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.

     

Top-down synthesis of polyoxometalate-like sub-nanometer molybdenum-oxo clusters as high-performance electrocatalysts

The top-down fabrication of catalytically active molecular metal oxide anions, or polyoxometalates, is virtually unexplored, although these materials offer unique possibilities, for catalysis, energy conversion and storage. Here, we report a novel top-down route, which enables the scalable synthesis and deposition of sub-nanometer molybdenum-oxo clusters on electrically conductive mesoporous carbon. The new approach uses a unique redox-cycling process to convert crystalline Mo^IVO₂ particles into sub-nanometer molecular molybdenum-oxo clusters with a nuclearity of ∼1–20. The resulting molybdenum-oxo cluster/carbon composite shows outstanding, stable electrocatalytic performance for the oxygen reduction reaction with catalyst characteristics comparable to those of commercial Pt/C. This new material design could give access to a new class of highly reactive polyoxometalate-like metal oxo clusters as high-performance, earth abundant (electro-)catalysts.

The top-down synthesis and deposition of polyoxometalate-like clusters on porous carbon is reported together with the high electrocatalytic oxygen reduction reactivity of the composite.     

Lithium–Lanthanide Bimetallic Metal–Organic Frameworks towards Negative Electrode Materials for Lithium-Ion Batteries

Novel lithium–lanthanide (Ln: cerium and praseodymium) bimetallic coordination polymers with formulas C₁₀H₂LnLiO₈ (Ln: Ce (CeLipma) and Pr (PrLipma)) and C₁₀H₃CeO₈ (Cepma) were prepared through a simple hydrothermal method. The three compounds were characterized by means of FTIR spectroscopy, X-ray diffraction, single-crystal X-ray diffraction, SEM, TEM, and X-ray photoelectron spectroscopy. The results of structural refinement show that they belong to triclinic symmetry and P space group with cerium (or praseodymium) and lithium cations, forming coordination bonds to oxygen atoms from different pyromellitic acid molecules, and leading to the construction of 3D structures. It is interesting to note that the frameworks exclude any coordination water and lattice water. As an electrode material for lithium-ion batteries, CeLipma exhibits a maximum capacity of 800.5 mAh g⁻¹ and a retention of 91.4 % after 50 cycles at a current density of 100 mA g⁻¹. The favorable electrochemical properties of the lanthanide coordination polymers show potential application prospects in the field of electrode materials.