3,488 research outputs found

    The role of Information Technology in Education

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    Education and study are vital processes in everyday life. From the first birthday to the last day a person learns every day. We are taught by our parents, people around us, nature, and circumstances. Education gives us certain knowledge and information necessary for our development. This is very important for each of us, and it should be accessible so that as few people in the world as possible are illiterate

    Application of functional analysis to perturbation theory of differential equations

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    The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point

    Internal Modes of Solitons and Near-Integrable Highly-Dispersive Nonlinear Systems

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    The transition from integrable to non-integrable highly-dispersive nonlinear models is investigated. The sine-Gordon and ϕ4\phi^4-equations with the additional fourth-order spatial and spatio-temporal derivatives, describing the higher dispersion, and with the terms originated from nonlinear interactions are studied. The exact static and moving topological kinks and soliton-complex solutions are obtained for a special choice of the equation parameters in the dispersive systems. The problem of spectra of linear excitations of the static kinks is solved completely for the case of the regularized equations with the spatio-temporal derivatives. The frequencies of the internal modes of the kink oscillations are found explicitly for the regularized sine-Gordon and ϕ4\phi^4-equations. The appearance of the first internal soliton mode is believed to be a criterion of the transition between integrable and non-integrable equations and it is considered as the sufficient condition for the non-trivial (inelastic) interactions of solitons in the systems.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

    Soliton complexity in the damped-driven nonlinear Schr\"odinger equation: stationary, periodic, quasiperiodic complexes

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    Stationary and oscillatory bound states, or complexes, of the damped-driven solitons are numerically path-followed in the parameter space. We compile a chart of the two-soliton attractors, complementing the one-soliton attractor chart.Comment: 12 pages, 7 figure

    How to improve computer performance

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    Nowadays a large number of people use computers for different purposes such as games, work, listening to music, watching videos, making presentations etc. However, while operating a computer, most users often have to cope with the low performance of their machines. And as some people do not know how to optimize the computers, they buy a new one, even more expensive, thinking that it will solve the problem. In this case basic knowledge of computer optimization can save both time and money

    Casimir dependence of transverse distribution of pairs produced from a strong constant chromo-electric background field

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    The transverse distribution of gluon and quark-antiquark pairs produced from a strong constant chromo-electric field depends on two gauge invariant quantities, C1=EaEaC_1=E^aE^a and C2=[dabcEaEbEc]2C_2=[d_{abc}E^aE^bE^c]^2, as shown earlier in [G.C. Nayak and P. van Nieuwenhuizen, Phys. Rev. D 71, 125001 (2005)] for gluons and in [G.C. Nayak, Phys. Rev. D 72, 125010 (2005)] for quarks. Here, we discuss the explicit dependence of the distribution on the second Casimir invariant, C_2, and show the dependence is at most a 15% effect.Comment: 5 fig
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