Sentence examples for estimates of the form from inspiring English sources
We would like to have estimates of the form bigl| u(t bigr| leqPsibigl |g|bigr), for some function (Psi(cdot)) which satisfies the condition (Psi (s)longrightarrow0) as (slongrightarrow0).
The effect of either operation is to generate a complex-valued signal estimates of the form: a x, y) exp (jφ x, y)), where the IA and phase functions will hopefully approximate the input AM-FM components.
These estimates imply earlier L2 L2 L2 results obtained by the second author as well as corresponding sharp, stable sublevel set estimates of the form studied by Christ [3] and Christ, Li, Tao, and Thiele [5].
Pragmatic difficulty for BIA Determining the measure of one's priors can be difficult, and Bayesian methods can be perceived as unscientific, especially in legal circles Does not produce estimates of the form typically desired (e.g., "a 77% chance"), and results logically pertain to the data itself, not to the prediction of new cases.
Besides, the function (omega_{k_{1}}^{d} tau,m,epsilon)) satisfies estimates of the form: there exist constants (nu>0) and (varpi_{d}>0) with bigl|omega_{k_{1}}^{d} tau,m,epsilon bigr| leq varpi_{d}bigl(1+|m|bigr)^{-mu }e^{-beta|m|} frac{|tau|}{1 + |tau|^{2k_{1}}} e^{nu|tau|^{kappa}} for all (tauin U_{d}), all (m inmathbb{R}), all (epsilonin D 0,epsilon_{0})); see Proposition 11.
By the integral inequalities method, Porzio derived the L∞ decay estimate of the form u ( t ) L ∞ ≤ C u 0 L q α t - λ, t > 0 (1.7).
with a constant C > 0. Operators whose principal symbols allow an estimate of the form (2.8) are also called N-elliptic with parameter.
Thus, as a further application, a two-sided estimate of the form c0|D+∥x t)∥R|⩽∥˙x t)∥R⩽c1|D+∥x t)∥R| can be derived, which is shown to be invalid for the norm ∥⋅∥2.
In this case the elementary domain (e={xi= xi_{1},xi_{2}): |xi_{alpha}-x_{alpha}|leq h_{alpha}}), and we again obtain the estimate of the form (27) (see, e.g., [17]).
By substituting (a_{F}^{(3)}) into (21) we see that we need an estimate of the form (h_{F} geqvarsigma_{1} h_{T}) in order for Theorem 2 to hold.
If the coefficients of top order are Hölder continuous of exponent τ∈ 0,1], we can derive the remainder estimate of the form O(t(n−θ)/2m) with any θ∈ 0,τ).
