Sentence examples for sharp estimation from inspiring English sources

which by Lemma 1 gives sharp estimation (2).

and by Lemma 1, we obtain the sharp estimation (14).

Putting μ = 0 in (4) we get the sharp estimation (3).

The following theorem gives the complete sharp estimation of the Fekete-Szegö functional in the class CW ( Φ ; P ).

Proof From Theorem 4, we have sharp estimation (23) for A B ≥ 0. Let now A ≥ C and B < 0.

Moreover, the type of the sharp estimation function will depend on the geometry of the domains of integration in the high dimensional cases.

Estimating high security levels assumes sharp estimations of FMRs when they are close to zero.

Moreover, we obtain sharp estimations for the evolution of the solution along the characteristic curves, which enable us to derive the uniform exponential decay of the associated energies.

In this paper, we use the algebra methods, the properties of the r-circulant matrix and the geometric circulant matrix to study the upper and lower bound estimate problems for the spectral norms of a geometric circulant matrix involving the generalized k-Horadam numbers, and we obtain some sharp estimations for them.

In the article, we present new bounds for the function (e^{tcot(t -1}) on t -1}nterval ((0, pi/2)) and find sharp estimations for the Sintervalgral and the Catalan constant based on a new monotonicity criterion for the quotient of power series, which refine the Redheffer and Becker-Stark type inequalities for tangent function.

To obtain a sharper estimation of (C_{p}(Omega)), we focus on the constants (D_{p}(Omega)) such that begin{aligned} biggl( int_{Omega} biglvert u(x -u_{Omega}(x -u_{Omega}^{p},dx bigrvertfrac{1}{p}}leq D_{p}(Omega) biggl( int_{Omega} biglvert nabla u(x) bigrvert ^{p},dx biggr)^{frac{1}{p}}leqD_{pox{for all } uin W^{1,q}(Omega).