Sentence examples for establish inequality from inspiring English sources

Now, to establish inequality between the extrinsic scalar curvature of M and the scalar curvature of ((overline{M},overline{g})), we shall need the following lemma.

In particular we establish inequality constraints on a control task's period and deadline whose satisfaction ensures that the closed loop system's induced ℒ2 gain lies below a specified performance threshold.

For this, we define for any non-negative sequence (a n ) and any integers N ≥ n ≥ 1, We then note that in order to establish inequality (1.2), it suffices to show that for any integer N ≥ 1, we have.

In this paper, we establish inequality relations of some degree-based indices such as Randić, GA, ABC, and harmonic indices with various distance-based indices such as eccentric connectivity, connective eccentric, augmented eccentric connectivity, Wiener, and third ABC indices.

However, motivating authors to establish inequality poses challenges, many of which can be overcome by means of the completeness of wavelet bi-frames in Lebesgue spaces and the stability of wavelet coefficients.

Also, we establish inequalities for the Wallis sequence.

For some special kernel functions, it is meaningful to establish inequalities in the whole plane.

Next we establish inequalities involving the second fundamental form, slant angle, and warping functions.

It is, therefore, of interest to establish inequalities for various variances as well.

A few of those properties are a key to establish inequalities for ECHFs and EGHFs.

Besides, we establish some inequalities for the edge lengths and altitudes of a spherical simplex, and we establish inequalities for the edge lengths and circumradius of Ω n.