Sentence examples for by using the sharp from inspiring English sources

First, we establish a sharp estimate for the operator T b ; and second, we prove the boundedness for the operator on L p spaces with variable exponent by using the sharp estimate.

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.

However, these findings are consistent with a previous study of serum Dkk-1 concentrations in inflammatory arthritis, which did not show an association with radiographic damage in rheumatoid arthritis (RA) (by using the Sharp score) or ankylosing spondylitis (by using the modified Stoke Ankylosing Spondylitis Spine Score (mSASSS)) [ 28].

In total, 2340 sets of hands and feet radiographs of 463 patients with RA were scored by using the Sharp-van der Heijde scoring (SHS) methods by one experienced reader with known time order (intra-class correlation coefficient of 0.91) [ 19].

Our data demonstrated a continuously significant joint space narrowing as measured by the Z-Score using the Sharp Score for joint space narrowing for assessment of RA severity.

They were scored by the BioClinica Corporation (Newtown, Pennsylvania, USA) using the Sharp score as modified by van der Heijde and colleagues (vdH-S).

A hole, sized 2 mm × 2 mm, was made using the sharp scalpel followed by irrigation of the bulla with Trizol.

The interface properties are defined by using the concept of a sharp Gibbs dividing surface, which in turn is used to define the interface internal energy and the interface stresses.

Study radiographs were read by an experienced reader blinded to all clinical and demographic data, who scored the radiograph for erosions and joint-space narrowing (JSN) by using the van der Heijde modified Sharp method [ 28, 29].

Calculations have been performed by using sharp and rounded corners, and by using the conventional and the constrained finite strip method.

Motivated by these papers, the main purpose of this paper is to introduce some Toeplitz type operator related to some singular integral operator satisfying a variant of Hörmander's condition and prove the boundedness for the operator on L p spaces with variable exponent by using a sharp estimate of the operator.