Sentence examples for basic theorem on from inspiring English sources

In addition, Dorflein [52] stated and proved that the basic theorem on coherence networks of concept lattices as an extension of the basic theorem on concept lattices.

As applications, an extended basic theorem on Hilbert-type inequalities with the decreasing homogeneous kernels of -degree is established, and some particular cases are considered.

As applications, an extended basic theorem on Hilbert-type inequalities with the decreasing homogeneous kernel of -degree is established; some particular cases are considered.

They allow us to derive some basic theorems, one of which we'll use in the next section: Theorem (\ \bwedge\ -distribution).

For investigating the impacts of parametric uncertainties on the overall stability, the basic theorem of the proposed robust control strategy, frequency-domain modeling of the microgrid, robustness and close-loop stability analyses are outlined.

The basic theorems of intuitionistic analysis — the bar theorem, fan theorem, and continuity theorem — are in "On the Domains of Definition of Functions" of 1927.

Section 2 gives the basic theorems of fractional calculus.

In Section 3, we prove some basic theorems for the CF Dirac system on (mathbb{T}).

Based on a basic theorem in mathematical statistics concerning unbiased estimators with minimum variance, Gurland [1] yielded a closer approximation to π than that afforded by (1.1), namely, begin{aligned} frac{4n+3}{(2n+1)^{2}} biggl( frac{(2n)!!}{(2n-1)!!} biggr)^{2}< pi< frac {4}{4n+1} biggl( frac{(2n)!!}{(2n-1)!!} biggr)^{2}, quad n in mathbb{N}.

A basic theorem says that there is a suitable σ-field containing all the intervals and a unique probability defined on this σ-field for which the probability of an interval is its length.

In Section 2, some notations and basic theorems or lemmas on time scales are given.