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Replica Oakleys,37 CAD,are closely related with the beam’s

Replica Oakleys,37 CAD,are closely related with the beam’s

Analytical formulas for the average intensity and decentered parameter of a decentered elliptical Gaussian beam (DEGB) propagating in a turbulent Replica Oakleys atmosphere are derived in a tensor form. The propagation properties of a DEGB in a turbulent atmosphere are investigated in detail, and found to be different from that in Fake Oakley Jawbone free space. Furthermore, as an application example, we investigate the propagation of a decentered elliptical flat-topped beam (DEFB) by expressing its electric field as a finite sum of DEGBs in a turbulent atmosphere. The properties of a DEGB or a DEFB in a turbulent atmosphere are closely related with the beam’s parameters and the structure constant of the turbulent atmosphere. In recent years, in trying to generalize the normality of subgroups, (semi-)(pp-)cover-avoiding subgroups were defined. Some valuable results on the structure of a finite group were set up, provided that its subgroups have the cover-avoiding property, semi-cover-avoiding property or semi-pp-cover-avoiding property. Since whether a subgroup covers or avoids in a group is connected to the chief series of the group, the results look interesting. Here the authors discuss the connection between the structure of a finite group and its (semi-)(pp-)cover-avoiding maximal or minimal subgroups, and obtain some sufficient conditions for a group being pp-nilpotent or supersolvable.
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