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Multi-hop teleportation is a quantum teleportation scheme for transferring quantum states on a large scale. In this paper, a new multi-hop teleportation protocol is investigated for transferring arbitrary N-qubit states between M-neighbor nodes. In this scheme, intermediate nodes are connected with each other by symmetric entangled Bell states as quantum channels. First, one-hop teleportation of single-qubit, two-qubit and N-qubit states are introduced, then this method is generalized to two-hop and multi-hop teleportation for N-qubit. Also, we calculate the efficiency of this scheme.

We consider the class of polynomial differential equations ẋ = λx + P_n(x, y), ẏ = μy + Q_n(x, y) in ℝ² where P_n(x, y) and Q_n(x, y) are homogeneous polynomials of degree n > 1 and λ ≠ μ, i.e. the class of polynomial differential systems with a linear node with different eigenvalues and homogeneous nonlinearities. For this class of polynomial differential equations, we study the existence and nonexistence of limit cycles surrounding the node localized at the origin of coordinates.

Two concepts have long dominated vertebrate nerve electrophysiology: (a) Schwann cell-formed myelin sheaths separated by minute non-myelinated nodal gaps and spiraling around axons of peripheral motor nerves reduce current leakage during propagation of trains of axon action potentials; (b) "jumping" by action potentials between successive nodes greatly increases signal conduction velocity. Long-held and more recent assumptions and issues underlying those concepts have been obscured by research emphasis on axon-sheath biochemical symbiosis and nerve regeneration. We hypothesize: mutual electromagnetic induction in the axon-glial sheath association, is fundamental in signal conduction in peripheral and central myelinated axons, explains the g-ratio and is relevant to animal navigation.

This paper presents a technique for the enumeration of minimal paths of two-terminal networks. The method is developed based on the multiway tree structure that has been used widely for sorting and searching. The new technique does not require any matrix multiplication; it only requires a connection matrix. Furthermore, this simple method has capability of evaluating the reliability of a network after a topological modification, without going through the entire evaluation process. The method is compared with the existing algorithms, and the application simplicity of this method is demonstrated through examples.