54 research outputs found

    On the Number of Unbordered Factors

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    We illustrate a general technique for enumerating factors of k-automatic sequences by proving a conjecture on the number f(n) of unbordered factors of the Thue-Morse sequence. We show that f(n) = 4 and that f(n) = n infinitely often. We also give examples of automatic sequences having exactly 2 unbordered factors of every length

    On unitarizability in the case of classical p-adic groups

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    In the introduction of this paper we discuss a possible approach to the unitarizability problem for classical p-adic groups. In this paper we give some very limited support that such approach is not without chance. In a forthcoming paper we shall give additional evidence in generalized cuspidal rank (up to) three.Comment: This paper is a merged and revised version of ealier preprints arXiv:1701.07658 and arXiv:1701.07662. The paper is going to appear in the Proceedings of the Simons Symposium on Geometric Aspects of the Trace Formul

    Threshold and linewidth of a mirrorless parametric oscillator

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    We analyze the above-threshold behavior of a mirrorless parametric oscillator based on resonantly enhanced four wave mixing in a coherently driven dense atomic vapor. It is shown that, in the ideal limit, an arbitrary small flux of pump photons is sufficient to reach the oscillator threshold. We demonstrate that due to the large group-velocity delays associated with coherent media, an extremely narrow oscillator linewidth is possible, making a narrow-band source of non-classical radiation feasible.Comment: revised version to appear in Phys.Rev.Lett., contains discussion on threshold conditions and operation on few-photon leve

    Homological algebra for Schwartz algebras of reductive p-adic groups

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    Let G be a reductive group over a non-Archimedean local field. Then the canonical functor from the derived category of smooth tempered representations of G to the derived category of all smooth representations of G is fully faithful. Here we consider representations on bornological vector spaces. As a consequence, if V and W are two tempered irreducible representations and if V or W is square-integrable, then Ext_G^n(V,W) vanishes for all n>0. We use this to prove in full generality a formula for the formal dimension of square-integrable representations due to Schneider and Stuhler.Comment: 34 pages, version 2 contains, in addition, a discussion about formal dimensions from the point of view of Schwartz algebras and von Neumann algebra

    An Ultra-Fast Optical Modulator: The Double-Well GaAs/GaAlAs Superlattice (DWSL)

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