961 research outputs found

    Boson Stars as Solitary Waves

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    We study the nonlinear equation i∂tψ=(−Δ+m2−m)ψ−(∣x∣−1∗∣ψ∣2)ψon R3i \partial_t \psi = (\sqrt{-\Delta + m^2} - m)\psi - ( |x|^{-1} \ast |\psi|^2 ) \psi \quad {\rm on}\,\mathbb{R}^3 which is known to describe the dynamics of pseudo-relativistic boson stars in the mean-field limit. For positive mass parameters, m > 0, we prove existence of travelling solitary waves, ψ(t,x)=eitμφv(x−vt)\psi(t,x) = e^{{i}{t}\mu} \varphi_{v}(x - vt) , for some μ∈R\mu \in {\mathbb{R}} and with speed |v| < 1, where c=1 corresponds to the speed of light in our units. Due to the lack of Lorentz covariance, such travelling solitary waves cannot be obtained by applying a Lorentz boost to a solitary wave at rest (with v = 0). To overcome this difficulty, we introduce and study an appropriate variational problem that yields the functions φv∈H1/2(R3)\varphi_v \in {\bf H}^{1/2}({\mathbb{R}}^3) as minimizers, which we call boosted ground states. Our existence proof makes extensive use of concentration-compactness-type arguments. In addition to their existence, we prove orbital stability of travelling solitary waves ψ(t,x)=eitμφv(x−vt)\psi(t, x) = e^{{i}{t}\mu}\varphi_v(x - vt) and pointwise exponential decay of φv(x)\varphi_v(x) in

    Modelling the geographical distribution of soil-transmitted helminth infections in Bolivia

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    The prevalence of infection with the three common soil-transmitted helminths (i.e. Ascaris lumbricoides, Trichuris trichiura, and hookworm) in Bolivia is among the highest in Latin America. However, the spatial distribution and burden of soil-transmitted helminthiasis are poorly documented.; We analysed historical survey data using Bayesian geostatistical models to identify determinants of the distribution of soil-transmitted helminth infections, predict the geographical distribution of infection risk, and assess treatment needs and costs in the frame of preventive chemotherapy. Rigorous geostatistical variable selection identified the most important predictors of A. lumbricoides, T. trichiura, and hookworm transmission.; Results show that precipitation during the wettest quarter above 400 mm favours the distribution of A. lumbricoides. Altitude has a negative effect on T. trichiura. Hookworm is sensitive to temperature during the coldest month. We estimate that 38.0%, 19.3%, and 11.4% of the Bolivian population is infected with A. lumbricoides, T. trichiura, and hookworm, respectively. Assuming independence of the three infections, 48.4% of the population is infected with any soil-transmitted helminth. Empirical-based estimates, according to treatment recommendations by the World Health Organization, suggest a total of 2.9 million annualised treatments for the control of soil-transmitted helminthiasis in Bolivia.; We provide estimates of soil-transmitted helminth infections in Bolivia based on high-resolution spatial prediction and an innovative variable selection approach. However, the scarcity of the data suggests that a national survey is required for more accurate mapping that will govern spatial targeting of soil-transmitted helminthiasis control

    Some Applications of the Lee-Yang Theorem

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    For lattice systems of statistical mechanics satisfying a Lee-Yang property (i.e., for which the Lee-Yang circle theorem holds), we present a simple proof of analyticity of (connected) correlations as functions of an external magnetic field h, for Re h > 0 or Re h < 0. A survey of models known to have the Lee-Yang property is given. We conclude by describing various applications of the aforementioned analyticity in h.Comment: 16 page

    Sequential intravenous-oral amoxycillin/clavulanate (Augmentin) therapy in paediatric hospital practice

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    The efficacy and safety of intravenous and sequential intravenous-oral clavulanate-potentiated amoxycillin therapy was evaluated in 71 hospitalized paediatric patients, one month to 16 years of age. The infections treated included peritonsillar abscess (2 patients), purulent tracheitis (1), acute epiglottitis (24), pneumonia (31), pansinusitis (4), mastoiditis (1), cellulitis (4), lymphadenitis (2) and pyelonephritis (2). The severity of disease was rated as moderate in 31 patients (44%), and as severe in 40 (56%). Bacterial pathogens could be cultured in 26 cases (37%). The response to therapy was prompt and followed by clinical cure in each patient. Adverse drug effects included phlebitis (in 6%), mild gastrointestinal complaints (6%), rash (4%) and transient neutropenia and elevation of transaminases (one case each). It is concluded that amoxycillin/clavulanate is effective and safe treatment for bacterial infections of the respiratory tract, urinary tract, skin or soft tissues in childre

    Long Time Motion of NLS Solitary Waves in a Confining Potential

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    Abstract.: We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schrödinger equations with a confining, slowly varying external potential, V(x). A Lyapunov-Schmidt decomposition of the solution combined with energy estimates allows us to control the motion of the solitary wave over a long, but finite, time interval. We show that the center of mass of the solitary wave follows a trajectory close to that of a Newtonian point particle in the external potential V(x) over a long time interval. Communicated by Rafael D. Benguri

    Maximal sublattices and Frattini sublattices of bounded lattices

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    We investigate the number and size of the maximal sublattices of a finite lattice. For any positive integer k, there is a finite lattice L with more that ]L]k sublattices. On the other hand, there are arbitrary large finite lattices which contain a maximal sublattice with only 14 elements. It is shown that every bounded lattice is isomorphic to the Frattini sublattice (the intersection of all maximal sublattices) of a finite bounded lattic

    Design of an N^7-Glycosylated Purine Nucleoside for Recognition of GC Base Pairs by Triple Helix Formation

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    Pyrimidine oligodeoxyribonucleotides bind in the major groove of DNA parallel to the purine Watson-Crick strand by formation of specific hydrogen bonds between thymine and adenine (T•AT triplet) and protonated cytosine and guanine (C+GC triplet) on the Hoogsteen face of the purine base. Alternatively, purine oligodeoxyribonucleotides bind in an antiparallel orientation relative to the purine Watson-Crick strand by formation of G•GC and A•AT triplets. The prerequisite protonation of cytosine in C+GC triplets leads to a considerable pH dependence in the binding affinity of C-containing oligodeoxyribonucleotides (Figure 1). Substitution of 5-methylcytosine (^mC) for cytosine results in increased binding affinities near physiological pH. In an attempt to eliminate the necessity for protonation, recent efforts have been directed toward the synthesis of nonnatural nucleosides which display the hydrogen bonding functionality of protonated cytosine

    Cocaine/Levamisole-Induced, Skin-Limited ANCA-Associated Vasculitis with Pyoderma Gangrenosum-like Presentation

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    The use of levamisole as the most frequent adulterant of cocaine has merged in previously unknown toxicities, notably a disease entity called cocaine/levamisole-associated autoimmune syndrome (CLAAS). Clinically, CLAAS can manifest with diverse cutaneous and extracutaneous features sharing common laboratory findings (neutropenia, autoantibody patterns). We report the case of a cocaine-abusing female patient with relapsing episodes of painful ulcers, worsening and expanding over a three-year period. The case exhibited all features of a drug-induced, skin-limited, ANCA-associated vasculitis, evolving over time to PG-like findings. In both disease stages, the patient responded well to the cessation of cocaine exposure and systemic glucocorticosteroids. This case demonstrates the continuous nature of cutaneous CLAAS manifestations in a single patient. CLAAS has become a major public health issue in the at-risk group of cocaine users, and clinicians should be alert of this condition when treating cocaine users presenting with single or multiple skin ulcerations
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