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Let T : X → X be a transformation. For any x ∈ [0, 1) and r > 0, the recurrence time τr(x) of x under T in its r-neighborhood is defined asFor 0 α β ∞, let E(α, β) be the set of points with prescribed recurrence time as followsIn this note, we consider the Gauss transformation T on [0, 1), and determine the size of E(α, β) by showing that dim H E(α, β) = 1 no matter what α and β are. This can be compared with Feng and Wu's result [Nonlinearity, 14 (2001), 81-85] on the symbolic space.

In this article, a new Aloha-based tag identification protocol is presented to improve the reading efficiency of the EPC C1 Gen2-based UHF RFID system. Collision detection (CD) plays a vital role in tag identification process which determines the efficiency of anti-collision protocols since most Aloha-based protocols optimize the incoming frame length based on the collisions in current frame. Existing CD methods are ineffective in identifying collision, resulting in a degradation of identification performance. Our proposed algorithm adopts an enhanced CD (ECD) scheme based on the EPC C1 Gen2 standard to optimize identification performance. The ECD method can realize timely and effective CD by detecting the pulse width of the randomly sent by tags. According to the ECD, the reader detects the slot distribution and predicts tag cardinality in every collision slot. The tags involved in each collision slot are identified by independently assigned sub-frames. A large number of numerical results show that the proposed solution is superior to other existing anti-collision protocols in various performance evaluation metrics.