By using the constraint condition of (MDII) and F(x, u; 0) = 0, inequality (111) implies
Suppose that there exist [mathematical expression not reproducible] is feasible for (MDII).
Suppose that ([bar.x], [bar.[lambda]], [bar.[mu]], [bar.t]) is not a weakly efficient solution of (MDII); then there exists another feasible solution (x, [lambda], [mu], t) of (MDII) such that
Hence ([bar.x], [bar.[lambda]], [bar.[mu]], [bar.t]) is a weakly efficient solution of (MDII).
Let [bar.x] and ([bar.x], [bar.[lambda]], [bar.[mu]], [bar.t]) be feasible solutions for (MP) and (MDII), respectively.
By using the constraint condition of (MDII) and F([bar.x], [bar.u]; 0) = 0, we obtain
The reaction mixture (200 [micro]l of final volume) for the measurement of MDII activity contained 1 [micro]M [sup.[125I]]r[T.sub.3], 2 nM r[T.sub.3], 10 [micro]l skin homogenate (approximately 1-100 [micro]g protein), 5 mM DTT, and 1 mM PTU.
Because the data exhibited a skewed distribution, the data of MDII, MDIII and MDIII/MDII were [log.sub.10] transformed before analysis.
The mean level of MDII activity was higher in the M compared with C group (p<0.05) in July and August, but there was no significant difference during other months.
Previous report indicated that the MDI activity was not detected in the goats skin but both MDII and MDIII activity could be detected (Villar et al., 2000b).
Implanted melatonin showed the differences in MDII activity and ratio of MDIII/MDII between M and C only in July and August, but no differences after September.
This study indicates that the skin MD activity showed a seasonal variation in Chinese Inner Mongolia cashmere goats, with the MDII activity increasing and the MDIII and MDIII/MDII ratio decreasing from June (the summer solstice) to November.