Based on careful analysis of the regularity of surface subsidence in mined-out area, we proposed a new time function based on Harris curve model in consideration of the shortage of current surface subsidence time functions.
This section is devoted to an analysis of the regularity of refinable functions (phi^{m,l,alpha}_{0}) with the mask (tau^{m,l,alpha}_{0} omega)) defined by (2).
In this section we will turn to the analysis of a lot i and in particular to the analysis of the regularity properties of function ( {T}_ileft({overline{mathbf{t}}}_{I-i}right)= inf left{kern0.5em tle {t}_{max }:;{widehat{Q}}_ileft tleft|;{overline{mathbf{t}}}_{I-i}right.right ge {k}_iright} ) in order to derive those of function T I. Lot i has potentially neighbouring lots j < i and/or k > i.
The main difficulty in proving (C^{1,1}) regularity is the analysis of points where the gradient of the function vanishes.
It is worthwhile pointing out that, without consideration of the dividend policy, Han et al. in [10] deduced that (partial _{x} ugeq0), which plays an important role in the analysis of the regularities of the free boundary.
Based on the analysis of the regularities of the Ag nanostructures growth and corresponding kinetics of SERS-signal intensity change, we revealed a parameter crucial for the formation of the SERS-active substrates, which can be defined as a product of the Ag salt concentration by the immersion deposition time.
Based on the performed analysis of the regularities of the Ag nanostructures growth via the Volmer Weber mechanism and the SERS-signal intensity dependence on the Ag immersion time, we have proposed a universal parameter crucial for the choice of the optimal formation conditions of SERS-active substrates.
The multi-level preconditioner is designed from an analysis of the gradient regularity loss.
It can be supposed that some potential regularity might be discovered by integrated analysis of the global literatures on the two diseases, in both English and Chinese.
Weyl's mathematical analysis of the foundations of quantum mechanics showed that regularities in a physical theory are most fruitfully understood in terms of symmetry groups.
