1,457 research outputs found

    Instability of steady states for nonlinear wave and heat equations

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    We consider time-independent solutions of hyperbolic equations such as \d_{tt}u -\Delta u= f(x,u) where ff is convex in uu. We prove that linear instability with a positive eigenfunction implies nonlinear instability. In some cases the instability occurs as a blow up in finite time. We prove the same result for parabolic equations such as \d_t u -\Delta u= f(x,u). Then we treat several examples under very sharp conditions, including equations with potential terms and equations with supercritical nonlinearities

    The Fictions of Surrealism

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    Surrealism is an attitude toward life, even more than a literary and artistic movement. It aspired to no less than the remaking of man and the world by reintroducing everyday magic and a new idealization of the Female. In many respects, its goal was spiritual renewal. This enterprise was most prominently successful in the domain of poetry and painting. The major spokesman for the movement, Andre Breton, disliked the novel. Nevertheless, the members of the movement and their associates made numerous ventures into prose fiction, with notable results. Four types of fiction are delineated: the neo-Gothic romance; the adventure diary of magic experience—this one being probably the most typical of all the kinds of narrative invented; the erotic (or pornographic) récit, and the linguistic extravaganza, in which language becomes the major instrument of sorcery. In many ways, the Surrealist experiment could be characterized as an attempt at the liberation of languages. This observation raises a number of questions about the impact of Surrealism on subsequent developments in French fiction (and the theatre), as well as upon its impact on Western fiction in general. The conclusion drawn is that Surrealist fiction has been a major contribution, a pioneering effort, in the shaking up of narrative concepts and techniques in the second half of the twentieth century

    Existence of Rotating Magnetic Stars

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    We consider a star as a compressible fluid subject to gravitational and magnetic forces. This leads to an Euler-Poisson system coupled to a magnetic field, which may be regarded as an MHD model together with gravity. The star executes steadily rotating motion about a fixed axis. We prove, for the first time, the existence of such stars provided that the rotation speed and the magnetic field are sufficiently small

    Gemini Near-infrared Spectroscopy of Luminous z~6 Quasars: Chemical Abundances, Black Hole Masses, and MgII Absorption

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    We present Gemini near-infrared spectroscopic observations of six luminous quasars at z=5.8∼\sim6.3. Five of them were observed using Gemini-South/GNIRS, which provides a simultaneous wavelength coverage of 0.9--2.5 μ\mum in cross dispersion mode. The other source was observed in K band with Gemini-North/NIRI. We calculate line strengths for all detected emission lines and use their ratios to estimate gas metallicity in the broad-line regions of the quasars. The metallicity is found to be supersolar with a typical value of ∼\sim4 Z_{\sun}, and a comparison with low-redshift observations shows no strong evolution in metallicity up to z∼\sim6. The FeII/MgII ratio of the quasars is 4.9+/-1.4, consistent with low-redshift measurements. We estimate central BH masses of 10^9 to 10^{10} M_{\sun} and Eddington luminosity ratios of order unity. We identify two MgII λλ\lambda\lambda2796,2803 absorbers with rest equivalent width W_0^{\lambda2796}>1 \AA at 2.2<z<3 and three MgII absorbers with W_0^{\lambda2796}>1.5 \AA at z>3 in the spectra, with the two most distant absorbers at z=4.8668 and 4.8823, respectively. The redshift number densities (dN/dz) of MgII absorbers with W_0^{\lambda2796}>1.5 \AA are consistent with no cosmic evolution up to z>4.Comment: 33 pages (including 7 figures and 6 tables), AJ in pres

    Global bifurcation theory for periodic traveling interfacial gravity-capillary waves

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    We consider the global bifurcation problem for spatially periodic traveling waves for two-dimensional gravity-capillary vortex sheets. The two fluids have arbitrary constant, non-negative densities (not both zero), the gravity parameter can be positive, negative, or zero, and the surface tension parameter is positive. Thus, included in the parameter set are the cases of pure capillary water waves and gravity-capillary water waves. Our choice of coordinates allows for the possibility that the fluid interface is not a graph over the horizontal. We use a technical reformulation which converts the traveling wave equations into a system of the form "identity plus compact." Rabinowitz' global bifurcation theorem is applied and the final conclusion is the existence of either a closed loop of solutions, or an unbounded set of nontrivial traveling wave solutions which contains waves which may move arbitrarily fast, become arbitrarily long, form singularities in the vorticity or curvature, or whose interfaces self-intersect.Comment: Corrected a typ
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