Polynomial solutions of a nonlinear difference equation

A class of nonlinear difference equations is considered. We show how their polynomial solutions can be computed in a systematic manner.     

A one‐pot method for synthesis of reduced graphene oxide‐supported Cu–Cu2O and catalytic application in tandem reaction of halides and sodium azide with terminal alkynes

Reduced graphene oxide (RGO)‐supported Cu–Cu₂O nanocomposite material (Cu‐Cu₂O@RGO) was prepared through a one‐pot reflux synthesis method. The morphology, crystal structure and composition of the prepared Cu‐Cu₂O@RGO were characterized using transmission electron microscopy, X‐ray diffraction, and X‐ray photoelectron, infrared and Raman spectroscopies. Cu‐Cu₂O@RGO as a heterogeneous catalyst was applied to tandem reactions of halides and sodium azide with terminal alkynes to synthesize effectively 1,4‐disubstituted 1,2,3‐triazoles. Moreover, the catalyst showed excellent recyclability performance with very little leaching of the metal. Compared with homogeneous catalysts, Cu‐Cu₂O@RGO as a green and efficient catalyst was recoverable, easy to separate and highly stable in the tandem method for the synthesis of 1,2,3‐triazole compounds.     

Liquid crystal mixtures for potential infrared applications

Liquid crystals (LCs) with diazo linkages have high dielectric and optical anisotropy. Two newly synthesized liquid crystalline compounds were dissolved in room temperature LC hosts, E7 and PTTP-24/36, to assess their properties. It was found that these mixtures have higher birefringence, larger dielectric anisotropy, and better elastic properties than the hosts. Satisfactory viscoelastic coefficients were also obtained for these mixtures, showing that they are promising LC materials for applications in the near IR region.     

Immersed boundary method for unsteady kinetic model equations

Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.     

Offline Arbitrated Quantum Blind Dual-Signature Protocol with Better Performance in Resisting Existential Forgery Attack

In this paper, we present an offline arbitrated quantum blind dual-signature protocol by using four-particle entangled Greenberger-Horne-Zeilinger(GHZ) states. By using the special relationship of four-particle GHZ states, we can not only support the security of quantum signature, but also guarantee the anonymity of the message owner. In our protocol, the authority of the arbitrator has been reduced, i.e., he will not help the receiver verify the signature in the verification. Compared with the previous quantum blind signature protocols, the presented arbitrator is offline. Finally, the security analysis and discussion are proposed.