“…In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. …”
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“…Quantum inverse scattering methods related to a fractal potential given by a Weierstrass function (continuous but nowhere differentiable) are applied to the fractal analog of the Comtet-Bandrauk-Campbell (CBC) formula in SUSY QM. It requires using suitable fractal derivatives and integrals of irrational order whose parameter $ \beta $ is one-half the fractal dimension ($ D = 1.5 $) of the Weierstrass function. …”
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“…Additionally, the validity facet scores are interpreted based on Shadish, Cook, and Campbell’s validity model. RESULTS AND DISCUSSION: An empirical validation of the three facets of the MQ (external, internal, and construct validity) and the interpretation of the scores were obtained based on a theoretical framework. …”
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“…Greenberg in 1987, although L. Campbell's 1997 classification cannot be ruled out. …”
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“…This occurred by colonization of slopes from nearby refugia located around the northern part of Scotia Arc, southern tip of South America, South Georgia, Bouvet Island, southern tip of the Campbell plateau and Kerguelen plateau. By 2100, the shrimp are likely to expand their distribution in east Antarctica but have a continued pole-ward contraction in west Antarctica. …”
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“…Eighty-three varsity female athletes from eight Campbell University sports teams completed the survey and a medical history form anonymously. …”
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“…Framing our arguments using Campbell and Stanley’s classic research design monograph, we show that several “quasi-experimental” designs, especially interrupted time series (ITS), can estimate valid effects (or non-effects) of health interventions and policies as diverse as public insurance coverage, speed limits, hospital safety programs, drug abuse regulation and withdrawal of drugs from the market. …”
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“…OBJECTIVE: There exist conflicting data regarding the accuracy of ICU nurses accurately assessing patient sleep using validated questionnaires. Using the Richards-Campbell Sleep Questionnaire (RSQ), we hypothesize that patient factors might influence nursing perception of their sleep. …”
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“…Two identical PWS100 (Campbell Scientific), one Laser Precipitation Monitor (Thies Clima) and a first-generation Parsivel (OTT) were collocated with a weighing rain gauge (OTT Pluvio(2)) at a site in Austria. …”
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“…Understanding a study’s data generating structure and translating that data structure into a DAG can be challenging, but these skills are often glossed over in training. Campbell and Stanley’s framework for causal inference has been extraordinarily influential in social science training programs but has received less attention in epidemiology. …”
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“…Satoshi ōmura and William C. Campbell won the 2015 Nobel Prize in Physiology or Medicine for the discovery of the excellent efficacy of ivermectin against parasitic diseases. …”
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“…In a cross-sectional survey, 240 participants (age range: 18-92) reported on frequency and clarity of possible selves, as well as general self-clarity (Campbell et al., 1996). Results indicate curvilinear moderation by age of the link between possible self-clarity and well-being, with the association being stronger among midlife adults than among younger adults and older adults. …”
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“…Each interruption was associated with a 1-point decrease in patient reported quality of sleep, as assessed by the Richards Campbell Sleep Questionnaire. Our observations suggest a possible relationship between acoustic interruptions and worsened perceived sleep.…”
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“…Measurements included the CTLS, GTLS, International Personality Item Pool, Personal Need for Structure Scale, and Campbell Index of Well-Being. RESULTS: The revised CTLS contained four items and retained a single-dimensional structure. …”
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