Periodic solutions of fourth-order functional differential equations with $p$-Laplacian

Yuji Liu

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Greedy and lazy representations in negative base systems

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We consider positional numeration systems with negative real base $- β$ , where $β > 1$ , and study the extremal representations in these systems, called here the greedy and lazy representations. We give algorithms for determination of minimal and maximal $(- β)$ -representation with respect to the alternate order. We also show that both extremal representations can be obtained as representations in the positive base $β^{2}$ with a non-integer alphabet. This enables us to characterize digit sequences admissible...