Sentence examples for by using the recurrence from inspiring English sources

By using the recurrence relation the minimal value of the objective function in (15) can be found at the last step of optimization.

In this paper, new bounds for the exponential function with cotangent are found by using the recurrence relation between coefficients in the expansion of power series of the function (ln (1-2x^{2}/15-px^{6})) and a new criterion for the monotonicity of the quotient of two power series.

In the present study, we first obtain some new bounds for the exponential function with cotangent by using the recurrence relation between coefficients in the expansion of power series of the function (ln (1-2x^{2}/15-px^{6})) and a new criterion for the monotonicity of the quotient of two power series.

This was accomplished by using the seismic recurrence and hazard curves developed for Mérida State by Bendito et al. (2001).

Proof Using the recurrence formula (2), by a simple calculation, we can easily get the recurrence (3), the proof is omitted.

Using the recurrence hypothesis, we have (4.11).

Using the recurrence formula (2.8) and, we have (2.11).

The relation between Pfmdr-1 86Y mutation in isolates from day 0 (or day of recrudescence, if available) and clinical response to CQ treatment by using the time of recurrence, showed a markedly difference between the two curves (Figure 4).

Second, we optimized these profiles by using the clinical data on local recurrence.

Now we find another recurrence relation by using the derivative operator.

Then we construct the exact solution of the canonical three-term recurrence relation, by using the R-sum key lemma.