Analysis of moving least squares approximation revisited

In this article the error estimation of the moving least squares approximation is provided for functions in fractional order Sobolev spaces. The analysis presented in this paper extends the previous estimations and explains some unnoticed mathematical details. An application to Galerkin method for partial differential equations is also supplied.Comment: Journal of Computational and Applied Mathematics, 2015 Journal of Computational and Applied Mathematic

Effect of drying process on antioxidant properties of date palm fruits

Aim. In order to identify antioxidant activities and phenolic compound, two varieties of date palm (Mazfati and Kalute varieties) (Phoenix dactylifera) fruits (DPF) from Iran systematically evaluated. Methods. Antioxidant activity determined using typical methods such as DPPH, reducing power and total antioxidant method. The total phenolic content of the dates was measured using Folin-Ciocalteau method. The included samples were gathered at three stages of khalaal, rutab, tamr and dried date from Sam and Jiroft date. The total phenolic content ranged from 1074, 856.4 and 723.8 in Mozafati variety and 921.5, 723.5 and 785.3 mg gallic acid equivalents (GAE/100-g-dw sample) in Kalute variety for khalal, rutab and tamr stage, respectively. Results. In both varieties antioxidant activities and total phenolic content decreased by ripening stages. Result of drying process showed that total phenolic content and antioxidant activities varied from temperature and decreased by increase of drying temperature. Conclusion. This research demonstrates Iranian dates could be potential rich resources of natural antioxidants, and could be developed into functional foods or drug for the prevention and treatment of diseases caused by oxidative stress

An Alloy Verification Model for Consensus-Based Auction Protocols

Max Consensus-based Auction (MCA) protocols are an elegant approach to establish conflict-free distributed allocations in a wide range of network utility maximization problems. A set of agents independently bid on a set of items, and exchange their bids with their first hop-neighbors for a distributed (max-consensus) winner determination. The use of MCA protocols was proposed, $e.g.$, to solve the task allocation problem for a fleet of unmanned aerial vehicles, in smart grids, or in distributed virtual network management applications. Misconfigured or malicious agents participating in a MCA, or an incorrect instantiation of policies can lead to oscillations of the protocol, causing, $e.g.$, Service Level Agreement (SLA) violations. In this paper, we propose a formal, machine-readable, Max-Consensus Auction model, encoded in the Alloy lightweight modeling language. The model consists of a network of agents applying the MCA mechanisms, instantiated with potentially different policies, and a set of predicates to analyze its convergence properties. We were able to verify that MCA is not resilient against rebidding attacks, and that the protocol fails (to achieve a conflict-free resource allocation) for some specific combinations of policies. Our model can be used to verify, with a "push-button" analysis, the convergence of the MCA mechanism to a conflict-free allocation of a wide range of policy instantiations