Examples of perturbative

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In order to ensure there are no further periodic points we introduce a second perturbative term.
All other symmetric and perturbative states will continue to be represented by (2.6) and (2.7) with no source term.
Nevertheless, both cases have the passage to a perturbative situation as a common starting point.
There can be problems with a perturbative treatment even for magnetic configurations that are only slightly asymmetric.
The results to be given are of perturbative type.
The broken lines denote (a) the standard perturbative solution and (b) the approximate solution described by (2.18) and (2.19).
The analysis of previous solutions is complicated by perturbative solutions that may include moving ions, but our analysis does not include moving ions.
Perhaps the answer is a non-trivial question of formalism: the '+' (the + sign) found in perturbative expansions certainly represents more than the simple addition of numbers.
In this case the solution can be found analytically and the expression for absorbed energy coincides with the one obtained using quantum mechanics with a first order perturbative approximation.
More recently, quantum field theory, which is the theory of elementary particles, is mostly perturbative, and certainly its most spectacular successes are down to perturbation theory.
Iterates of the -perturbative operators, restricted to suitable finite-dimensional subspaces of generalized functions, give rise to finite-dimensional matrices, whose traces approximate the flat traces of these iterates.
For small perturbative forces acting over short timescales, these interactions act in a way similar to that of permanent junction points and confer elastic properties on the biofilm.
Since the main quantity in the problem of plasma radiation is the dipolar autocorrelation function of the radiator, we derive it using the path integral technique in its perturbative form.
We should, however, bear in mind that no matter whether perturbative results have been positive or negative, they have always been a great source of progress.

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