In this section, we first generalize
the notion of the generalized (ph, , p, th, m)-invexities, and then recall some important auxiliary results for the problem (P) on hand.
The purpose of survey design is to generalize
research finding to larger groups of a population based on a studying a subset of the target population.
This suggests an alternative criterion by which to judge changes in student performance--namely, that achievement gains on test items that measure particular skills or understandings may be meaningful even if the student's overall test score does not fully generalize
to other exams.
However, research suggests that when skills are taught in one setting, they do not necessarily generalize
to other settings, especially when those other settings are substantially different from the one in which the training took place (Stokes & Baer, 1977).
the concept from individual examples in order to discuss its structures and light propagation properties.
In this paper, we generalize
some of the results in  which carry over when nilpotent groups are replaced by solvable groups.
Even if the outcomes of the treatment and control groups differ significantly, we cannot be sure that the results will generalize
to other locations and to other grades.