32,639 research outputs found

    SDSS J142625.71+575218.3: the First Pulsating White Dwarf With A Large Detectable Magnetic Field

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    We report the discovery of a strong magnetic field in the unique pulsating carbon- atmosphere white dwarf SDSS J142625.71 + 575218.3. From spectra gathered at the MMT and Keck telescopes, we infer a surface field of B(s) similar or equal to 1.2 MG, based on obvious Zeeman components seen in several carbon lines. We also detect the presence of a Zeeman- splitted He I lambda 4471 line, which is an indicator of the presence of a nonnegligible amount of helium in the atmosphere of this "hot DQ" star. This is important for understanding its pulsations, as nonadabatic theory reveals that some helium must be present in the envelope mixture for pulsation modes to be excited in the range of effective temperature where the target star is found. Out of nearly 200 pulsating white dwarfs known today, this is the first example of a star with a large detectable magnetic field. We suggest that SDSS J142625.71 + 575218.3 is the white dwarf equivalent of a rapidly oscillating Ap star.NSERCNSF AST 03-07321Reardon FoundationAstronom

    A computer-aided design for digital filter implementation

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    Combinatorics of linear iterated function systems with overlaps

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    Let p0,...,pm1\bm p_0,...,\bm p_{m-1} be points in Rd{\mathbb R}^d, and let {fj}j=0m1\{f_j\}_{j=0}^{m-1} be a one-parameter family of similitudes of Rd{\mathbb R}^d: fj(x)=λx+(1λ)pj,j=0,...,m1, f_j(\bm x) = \lambda\bm x + (1-\lambda)\bm p_j, j=0,...,m-1, where λ(0,1)\lambda\in(0,1) is our parameter. Then, as is well known, there exists a unique self-similar attractor SλS_\lambda satisfying Sλ=j=0m1fj(Sλ)S_\lambda=\bigcup_{j=0}^{m-1} f_j(S_\lambda). Each xSλ\bm x\in S_\lambda has at least one address (i1,i2,...)1{0,1,...,m1}(i_1,i_2,...)\in\prod_1^\infty\{0,1,...,m-1\}, i.e., limnfi1fi2...fin(0)=x\lim_n f_{i_1}f_{i_2}... f_{i_n}({\bf 0})=\bm x. We show that for λ\lambda sufficiently close to 1, each xSλ{p0,...,pm1}\bm x\in S_\lambda\setminus\{\bm p_0,...,\bm p_{m-1}\} has 202^{\aleph_0} different addresses. If λ\lambda is not too close to 1, then we can still have an overlap, but there exist x\bm x's which have a unique address. However, we prove that almost every xSλ\bm x\in S_\lambda has 202^{\aleph_0} addresses, provided SλS_\lambda contains no holes and at least one proper overlap. We apply these results to the case of expansions with deleted digits. Furthermore, we give sharp sufficient conditions for the Open Set Condition to fail and for the attractor to have no holes. These results are generalisations of the corresponding one-dimensional results, however most proofs are different.Comment: Accepted for publication in Nonlinearit

    A note in inverse and dual semigroups

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