Sentence examples for the sharp inequality from inspiring English sources

Take a look at most riots in the 20th century: the one underlying similarity is unemployment and poverty among people who are keenly aware of the sharp inequality between themselves and their country's wealthy elite.

Then there holds the sharp inequality (3.7).

Next we note that the proof above only consists of suitable substitutions and equalities to reduce all inequalities to the sharp inequality (2.3) and we obtain a proof also of the statements (e) and (f) according to Theorem 2.1.

Then for the same collection of parameters and, for every f ∈ L p, s r, the sharp inequality ∥ D ± k f ∥ L q ⩽ K ∥ f ∥ L p μ ∥ D r f ∥ L s λ. holds true.

In this paper, we introduce the norm squares Bp for Qp spaces on a hyperbolic Riemann surface R so that Bp(f)="1 for 0⩽p⩽∞ if R is the unit disk and f is the identity function, and prove the sharp inequality Bp(f)⩽Bq(f) for 0⩽q<p⩽∞.

In [2], Anglesio showed that the sharp inequality biggl( frac{sin x}{x} biggr) ^{2}+frac{tan x}{x}>2+ frac {16}{pi^{4}}x^{3}tan x (3) is valid and the best possible constant is (frac{16}{pi^{4}}) for the constant c in inequality (2).

This apparently implies the sharp inequalities 1 4 < θ ( x ) < 1 2 (40).

In this paper, the sharp inequalities for some vector-valued multilinear integral operators are obtained.

First, we establish some sharp inequalities for the Toeplitz type operator T b, and, second, we prove the boundedness for the Toeplitz type operator by using the sharp inequalities.

The main purpose of this paper is to prove the sharp inequalities for the multilinear integral operators S ψ A and μ S A when D α A j ∈ B M O ( R n ) for all α with | α | = m j.

Much of what is written on race focuses on how it impacts on those suffering the sharpest inequality: unemployment, criminalisation, underachievement in school, poor housing.