Sentence examples for application of the proof from inspiring English sources

As an application of the proof of Theorem 2.8, one has the following.

Here we extend the application of the proof load design to estimate the parameters of a bivariate Weibull distribution.

NFP is equivalent to a weaker fragment of arithmetic, but does (unlike NFU) prove Infinity: this is the only application of the Specker proof of ¬AC to a provably consistent theory.

The results of the current application of both proof that the resulting time series trajectories are comparable and matching the data available on periodical basis like intended by the design of the methods.

Decision theory cannot therefore be used to support a variable application of the standard of proof beyond reasonable doubt.

Finally, note that all solutions with initial conditions on the positive x-axis enter the region ( 0, ∞ ) 2 under a single application of the map T. The proof of the case α 1 ≠ 0 and α 2 = 0 in (11) is similar to the previous case and we skip it.

We shall see its application in the proof of Theorem 3.2.

It is indeed a matter of time before the application of automated proof assistants becomes an everyday affair in the life of the mathematician; it is the grand challenge of the automated reasoning community to make it happen sooner than later.

We present an application of the Natural Approach algorithm in the proof (Application 1 - Theorem 9) of certain new rational (Padé) approximations of the function cos2 x, as well as in the improvement of a class of inequalities (20) by Yang (Application 2, Theorem 10).

As applications we simplify part of the proof the Bost Connes theorem on phase transition with spontaneous symmetry breaking and we discuss generalizations to other systems associated to subsets of primes and to number fields of class number 1.

The application of the method in a proof-of-concept pilot study of the Eagle Ford formation is introduced.