Previous research studies mostly focused on enhancing the security of radio frequency identification (RFID) protocols for various RFID applications that rely on a centralized database. However, blockchain technology is quickly emerging as a novel distributed and decentralized alternative that provides higher data protection, reliability, immutability, transparency, and lower management costs compared with a conventional centralized database. These properties make it extremely suitable for integration in a supply chain management system. In order to successfully fuse RFID and blockchain technologies together, a secure method of communication is required between the RFID tagged goods and the blockchain nodes. Therefore, this paper proposes a robust ultra-lightweight mutual authentication RFID protocol that works together with a decentralized database to create a secure blockchain-enabled supply chain management system. Detailed security analysis is performed to prove that the proposed protocol is secure from key disclosure, replay, manin-the-middle, de-synchronization, and tracking attacks. In addition to that, a formal analysis is conducted using Gong, Needham, and Yahalom logic and automated validation of internet security protocols and applications tool to verify the security of the proposed protocol. The protocol is proven to be efficient with respect to storage, computational, and communication costs. In addition to that, a further step is taken to ensure the robustness of the protocol by analyzing the probability of data collision written to the blockchain. INDEX TERMS Blockchain, distributed ledger technology, radio frequency identification.

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The nature of normal state charge-carriers' dynamics and the transition in conduction and gap dimensionalities between 2D and 3D for YBa2Cu3O 7−δ and Bi2Sr2Ca1−xYxCu2O8 high-Tc superconductors were described by computing and fitting the resistivity curves, ρ(T, δ, x). These were carried out by utilizing the 2D and 3D Fermi liquid (FL) and ionization energy (EI) based resistivity models coupled with charge-spin (CS) separation based t-J model [Phys. Rev. B 64, 104516 (2001)]. ρ(T, δ, x) curves of Y123 and Bi2212 samples indicate the beginning of the transition of conduction and gap from 2D to 3D with reduction in oxygen content (7−δ) and Ca 2+ (1−x) as such, c-axis pseudogap could be a different phenomenon from superconductor and spin gaps. These models also indicate that the recent MgB2 superconductor is at least not Y123 or Bi2212 type.

SUMMARYA new formulation of the Navier-Stokes equations is introduced to solve incompressible ow problems. When ÿnite element methods are used under this formulation there is no need to worry whether Babuska-Brezzi condition is satisÿed or not. Both velocity and pressure can be obtained separately and the pressure can be simply obtained by a substitution. Moreover, fully explicit time integration can be applied for easy implementation. Implementation issues are discussed and a couple of ow examples are simulated. Parallel implementation based on domain decomposition is incorporated as well.

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