14,530 research outputs found

    On Nonoscillation of Mixed Advanced-Delay Differential Equations with Positive and Negative Coefficients

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    For a mixed (advanced--delay) differential equation with variable delays and coefficients x˙(t)±a(t)x(g(t))∓b(t)x(h(t))=0,t≥t0 \dot{x}(t) \pm a(t)x(g(t)) \mp b(t)x(h(t)) = 0, t\geq t_0 where a(t)≥0,b(t)≥0,g(t)≤t,h(t)≥t a(t)\geq 0, b(t)\geq 0, g(t)\leq t, h(t)\geq t explicit nonoscillation conditions are obtained.Comment: 17 pages; 2 figures; to appear in Computers & Mathematics with Application

    A delay differential model of ENSO variability: Parametric instability and the distribution of extremes

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    We consider a delay differential equation (DDE) model for El-Nino Southern Oscillation (ENSO) variability. The model combines two key mechanisms that participate in ENSO dynamics: delayed negative feedback and seasonal forcing. We perform stability analyses of the model in the three-dimensional space of its physically relevant parameters. Our results illustrate the role of these three parameters: strength of seasonal forcing bb, atmosphere-ocean coupling κ\kappa, and propagation period τ\tau of oceanic waves across the Tropical Pacific. Two regimes of variability, stable and unstable, are separated by a sharp neutral curve in the (b,τ)(b,\tau) plane at constant κ\kappa. The detailed structure of the neutral curve becomes very irregular and possibly fractal, while individual trajectories within the unstable region become highly complex and possibly chaotic, as the atmosphere-ocean coupling κ\kappa increases. In the unstable regime, spontaneous transitions occur in the mean ``temperature'' ({\it i.e.}, thermocline depth), period, and extreme annual values, for purely periodic, seasonal forcing. The model reproduces the Devil's bleachers characterizing other ENSO models, such as nonlinear, coupled systems of partial differential equations; some of the features of this behavior have been documented in general circulation models, as well as in observations. We expect, therefore, similar behavior in much more detailed and realistic models, where it is harder to describe its causes as completely.Comment: 22 pages, 9 figure

    Gravitational Atom in Compactified Extra Dimensions

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    We consider quantum mechanical effects of the modified Newtonian potential in the presence of extra compactified dimensions. We develop a method to solve the resulting Schroedinger equation and determine the energy shifts caused by the Yukawa-type corrections of the potential. We comment on the possibility of detecting the modified gravitational bound state Energy spectrum by present day and future experiments.Comment: 12 pages, 2 figure

    Differential/Difference Equations

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    The study of oscillatory phenomena is an important part of the theory of differential equations. Oscillations naturally occur in virtually every area of applied science including, e.g., mechanics, electrical, radio engineering, and vibrotechnics. This Special Issue includes 19 high-quality papers with original research results in theoretical research, and recent progress in the study of applied problems in science and technology. This Special Issue brought together mathematicians with physicists, engineers, as well as other scientists. Topics covered in this issue: Oscillation theory; Differential/difference equations; Partial differential equations; Dynamical systems; Fractional calculus; Delays; Mathematical modeling and oscillations
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