Sentence examples for uniform regularity from inspiring English sources

A law of nature, as Hume interprets it, involves a uniform regularity of events.

Jin and Fan [14] proved a global uniform regularity in the vanishing viscosity limit in a domain (Omega= -infty,+infty)times(0,1)) with a slip bOmega= -inftytion.

We remark that this uniform regularity can be violated even in the semilinear case: (G = {1over 2} sigma ^{2} t,omega) : gamma + f t,omega, y,z)).

By the uniform regularity of w, and using (19) we see that begin{array}rcl@ overline{mathcal{E}}^{L}left[w^(delta,B_{delta}) mathbf{1}_{{textsc{H} >delta}}right] leq overline {mathcal{E}}^{L} left[e^{L (textsc{H} - delta)}w^left textsc{H},B_{textsc{H}}right)mathbf{1}_{{textsc{H} >delta}}right] leq overline {mathcal{E}}^{L} left[e^{L textsc{H}}w^left textsc{H},B_{textsc{H}}right)right].

Further, if x lies in a bounded set (Bsubset X), the uniform asymptotic regularity on B follows.

In this section, we show the uniform maximal regularity properties of the nonlocal initial value problem for nonstationary Stokes equations (1.6).

The uniform maximal regularity properties of the corresponding stationary Stokes operator, well-posedness of a nonstationary Stokes problem and the existence, uniqueness and uniformly L p estimates for the solution of the Navier-Stokes problem are established.

We further remark that the notion of uniform asymptotic regularity introduced by Edelstein and O'Brien [21] plays an important role for studying property ( A ) of nonlinear Lipschitzian-type operators.

The conditions of closedness and uniform asymptotic regularity on the maps { T k } k = 1 m can be replaced by the condition that each of the maps { T k } k = 1 m is uniformly Lipschitz.

By others, this mesh-refinement ensures uniform shape regularity of T ℓ.

According to the almost minimal cardinality of M ℓ, assumption  (8.4), and uniform shape regularity, it follows that | M ℓ | ≤ | M | ≤ C 9 | ω k (T ℓ ; M ˜ ) | ≃ | M ˜ | ≃ | R ˜ (ε 0 ; T ℓ, T ^ ) |.