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We obtain similar results for uniformly regular families of commuting operators on a Banach space.
A new non-singular, analytical theory with respect to the Earth's zonal harmonic terms J2, J3, J4 has been developed for short-periodic motion, by analytically integrating the uniformly regular K-S canonical equations.
Case (i): A uniformly regular.
Let ({S_{h}}) be a uniformly regular family of triangulation of Ω̄ with diameters bounded by h (see [14]).
We divide the domain Ω̄ into small triangular elements, which leads to a uniformly regular triangulation (S_{h}) with (hle 0.05).
A is uniformly regular, ({mathcal {F}}) satisfies F2 and F5, with (b=infty ), and (B -pcdot D_pBle o(|p|^2)) in (1.22); ({mathcal {F}}) is orthogonally invariant satisfying F7, (A = o(|p|^2)) in (1.22) and (beta = nu ).
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Finally, the magnetostatic self-energy of a uniformly magnetized regular polygonal disk of arbitrary order is analyzed.
Now, we recall the concept of uniformly asymptotically regular semigroup.
Also is uniformly asymptotically regular, we have from (2.8) (2.8).
Since T is uniformly asymptotically regular and from (3.24), we obtain that (3.25).
Since S is uniformly asymptotically regular and (3.33), we obtain that (3.34).
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