29 research outputs found

    Long Range Scattering and Modified Wave Operators for some Hartree Type Equations

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    We study the theory of scattering for a class of Hartree type equations with long range interactions in space dimension n > 2, including Hartree equations with potential V(x) = lambda |x|^{- gamma} with gamma < 1. For 1/2 < gamma < 1 we prove the existence of modified wave operators with no size restriction on the data and we determine the asymptotic behaviour in time of solutions in the range of the wave operators.Comment: TeX, 89 pages, available http://qcd.th.u-psud.f

    Uniqueness and Nondegeneracy of Ground States for (Δ)sQ+QQα+1=0(-\Delta)^s Q + Q - Q^{\alpha+1} = 0 in R\mathbb{R}

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    We prove uniqueness of ground state solutions Q=Q(x)0Q = Q(|x|) \geq 0 for the nonlinear equation (Δ)sQ+QQα+1=0(-\Delta)^s Q + Q - Q^{\alpha+1}= 0 in R\mathbb{R}, where 0<s<10 < s < 1 and 0<α<4s12s0 < \alpha < \frac{4s}{1-2s} for s<1/2s < 1/2 and 0<α<0 < \alpha < \infty for s1/2s \geq 1/2. Here (Δ)s(-\Delta)^s denotes the fractional Laplacian in one dimension. In particular, we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for s=1/2s=1/2 and α=1\alpha=1 in [Acta Math., \textbf{167} (1991), 107--126]. As a technical key result in this paper, we show that the associated linearized operator L+=(Δ)s+1(α+1)QαL_+ = (-\Delta)^s + 1 - (\alpha+1) Q^\alpha is nondegenerate; i.\,e., its kernel satisfies kerL+=span{Q}\mathrm{ker}\, L_+ = \mathrm{span}\, \{Q'\}. This result about L+L_+ proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for nonlinear dispersive PDEs with fractional Laplacians, such as the generalized Benjamin-Ono (BO) and Benjamin-Bona-Mahony (BBM) water wave equations.Comment: 45 page

    Uniqueness Properties of Solutions to the Benjamin-Ono equation and related models

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    We prove that if u1, u2 are solutions of the Benjamin- Ono equation defined in (x, t) ∈ R × [0, T ] which agree in an open set Ω ⊂ R × [0,T], then u1 ≡ u2. We extend this uniqueness result to a general class of equations of Benjamin-Ono type in both the initial value problem and the initial periodic boundary value problem. This class of 1-dimensional non-local models includes the intermediate long wave equation. Finally, we present a slightly stronger version of our uniqueness results for the Benjamin-Ono equation

    Group B Streptococcus GAPDH Is Released upon Cell Lysis, Associates with Bacterial Surface, and Induces Apoptosis in Murine Macrophages

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    Glyceraldehyde 3-phosphate dehydrogenases (GAPDH) are cytoplasmic glycolytic enzymes that, despite lacking identifiable secretion signals, have been detected at the surface of several prokaryotic and eukaryotic organisms where they exhibit non-glycolytic functions including adhesion to host components. Group B Streptococcus (GBS) is a human commensal bacterium that has the capacity to cause life-threatening meningitis and septicemia in newborns. Electron microscopy and fluorescence-activated cell sorter (FACS) analysis demonstrated the surface localization of GAPDH in GBS. By addressing the question of GAPDH export to the cell surface of GBS strain NEM316 and isogenic mutant derivatives of our collection, we found that impaired GAPDH presence in the surface and supernatant of GBS was associated with a lower level of bacterial lysis. We also found that following GBS lysis, GAPDH can associate to the surface of many living bacteria. Finally, we provide evidence for a novel function of the secreted GAPDH as an inducer of apoptosis of murine macrophages

    Convergence Rates of a Fully Discrete Galerkin Scheme for the Benjamin–Ono Equation

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    We consider a recently proposed fully discrete Galerkin scheme for the Benjamin–Ono equation which has been found to be locally convergent in finite time for initial data in L 2 (R). By assuming that the initial data is sufficiently regular we obtain theoretical convergence rates for the scheme both in the full line and periodic versions of the associated initial value problem. These rates are illustrated with some numerical examples.submittedVersionThis is a pre-print of an article published in [Theory, Numerics and Applications of Hyperbolic Problems I]. The final authenticated version is available online at: https://doi.org/10.1007/978-3-319-91545-6_4

    Structural and morphological characterizations of pure and Ce-doped ZnO nanorods hydrothermally synthesized with different caustic bases

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    This investigation concerns the synthesis as well as structural and morphological characterizations of pure and Ce-doped ZnO nanorods. The samples were synthesized by simple low-temperature hydrothermal process using respectively NaOH and KOH as caustic bases. The as-synthesized nanorods were characterized in terms of their morphological, structural, compositional and vibrational properties. The sizes of the rods were found to be 1.5 μm to 2 μm in length and 250 nm to 300 nm in diameter. The presence of Ce ions in ZnO (NaOH) favored the agglomeration of the rods to form flower-like nanostructures. EDAX measurements showed Zn rich materials with high oxygen vacancy concentration. XRD results indicated that the synthesized ZnO nanorods possess a pure wurtzite structure with good crystallinity. It has also been found that Ce doping deteriorates the crystalline quality of ZnO (NaOH) and improves that of ZnO (KOH). The insignificant intensities observed in FT-IR signals confirm that the synthesized nanorods are of high purity. The Raman spectroscopy studies showed that Ce ions shift the vibrational modes towards lower frequencies. The peaks related to E2 (high) mode in ZnO (KOH) are relatively intense compared to those of ZnO (NaOH). The peaks are found to be shifted and asymmetrically broadened due to anharmonic effects originating from quantum-phonon-effect confinement

    Convergence Rates of a Fully Discrete Galerkin Scheme for the Benjamin–Ono Equation

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    We consider a recently proposed fully discrete Galerkin scheme for the Benjamin–Ono equation which has been found to be locally convergent in finite time for initial data in L 2 (R). By assuming that the initial data is sufficiently regular we obtain theoretical convergence rates for the scheme both in the full line and periodic versions of the associated initial value problem. These rates are illustrated with some numerical examples

    Investigation of the milling route for the development of colloidal suspensions to be used as binder in refractory castables

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    Refractories castables bonded with CAC (calcium aluminate cement) have a limitation when they are used at high temperature in micro-silica containing system and/or in acidic corrosive environments. The CAC binder reacts with the micro-silica and/or acidic components to form liquid/viscous compounds deteriorating the refractory material.Refractory castables bonded with HA (hydratable alumina) perform better in these environments. However, the drying step of such materials needs time and energy for the water evacuation to avoid the lining cracking.The use of CS (colloidal silica) as binder seems to hinder the drawback of CAC and HA binders. However, the presence of free amorphous silica in the castable composition limits their uses in basic environments by forming liquid/viscous phases at high temperature with a reduction of castable refractoriness.In this context, new colloidal bonding systems that could improve the high performances of refractory castables such as boehmite and spinel colloidal suspensions, were developed
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