3,488 research outputs found
The role of Information Technology in Education
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
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
The transition from integrable to non-integrable highly-dispersive nonlinear
models is investigated. The sine-Gordon and -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
-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
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
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
The transverse distribution of gluon and quark-antiquark pairs produced from
a strong constant chromo-electric field depends on two gauge invariant
quantities, and , 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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