For UMDA, three methods, i.e., the first order interval Taylor expansion method, the interval vertex theorem, the direct optimization approach are formulated.
Increasing moisture following these arid intervals allowed expansion, creation and maintenance of a more diverse landscape vegetation mosaic around Lake Malawi including Zambezian miombo woodland, humid evergreen woodland and afromontane forests.
After several rounds of chemotherapy (b) the endoluminal metastatic renal cell carcinoma is now seen (arrowhead) and is no longer obstructive with interval re-expansion of the left lung.
The 95% confidence intervals on expansion parameter τ suggest the onset of expansions has overlapped the LGM in most population groups and regions analyzed, and lower 95% confidence intervals extending into the present may be indications that expansion is on-going or ceased only recently, e.g. in north Florida (Table 3; Figure 5).
Reliability sensitivities provide useful information to increase the safety level and can be also exploited in the context of first-order interval Taylor series expansion to estimate the bounds of interval reliability when slight uncertainties are involved.
Then, based on the perturbation principle and the Taylor extension approach, a new interval perturbation series expansion method (PSEM) to predict boundary rules of the fatigue crack length a(t) is derived.
Thus, zygotic γCOP function is required before and during the diameter expansion interval.
The tracheal tubes on the other hand, elongate continuously and the programmed boost of secretory activity precedes the short interval of diametric expansion.
We use photogrammetry for both analyzing frequencies ("Measurements of pulsation intervals" section) and expansion rates ("Measurements of pulse evolution" section) of pulses as they are released from the vent and also for deriving eruption source parameters of individual pulses ("Pulse volume at transitional level methodology and results" and "Pulse velocity-derived model" sections).
