14,396 research outputs found

    Regular finite decomposition complexity

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    We introduce the notion of regular finite decomposition complexity of a metric family. This generalizes Gromov's finite asymptotic dimension and is motivated by the concept of finite decomposition complexity (FDC) due to Guentner, Tessera and Yu. Regular finite decomposition complexity implies FDC and has all the permanence properties that are known for FDC, as well as a new one called Finite Quotient Permanence. We show that for a collection containing all metric families with finite asymptotic dimension all other permanence properties follow from Fibering Permanence

    Radial excitations of heavy-light mesons from QCD sum rules

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    QCD sum rules are commonly used to predict the characteristics of ground-state hadrons. We demonstrate that two-point sum rules for the decay constants of charmed (D(),Ds()D^{(*)},D_s^{(*)}) and bottom (B(),Bs()B^{(*)},B_s^{(*)}) mesons can also be modified to estimate the decay constants of the first radial excitations, D(),Ds()D^{(*)'},D_s^{(*)'} and B(),Bs()B^{(*)'},B_s^{(*)'}, respectively, provided the masses of these resonances are used as an input. For the radially excited charmed mesons we use available experimental data, whereas the masses of analogous bottom mesons are estimated from the heavy-quark limit. The decay constants predicted for the radial excitations of heavy-light pseudoscalar and vector mesons are systematically smaller than those of the ground states and we comment on the possible origin of this difference. Our results can be used in the sum rule calculations of heavy-to-light form factors and in the factorization approximations for nonleptonic BB-meson decays where the decay constants of charmed mesons enter as input parameters.Comment: 16 pages, a few comments added, version to appear in EPJ

    Reading Too Much into What the Court \u3ci\u3eDoesn\u27t\u3c/i\u3e Write: How Some Federal Courts Have Limited Title VII\u27s Participation Clause\u27s Protections after \u3ci\u3eClark County School District v. Breeden\u3c/i\u3e

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    In 2001, the Supreme Court issued its opinion in Clark County School District v. Breeden, in which it refused to determine what a plaintiff must prove to demonstrate that she engaged in “protected activity” under Title VII’s anti-retaliation provision’s opposition clause. Although the Court declined to answer this question, courts have interpreted Breeden as requiring an opposition-clause plaintiff to prove a good-faith, objectively reasonable belief of an unlawful employment practice. Although Breeden involved Title VII’s opposition clause, some courts are now applying Breeden to cases involving Title VII’s participation clause. This is baffling for two reasons. First, Breeden involved the opposition clause, not the participation clause, and prior to Breeden, federal courts had concluded that the participation clause provided more protection than the opposition clause provided. Second, Breeden never definitively established the standard for opposition-clause cases. Despite this, some courts are now applying Breeden’s objectively reasonable standard to participation-clause cases. This Article argues that courts should not apply Breeden in participation-clause cases and should protect participation-clause plaintiffs even if the plaintiffs’ beliefs about unlawful employment practices are unreasonable. Courts should do this because of (1) the participation clause’s plain language; (2) the Equal Employment Opportunity Commission’s (EEOC) position on this issue; (3) the canon of statutory construction that requires remedial statutes such as Title VII to be interpreted broadly; and (4) the fact that Breeden neither addressed the participation clause nor provided a definitive standard for opposition-clause cases

    The Legality and Practicality of Condominium Conversion Moratoriums

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    Condominium conversions have been a source of increasing concern among Florida apartment dwellers as the number of available rental units has continued to decline. The author examines the constitutionality of condominium conversion moratoriums enacted or proposed by counties and municipalities. She then asks whether moratoriums are a practical solution to the housing crisis

    Regularization of the second-order gravitational perturbations produced by a compact object

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    The equations for the second-order gravitational perturbations produced by a compact-object have highly singular source terms at the point particle limit. At this limit the standard retarded solutions to these equations are ill-defined. Here we construct well-defined and physically meaningful solutions to these equations. These solutions are important for practical calculations: the planned gravitational-wave detector LISA requires preparation of waveform templates for the potential gravitational-waves. Construction of templates with desired accuracy for extreme mass ratio binaries, in which a compact-object inspirals towards a supermassive black-hole, requires calculation of the second-order gravitational perturbations produced by the compact-object.Comment: 12 pages, discussion expanded, to be published in Phys. Rev. D Rapid Communicatio