The differentiation operator in the space of uniformly convergent Dirichlet series

Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fréchet space of all Dirichlet series that are uniformly convergent in all half-planes for each . The properties of the formal inverse of the differentiation are also investigated.     

Assessment of different reconstruction techniques for implementing the NVSF schemes on unstructured meshes

Three new far‐upwind reconstruction techniques, New‐Technique 1, 2, and 3, are proposed in this paper, which localize the normalized variable and space formulation (NVSF) schemes and facilitate the implementation of standard bounded high‐resolution differencing schemes on arbitrary unstructured meshes. By theoretical analysis, it is concluded that the three new techniques overcome two inherent drawbacks of the original technique found in the literature. Eleven classic high‐resolution NVSF schemes developed in the past decades are selected to evaluate performances of the three new techniques relative to the original technique. Under the circumstances of arbitrary unstructured meshes, stretched meshes, and uniform triangular meshes, for each NVSF scheme, the accuracies and convergence properties, when implementing the four aforementioned far‐upwind reconstruction techniques respectively, are assessed by the pure convection of several scalar profiles. The numerical results clearly show that New‐Technique‐2 leads to a better performance in terms of overall accuracy and convergence behavior for the 11 NVSF schemes. Copyright © 2013 John Wiley & Sons, Ltd.     

Properties of cat-eye modulating retro-reflector and its application with piezoelectric transducer

Piezoelectric cat-eye modulating retro-reflector (MRR) is the core component of an acousto-optic retro-identification system. The influence of the optical parameters (link distance l, lens focal length f and the detector diameter r) to the cat-eye effect was analyzed theoretically and experimentally. A piezoelectric cat-eye retro-identification (PCERI) system was built, and an information transmission ratio of 2 kHz was achieved which can satisfy an access control system.     

Higher integrability for nonlinear elliptic equations with variable growth and discontinuous coefficients

In this paper, based on the theory of variable exponent spaces, we study the higher integrability for a class of nonlinear elliptic equations with variable growth and discontinuous coefficients. Under suitable assumptions, we obtain a local gradient estimate in Orlicz space for weak solution.