Sentence examples for key theorem from inspiring English sources

Take, for instance, Keynes' key theorem: that monetary events — government deficits, interest rates, credit volume and volume of money in circulation — determine demand and with it economic conditions.

One can obtain the double inequality (1.12) using the key theorem of Wu and Debnath [28].

Then the key theorem, i.e. the following Theorem 3.1 will be proved in next subsection.

So, for instance, Hacking has argued that we should really be committed to a second-order formulation of set theory and that Putnam's key theorem doesn't apply to such formulations (Hacking 1983).

The result serves as a crucial ingredient in the proof of the key theorem of the paper, providing a characterization of the common zero data of two square-size rational matrix functions in terms of the kernel of their Bezoutian.

The paper proposes a unified approach to many key theorems proved in the last twenty years in different areas of abstract harmonic analysis.

We then describe the challenges and opportunities encountered in adapting ranking-and-selection techniques to stochastic simulation problems, along with key theorems, results and analysis tools that have proven useful in extending them to this setting.

}}y= y_{1},ldots,y_{k-1} in H. end{cases} The key equivalent theorem for problems (P) and (Q) is given as follows.

On the other hand, it is well known from the key renewal theorem that lim t → ∞ ( p ( ⋅, S − x ) ∗ U θ ) ( t ) = 1 E [ τ 1 ] ∫ 0 ∞ p ( t, S − x ) d t.

We would like to mention that our key result Theorem 2.1 could be regarded as either an extension or an improvement of the corresponding results in the existing literature given by the authors of [6 9, 11 13, 15, 16, 18, 20, 21, 30].

Decision procedures are key components of theorem provers and constraint satisfaction systems.