The regularity, Hopf principle, maximum principle as well as a Harnack inequality for (1.3) or for its extension equation (1.2) (in this case b = 1 ) were given.
Furthermore, the genotypic entities in this hierarchy are governed by various transformations and regularities (principles of inheritance), such as segregation, linkage, and mutation.
This is partly due to the fact that the regularities override each other: morphological regularities override semantic regularities, such as the natural gender principle,2 and semantic regularities override phonological regularities (see Wegener, 1995).
Moreover, such regularities can in principle be used to predict lifetimes of rank occupancy, thus increasing our ability to forecast stratification in the presence of competition.
A key element of our approach is that we turned requirements on the cross-level principles (regularity, IIA and consistency) into requirements for the analysis, not the biophysical process, thereby ensuring the universality of our result.
Results of existence, maximum principle and regularity of solutions are derived for these new variational inequalities.
By regularity and the maximum principle, we obtain that (vert tilde {u} vert, vert tilde{v}vert >0) in (mathbb{R}^{N}).
Systematic and satisfactory results on the weak solutions to the Cauchy problem to the fractional porous medium problem have been obtained, including the existence, uniqueness, comparison principle, and regularity to the suitable weak solutions.
Moreover, the addition of an irrelevant third option should not determine an increase of the absolute preference for any of the options in the set (principle of regularity, Tversky and Simonson 1993).
Griffin emphasizes the regularity provided by metaphysical principles.
Regularity results and comparison principles are the basis of the sub-supersolution method.
