Sentence examples for the introduced basis from inspiring English sources

The introduced basis states are completed and normalized as: sum_{gamma}int {rm d}{mathbf{p}}int {rm d}{mathbf{q}} |{mathbf{p}}{mathbf{q}}gammaranglelangle{mathbf{p}}{mathbf{q}}gamma|= 1, (4) langle{mathbf{p}}^{prime}{mathbf{q}}^{prime}gamma^{prime}|{mathbf{p}}{mathbf{q}}gammarangle= delta({mathbf{p}}^{prime}-{mathbf{p}}) delta({mathbf{q}}^{prime}-{mathbf{q}}) delta_{gamma^{prime}gamma}.

An efficient routing function is developed and used as a basis for the introduced algorithm.

Table 3 shows the results obtained using the different methods on the basis of the introduced evaluation criteria.

Further, on the basis of the introduced notion of soft element, we give a natural definition of a soft mapping, the image and the inverse of a soft mapping and discuss its properties.

The proposed production technology of the tubular BNC material is quite simple, and accordingly other hollow BNC materials in different shapes could also be produced on the basis of the introduced concept.

Xiao et al. [8] proved that only enforcing the orthonormality constraints is not enough for the factorization-based method; therefore, they introduced the basis constraints to reduce ambiguity.

We end the section by introducing the basis for our proposed imagery of thought bubbles for an innovator.

Starting from the concept introduced on the basis of this case study, future research could develop in-depth studies in at least two directions.

The basic foundations of EPR spectroscopy are supposed to be known by the reader, while we introduce the basis of magnetic interactions between spins.

With a set of orthogonal unit basis introduced as the contravariant basis, the helical coordinate is firstly considered, where components of tensor retain the dimension of original quantity.

This paper aims at introducing the basis of the formalization of the Sachem perception based monitoring and diagnosis approach.