Sentence examples for continuity estimates from inspiring English sources

Fault rock continuity estimates suggest displacements of 50 200 m are required to form a continuous low-permeability cataclasite veneer in the studied sequence.

For a compact set K⊆Rd we present a rather easy construction of a linear extension operator E E(K →C∞(Rd) for the space of Whitney jets E(K) which satisfies linear tame continuity estimates sup{|∂αE(f)(x)|:|α|⩽m,x∈Rd}⩽Cm,ε∥f∥(r+ε m, where ∥⋅∥s denotes the s-th Whitney norm.

More generally it provides a modulus of continuity estimate for solutions of (1.1) that are admissible in (Gamma _k) for (k>n/2).

The Hölder continuity estimate for solutions of nonlinear elliptic equations has always been an important subject in the theory of differential equations and dynamical systems, see, e.g., [1 4].

Note that in the analogous natural growth conditions in the uniformly elliptic theory, the "o" lower bounds on (D_z A) and (D_z B) in (1.22) can be dispensed with as a continuity estimate is available [7, 25].

In Section 4, we give the rate of convergence by using the modulus of continuity and estimate a convergent theorem for the Lipschitz continuous functions.

The stand continuity was estimated as dead wood diversity and past management intensity (number of stumps).

This work highlights the heterogeneity in the distribution and fabric of carbonate fault rocks within fault zones hosting tens of meters displacement, and the importance of considering fault rock thickness and continuity when estimating the sealing capacity of a carbonate-hosted fault zone.

This thresholding function also assures the continuity of estimated wavelet coefficients.

The acoustic context information along both time axis (with multiple neighboring frames) and frequency axis (with full frequency bins) can be fully utilized by DNN to improve the continuity of estimated clean speech, and context information is more important in reverberant condition.

On the other hand, the Lasso regularization possesses continuity but the estimates are biased, because in addition to small, large-amplitude coefficients are "shrunk" too. Figure 2 Regularized LS estimation rules in the scalar case: (a) (group) Lasso, (b) Schwarz-type regularization, and (c) SCAD.