Sentence examples for establishing regularity from inspiring English sources

These so called distance estimates have wide-spread application in state constrained optimal control, including justifying the use of the Maximum Principle in normal form and establishing regularity properties of value functions.

Establishing regularities of the phase layer formation processes in multicomponent systems on a nano- and sub-nanoscale will enable the development of novel surface engineering techniques for obtaining functional coatings with desired functional properties.

Based on the established regularity, an algorithm for the process duration control is proposed.

The flexibility of these classes allows us to also establish regularity of solutions to rather general nonlinear integral equations.

When this repetition is omitted, the thematic balance of the movement is upset and the dramatic effect of the development's sudden departure from an established regularity can be ruined.

We also establish regularity and positivity of the groundstates and prove that all positive groundstates are radially symmetric and monotone decaying about some point.

The aim of this paper is to establish regularity for weak solutions to the nondiagonal quasilinear degenerate elliptic systems related to Hörmander's vector fields, where the coefficients are bounded with vanishing mean oscillation.

Dong and Chen [15] established regularity criteria of weak solutions to the three-dimensional micropolar fluid equations.

Later, in [3] Zhou and Fan studied the Cauchy problem of certain Boussinesq-α equations in n dimensions with n = 2 or 3. We establish regularity for the solution under ∇ u ∈ L 1 ( 0, T ; Ḃ ∞, ∞ 0 ).

The established regularity of diffusion acceleration of substitution atoms under multiple γ-α-γ martensitic transformations can be used to intensify treatment modes of chemical and thermal treatment, in particular for surface saturation of iron alloys with metals.

Even in countries with formalised or long established BS, there is often no established regularity in the timing of BS in the different populations, possibly indicating instability of the system.