Sentence examples for basic concepts and fundamental from inspiring English sources

In Section 2.1, some basic concepts and fundamental results about subspaces are listed.

In this section, first, we introduce some basic concepts and fundamental results on time scales.

In Section 2, some basic concepts and fundamental results about subspaces and Eq. (1.1) are introduced.

In Section 2, some basic concepts and fundamental results about subspaces in Hilbert spaces and second-order symmetric linear difference equations are introduced.

Section 2 introduces some basic concepts and fundamental results about time scales, which will be used in Section 3. In Section 3 we first give the Picone identity on time scales, then we will employ this to prove our main result: Sturm-Picone comparison theorem of (1.1) and (1.2) on time scales.

Finally, several criteria of the limit-point case are established, and the invariance of the limit cases is shown under a bounded perturbation for the potential function q in Section 4. In this section, some basic concepts and fundamental results on time scales are introduced.

The basic concepts and fundamentals of structural phase transition and the two properties are briefly introduced.

In this section, some basic concepts and some fundamental results on time scales are introduced.

In Section 2, some basic concepts and a fundamental theory about time scales are introduced.

In this section, we introduce some basic concepts and give some fundamental results about subspaces in a product space and present two results about Eq. (1.1).

In each case the aim was to formulate the basic concepts and principles in terms of geometric and numerical quantities and then to derive the fundamental phenomena of the field by geometric constructions and proofs.