Sentence examples for rational bound from inspiring English sources

In the following we will determine a lower rational bound for the sine function.

Using the lower rational bound founded in Lemma 2.2, we will provide a refined version of the classical Jordan inequality (1.7): The inequality operatorname {sinc}( x ) >frac{60-7x^{2} >frac{60-7x^{2}c{2}{60+3x^{2}rue for all (xin ( 0,sqrt{frac{60pi -120}{7pis+6}} ) ).

Russell claimed that rather than postulating entities in such a case, an irrational number should simply be defined as a class of rational numbers without a rational upper bound.

Meanwhile, some discussions between the variance and its rational upper bound are presented to show the rationality of the latter.

Since the whole calculation processes are too intricate, an inequality about the variance is proved, which is used for defining a rational upper bound of the variance (RUBV).

In order to tackle this problem, in this section, we suggest a rational upper bound of the variance and its calculation formula for some special fuzzy variables on account of the following theorem.

Furthermore, two inequalities regarding the rational upper bound of variance and standard deviation of the sum of two fuzzy variables and their individual variances and standard deviations are proved.

Then the rational upper bound of the variance (RUBV) is defined by overline{V}[xi]= int_{0}^{+infty} bigl( 1-Phi(e+sqrt {x})+Phi e-sqrt {x}) bigr),mathrm{d}x.

Thus, in order to better implement variance in real-life projects like risk control and quality management, we suggest a rational upper bound of the variance based on an inequality, together with its calculation formula, which can largely simplify the calculation process within a reasonable range.

In these rational bounds, either the lower bound or the upper bound will always be the absolute best rational approximation.

Due to the fact that EEs are usually featured by lack of information and time pressure, decision makers (DMs) are often bound rational and their psychological behaviors are very crucial to the GEDM process.