Sentence examples for fundamental estimates from inspiring English sources

We have the following fundamental estimates for the evolution family.

The following fundamental estimates for the resonance function can be proved easily.

The following fundamental estimates can be proved with a slight modification in [14, 28].

In Section 3, we give some fundamental estimates for the solution ((u,v,w)) to system (1.2) and then prove Theorem 1.1.

For simplicity of presentation, we assume (T = K Delta t) with an integer K. Our approach is based upon the following simple, but fundamental estimates [33].

and Schauder estimates, which play important roles in the theory of partial differential equations, are two fundamental estimates for elliptic and parabolic equations and the basis for the existence, uniqueness, and regularity of solutions.

from the fundamental estimate of the logarithmic derivative.

Figure 5 RMSE as a function of N for SNR = 40 dB evaluated on single-pitch signal with unit amplitude: (a) fundamental frequency estimates; (b) DOA estimates.

Figure 6 RMSE as a function of SNR for N = 64 evaluated on single-pitch signal with unit amplitudes: (a) fundamental frequency estimates; (b) DOA estimates.

Figure 9 RMSE as a function of Δ ω: (a) joint fundamental frequency estimates; (b) joint DOA estimates.

Figure 8 RMSE as a function of SNR for N = 64 evaluated on multi-pitch signal with unit amplitudes: (a) joint fundamental frequency estimates; (b) joint DOA estimates.