Sentence examples for by using the approximation from inspiring English sources

Again by using the approximation of for very small, the above sum rate becomes (32).

By using the approximation method which is due to Ionescu Tulcea (see [16]), we provide a new proof for the random version of Ky Fan's fixed point theorem.

by using the approximation of the gamma function: (Gamma (x approx sqrt {2pi }x^{x-1/2}e^{-x}~text {as}~xrightarrow infty).

Consequently, the probability density function can be estimated according to (7) by using the approximation of φ X (t) given in (9).

Usually the test results are analysed using the maximum likelihood method (MML), either directly or by using the approximation by Dixon and Mood.

The positive constant C ( h ) appearing here is numerically determined in Section 5 by using the approximation property of K h expressed by P K F ( u ) − R ( P K F ( u ) ) ∈ RE ( P K F ( u ) ), ∀ u ∈ U.

Recently, by using the idea of piecewise approximation, the simple Taylor-series expansion method has been further modified in [28].

To achieve a convex feasible set of C6, a convex approximation of C6 should be performed, which can be achieved by using the Bernstein approximation method [25, 27].

We tested against the null hypotheses of classification at the chance level (r = 0.5) by using the normal approximation to the binomial density, which allowed us to compute p values.

By using the statistical approximation for the effective SNR, which we introduced in [21], we now derive an analytical, tractable approximation for the EGP, which we call the approximate EGP (AEGP).

random variables by using the strong approximation method.