Sentence examples for a basis set of from inspiring English sources

Still, the quaternions can be regarded as a four-dimensional vector space formed by combining a real number with a three-dimensional vector, with a basis (set of generating vectors) given by the unit vectors 1, i, j, and k such that i2 = j2 = k2 = ijk = −1.

The B functions are used as a basis set of atomic orbitals.

We employ a basis set of orthogonal polynomials dynamically adapted to allow for emergence of chemical non-equilibrium.

The wave functions are expanded on a basis set of double-ζ orbitals plus one polarization orbital (DZP).

In computations, we have used a hybrid exchange correlation functional within the density functional theory and a basis set of localized atomic orbitals.

QUEST is a non-linear least-squares algorithm that fits a time-domain model function, made up from a basis set of quantum-mechanically simulated whole-metabolite signals.

The calculation procedures for constructing a basis set consisting of nonorthogonal SDs for N- electron systems using single and multiple correction vectors are described here.

The results demonstrate bilateral activation in the hippocampal formation in identification of novel complex scenes distinct from a learned basis set of complex scenes.

The aromatic nuclei, labile bridges, char links, and peripheral groups in FLASHCHAIN® comprise a suitable basis set of structural components to describe tar decomposition, without modification.

Recently, a hybrid approach has also been applied in 1D to spectral fitting of high resolution H NMR spectra in rat brain extracts given a prior basis set of 29 compounds.

Given a complete orthonormal basis set of functions {φn} in a separable Hilbert space, for example, the normalized eigenvectors of a compact self-adjoint operator, any vector f can be expressed as: :f = \sum_{n=1}^\infty \alpha_n \varphi_n.