700 research outputs found

    A quadratic stability result for singular switched systems with application to anti-windup control

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    In this note we consider the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices are of the form A, A−ghT , and where one of the matrices is singular. We then apply this result in a study of a feedback system with a saturating actuator

    Renorm-group, Causality and Non-power Perturbation Expansion in QFT

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    The structure of the QFT expansion is studied in the framework of a new "Invariant analytic" version of the perturbative QCD. Here, an invariant (running) coupling a(Q2/Λ2)=β1αs(Q2)/4πa(Q^2/\Lambda^2)=\beta_1\alpha_s(Q^2)/4\pi is transformed into a "Q2Q^2--analytized" invariant coupling aan(Q2/Λ2)A(x)a_{\rm an}(Q^2/\Lambda^2) \equiv {\cal A}(x) which, by constuction, is free of ghost singularities due to incorporating some nonperturbative structures. Meanwhile, the "analytized" perturbation expansion for an observable FF, in contrast with the usual case, may contain specific functions An(x)=[an(x)]an{\cal A}_n(x)= [a^n(x)]_{\rm an}, the "n-th power of a(x)a(x) analytized as a whole", instead of (A(x))n({\cal A}(x))^n. In other words, the pertubation series for F(x)F(x), due to analyticity imperative, may change its form turning into an {\it asymptotic expansion \`a la Erd\'elyi over a nonpower set} {An(x)}\{{\cal A}_n(x)\}. We analyse sets of functions {An(x)}\{{\cal A}_n(x)\} and discuss properties of non-power expansion arising with their relations to feeble loop and scheme dependence of observables. The issue of ambiguity of the invariant analytization procedure and of possible inconsistency of some of its versions with the RG structure is also discussed.Comment: 12 pages, LaTeX To appear in Teor. Mat. Fizika 119 (1999) No.

    Engagement with care, substance use, and adherence to therapy in HIV/AIDS

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    Engagement with care for those living with HIV is aimed at establishing a strong relationship between patients and their health care provider and is often associated with greater adherence to therapy and treatment (Flickinger, Saha, Moore, and Beach, 2013). Substance use behaviors are linked with lower rates of engagement with care and medication adherence (Horvath, Carrico, Simoni, Boyer, Amico, and Petroli, 2013). This study is a secondary data analysis using a cross-sectional design from a larger randomized controlled trial (n = 775) that investigated the efficacy of a self-care symptom management manual for participants living with HIV. Participants were recruited from countries of Africa and the US. This study provides evidence that substance use is linked with lower self-reported engagement with care and adherence to therapy. Data on substance use and engagement are presented. Clinical implications of the study address the importance of utilizing health care system and policy factors to improve engagement with care

    Stable, metastable and unstable states in the mean-field RFIM at T=0

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    We compute the probability of finding metastable states at a given field in the mean-field random field Ising model at T=0. Remarkably, this probability is finite in the thermodynamic limit, even on the so-called ``unstable'' branch of the magnetization curve. This implies that the branch is reachable when the magnetization is controlled instead of the magnetic field, in contrast with the situation in the pure system.Comment: 10 pages, 3 figure

    The Newtonian limit of spacetimes for accelerated particles and black holes

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    Solutions of vacuum Einstein's field equations describing uniformly accelerated particles or black holes belong to the class of boost-rotation symmetric spacetimes. They are the only explicit solutions known which represent moving finite objects. Their Newtonian limit is analyzed using the Ehlers frame theory. Generic spacetimes with axial and boost symmetries are first studied from the Newtonian perspective. The results are then illustrated by specific examples such as C-metric, Bonnor-Swaminarayan solutions, self-accelerating "dipole particles", and generalized boost-rotation symmetric solutions describing freely falling particles in an external field. In contrast to some previous discussions, our results are physically plausible in the sense that the Newtonian limit corresponds to the fields of classical point masses accelerated uniformly in classical mechanics. This corroborates the physical significance of the boost-rotation symmetric spacetimes

    Real world challenges in delivering person centred care: A community based case study

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    Community nurses face many challenges when trying to practice evidence-based, person-centred care. Ongoing concerns regarding the impact of the 2013 Francis Report (Ford and Lintern, 2017) suggest that individualised and holistic care is an impossible dream, one made harder when the client appears uncooperative. This paper presents a case study that sets out how some of these challenges were met in a potentially difficult situation experienced by a student nurse and her mentor in practice, in which the student was supported to further examine and explore issues that may have influenced the situation. In this instance, the solution came with the recognition that the client had expertise and knowledge that needed to be taken into account, alongside that of the nurses looking after him. His care became a partnership, not an imposition of expertise; a principle which is transferable to many other situations. Underpinning it was the recognition of our shared humanity, wherein lies the essence of truly holistic care, and student nurses learning this, through the guidance and support of their mentor.

    A novel series solution to the renormalization group equation in QCD

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    Recently, the QCD renormalization group (RG) equation at higher orders in MS-like renormalization schemes has been solved for the running coupling as a series expansion in powers of the exact 2-loop order coupling. In this work, we prove that the power series converges to all orders in perturbation theory. Solving the RG equation at higher orders, we determine the running coupling as an implicit function of the 2-loop order running coupling. Then we analyze the singularity structure of the higher order coupling in the complex 2-loop coupling plane. This enables us to calculate the radii of convergence of the series solutions at the 3- and 4-loop orders as a function of the number of quark flavours nfn_{\rm f}. In parallel, we discuss in some detail the singularity structure of the MSˉ{\bar{\rm MS}} coupling at the 3- and 4-loops in the complex momentum squared plane for 0nf16 0\leq n_{\rm f} \leq 16 . The correspondence between the singularity structure of the running coupling in the complex momentum squared plane and the convergence radius of the series solution is established. For sufficiently large nfn_{\rm f} values, we find that the series converges for all values of the momentum squared variable Q2=q2>0Q^2=-q^2>0. For lower values of nfn_{\rm f}, in the MSˉ{\bar{\rm MS}} scheme, we determine the minimal value of the momentum squared Qmin2Q_{\rm min}^2 above which the series converges. We study properties of the non-power series corresponding to the presented power series solution in the QCD Analytic Perturbation Theory approach of Shirkov and Solovtsov. The Euclidean and Minkowskian versions of the non-power series are found to be uniformly convergent over whole ranges of the corresponding momentum squared variables.Comment: 29 pages,LateX file, uses IOP LateX class file, 2 figures, 13 Tables. Formulas (4)-(7) and Table 1 were relegated to Appendix 1, some notations changed, 2 footnotes added. Clarifying discussion added at the end of Sect. 3, more references and acknowledgments added. Accepted for publication in Few-Body System
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