Sentence examples for using the simple inequality from inspiring English sources
By using the simple inequality, one concludes that in all cases.
Now, using the simple inequality (|a-b|^{r} le|a^{r} - b^{r}|) for (rge 1) and (a,binmathbb{R}^), we have biglvert biglVert X^{n}bigl(s^bigr bigrVert ^{p-2} - biglVert Xbigl(s^bigr bigrVert ^{p-2}bigrvert lebiglvert biglVert X^{n}bigl(s^bigr bigrVert ^{p}-biglVert Xbigl(s^bigr bigrVert ^{p}bigrvert ^{frac{p-2}{p}}.
For the initial conditions by using (3.4), (3.25) and the simple inequality u - u 0 H 0 2 ≤ u - u i H 0 2 + u i - u i ( 0 ) H 0 2 + u i ( 0 ) - u 0 H 0 2 , we get the first initial condition immediately.
This requires the use of equivalence limits as maximum acceptable deviations because the simple inequality Δ≠0 does not qualify as a testable hypothesis.
This inequality has diminished mildly, although the inequality in emissions across countries ordered in the increasing value of income (inequality between rich and poor countries) has diminished less than the "simple" inequality in emissions.
Use the simple displacement method.
We show that points can be removed from the design space during the search for a D-optimum design, using a simple inequality satisfied by support points of a D-optimum design measure.
But, using a simple inequality, he shows that each such pair works exactly once: either as a sum of an odd number of integers with the even integer as the middle, or a sum of an even number of integers with odd/2 as the middle.
Depending on the controller form, constraints are enforced (i) using simple inequalities guaranteeing SPRness, (ii) in the frequency domain or, (iii) by implementing the Kalman Yakubovich Popov Lemma.
In this paper, we shall use some simple inequalities and a deep result on the existence of primitive divisors of Lucas numbers to prove the following result.
