular, by utilizing a recent inequality due to Jia, Erbe, and Peterson, we are able to improve some of the existing results in the literature. As part of this study we illustrate the improvements that our results afford by providing several specific examples of their application. Mathematics subject classification (2010): Primary: 26A51, 39A12, 39B62; Secondary: 26A33, 39A70, 39A99.

The ELISpot assay is used for the detection of T cell responses in clinical trials and vaccine evaluations. Standardization and reproducibility are necessary to compare the results worldwide, inter- and intra-assay variability being critical factors. To assure operator safety as well as high-quality experiment performance, the ELISpot assay was implemented on an automated liquid handling platform, a Tecan Freedom EVO. After validation of the liquid handling, automated loading of plates with cells and reagents was investigated. With step by step implementation of the manual procedure and liquid dispensing optimization on the robot platform, a fully automated ELISpot assay was accomplished with plates remaining in the system from the plate blocking step to spot development. The mean delta difference amounted to a maximum of 6%, and the mean dispersion was smaller than in the manual assay. Taken together, we achieved with this system not only a lower personnel attendance but also higher throughput and a more precise and parallelized analysis. This platform has the potential to guarantee validated, safe, fast, reproducible and cost-efficient immunological and toxicological assays in the future. Funding was provided by Ministerium für Wirtschaft, Arbeit, Energie und Verkehr des Saarlandes (Grant Nos. C71-LdZ-2011, 01/2014), Spanish Ministry of Economy and Competitiveness and FEDER (Grant No. SAF2013-46077-R).

Background: Many laboratories use 4 delta check methods: delta difference, delta percent change, rate difference, and rate percent change. However, guidelines regarding decision criteria for selecting delta check methods have not yet been provided. We present new decision criteria for selecting delta check methods for each clinical chemistry test item. Methods: We collected 811,920 and 669,750 paired (present and previous) test results for 27 clinical chemistry test items from inpatients and outpatients, respectively. We devised new decision criteria for the selection of delta check methods based on the ratio of the delta difference to the width of the reference range (DD/RR). Delta check methods based on these criteria were compared with those based on the CV% of the absolute delta difference (ADD) as well as those reported in 2 previous studies. Results: The delta check methods suggested by new decision criteria based on the DD/ RR ratio corresponded well with those based on the CV% of the ADD except for only 2 items each in inpatients and outpatients. Delta check methods based on the DD/RR ratio also corresponded with those suggested in the 2 previous studies, except for 1 and 7 items in inpatients and outpatients, respectively. Conclusions: The DD/RR method appears to yield more feasible and intuitive selection criteria and can easily explain changes in the results by refl ecting both the biological variation of the test item and the clinical characteristics of patients in each laboratory. We suggest this as a measure to determine delta check methods.

The international Rosetta mission, the 3/sup rd/ cornerstone mission of the European Space Agency (ESA) has been in operations since March 2, 2004. This year, Rosetta conducted observations of comet 9P/Tempel 1 in support of NASA's deep impact mission. Observations of this comet target were conducted from a distance of approximately 0.5 AU, and provided for approximately 2 weeks of observation time to complement the 800 seconds of observation time afforded Deep Impact's cameras. In this paper we have updated the status of the instruments following the commissioning exercise, an exercise that was only partially complete when a report was prepared for the 2005 IEEE conference. We have presented an overview of the 2005 Earth/Moon activities, and the deep impact set of observations. The paper also provides an update of the role of NASA's deep space network in supporting an ESA request for delta difference one-way ranging to provide improved tracking and navigation capability in preparation for the Mars flyby in 2007.