A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Cryptanalysis and Improvement of Ye et al’s Quantum Private Comparison Protocol

Recently, Ye et al. (Int. J. Theor. Phys. 56, 1517–1529, 2017) proposed a quantum private comparison (QPC) protocol based on five-qubit entanglement state. Two parties can verify that their secret information is equal or not with the help of the semi-honest third party (TP). However, in this paper we will point out the Ye et al.’s initial protocol is not safe under a special participant attack. That is a malicious participant can get the other party’s secret input information illegally under the forgery attack. Furthermore, we give two possible improvement protocols, which can perform this protocol secure against this kind of attack.

     

Effect of nano-fillers on conductivity of polyethylene/low melting point metal alloy composites

A novel method for preparing conductive polyethylene(PE) composites has been developed. In the method, the powder of low melting point metal alloy(LMPA) is filled into the PE matrix by using twin screw extruder at a temperature below the melting point of the LMPA, and followed by a die drawing process at a temperature around the melting point of the metal alloy. It has been found that die drawing process, repeating the die drawing process and adding nano-fillers, such as montmorillonite(MMT) and multi-wall carbon nanotubes(MWCNTs), all help reduce the metal particle size in the PE matrix, thus improve the conductivity of the composite. The conductivity improvement is attributed to an increased number of the smaller metal particles. Therefore, conductive composites of polymer/metal alloy/nano-filler with high conductivity are possible to be prepared by using the new method.