Cognitive radios shall form cognitive radio network (CRN) to complete the packets delivery. As cognitive radio network is a general multihop wireless heterogeneous network, trust becomes a critical factor for network layer functions and network operation. We explore and develop the mathematical framework of trust in CRN, to further develop trusted routing with relevant explorations on network layer and above functions.

Cognitive radio has been considered as a key technology for future wireless communications and mobile computing. We note the cognitive radios can form cognitive radio networks (CRN) by extending the radio link features to network layer functions and above. We categorize CRN architecture into several structures and classify the unidirectional links in such structures, to pave the way for future systematic CRN research.

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This paper aims to construct the bracket formalism of mixture continua by using the method of Lagrangian- to-Eulerian (LE) transformation. The LE approach first builds up the transformation relations between the Eulerian state variables and the Lagrangian canonical variables, and then transforms the bracket in Lagrangian form to the bracket in Eulerian form. For the conservative part of the bracket formalism, this study systematically generates the noncanonical Poisson brackets of a two-component mixture. For the dissipative part, we deduce the Eulerian-variable-based dissipative brackets for viscous and diffusive mechanisms from their Lagrangian-variable-based counterparts. Finally, the evolution equations of a micromorphic fluid, which can be treated as a multi-component mixture, are derived by constructing its Poisson and dissipative brackets.

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