infinitesimal generator


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infinitesimal generator

[¦in‚fin·ə¦tes·ə·məl ′jen·ə‚rād·ər]
(mathematics)
A closed linear operator defined relative to some semigroup of operators and which uniquely determines that semigroup.
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sigma]]) is really the infinitesimal generator of the composition [PHI]([[PSI].
tau]] is called the exponential map, corresponding to the vector field F; the vector field F is called the infinitesimal generator of [[PHI].
Because the vector field [XI] is the infinitesimal generator of the flow [[PSI].
II) find the system of determining equations used to obtain the variable coefficients present in the infinitesimal generators of the symmetry groups;
V) map the unique solution by using the exponential of a linear combination of the infinitesimal generators obtained;
This is because it is necessary to calculate prolongation (4) of Second degree of the infinitesimal generators of the symmetry group and []tell apply the criterion of infinitesimal variation [15][16].
In case there arc odes available for the manipulation of the exponential or the infinitesimal generators obtained, the number or resulting operations is rather reduced--often being of the same order as the number of infinitesimal generators (5).
His topics include semigroups and infinitesimal generators, analytic subgroups, weak formulations for second-order systems, inverse or parameter estimation problems, and families of approximate control problems.