Sentence examples for regular assumptions from inspiring English sources
Indeed, the regular assumptions made in Caristi's theorem imply that any chain (for ≺ α ) has a lower bound, which is stronger than having a minimal element.
One is our minimal regular assumptions which are concerned with elliptic obstacle problems (1.1) with partially BMO coefficients over the bounded nonsmooth domain.
It is noted that in this paper we only give the homogenization result of PDEs system with Markov chains when there exists the classical solution under sufficiently regular assumptions.
(1.3) As we know, it is very necessary that some structural and regular assumptions are imposed on the tensorial-valued operator (A x,u)) and the inhomogeneity (B x,u,Du)).
Here I show that, given regular assumptions on the primitives of the design problem, a weaker condition that includes the case of non-smooth valuations is sufficient and necessary for the uniqueness of Groves mechanisms among all efficient, dominant strategy mechanisms.
To this end, it is necessary to impose some suitable minimal regular assumptions on the coefficients (A x)) and geometric restriction on the boundary of the domain under the assumption that the given variable exponent (p(x)) has log-Hölder continuity.
If we assume the matrix A satisfies the following condition begin{aligned} D_z A x,z,p) ge c |p|^2I, end{aligned} (3.70)as (|p|rightarrow infty ), (xin Omega ), (|z|le M), (pin {mathbb {R}}^n) for any (M>0) and for some (c>0), we can dispense with the uniformly regular assumption on A in Theorem 1.3 and Theorem 3.1 and the proof is much simpler.
The frequent experimental observation of a semi-regular system of patches, centered on the site of a small injection of tracer, lead us to propose an intuitive model of projections onto a regular grid (assumption 2) that shifts smoothly across the cortical surface.
With the research he funds, Grove demands regular updates, challenges assumptions and asks for new experiments.
The findings from the models were compared under the regular normal distribution assumption for the residuals against Student's t-distribution.
Assuming that the property of being a square is the same as the property of being a regular diamond (an assumption defended by Peacocke in 1993, contested by Tye 2003, but granted by Tye 2004), this appears to be a case in which there is a phenomenal difference without any difference in the properties represented.
